Introduction to Polarography and Allied Techniques

7+,6 3$*( ,6 %/$1.

Copyright © 2006, 2002, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to [email protected]

ISBN (10) : 81-224-2337-X ISBN (13) : 978-81-224-2337-2

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com

Dedicated to fond memory of brother Sh. P.K. Zutshi who passed away on 3rd August 2001

7+,6 3$*( ,6 %/$1.

PREFACE TO THE SECOND EDITION The foundation of Polarography was laid by Late Professor Jaroslov Heyrovsky in 1922. The theory and practical implications were further extended by Professors : Jaroslov Kuta, B. Kucera, VI•cek, Kalousek Switch, R. Bridicka, I.M. Kolthoff, P. Zuman, L. Meites, J. O’M Bockris and other distinguished electrochemists. Significant progress has been made in this field, since then and I have been motivated to bring out this book which covers both the fundamentals as well as the recent developments. This volume is intended as a text book and includes questions and chemical examples. The book can be used in formal courses at the senior under graduate levels. The problems following each chapter have also been included along with some general questions. Some more topics have been added in this second edition. This has helped to cover the courses prescribed in other north Indian universities of the country. The chapter on corrosion has been given special attention and as such the chapter has been divided in two A and B. The details of laboratory procedure, such as the design of cells and the construction of electrodes has also been attended. The main feature lies in the important developments resulting from polarographic analysis in the study of organic systems by electrochemical method. The level at which the fundamental principles pertaining to the methods described in this text are presented and would help in understanding the essential principles underlying the applications of the methods described in the text. In addition to the treatment of the fundamental principles, some chapters do certain examples describing the applications of the methods described in the text. Apart from the general coverage, importance is given to the study of organic systems by electrochemical methods. The electro-organic synthesis involving direct and indirect electrode reactions has also been described in this text. The matter provided in this area of electrochemistry has been described mainly under categories like : Theory, Methods and Instrumentation. The incentive to prepare this work for publication has been provided by the members of my family. I wish to express my sincere thanks to my brothers and my niece for their interest and constant encouragement to complete this work. For bringing out the second edition as well as to include few more chapters has been given by one of my students : Prof. P.S. Verma of the Dept., University of Rajasthan, Jaipur. Kamala Zutshi

7+,6 3$*( ,6 %/$1.

PREFACE TO THE FIRST EDITION The foundation of Polarography was laid by Late Professor Jaroslov Heyrovsky in 1922. The theory was further extended by Professors : Jaroslov Kuta, B. Kucera, Vl•cek, Kalousek Switch, R. Bridicka, I.M. Kolthoff P. Zuman, J.O.M Bockris, L. Mcites and other distinguished scientists. Significant progress has been made in this field in recent times and this has motivated me to bring out this book which covers both the fundamentals as well as the recent developments. The book has been written to serve mainly the postgraduate students of the various Indian universities. The contents of the current research and modern textbooks in this area of Electrochemistry indicate beyond doubt that students of electrochemistry must have a working knowledge of various methods in this field. It is also necessary to understand the basic principles and limitations of these experimental methods in order to proceed for good research, unless the students have already had an introductory electrochemistry course. The level at which the fundamental principles pertaining to the methods described in this text are presented, shall help in understanding the essential principles underlying the applications of the methods described in the text. In addition to the treatment of the fundamental principles, some chapters do contain examples describing the applications of these methods, though the coverage may not be very detailed. The main feature lies in the important developments resulting from polarographic analysis in the study of organic systems by electrochemical methods. As a whole the text has been detailed as: The methods and instrumentation, Various types of electrodes and their working. Non aqueous systems, Inorganic systems as well as the Electrode processes. Apart from the general coverage, importance is given to the study of organic systems by electrochemical methods. The electro organic synthesis involving direct and indirect electrode reactions has also been described in this text. The matter provided in this area of electrochemistry has been described mainly under categories like: Theory, Methods and Instrumentation. The incentive to prepare this work for publication has been provided by the members of my family. I wish to express my sincere thanks to my brothers and my niece for their interest and constant encouragement to complete this work. Kamala Zutshi Jaipur, India

7+,6 3$*( ,6 %/$1.

CONTENTS PART–I : POLAROGRAPHY 1.

POLAROGRAPHY 1.1 Introduction and Basic Principles 1.2 Polarographs and their Applications 1.3 The Polarographic Cells and the Experimental Set Up 1.4 The Half-wave Potential and its Significance 1.4.1 Significance of Half-wave Potentials 1.4.2 Influence of Ionic Strength on Half-wave Potentials 1.4.3 Factors which Affect the Half-wave Potentials References

3 3 5 5 6 7 7 8 10

2.

THE ELECTRODES 2.1 Mercury Electrodes 2.1.1 Dropping Mercury Electrode 2.1.2 Flow of Mercury from Capillaries 2.1.3 Advantages of DME 2.1.4 Hanging Mercury Drop Electrode 2.2 Carbon Electrodes 2.2.1 Carbon Paste Electrodes 2.2.2 Glassy Carbon Electrode 2.3 Polarographic Cells and Saturated Calomel Electrode 2.4 Mercury Pool Electrode References

11 11 12 12 14 15 17 17 19 19 22 22

3.

THE TECHNIQUE 3.1 Polarographic Circuit 3.2 The Significance of Diffusion in Classical Polarography 3.3 Solvents and Supporting Electrolytes 3.3.1 Recommended Solvents and Electrolytes 3.4 Polarographic Maxima 3.4.1 Maxima of the First Kind 3.4.2 Suppression of Maxima of the First Kind 3.4.3 Polarity of Maxima of the First Kind

23 23 23 28 30 31 31 32 32

(xii)

3.4.4 Streaming of Electrolyte and Maxima of the First Kind 3.4.5 Maxima of the Second Kind 3.4.6 Suppression of Maxima of the Second Kind 3.4.7 Streaming of Electrolyte with Maxima of the Second Kind 3.4.8 Interpretation of Maxima of the Second Kind 3.4.9 Practical Applications of Polarographic Maxima 3.5 Polarography in Non-aqueous Solvents 3.5.1 Solvents that are Frequently Used References

34 35 35 36 36 37 37 38 40

4.

THEORY OF CURRENT POTENTIAL CURVES 4.1 The Ilkovi•c Equation 4.1.1 Consequences of Ilkovi•c Equation 4.2 Reversible and Irreversible Electrode Processes 4.3 Reversible Polarographic Wave 4.3.1 Cathodic Wave 4.3.2 Anodic Wave 4.3.3 Cathodic-Anodic Waves 4.4 Coupled Chemical Reaction and Chemical Reversibility References

42 42 44 46 48 49 52 53 55 57

5.

TYPES OF CURRENTS 5.1 Mass Transfer and Electrochemical Processes 5.2 Diffusion Current 5.2.1 Diffusion to Stationary Electrodes 5.2.2 Diffusion-Controlled Current 5.2.3 Linear Diffusion to a Growing Dropping Electrode 5.2.4 Diffusion Coefficient 5.2.5 Spherical Diffusion 5.3 Influence of Viscosity and of Complex Formation on Diffusion Current 5.4 Factors Affecting the Diffusion Current 5.4.1 The Limiting Current 5.4.2 The Residual Current 5.4.3 Migration Current 5.4.4 Kinetic Currents 5.4.5 Catalytic Currents 5.5 Adsorption Waves References

58 58 58 59 60 61 61 63

POLARIZATION 6.1 Polarization of the Dropping Mercury Electrode and Depolarization Processes 6.2 Reduction of Hydrogen Ions and Hydrogen Over Voltage

77

6.

64 64 67 67 68 71 73 74 76

77 78

(xiii)

6.3 Double Layer 6.4 Reduction of Cations References

80 81 82

7.

AMPEROMETRIC TITRATIONS 7.1 Types of Amperometric Titrations 7.1.1 Theory of Amperometric Titration Curves 7.2 Kinds of Amperometric Titrations 7.2.1 Redox Titrations 7.2.2 Complexometric and Chelometric Titrations 7.2.3 Compensation and Diffusion-Layer Titrations 7.3 Amperometric Titrations with Two Polarized Electrodes 7.4 Apparatus and Techniques 7.4.1 The Working Electrode : Reference Electrode 7.5 Two Working Electrodes 7.6 Chronoamperometry References

83 83 83 84 85 85 86 86 87 88 88 89 91

8.

POLAROGRAPHY OF METAL COMPLEXES 8.1 Reversible, Diffusion-controlled Systems Determination of Formulae and Stability Constants of Complexed Metal Ions 8.2 Determination of Stability Constants and Coordination Numbers of Metal Complexes 8.2.1 Calculation of Individual Complex Stability Constants 8.3 Mixed Ligand Systems–the Method of Schaap and McMasters References

92

9.

POLAROGRAPHY OF ORGANIC COMPOUNDS 9.1 Structural Effects 9.2 Nature of Electroactive Group 9.3 Steric Effects 9.4 Substituent Effects References

92 93 96 96 97 98 99 100 101 102 104

PART–II : ALLIED TECHNIQUES 10.

MISCELLANEOUS POLAROGRAPHIC METHODS : PRINCIPLES, THEORY TECHNIQUES AND ANALYTICAL APPLICATIONS 10.1 Square Wave Polarography 10.2 Alternating Current Polarography 10.2.1 The Technique and Instrumentation

107 107 114 117

(xiv)

10.3 Coulometry 10.3.1 Coulometry with Large Area Mercury Electrodes 10.3.2 Coulometry with a Dropping Mercury Electrode 10.3.3 Determination of n by Analysis of the Decrease in Limiting Current 10.3.4 Determination of n by Electrolysis at Constant-Current 10.4 Coulometry in Polarographic Analysis 10.5 Controlled-potential Electrolysis 10.6 Chronopotentiometry 10.7 Theory of Reversible Processes 10.7.1 Irreversible Processes 10.8 Experimental Methods 10.8.1 Apparatus 10.8.2 Cells and Electrodes 10.9 The Techniques 10.9.1 Measurement of Transition Times 10.10 Applications 10.10.1 Concentration Measurements 10.10.2 Electrode Kinetics 10.10.3 Electrode Pretreatment 10.10.4 Differential and A.C. Chronopotentiometry 10.10.5 Thin-Layer Chronopotentiometry 10.10.6 Chemical Kinetics 10.11 Adsorption 10.12 Applications References 11.

ADVANCES IN D.C. POLAROGRAPHY 11.1 Developments in D.C. Polarography 11.1.1 Principle of Potentiostatic (Controlled-Potential) Electrolysis 11.2 Time-derivative D.C. Polarography 11.2.1 Direct Proportionality of First Derivative Peak Heights to id 11.2.2 Relative Signal Levels in Regular and in First, Second, and Third Derivative D.C. Polarography 11.2.3 Criterion for Relative Resolving Power of Various Methods of Polarography 11.2.4 Geometrical Overlapping for Successive Waves 11.2.5 Mathematical Resolution of Overlapped First Derivative d.c. Polarograms 11.2.6 Mathematical Resolution of Regular Polarography Compared to First Derivative d.c. Polarography 11.2.7 D.C. Polarography in Non-aqueous Solvents and Particularly in Solvent Extracts

119 120 120 121 122 123 123 126 127 128 129 130 130 130 131 131 131 131 131 131 132 132 132 132 133 135 135 135 136 139 139 139 140 141 142 143

(xv)

11.3 Theory, Principles and Applications 11.3.1 Single Sweep Methods 11.3.2 Electrolytic Current 11.3.3 Kinetic Currents 11.3.4 Types and Forms of Voltage Sweeps 11.4 Multi-sweep Methods 11.5 Apparatus for Applied Voltage Oscillographic Polarography 11.6 Controlled Current Oscillographic Polarography 11.7 Pulse Polarography 11.8 Stripping Analysis References

143 144 146 149 149 149 150 150 152 153 160

12.

VOLTAMMETRIC METHODS 12.1 Voltammetry 12.1.1 Coulometric Methods 12.1.2 Voltammetric Methods 12.2 Large-amplitude Pulse Voltammetry (LAPV) 12.3 Differential and Derivative Voltammetry References

162 162 163 164 167 170 172

13.

CONTROLLED POTENTIAL ELECTROLYSIS

173

13.1 Electro-organic Synthesis and the Technique 13.1.1 Pure Electron Transfer 13.1.2 Conversion of Functional Groups 13.1.3 Substitution Reactions 13.1.4 Addition Reactions 13.1.5 Elimination Reactions 13.1.6 Coupling Reactions 13.1.7 Cyclization (Intramolecular and Intermolecular) 13.2 Electrochemical Activity in Heterocyclic Systems 13.2.1 Ring Closure Reactions 13.3 Experimental Technique 13.4 Circuit for Potentiostatic Method 13.4.1 Polarization Study 13.5 Current Efficiency References

173 173 174 174 174 175 175 175 176 176 177 178 179 184 185

CORROSION

186

14.

Part A : Principles and Control 14.1 Corrosion and Control 14.1.1 Ion Selective Electrodes 14.1.2 Operational Amplifiers 14.1.3 Potentiostat 14.1.4 Galvanostat

186 187 189 189 190

(xvi)

14.1.5 Polarography 14.1.6 Pulse Plating Sources 14.1.7 Micro Processor Based Instrumentation 14.1.8 Damage and Control 14.1.9 Sources of Hydrogen and Modes of Entry 14.1.10 Mechanism of Corrosion of H2S CO2 14.2 Mechanism of Carbon Dioxide Corrosion References

190 190 191 191 191 192 193 194

Part B : Stability of Metals 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11

Thermodynamics and the Stability of Metals Potential–pH (or Pourbaix) Diaphragms: Uses and Abuses Electronation Reaction in Corrosion The Corrosion Current and Corrosion Potentials The Basic Electrodics of Corrosion in the Absence of Ozide Films Factors Affecting the Rate of Corrosion and Evans Diagrams Some Common Examples of Corrosion Control of Corrosion Current in the Corrosion Process Various Factors in Determining Corrosion

195 198 200 201 203 204 208 209 209

Part C : Passivation 14.12 Passivation : Transformation from a Corroding and Unstable Surface to a Passive and Stable Surface 212 14.13 The Mechanism of Passivation 213 14.14 The Thermodynamics of Passivation 213 14.15 Role of Hydrogen in Corrosion 214 15.

CONVERSION AND STORAGE OF ELECTROCHEMICAL ENERGY

216

Section A 15.1 15.2 15.3 15.4 15.5 15.6 15.7

Present Status of Energy Consumption Status of Energy Consumption Direct Energy Conversion by Electrochemical Means Direct Energy Conversion by Electrochemical Means The Maximum Intrinsic Efficiency of an Electrochemical Converter The Actual Efficiency of an Electrochemical Energy Converter Physical Interpretation of the Absence of the Carnot Efficiency Factor in Electrochemically Energy Converters 15.8 The Power Output of an Electrochemical Energy Converters

216 217 218 218 219 220 220 222

Section B Electrochemical Generators (Fuel Cells) Cells Using Fuels other than Hydrogen The Hydrogen-Oxygen Cell Hydrogen Air Cells

222 223 224 225

(xvii)

16.

17.

18.

ELECTROCHEMICAL ENERGY STORAGE : THE IMPORTANT QUANTITIES IN ELECTRICITY STORAGE

226

16.1 Electricity Storage Density 16.2 Energy Density Power Electricity Storage Classical Batteries Zinc Manganese Dioxide Relatively New Electricity Stores Silver Zinc Cell Storers with Zinc in Combination with an Air Electrode Future Electricity Storers Storage by Using Alkali Metals Storers involving Non-aqueous Solutions

226 226 229 230 233 234 235 236 237 238 239

KINETICS OF ELECTRODE PROCESS Introduction 17.1 Essentials of Electrode reaction 17.2 Butler – Volmer Model of Electrode Kinetics R Effects of Potential on Energy Barriers One Step, One-Electron Process 17.3 Implications of the Butler-Volmer Model for the One Step, One Electron Process 17.4 The Current Overpotential Equation 17.5 The Standard Rate Constant 17.6 The Transfer Coefficient 17.7 Approximate Forms of the i- n Equation (a) No Mass-Transfer effects (b) Linear Characteristic at Small η (c) Tafel Behaviour at Large η (d) Tafel Plots Exchange Current plots (Tafel Plots) 17.8 Effects of Mass Transfer References

241 241 243 244 244 246

BIOELECTRODICS Introduction Useful Preliminaries Membrane Potentials Simplistic Theory Modern Approaches to the Theory of Membrane Potentials Electrical Conduction in Biological Organisms Electrical Conduction in Biological Organisms Protonic

257 257 257 259 261 262 264 265

248 249 249 250 252 252 252 253 254 254 255 256

(xviii)

The Electrochemical Mechanisms of the Nervous System an Unfinished Section Enzymes as Electrodes Enzymes Electrodes Carrying Enzymes The electrochemical Enzyme-Catalyzed Oxidation of Styrene

266 267 267 267 269

APPENDIX Questions

270 279

PART-I

POLAROGRAPHY

7+,6 3$*( ,6 %/$1.

CHAPTER 1

POLAROGRAPHY 1.1 INTRODUCTION AND BASIC PRINCIPLES Polarography is the branch of voltammetry in which a dropping mercury electrode is used as the indicator electrode. It is the electroanalytical technique that deals with the effect of the potential of an electrode in an electrolysis cell on the current that flows through it. The electrode whose potential is varied is called the indicator electrode voltammetric indicator electrodes may be made from quite a large number of materials say for instance mercury, platinum, gold and graphite, having varying shapes and construction. They may be stationary or is motion and the solutions in which these are used may be stationary or quiet. Polarography was the first of the voltammetric techniques to gain prominence. Certainly the most popular constant potential method is d.c. polarography at a dropping mercury electrode (DME). The reason being that there are several advantages peculiar to the DME, these are described further. The essential features of current potential curves obtained with DME are shown in Fig. 1.1. Curve b is the polarogram of a dilute solution of hydrochloric acid and the curve a being obtained under exactly the same conditions after addition of a small concentration of cadmium ion. Here, each oscillation represents the life cycle of one drop. It is the difference between the currents on the two curves which is of interest. No detectable change of current results at potentials less negative than about – 0.5 V from the addition of cadmium ion. The reason being that these potentials are insufficiently negative to bring about the reduction of any appreciable fraction of the cadmium ion at the surface of the drop. At potentials more negative than this, however, a wave appears, i.e., the reduction of cadmium ion proceeds more and more rapidly as the potential becomes more negative until eventually, at potentials more negative than about – 0.7 V is attained. It is so fast that cadmium ions are reduced as rapidly as they get diffused from the bulk of the solution upto the surface of the electrode. The rate of this diffusion depends on a number of factors. Out of these the concentration of cadmium ion in the bulk of the solution is of special importance. More concentrated the solution, the greater the rate at which cadmium ions reach, the electrode surface, and the greater the diffusion current that results from their reduction. The proportionality between the diffusion current and the concentration of the substance responsible for the wave is the basis for nearly all quantitative polarographic analysis. The ease of reduction or oxidation differs for different substances, and is reflected by the position of the wave with respect to the potential

4

Introduction to Polarography and Allied Techniques

axis. This is termed by a parameter called the half wave potential (– E ½). This is defined as the potential at which the current due to the reduction or oxidation of the substance responsible for the wave, is half as large as on the plateau. The half wave potential of cadmium ion can be seen in Fig. 1.1 (a). Under a set of defined experimental condition, each ion has its own characteristic half wave potential which is the basis of qualitative polarographic analysis. In cases, the electrode reaction may be so rapid that equilibrium is closely approached at every potential in a time much shorter than the drop life. This indicates the wave to be reversible. Studying the effects of potential and solution composition on the currents along the rising part of the wave provides information on the thermodynamics of the half reaction.

C ur rent in micr o a mp e res

20

15

(a) 10 Diffusion Current E½

5

(b) 0 0

–0.3

–0.6 –0.9 E d.c Volts in S.C.E.

(a) 1 F hydrochloric acid with 0.5 mM Cadmium ion

–1.2

(b) 1 F hydrochloric acid alone

Fig. 1.1 : Polarogram

In some cases the electrode reaction may involve a step having a large activation over potential than the variation of the current potential and solution composition are due to kinetic rather than thermodynamic effects. In such cases information on the mechanism of the rate determining step can be secured. Polarographic analysis can be used directly for the determination of any substance solid, liquid or gaseous, organic compounds containing conjugated double or triple bonds including polynuclear aromatic ring systems, as well as compounds like oximes, imines, ketones, aldehydes nitro diazo compounds and halo substituted compounds.

Polarography

5

One of the most important advantage of polarography and other voltammetric techniques is that two or even more substances can be determined by a single current potential curve. Another important analytical technique closely related to polarography is that of amperometric titration. Polarography is getting more widely used in fields as biochemistry and pharmaceutical chemistry. Even it has been used to study such diverse topics like hydrolysis, solubility, complex formation, absorption, kinetics of chemical reaction and mechanism of electrode reactions.

1.2 POLAROGRAPHS AND THEIR APPLICATIONS There are two kinds of polarographs: manual and recording. With a manual instrument, the potential applied to the cell is adjusted to some desired value and the current is measured. A single point on the polarogram is thus obtained. If the whole curve is wanted, the procedure must be repeated many times. This is tedious, specially when several waves or a complex polarogram is to be observed as such, the manual polarograph is not very convenient. For such observations a recording instrument is most suitable. The manual polarographs are not a disadvantage either. The diffusion-current measurements can be made more precisely and more quickly with manual than with recording polarograph. In a recording polarograph, the potential applied to the cell is obtained from a motor-driven voltage divider. Two procedures have been most frequently employed for recording the current. In one, the current is passed through a galvanometer, and the deflections of the galvanometer are recorded photographically or a piece of photographic paper moving at a known rate past a slit. In the other, which is now by for the more common, the current is passed through a standard resistor in series with the cell, and the resulting iR drop is presented to a strip-chart recording potentiometer, which plots the iR drop against time. Correlating the rates of motion of the chart and the voltage divider makes it possible to interpret the curve as a plot of current against applied potential. Usually, a recording polarograph employs a rate of change of potential of about 0.2 volt per minute and furnishes a complete polarogram in about 10 minutes.

1.3 THE POLAROGRAPHIC CELLS AND THE EXPERIMENTAL SET UP The cell is that portion of the apparatus that contains the solution which being studied. It also includes a non-polarizable electrode to which the potential of the dropping electrode is referred. The most important part of a cell is its reference electrode. Two kinds of reference electrodes, “internal” and “external” are in general use. An internal electrode is in direct contact with the solution being studied, while an external electrode is separated from it by a salt bridge or a porous membrane. Internal electrodes are chiefly valuable in routine analyses in which a limited constancy of potential is unimportant. They are also often used in work (when very high negative potentials) where contamination by alkali metal ions or other constituents of a salt bridge would be harmful; in cells containing

6

Introduction to Polarography and Allied Techniques

only one or two drops of solution are used. Here the difficulty arises by bringing an external electrode into contact with so small a volume of the sample. In continuous polarographic analysis, where the slow contamination of an external electrode would eventually render its potential as uncertain as that of an internal one. Internal reference electrode is made by coiling about 15–20 cm of 14 gauge silver wire into a helix. It is often Galvanometer convenient to coil it around – + the dropping electrode. In a G solution containing an ion X– that forms an insoluble silver salt, the potential of – this electrode depends only – on the activity of X in the Mercury reservoir solution, provided of course, that the solution in saturated with Ag X. If its oxygen free nitrogen solubility is very small, enough Ag X to satisfy this requirement will be formed by reaction with dissolved oxygen, an air saturated solution of unknown subs. with excess inert salt solution is placed in contact with the electrode before + deaeration. If the solution is neutral and unbuffered, it may involve partial Fig. 1.2 : Experimental set up in Polarographic Experiment hydrolytic precipitation of heavy metal ions. The electrode should not be used unless a precipitate results when a drop of solution containing 0.01 M silver ion is added to 10 ml of the sample solution. Otherwise the concentration of dissolved silver ion, and hence the potential of the silver electrode, may change considerably during the recording of the polarogram. In addition the concentration of silver ion may become high enough to give rise to substantial current at the dropping electrode. The silver electrode is not workable in solutions containing ammonia, cyanide, thiosulphates and high concentrations of halides as well as in solutions containing only nitrate, acetate perchlorate and other ions whose silver salts are appreciably soluble. The coating of insoluble salts that terms on the electrode when it is used as the anode cell should be removed by treatment with ammonia, thiosulphate, or cyanide, followed by rinsing with distilled water.

1.4 THE HALF-WAVE POTENTIAL AND ITS SIGNIFICANCE The most important constant in polarography is the half-wave potential. Chemical, thermodynamic and structural information may be obtained from the measurements of the half-wave potentials of reversible and irreversible waves under varying experimental conditions.

Polarography

7

The manner in which the current is affected by electrode potential on the rising part of the wave is to be noted. On the plateau, electron transfer is so fast that the ions or molecules of the electroactive substances are reduced or oxidized as rapidly as they arrive or are formed at the electrode surface. As the potential moves from the plateau of the wave towards its foot, the rate of the electron-transfer process decreases and the reduction or oxidation becomes less and less complete. It is convenient to divide electrode reactions into two extreme classes : (i) Reversible reactions, and (ii) irreversible reactions. (i) The reversible reactions are so rapid that thermodynamic equilibrium is very nearly attained at every instant during the life of a drop at any potential. For such reactions the variation of current with potential reflects the changing position of the equilibrium and is described by Nernst equation. The other extreme is that of totally irreversible reactions, which are so slow that they proceed only by a fraction of the way towards equilibrium during the life of each drop. For these reactions it is the rate of the electron-transfer process and the manner in which this is influenced by the electrode potential that governs the relationship between current and potential. The polarographic data serve to elucidate the kinetics of the rate determining step in totally irreversible processes.

1.4.1 Significance of Half-wave Potentials It follows from the equation derived on current potential curves that the half-wave potentials given by the term, RT/nF. In D /v′, equals the standard oxidation-reduction potential found with other indicator electrodes such as platinum electrodes. This property holds only for an oxidation-reduction system, whose oxidized and reduced terms are both present in the solution, e.g., Fe2+/Fe3+. This was confirmed by many previous workers. If one of the two terms (may be the reduced one) reacts with the material of the electrode (metals with information of an amalgam), then the half-wave potential differs from the standard oxidation-reduction potential for the metal/ion system. It can be readily shown that the difference between the half-wave and the standard potential is given by the free energy of amalgamation.

1.4.2 Influence of Ionic Strength on Half-wave Potentials Very accurate measurements point to the fact that the half-wave potentials of cations depend on the ionic strength. Get shifted to more negative potentials with increasing ionic strength. This is caused by the dependence of E ½ on the activity coefficients of both the oxidized form f and the reduced form f ′. This is when the activities are considered instead of concentration. The potential of an oxidation-reduction system is given by the formula: E = E0 –

RT ( Red) ln nF (ox ) 0

...(1)

where ( ) denote the activities. On expressing the above equation in terms of concentrations the following equation results:

8

Introduction to Polarography and Allied Techniques

RT f ′ RT [Red]0 E = E 0 – nF ln f – nF [OX ] 0

...(2)

The half-wave potential is defined by the relationship

[Red]0 [ox ]0

=

D D′

...(3)

On obtaining this condition, we obtain E ½ = E0 –

RT f ′ RT D ln − ln nF f nF D′

...(4)

For the half-wave potential. In this equation the last two terms depend on the ionic strength. If cations are deposited a very dilute amalgam is formed and f ′ is virtually one. The activity coefficient f of the cation in the supporting electrolyte is, however, less than one and since f decreases with increasing ionic strength, E ½ is shifted to more negative potentials. Lingane studied it first [2]. Vlcek [1] mode more accurate thermodynamic calculations and recommended that E ½ be extrapolated to μ = 0 : (E ½)μ = 0 = E 0 –

RT D0 ln nF D′0

...(5)

[D0 and D0′ are the corresponding diffusion coefficient for μ = 0]. The half-wave potentials calculated from the thermodynamic standard potentials for μ = 0 agreed with the extrapolated half-wave potentials as was shown by Vl•cek [1] in cases of Tl+, Pb2+ and alkali metals.

1.4.3 Factors which Affect the Half-wave Potentials 1. The temperature coefficient of the half-wave potential is mostly between –2 and +2 mv/degree. For a reversible wave it may be either positive or negative. For an irreversible wave it is usually positive and may exceed several millivolts per degree. 2. The half wave potential is almost always independent of the concentration of the electroactive species (i.e., of the diffusion current) after proper correction is applied for the iR drop. However, the half-wave potential of a reversible wave does not vary with concentration if a solid product is termed, or more generally, whenever the number of the ions or molecules of the product of variable activity differ from the number of ions or molecules of reactant of variable activity in the equation for the half-reaction. Such variations can be described only by thermodynamic equations. The half-wave potential of an irreversible wave may also vary with concentration of the reaction mechanism involving some rate governing step that is not the first- or pseudo-first order. When it does vary, it most often becomes more negative as the concentration increases.

Polarography

9

3. The half-wave potential of a reversible wave is nearly independent of the capillary characteristics, i.e., m and t. When the diffusion current obeys the Koutocky equation and when the diffusion coefficient of the oxidized and reduced species differ a small dependence of the half-wave potential on t1/6 and m1/3 can be predicted. Changes in m, t and the concentration of the electroactive species may, however, produce apparent variations of the half-wave potential unless both are corrected. The iR drop always produces an apparent shift of the half-wave potential toward more negative values for the cathodic waves and toward more positive values for anodic waves and the shift is proportional to the limiting current. 4. The half-wave potential of a totally irreversible wave, however, varies significantly with t, becoming more positive for a cathodic wave as t increases. The magnitude of the variation depends on αn a and may be used for its evaluation. Typically, if αn a = 0.5, the half-wave potential becomes about 20 mV more positive if t is doubled. 5. Changes in the nature and concentration of supporting electrolyte may effect the half-wave potential in many ways. For reversible waves the effect is due to complex formation. Quite some information about the identities and dissociation constants of reversibly reduced metal complexes can be obtained from polarographic measurements. In the reversible reduction or oxidation of an organic compound it is the pH of the supporting electrolyte that is most important. For such processes it is possible to obtain information concerning the occurrence and equilibrium constants of acid-base reactions involving the oxidized and reduced forms of the couple. 6. When a complex metal ion is reversibly reduced to a metal soluble in mercury, its half-wave potential is always more negative than that for the reversible reduction of the corresponding simple or aquo-complex ion. The difference being related to the free energy of dissociation of the complex. When complex formation takes place the half-wave potential is usually more negative when a metal ion is reduced to a lower oxidation state and when the product remains dissolved in the solution phase. The opposite effect is only occasional and when it takes place it signifies that the reduced complex is more stable than the oxidized one. Hydrogen ion is nearly always consumed in the reversible reduction of an organic compound, and as such the half-wave potential for such a process always becomes more negative as the pH is increased. It may remain constant over a certain range of pH values because of the influence of prior or subsequent proton transfer reactions. 7. Complex formation may cause the half-wave potential in the irreversible reduction of a metal ion to become either more negative or more positive. This depends on the nature of the ligand used. Example could be of nickel ion. The half-wave potential is –1.01 V vs. SCE in 0.1 F sodium per chlorate but no wave in ethylene diamine tetra acetate solutions. Where as in media containing thiocyanate or high concentration of halide, the half-wave potentials of nickel (II) are considerably more positive than –1.0 V. The reason being that these

10

Introduction to Polarography and Allied Techniques

ligands facilitate electron transfer and decrease activation energy involved in the reduction. The half-wave potentials for the irreversible reduction of an organic compound may also get affected by a chemical reaction with the supporting electrolyte. The example could be of carbonyl compounds. The halfwave potentials are altered by addition of ammonia or hydroxylamine, which converts them into imines or oximes. In the absence of any reaction with the supporting electrolyte the double layer effects and the liquid-junction potential can also produce changes in the half-wave potentials. 8. When there a change made in the supporting electrolyte concentration, the half-wave potential may be affected in irreversible waves. Where upon the rate of electron-transfer steps on equilibrium position of some fast chemical reaction that precedes it, could be the reason and also the potential difference between the electrode and that surface and thus the rate of electron transfer. The direction and magnitudes of these double-layer effects depend on the potential at which the wave occurs, on the nature of ionic medium, on the charge on the species actually reduced and on the mechanism by which the reduction occurs. In some cases the half-wave potential become more negative on increasing the salt concentration while in others it becomes more positive. Large shifts have been observed. It is therefore desirable to keep the nature and concentration of the supporting electrolyte nearly constant specially while studying irreversible processes. In studying the behaviour of an organic compound, the results can be obtained consistent by using buffers of identical ionic strengths [3]. 9. In reversible waves, the effects of salt concentration on the half-wave potentials are due to mass-action effects on complex equilibria, changes of activity coefficients of the species involved in the half reaction and variations of liquidjunction potential [4]. All these can be referred to the data (5) on the half-wave potential of cadmium ion in nitrate solutions at ionic strengths up to 12 M. 10. In non-aqueous solutions having low dielectric constants, electroactive ions will be largely converted with ion pairs or higher ionic aggregates. In this, it may be pointed out that one consequence of the Stern double-layer theory is that the dielectric constant decreases rapidly as the electrode surface is approached, becoming as small as 2 or 3 or the electrode-solution interface even in an aqueous solution. The transient formation of an ion-aggregate under these condition has no effect on the half-wave potential of a reversible wave, but because it may alter the charge borne by the electroactive species it may affect that of an irreversible one.

References 1. Vl•cek A.A., Chem. List Y. 48, 1474 (1954); Collection Czechoslov, Chem. Communs. 19, 862 (1954). 2. Lingane J.J.: J. Am. Chem. Soc. 61, 2099 (1939). 3. Meites L.J. Electroanal. Chem. 5, 270, (1963). 4. Moros, S.A. and Meites, L.J. Electrochem. 5, 103, (1963). 5. Lingane J.J., Electroanalytical Chemistry, Ins., N.Y., 2nd ed. 1958, pp. 351–415.

CHAPTER 2

THE ELECTRODES 2.1 MERCURY ELECTRODES Mercury is widely used in the practice of electroanalytical chemistry both for working electrodes and for reference electrodes, in the latter case usually as an electrode of the second kind. The use of mercury is nearly an ideal choice for the construction of working electrodes for several reasons. Mercury has a large liquid range (–38.9 to 356.9°C at normal pressure) and therefore electrodes of various shapes can easily be prepared. The surface of such electrodes is highly uniform and reproducible, if the mercury is clean. The preparation of pure mercury is not very difficult. All metals with a standard potential more negative than that of mercury may be oxidized easily (exception being Nickel, which forms an inter metallic compound) by dispersing mercury into a solution of its salts acidified with nitric acid and saturated with oxygen. The elimination from mercury of metals more noble than itself to accompanied by repeated distillation under reduced pressure. One of the most important reasons for the application of mercury to the construction of working electrode is the very high over voltage for hydrogen evolution on such electrodes. Relative to a platinum electrode, the over voltage of hydrogen evolution under comparable conditions on mercury will be –0.8 to –1.0 V. It is, therefore, possible in neutral or (better) alkaline aqueous solutions to reduce alkali metal cations at mercury electrodes giving relatively well-defined polarographic waves at potentials more negative than –2.0 V vs SCE. Using supporting electrolytes such as tetra alkyl-ammonium salts, potentials as high as –2.6 V vs SCE in aqueous solutions, while in some non-aqueous systems even –3.0 V vs SCE (aqueous) is possible. Mercury electrodes do have serious limitations in applications at positive potentials. Solid metal and carbon electrodes are useful in such cases. Oxidation of mercury occurs at approximately +0.4 V vs SCE in solutions of perchlorates or nitrates since these anions do not form insoluble salts or stable complexes with mercury cations. In all solutions containing anions which form such compounds, oxidation of the mercury proceeds at potentials less than +0.4 V vs SCE. For example, in 0.1 M KCl this occurs at +0.1 V, in 1.0 M KI at –0.3 V, and so on. A number of mercury electrodes have been widely used for voltammetry. Of these, the dropping mercury electrode (DME) has been extensively used both for analytical and fundamental studies. Others are hanging mercury drop electrode (HDME), streaming mercury electrode (SME), and mercury film electrode (MFE) so also the static mercury drop electrode (IMDE) which is recently developed.

12

Introduction to Polarography and Allied Techniques

2.1.1 Dropping Mercury Electrode The DME is the essential component of all polarographic experiments. It was introduced by Kucera in 1903 [1]. Later in 1921, Heyrovsky applied this electrode in the original polarographic apparatus [2]. Usually, the DME is formed of glass capillary tubing connected to a stand pipe of plastic or glass attached to a mercury reservoir. When the level of the mercury in the standpipe is sufficiently high with respect to the tip of the capillary, mercury flows from the capillary at a steady rate and small drops from at the end and fall at a regular interval. These drops have nearly spherical shape if their mass is not greater than about 15 mg and the radius of the capillary is of the order of 0.05 mm. Electrolysis is carried out on the surface of the mercury drops. One of the most important advantages of (DME), as given further, is the continuous renewal of the electrode surface. The periodicity of this renewal is governed by the life of an individual drop. The basic concept involved in the formation of mercury drops are used to define the capillary characteristics required for satisfactory electrodes. This is partially discussed by Kolthoff and Lingane [3].

2.1.2 Flow of Mercury from Capillaries The rate of flow of a liquid through a capillary can be defined by the Poiseuille equation. The volume V of liquid that flows in time t is given by V =

π rc4 Pt 8ln

...(i)

where rc and l are the internal radius of a capillary and its length, n is the viscosity of the flowing liquid, and P is the effective hydrostatic pressure (i.e., P is not exactly equal to the pressure created by the difference between the level of liquid in the reservoir and the lower end of the capillary). The above equation can be rearranged to from m=

Vd π rc4 Pd = t 8ln

...(ii)

where d is the density of the liquid. The effective pressure that acts on the mercury is not exactly equal to the total pressure, Pt, which is given by the equation Pt = h t gd

...(iii)

where h t is the vertical distance between the end of the capillary and the level of the mercury in the reservoir and g is gravitational constant. Mercury flows from the capillary in small drops. The size of these drops is determined by the interfacial tension at the mercury solution interface. The internal pressure in the drop acting against Pt is, according to Ku•cera [1], given by the relation

The Electrodes

13

Pb =

2r r

...(iv)

This internal pressure Pb, often called back pressure is proportional to the interfacial tension r at the mercury solution interface and is inversely proportional to the radius of the drop. Equation (iv) shows that the back pressure in a given solution changes with the growth of a drop and reaches the smallest value at the moment of detachment of a drop from the capillary. Taking an example, a capillary with an internal diameter of 0.06 mm placed into 3 M KCl at a potential –0.6 V, the back pressure changes from 10.44 to 0.97 cm of mercury during the life of the drop. If the mercury column is lower than the first value, obviously the outflow of mercury will not be observed. For construction of the electrode (DME) capillaries are commercially available. In case it is to be prepared from capillary tubing manually, the uniformity is the prime consideration. The length of the capillary used depends on its internal diameter and on the experimental objectives. Usually, the largest drop times should Mercury not exceed 7–8 sec. In general, the capillary Reservoir should be such as to give a drop time of the order of 3–4δ with h t equal to ca. 40 cm when the capillary is dipped into solution. If drop times are too long, it should be cut because a linear dependence exists between length of the capillary and td. The mercury reservoir usually has a volume varying between 100 and 200 cm3. The platinum wire used to make contact to the DME may be dipped in mercury reservoir or sealed in the stand tube. The common assembly used is shown in Fig. 2.1. The connection to the mercury Drop knocking reservoir in normally made using a soft plastic device tubing such as Tygon. The inside diameter of this tubing should be of the order of 5–7 mm Capillary and the connection to the capillary should be reinforced with wire. Once the capillary has been connected, the mercury reservoir should be filled with pure mercury (triply distilled mercury). While filling entrapping of air bubbles should be minimised. The DME requires a stand that facilitates changing position of the mercury reservoir. The mercury reservoir should always be elevated and Fig. 2.1 : Mercury reservoir assembly the flow of mercury observed, before the capillary for use in dropping mercury electrodes

14

Introduction to Polarography and Allied Techniques

is placed in an experimental solution. When the experiment is over, the capillary be placed in distilled water, washed well with it (if required non-aqueous solvent). Mercury should drop there before washing. For parameters characterizing the DME could be determined in the following way. The capillary is placed in a solution of the supporting electrolyte. The mercury reservoir is adjusted to a given h t and a potential is applied, either a value related to experimental measurements or in the range –0.5 to –0.6 V vs S.C.E. A stop watch is used to measure the time for 10–20 drops to form and the drop time, td, is obtained by dividing the elapsed time by the number of drops collected. Mass flow rate of mercury, m, can be measured by collecting drops for a measured time and then weighing the washed and dried mercury. Usual units are milligrams per second.

2.1.3 Advantages of DME The dropping mercury electrode has several advantages over solid electrodes, these are summarized as follows : 1. The drops are very easily reproduced and thus give reproducible results. The regular dropping of pure mercury ensures that the electrochemical process always occurs at a fresh surface, virtually independent of the preceding polarization. As already indicated the results obtained in this manner are reproducible regardless of the irregular dropping in case precipitates are formed. The regular renewal of the surface ensures that the current is independent of the time of electrolysis and that the current voltage curve is the same whether recorded with increasing or decreasing voltages or even rapidly or slowly. 2. Owing to the very high over voltage of hydrogen towards mercury, the DME can be used over a considerable cathodic range of potentials without interference from hydrogen evolution. Polarographic curves for alkali metal ions may be recorded before hydrogen evolution takes place. Instead of mercury dilute amalgams may drop from the dropping electrode and anodic processes in the dissolution of the less noble metals may be studied. With commonly used supporting electrolytes, such as potassium chloride and potassium nitrate, the range extends to about 1.8 V (vs SCE). 3. In view of the behaviour of mercury as a noble metal, relatively positive potentials, but not of course exceeding that for the dissolution of mercury (about +0.4 V vs NCE) may be applied to the DME and the electrode may serve as an indifferent redox electrode for the study of oxidation reduction systems. Moreover, it is not subject to passivation or poisoning owing to constant renewal of mercury surface. This is in contrast to other electrodes. 4. Only small quantities of substances are deposited in the vicinity of the dropping electrode during electrolysis. For the reason there is no depletion of the depolarizer in the solution provided the volume of the electrolyzed solution is not too small. The curves obtained are identical even after several runs. 5. There is also an important factor for the application of polarogaphy is microanalysis because with a thin drawnout capillary the electrolysis of very small volumes (0.01 – 0.005 ml) may be studied.

The Electrodes

15

6. Processes may be studied that take place in aqueous solution in the potential range +0.4 to –2.6 V; and in non-aqueous solution upto –3.0 V (mix of dioxan and water) against the (NCE) normal calomel electrode. At potentials more positive than +0.4 V anodic dissolution of mercury and at potentials more negative than –2.6 V (or –3.0 V) decomposition of water or of the given solvent takes place. Besides, the advantages the use of DME is somewhat restricted. At positive potentials mercury undergoes oxidation and therefore other type of electrodes (standing mercury electrode or solid electrodes) must therefore be used. The volatility of mercury prevents the use of the DME in melts at higher temperatures. Good results are obtained at temperatures upto 100°C.

2.1.4 Hanging Mercury Drop Electrode (a) HMDE Suspended on a Metallic Contact : A simple HMDE was developed by Gerischer [4]. Using this approach 1 or 2 mercury drops falling from the classical DME are collected on a miniature spoon and transferred to a small metal contact scaled is glass or plastic material (Fig. 2.2). The length of the exposed contact wire is usually on the order 0.1–0.5 mm and its diameter is about 0.5 mm. Electrodes of this sort have many different Threaded plunger chemical properties from pure mercury electrodes, because of the formation of a gold or platinum amalgam [5]. Normally, a drop is suspended just prior to an experiment and this problem will, therefore, be of no consequence. Nevertheless, Plastic collar since the solubility of these noble metals in mercury is of the order of 0.05 M, the concentration of gold or platinum in mercury may be quite significant on a longer time scale. In such Reservoir and cases gold or platinum may form intermetallic Capillary (glass) compounds with several metals which are electrodeposited into the mercury [5]. (b) Capillary HMDE : This type of the HMDE consists of a small mercury drop with radius usually not exceeding 1 mm which hangs on a thin mercury thread in a glass capillary. The inner diameter of this capillary is about 0.15–0.21 mm, considerably Fig. 2.2 : Assembled unit, larger than for the DME. An electrode of this Hanging Mercury Drop type was used for the first time by Antweiler [6]. Electrode Preparation of reproducible HMDE as per this original model was very difficult. Kemula and Kublik [7] pointed out that suspended HMDE is more reproducible in comparison to the early design capillary HMDEs.

16

Introduction to Polarography and Allied Techniques

In the most successful designs, the mercury is pushed out mechanically. Randles and White [8] used this type of electrode, where mercury was pushed from the capillary by turning micrometer screw. The most popular electrode used these days was developed by Kemula and Kublik [7]. A detailed assembly of this electrode is shown in Fig. 2.2. It is composed of a thick walled glass tubing with an internal diameter of 4 mm, approximately 5 cm long. This forms a mercury reservoir which is sealed to a thick wall capillary. The internal diameter of this capillary is commonly 0.18 mm, but may vary somewhat around this value. The length of the capillary will depend on the size of the electrolytic cell. A groundglass joint on the mercury reservoir can provide a convenient means of supporting electrode in a cell. A Teflon thermometer adapter also works well. The top of the reservoir resembles a glass ring which is flat and very smoothly polished. This part of the electrode is connected to the plastic head, which is composed of two parts. These parts are shown in Fig. 2.2. After the capillary is inserted through part b, part c is screwed rather tightly into part b. The end of the mercury reservoir should then be tightly sealed by the bottom part c. To provide a tight seal a small plastic cylinder is extended from part c, being bit thicker than the internal diameter of the glass tubing. This small cylinder, schematically shown in Fig. 2.2, should enter into the reservoir tubing with a pressed fit when all parts of the HMDE are put together. A threaded steel piston of 2 mm in diameter moves in part c. By turning this screw by a fixed angle, for instance 90° or 180° mercury will be pushed out from the capillary and will hand as a drop from its end. It is important that the piston screw be set tight in the polyethylene part as shown in Fig. 2.2. In Fig. 2.2 the HMDE is shown ready for use. To ensure that the electrode works properly, special care should be taken to coat the internal part of the capillary with a hydropholic silicone film. The capillary should be thoroughly cleaned before a new coating is applied. Sodium hydroxide (2 M) should be used to remove any residual silicone. The capillary should them be washed with 3 M nitric acid, rinsed with distilled water, and dried thoroughly. Then a 5% solution of dichlorodimethylsilane in CCl4 is pulled through the capillary, followed by air. After several hours at room temperature or about 15 min. at 110°C, the capillary is ready for use. The silicone coating should be renewed from time to time. Specially when ranging drop tends to fall during an experiment. This happens when the silicone coating and the capillary wall is partly destroyed and solution enters between the glass and the mercury thread. The mercury reservoir and the capillary should be completely filled with mercury. There must be no entrapped air. The vessel should be filled with mercury such that the end of the capillary is covered when the vessel is placed in a horizontal position. With all of the mercury in part b, the vessel in connected to a vacuum pump, with a three way stop cock to decrease the pressure in the vessel and in the electrode down to 0.01 mm. After evacuation, the vessel is tilted into the horizontal position as shown in the Fig. 2.3 and the stop cock is turned to disconnect the pump and then turned further to admit air into the vessel. The pressure of air acting on the mercury in the vessel

The Electrodes

17

pushes it into the reservoir and the capillary of the HMDE. If the pressure had been decreased to 0.01 mm, mercury fills in the reservoir and capillary completely. The HMDE is now ready for use. By turning the screw to a fixed angle, a known amount of mercury is pushed out, forming a drop. Such an electrode can be prepared in the laboratory. These electrodes are equipped with a micrometer type of screw of pressing out a well-defined amount of mercury.

2.2 CARBON ELECTRODES Many interesting reactions can be studied which are not accessible at a mercury surface. A wide range of materials have been employed as solid electrodes, but the noble metals particularly platinum and gold, and carbon have emerged as the most popular ones. The ideal properties of a material for use as solid electrode are that: (i) it should be easy to incorporate into an electrode, (ii) it should have a large potential range, a low electrical resistance, and (iii) an easily reproducible surface. These criteria are met only to some degree by many materials. The properties of various types of carbon make it the material of choice for many applications.

2.2.1 Carbon Paste Electrodes The carbon paste electrodes (CPE) was introduced by Adams [8] and generally consists of a Teflon well into which is inserted a platinum, copper, steel or graphite 3 mm spectroscopic contact. The Teflon well may be mounted graphite in the end of a suitable glass tube or consists simply of a piece of Teflon tube as illustrated in the Fig. 2.3. 7 mm O.D. Pyrex The well is filled with a paste, made tubing by mixing powdered graphite with a suitable mulling liquid. Practical consideration require that the mulling liquid should have a low volatility, purity with respect to electroactive impurities, and very low solubility in the medium to be employed. These consideration generally limit the choice of mulling liquid to bromoform, bromonaphthalene, or mineral oil (Nujol). Preparation : A typical paste for CPE may be prepared by mixing Nujol 10 mm Teflon insert machined and graphite powder thoroughly (could for press fit be UCP 1 M from ultra carbon corporation) until the mixture is Polished flat uniformly wetted. The resultant paste should have a consistency similar to that Fig. 2.3 : Conventional Carbon Paste Electrode

18

Introduction to Polarography and Allied Techniques

of peanut butter. The best would be to take 3 gm of carbon to 2 ml of oil. Carbon rough surface should not be used since they give poorer peak current reproducibility. Pastes that appear satisfactory for conventional experiments at millimolar concentration may give rise to many disconcerting background peaks when pulse voltammetry at the micromolar level is tried. High purity graphite is important and the graphite (and paste) should not be unnecessarily exposed to the laboratory atmosphere. It is advisable to divide freshly prepared paste into lots of about 1 gm and to store these in small wide mouth vials. In practice a small amount of paste is placed on a clean card (could be an unused IBM computer card); the electrode is gently pressed into this pile and then rubbed on the card to remove excess paste and to attain a flat surface. The well is filled completely, leaving no holes or channels. Any paste remaining on the mantle is carefully wiped away with a paper tissue. Electrodes may be assembled and packed in quantity and stored in covered box. Electrodes may be renewed by removing a small amount of paste from the surface with a paper tissue and repacking with fresh paste. It is important to note that when packing the well, avoid applying too much pressure. This may result is separation of the carbon and oil. This would result in high resistance contact between the paste and the metal. Other methods of pastes and electrode preparation are being described by many workers. The formulations and methods of preparation of the CPE as described above are quite satisfactory for use in aqueous solutions containing perhaps as much as 25% alcohol or other solvents. However, when carbon paste electrodes of this type are used in non-aqueous media (e.g., acetonitrile, nitromethane, propylene carbonate), the pool of carbon paste tends to disintegrate. The cause of this disintegration appears to be dissolution of the mulling liquid or the preferential wetting of the graphite by the solvent. This difficulty can be overcome by addition of a surface active agent, such as sodium lauryl sulphate, to the paste [15]. The advantage is that the latter compound causes the graphite to be wetted equally well by both, mulling liquid and the nonaqueous solvent. It is a normal practice to prepare a new electrode surface before running each voltammogram. This is done by removing the surface layer of paste and refilling the Teflon holder. This is quickly reproducible manually as recommended by many workers. The preparation of a CPE with an increased positive potential range (+ 1.7 V vs SCE is 0.1 M H2SO4) has also been described [17]. It has been reported by several authors that adsorption of electroactive species at the electrode surface takes place while using CPE. This may be due primarily to the dissolution of the electroactive species in the organic phase of the CPE, although the effect is not of a major importance. All carbon paste electrodes described in the literature have been designed for voltammetric studies. The range of potentials over which the CPE can be used in quite large (large literature values are available).

The Electrodes

19

2.2.2 Glassy Carbon Electrode Glassy carbon was first used as an electrode material by Zittel and Miller [34], although it is commercially available. For this electrode a length of 3 mm diameter glassy carbon rod is scaled into a length of 5-mm tubing with epoxy cement. A few millimeters of carbon are then exposed then from the end of the glass tube using a glass cutting wheel. The end of glass tubecarbon rod assembly is then polished with emery paper, followed by polishing alumina until a mirror finish is obtained. Before each voltammogram is run the electrode is buffed for about 5 sec. with 1μ m alumina, rinsed and placed in the electrochemical cell. Some authors also used the electrode for stripping analysis and others have used it in molten salts as well. Typical data on positive and negative potential limits at GCE are given in the literature. Methods to modify the electrode are already in progress.

2.3 POLAROGRAPHIC CELLS AND SATURATED CALOMEL ELECTRODE

5 mm O.D. Pyrex tubing

Mercury

3 mm Glassy Carbon sealed with epoxy resin

Fig. 2.4 : Typical Glassy Carbon electrode for Voltammetric Studies

It is a long-standing custom of referring all polarographic potentials to the saturated calomel electrode. This is done to permit comparison of half-wave potentials measured in different media. Since the potential of an internal reference electrode varies from one medium to another such comparisons can be made only if the potential of the internal electrode is measured against an external saturated calomel electrode. The cell is that portion of the apparatus which contains the solution being studied. It also includes a non-polarizable electrode to which the potential of the dropping electrode is referred. Oxygen must usually be removed by bubbling an inert gas through the solution before measurement, because oxygen is reducible at the dropping electrode over most of the range of potentials which are important in polarography. It may also have other undesirable effects. The most important part of a cell is its reference electrode. The polarograph applies a voltage across the cell; even neglecting for the moment the iR drop. Any variation or error in the potential of the reference electrode leads to a corresponding uncertainty in the potential of the dropping electrode. It is also important that the potential of the reference electrode be not only known but also essentially independent of the current flowing through it. Two kinds of reference electrodes are in general use. These are “internal” and “external” electrodes, which are generally used. An internal electrode is in direct contact with the solution being studied, while the external electrode is separated

20

Introduction to Polarography and Allied Techniques

from it by a salt bridge or a porous membrane. Internal reference electrodes cannot be used in solutions containing oxidizing agents which have powerful energy to oxidize the electrode metal, or reducing agents are powerful enough to reduce the poising salt (Ag X, Hz 2 X2). Not are they as useful when the dropping electrode is the anode or when it is the cathode. In the former case the solution is usually capable of reducing the poisoning salt chemically, and even of this reaction were slow the poisoning salt would be reduced at the reference electrode as the polarogram was recorded. External reference electrodes, on the other hand have potentials that are either accurately known or can be measured once and for all (usually the SCE is used) and that are independent of the composition of the sample solution. With this only very frequent checking is needed to ensure that no contamination has occurred. When carefully used they rarely need renewing. They may be used with solution containing strong oxidizing or reducing agents. They also render the presence of a depolarizing anion in the sample unnecessary, thereby permitting the range of the dropping electrode to be extended to somewhat more positive potentials. The most widely used cell with an external reference is the H-cell. For Contact to A sample is shown in Fig. 2.5. It consists Mercury Column of two compartments. One containing the solution being studied and the other containing the reference electrode. To avoid ConstantHead polarization of the reference electrode, the Mercury Reservoir compartment containing it should be made from tubing of at least 20 mm i.d. The dimension of the solution compartment can 75 cm be varied widely to accommodate any desired volume of solution. As per the LinganeLaitinen cell as shown in the Fig. 2.5, these compartments are separated by a crossCapillary Tube member filled with a 4% agar-saturated potassium chloride gel, which is held in place Annular For Contact by a medium-parosity sintered-Pyrex disc. Space for To Reference Escape of Nitrogen Electrode In order to facilitate rapid and complete Nitrogen Inlet Tubes deaeration of the solution, the disc should be placed as near to the solution Agar compartment as possible. At the same time Plug Reference the side tube through which the inert gas is 10 cm. Cell passed through the solution should be as near to the bottom of the cell as possible. Sintered Solution The agar gel is prepared by warming 4 Glass Disc of Sample gm of agar and 90 ml of water in a small flask which is put in large beaker filled with boiling water or on a steam bath until Fig. 2.5 : H-cell and stand tube according to Lingane and Laitinen solution is complete. After this 30 gm of

The Electrodes

21

potassium chloride are added and the whole thing is stirred thoroughly. After this the gel is allowed to solidify which must be white to avoid contamination of the solution coming in contact with it. When the salt is dissolved, the clean dry cell is clamped with the cross-member vertical and the solution compartment down. The gel is pipetted into the cross-member until it is almost completely filled. The cell is then allowed to stand undisturbed until the gel is solidified. The unused gel may be stored in a lightly stoppered flask which could be used again after reliquing it. After the gel is solidified, the cell is turned upright the enough pure mercury is added to the reference-electrode compartment to give a layer 1 to 2 cm deep. This is then covered with an equally thick layer of a paste made by stirring equal weights of mercurous and potassium chlorides with a little saturated potassium chloride. The compartment is then filled with saturated potassium chloride solution containing a large excess of solid salt. Electrical connection to the mercury is made by means of a glass tube through which a small platinum wire is sealed so as to project into the mercury for a few millimeters. This tube is filled with mercury and inserted into a rubber stopper which serves to seal the reference-electrode compartment lightly. The wire leading to the reference-electrode terminal of the polarograph is simply dipped into the mercury in this tube. The solution compartment of the cell should finally be filled with saturated potassium chloride solution and a day or two should be allowed for the SCE to attain equilibrium. While in use, the solution compartment is emptied, washed with water and either dried or rinsed with several portion of the sample. Then enough solution is added to cover the entire fritted disc. Dissolved air is removed by passing nitrogen into the side tube so that it bubbles through the solution. Measurements should not be attempted while the gas is bubbling through the solution. Stirring may cause high erratic currents. Finally the dropping electrode is inserted through another hole in the stopper and the measurements be carried out. It is advisable to keep two cells available in routine work so that the solution can be deaerated in one while the other solution is being examined in the other cell. Insertion of dropping electrode should be deferred to avoid prolonged contact between mercury and the solution. If it is inserted before deaeration is complete, mercurous or mercuric ion may be formed according to the reaction: 4 Hg + O2 + 4H+ = 2Hg2++ + 2H2O In case, the solution in acidic and contains no ion yielding in soluble mercury salt, or an appreciable fraction of a heavy metal ion may be lost by a reaction like Pb++ + 2Hg + 2Cl– +

1 O + H2O = Hg2Cl2 + Pb(OH)2 2 2

if the solution is neutral and unbuffered. The solution compartment of an H-cell should never be allowed to stand empty for more than a few minutes at a time. The agar bridge will dry out and shrink, allowing bulk flow of the liquid between the two compartments of the cell. It should always be

22

Introduction to Polarography and Allied Techniques

kept filled with either water or, for overnight or longer period with saturated potassium chloride. Mercury must also be removed before the cell is allowed to stand even overnight to avoid air oxidation of mercurous salts. Contamination of H-cell must be avoided using various samples.

2.4 MERCURY POOL ELECTRODE Mercury pool reference electrode has been widely used since the beginning of polarography. It is simply a pool of pure mercury on the bottom of the cell, connected to the polarograph via a platinum wire sealed through the wall of the cell. The area of the mercury pool electrode should not be too small but need not exceed several square centimeters. Micro cells of various sizes can also be used which may contain small volumes of solution. Mercury pool electrodes should be used only in solutions that contain ions giving insoluble mercurous or mercuric ions.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Ku•cera, B. Ann. Phys. 11:529 (1903). Heyrovspy, J., Chem. Listy 16:256 (1992) Philos. Mag. J. Sci. 45:303 (1923). Kolthoff, I.M., and Lingane J.J., Polarography, Vol. I, Inter Science, N.Y. 1952. Gerischer, M., Z. Phys. Chem. 202:302 (1953). Kemula M. and Coworbers, Bull. Acad., Pol. Sci. Cl. 111 7:73 (1959). Ant Weiler, H.J., Z. Electrochem. 44:831 (1938). Kemula W., and Kublik Z., Advances in analytical Chemistry and Instrumentation, Vol. 2, Wiley Int. N.Y. (1963) p. 123. Randles, J.E.B. and White. W., Z. Electrochem. 59:666 (1955). Adams R.N., Anal. Chem. 30:1576 (1958). Marcoux, L.S. and Coworbers, Abel. Chem. 37:1446 (1965). Lind quist, J. Anal. Chem. 45:1006 (1973). Zittel, H.E. and Miller, F.J., Anal. Chem. 37:200 (1965).

CHAPTER 3

THE TECHNIQUE 3.1 POLAROGRAPHIC CIRCUIT Polarography constitutes a unique type of electrolysis in that it involves the study of current voltage relationships at a dropping mercury electrode under certain controlled conditions. A current-voltage (or current-potential) curve can be obtained by gradually increasing the applied voltage and measuring the corresponding mean currents; plotting the currents against voltage. In order to avoid time consuming measurements and curveplotting, automatic recording polarographs are available. These instruments serve for recording based on electrochemical polarization. Any electrolysis involves two main types of processes, e.g., transference of matter through a solution towards and away from electrodes and electrochemical processes involving as an essential part the exchange of electrons at the electrode surfaces. During an electrolysis, three mass transfer processes are of importance, namely, migration, diffusion and convection. The first of these is an electrical effect depending upon the charge carried by an electroactive species and upon its transference number. Thus, the effect is encountered only with charged species. Since processes of diffusion are non electrical in origin, these are for all species in solution whether they are charged or not. Convection effects include motion of small particles under the influence of stirring, mechanical agitation, and temperature gradients.

3.2 THE SIGNIFICANCE OF DIFFUSION IN CLASSICAL POLAROGRAPHY While studying the polarographic work, the migration effect is usually eliminated and it is usual to study the oxidation or reduction of electroactive species in solution under conditions such that the latter arrives at the indicator electrode by natural diffusion only. Suppression of migration effect is achieved by mixing together with the species under study, an excess of supporting “electrolyte” or “indifferent” electrolyte normally 50–100 fold is excess of the electroactive component of the solution. This added electrolyte is so chosen that no electrode reactions characteristic of it interferes with those of the species under investigation. Supporting electrolytes serve as current carriers and, by virtue of being in excess effectively reduce their transference numbers to zero. Convection effects are eliminated by carrying out the electrolysis in adequately controlled thermostats so as to protect the apparatus from all forms of shocks and vibrations.

24

Introduction to Polarography and Allied Techniques

Current i

Basically, polarography consists of electrolysing a solution containing several cations between a dropping mercury electrode and some reference electrode. The –ve dropping mercury electrode (DME) usually functioning as cathode. A potential is applied between these electrodes and increased in a step-wise manner. During this process, corresponding current changes being observed at each applied potential. Essentials of the electrical circuit required +ve are shown in the Fig. 3.1. The applied potential is varied by means of a potential divider circuit while the current flowing is indicated on a sensitive galvanometer. Diffusion-controlled currents observed in Fig. 3.1 : Essential Polarographic Circuit polarography are usually of the order of a few micro-amperes since the electroactive material used is of the order of 10–3 molar. As already given in Chapter 2, a dropping mercury electrode consists of a series of small mercury droplets which emerge, at a constant rate, from the tip of a capillary attached to a constant head device. The life-duration of each drop normally lies between 3–7s. Considering the reference electrode and anode a large area mercury pool on the bottom of the electrolysis cell is shown to be used. This is just for the sake of simplicity. Due to its large area and the small magnitude of the currents normally encountered, the potential of such a electrode remains fairly constant with varying applied potential. For most practical measurements, it is normal to replace this by a saturated calomel electrode (SCE) [see Chapter 2] or some other reliable reference electrode whose potential is independent of the imposed Diffusion current id potential. To examine the nature of the current voltage relationships Residual current observed on reduction of a metal ion in solution, it is necessary to flush the working solution with some inert gas, such as nitrogen or hydrogen, so as to remove dissolved oxygen which may cause Half wave applied e.m.f. potential E½ interference by itself undergoing reduction, in two stages, within the Fig. 3.2 : Essential features of a polarographic currents normal potential working range. voltage curve/polarogram or polarographic wave When this interference is removed

The Technique

25

the current-voltage curve for the reduction of the metal ion will have the appearance of that shown in Fig. 3.2. At first, as the potential is increased cathodically from zero, only a very small currents flows. This is called the residual current. This is essentially a charging current arising from the charging of the double layer at each drop and is non-faradaic. The residual current may also contain small (faradaic) components due to the presence of reducible impurities in the solution. These may be introduced through the high concentration of the supporting electrolytes used. Only the residual current flows until the decomposition potential of the reducible ionic species is reached. At this point the ions, designated mn+, begin to be discharged owing to their reduction by the process: Mn+ + ne

M (Hg)

...[1]

↓ (Product of electrode reaction) Very often the metal atoms produced are absorbed into the mercury drop in the form of amalgam. A steep rise in current is now observed and, with a further small increase in applied, potential, the rise will continue. However, the Mn+ ions Depolarizer Concentration arrive at the DME by the relatively slow process of natural diffusion. Since C0 = Bulk concentration the rate of reduction increases with the applied potential, a point is eventually reached at which the ions Electrode are reduced as fast as they diffuse Surface C = Surface concentration solution across the concentration gradient set up at the electrode surface. The Fig. S = Diffusion layer thickness 3.3, represents the concentration gradient in the immediate vicinity of planar section of the electrode surface. Distance from electrode surface→ When the concentration of ions at the electrode surface approaches zero, the Fig. 3.3 : Concentration gradient at coplanar section of electrode surface induced by the current no further increases in the occurrence of an electrode process. overall electrode reaction rate which is now the decomposition potential of some other reducible species present in solution is reached. This could be regarded as the discharge of supporting electrolyte cation, though not hydrogen due to the exceptionally large hydrogen overvoltage on mercury. Particles reduced at the mercury surface subsequently diffuse away from the surface and this may occur in one of the two ways: (i) If an amalgam is formed, e.g., with thallium, lead, cadmium, zinc and alkali metals. In this case, the reduced particles diffuse from the drop surface into the bulk of mercury forming the drop which subsequently detaches from the capillary tip;

26

Introduction to Polarography and Allied Techniques

(ii) If amalgam formation does not occur, e.g., for the reduction processes Fe3+ Fe2+ and Sn4+ Sn2+. The reduced species simply diffuse back into the bulk of the solution. The importance of polarography for quantitative analysis lies in the direct proportionality which exists between the limiting diffusion current and the concentration of the reducible species or “depolarize”. It is to be noted that at the foot of the currentvoltage curve, or polarographic “wave”, and at the limiting current plateau, the dropping electrode behaves is accordance with the definition of a “polarized” electrode. That is to say, the potential applied to it may be altered at will within these regions without sifnificantly altering the current flow. On the rising part of the wave, the current changes considerably for only a small variation in applied potential and the DME is said to be “depolarized”. In the region of the plateau current, id, the dropping electrode is completely “concentration polarized”, since the electrode reaction rate is controlled by the diffusion rate and hence by the concentration gradient at the electrode surface. The potential corresponding to the mid-point of the wave, where the current is exactly one-half of the maximum value id/2, is known as the “half-wave potential”, E ½. This is depolarized under fixed solution condition. Measurement of half-wave potentials therefore serves as a means of identification of different reducible species. (ii) Experimental Technique : For experimental purpose let us consider the electrolysis of a solution containing a cation or a solution containing several different cations, e.g., Cu+2, Tl+, Zn+2, etc. There is a certain reversible potential at which each ion is discharged at the cathode. The potential depends on the standard E 0 of the electrode M/M+2 and on the concentration of M+2 in the solution. At 25°C, E = E0 +

00592 . +2 log aM [z ]

...[2]

Thus a tenfold change in the ionic activity changes the discharge potential of the ions by 0.0592/(z) volts. A factor of 102 in activity corresponds to 0.1184/(z) volts. On gradually increasing the potential applied to the cell, the cation with the highest value of E deposits first. On continuing to increase the applied potential, the current density also increase. As the current density rises, the concentration of the ion being discharged becomes more and more depleted in the neighbourhood of the cathode, particularly if the solution is not stirred. This is the phenomenon of concentration polarization. Eventually the limiting value of Id′ is reached for the care of stationary electrodes. The Id vs voltage curve becomes flat and the potential rises to a value determined by the reversible discharge potential of the cation with next higher E. When this happens the second ion begins to be discharged, even though there may still be an appreciable concentration of the first ion in the bulk of the solution. With increasing E, this process may be repeated with a third kind of ion, and so on. If concentration polarization is used to differentiate reducible substances in a solution, it is necessary to have a cathode of tiny area, since otherwise the current

The Technique

27

through the cell would become very high. Transference must also be eliminated on the part of the electroactive ion so that the current is not strongly dependent upon the mobility of the anion present. Also the cathode surface should be clean, reproducible and, readily renewable. These conditions are met by the DME, which provides a continuous flow of droplets of mercury, about 0.5 mm in diameter. The anode should be practically non-polarizable. A pool of mercury located at the bottom of the cell can serve as a reference electrode and anode. It is negligibly polarized because of its large area. Alternatively, standard reference electrodes of large area can be used as reference anodes. These specifications are already given in previous chapters. A typical current density vs voltage curve in shown in Fig. 3.4.

Current , microamperes

2

a

b

c

1

0 –1.2

–1.2

–1.2 Ed.e. , volts vs. S.C.E

–1.6

Fig. 3.4 : Polarograms of 0.5 mM zinc (II) in 2F sodium hydroxide. The drop time at – 1.6 V. vs. S.C.E. was (a) 12, (b) 4, and (c) 1.4 sec.

The high over voltage for hydrogen discharge on mercury is a great advantage in the polarographic study since, it allows many ions to be studied which have reversible electrode potentials below H2 / H+. Even Na+ and K+ may be discharged before H+ at the dropping mercury electrode. During the process of experiment, the current oscillates between a maximum and a minimum as each mercury drop grows and falls. The overall rise from one flat portion

28

Introduction to Polarography and Allied Techniques

of the curve to the next is called the polarographic wave (as already described). The half-wave potential (already shown in figures) serves to identify the reducible ion. The value of the diffusion limited current for each ion is proportional to the concentration of the ion. The theoretical calculation of diffusion current is a solution of the diffusion equation given by Ilkovi•c, [2] I = 0.732F |z| D1/2 cm2 t1/6

...[3] where m is the mass of mercury flowing per second, D is the diffusion coefficient of the ion, t the drop time and c the molar concentration. This proportionality is the basis of quantitative application of polarography. It is to be noted that the current is proportional to the concentration for a given capillary and for a given ion. The Ilkovi•c equation can also be used to estimate [z] or D under the conditions of the experiment. Stationary micro electrodes are seldom used in practical polarography because the diffusion current decreases markedly with time as the thickness of the diffusion layer, δ, increases. In such experiments rotating platinum electrodes are used. From the equation [3] it is predicted that the plot of Ed.m.e. vs log [I / I ′ –I ] should be linear for a reaction that behaves reversibly under diffusion controlled conditions and the slope of this linear plot should be RT/2.303/z/F and that the intercept denotes the E ½. Polarography is useful in research because it is a convenient method for measuring electrode potentials and for studying electrode reaction.

3.3 SOLVENTS AND SUPPORTING ELECTROLYTES All electrochemical phenomena occur in a medium, which generally consists of a solvent containing a supporting electrolyte. The “solvent system” is a term to describe the medium consisting of both the solvent and the supporting electrolyte. As a matter of fact there is no universal solvent, and generally a system is used whose merits outweighs its disadvantages for a particular application. It may happen that a good solvent system for one type of experiment or compound may be totally unacceptable for other application. It is therefore one’s choice as to how the chemical and electrochemical properties of the electrode reaction in which one is interested may be affected by a particular solvent system. For all practical purposes, the solvent system should not undergo any electrochemical reaction over a range of potentials on which the reaction is to be carried out. A solution of tetrabutyl ammonium hexafluorophosphate in acetonimile exhibits positive and negative decomposition potentials of +3.4 and –2.9 V (SCE) respectively. In practice one rarely needs both positive and negative ranges in a single set of experiments. Solvents are often used which exhibit either a very negative or very positive decomposition potential, but not both. For example both nitrobenzene [3] and methylene chloride [3] have been used for studies of oxidation processes because they are oxidized with difficulty, not withstanding with the fact that they are actually quite easily reduced. On the contrary, liquid ammonia and methlamine are good solvents for electrochemical reduction, although poor for oxidation.

The Technique

29

As a matter of fact the potential limit in a given solvent system is set not by the solvent itself but by the electrochemical behaviour of the supporting electrolyte. It has been known for years that the reduction of alkali metal ions to the corresponding metals (–2 V vs SCE) is generally the potential limiting process in aprotic solvents and that by use of tetra alkyl ammonium salts one can reach considerably more negative potentials. The decomposition potentials of tetra alkys ammonium ions of mercury become more negative as the alkyl groups become larger, e.g., Me4 N+ : 2.65 V; Bu4 N+ : – 2.88 V. In order to support passage of an electrical current, the solvent system should have low electrical resistance and a moderately high dielectric constant (≥ 10). A number of most commonly used solvents used in organic electro chemistry have satisfactory dielectric constants, e.g., dimethyl formanide (3.6), acetonitrile (37.5) and dimethyl sulphoxide (46.7). So also their electrolytic solutions have acceptably high conductances. Considering the solvent power, an electrochemical solvent must be able to dissolve a wide range of substances at acceptable concentrations. This generally means that electrolytes must be soluble at least to the extent of 0.1 M, while the electroactive material must form approximately millimolar solution for application of the various electroanalytical techniques or greater for preparative electrolyses. Tetra alkyl ammonium perchlorates, hexafluoro phosphates and tetra fluoroborates generally exhibit the most satisfactory solubility as electrolytes in organic solvents. As a matter of fact chemical inertness of the solvent is an important aspect to be considered. The solvent, as such should not react with the electroactive material, nor with intermediates or products of the electrode reaction under investigation. No one solvent could reasonably be expected to be unreactive toward all of the many kinds of reactive species which can be generated electrochemically. It is known that many anodic organic reactions generate cationic species [1] and hence to use a nucleophilic solvent is not desirable. Acetonitrile is commonly used in anodic studies but it is moderately nucleophilic. Therefore attempts to characterize electrochemically generated cations may require a less reactive solvent, e.g., methylene chloride or one of the “super acid” solvents. On the other hand, reductions of organic species generally form anions, and use of protic solvents to avoid acid-base reactions between the solvent and cathodically generated intermediates. On the whole solvent should reasonably be stable so that purification, preparation, and storage of standard solution does not create major problems. Also the solvent should have a convenient liquid range. No doubt this depends on the experiment involved. Much depends whether the experiment is to be carried out at room temperature or otherwise. Moreover the solvents and electrolytes should be inexpensive, nontoxic, and non-flammmable. The latter two characteristics are not well satisfied by most organic solvents. They can be used with in acetonitrile and are stable to very positive and negative potentials salts like hexa fluorophosphate are rather insoluble in water, which means that they are non-hydroscopic and can often be separated from reaction products by evaporation of the acetonitrile followed by appropriate treatment (e.g., extraction with a non-polar solvent). Inorganic electrolytes like NaBF4 or NaClO4 may be useful in such cases. Methylene chloride is useful in organometallic

30

Introduction to Polarography and Allied Techniques

electrochemistry in situations where acetonitrile is found to displace ligands coordinated to a metal center. Dimethyl formamide, acetonitrile, and dimethyl sulphoxide are all excellent solvents for reductive electrochemistry of organic compounds. Water and alcohols are useful for inorganic electrochemistry. Dimethyl sulfoxide is particularly useful solvent for cathodic electrochemistry, although with inconvenient liquid range (18–189°C). TBAHFP and TBATFB are good electrolytes for use in organic solvents. Dimethyl sulphoxide is an excellent solvent for both organic and inorganic compounds. Water which is always present in dipolar aprotic solvents is a poor proton donor in DMSO. TBAHFP and TBATFB are two of many electrolytes for use in DMSO. Irregular drop time behaviour is observed in polarography in DMSO, possibly due to strong proper ventilation and safety precautions. Nevertheless, the property, viscosity may be of importance. When time interval is wished to be extended, i.e., the time interval over which mass transfer is occurring solely by diffusion (e.g., potential-step experiments) but would be a disadvantage where efficient mass transfer is required, as in preparative-scale electrolyses.

3.3.1 Recommended Solvents and Electrolytes Much inorganic oxidative and reductive electrochemistry has been carried out in water with little difficulty. Organic and organometallic compounds generally either are not very soluble in water or are reactive towards it. This has created interest in the use of non-aqueous solvents in electrochemistry. Ethanol and methanol are good organic solvents, inexpensive, readily available in high purity and dissolve salts readily. Alcohols, like water are rather easily oxidized and are highly nucleophilic. Hence it has been more common to use aprotic organic solvents for electrochemical oxidations. At the present time acetonitrile is the most commonly used organic solvent for anodic electrochemistry. It is preferred solvent for most purposes having a convenient liquid range (–45.7– 81.6°C). Tetrabutyl ammonium hexafluorophosphate or tetrafluoroborate salts are highly soluble adsorption of DMSO or dimethyl sulphide on the mercury surface. Most widely used organic solvent for cathodic chemistry has been DMF. It has a number of desirable properties at the same time it is quite toxic and undergoes undesirable reactions on storage. It is felt that acetonitrile and dimethyl sulphoxide are preferable to DMF as solvents for most applications. Hexamethyl phosphoramide (HMPA), ammonia and methylamine are excellent solvents for electrochemical generation of solvated electrons. Lithium chloride is recommended as the supporting electrolyte for this application. The properties of HMPA are otherwise generally similar to those of DMF and DMSO. Tetrahydrofuran (THF) and other ether solvents are useful aprotic solvents for cathodic electrochemistry inspite of their low dielectric constants, because they can be dried more efficiently than the other polar solvents. Note : More details are given in the chapter describing non-aqueous solvents.

The Technique

31

3.4 POLAROGRAPHIC MAXIMA It is often observed on polarographic curves that an increase of current above the limiting value takes place in the form of various shapes. In some cases the origin of the current maximum is connected with the mechanism of the electrode process, as happens during the catalytic discharge of hydrogen ions. More frequently, the polarographic maxima are caused by increased transport of the depolarizer towards the electrode by a streaming motion of the solution. Such maxima are reproducible and are called streaming maxima. These are divided into maxima of the first and of the second kind. Maxima of the first kind appears on the rising portion of the polarographic curve and usually occur in dilute solutions. The maxima of the second kind are observed in more concentrated solutions and at high mercury flow rates. They appear only over the range of the limiting current. These are usually rounded and do not fall discontinuously to the limiting current like the maxima of the first kind.

3.4.1 Maxima of the First Kind Kucera [3] put forth that streaming maxima of the first kind are connected with the anomalies observed on electrocapillary curves. Maxima of this kind appears on polarographic curves for currents governed by diffusion, usually in dilute solution of the supporting electrolyte used (below 1 N), the ratio of the concentration of depolarizer to that of the supporting electrolyte being from 1 : 1 to 1 : 100. Maxima have been observed during the polarographic reduction and oxidation [4] of cations, anions and neutral molecules and with anodic waves for the dissolution of amalgam [5], in both aqueous and non-aqueous [6] solutions and in melts [7]. Their shape is characteristic. The increase in current starts on the rising portion of the polarographic wave. The current rises rapidly with increasing voltage until it is several times greater than the limiting current. The maximum for the reduction of mercurous ions can be as much as 40-times higher than the limiting current [8] and then falls discontinuously to the normal current. Thus, a more or less sharp current peak which is typical of this kind of maxima is formed on the curve. The height of the maximum varies with different depolarizers. With the same substance it depends on the supporting electrolyte, on its concentration and on the presence of other substances present in the solution. At constant depolarizer concentration, the maximum increases with increasing concentration of supporting electrolyte upto a certain limit and then decreases again. The dependence of the maximum on temperature, drop-time and mercury flow-rate cannot be expressed by simple a relationship [9]. The height of the maximum is virtually independent of the height of the mercury head. In addition to other factors (depolarizer concentration, conductivity of the solution and drop-time), the voltage at which the decrease in maximum current starts depends on the direction in which the applied electromotive force is varied. The peak of the maximum on a reduction wave is upto 100 mV more negative with an increasing applied electromotive force than with a decreasing one. This phenomenon, called “hysteresis of the maximum” [10] is specially evident with longer drop-times and solutions of low conductivity.

32

Introduction to Polarography and Allied Techniques

Streaming mercury electrodes do not give maxima. Particularly high maxima are termed during reduction of silver, mercury, copper, indium and alkali metals, persulphates and molecular oxygen. The cations of alkali metals, on the other hand, give small maxima. Cadmium which is reduced at the same potential as indium forms no maxima. As a rule, no maxima are observed with aldehydes and most nitro compounds. Maxima on the anodic waves for dissolution of amalgams exhibit the same features as those on the polarographic curves for depolarizers present in solution. The highest maxima about twice as high as the limiting current are given by amalgam of thallium, cadmium, and zinc. Smaller maxima were observed with tin and lead [11].

3.4.2 Suppression of Maxima of the First Kind The height of a maximum of the first kind is very sensitive to the presence of surface active substances in solution. Due to maxima it is impossible to evaluate precisely the polarographic curves. Hence, it is necessary to remove maxima by adding surface active agents. In practice, gelatin is usually employed but also, similar effect is found with other higher-molecular organic substances such as various acids and alcohols, dyes, terpenes and neutral detergents like Triton X and some others. These substances suppress maxima over potential range within which they are adsorbed on the mercury surface, hence the influence of the same surface agent on the maxima of different depolarizers is different. In cases where individual substances do not suppress maxima sufficiently, their mixtures are often used [6]. It is important not to add more surface active agent than is necessary. Even a slight excess may affect the electrode process which would not allow correct evaluation of the polarographic curve. Substances with a higher molecular weight or a low solubility suppress the maxima more efficiently than low molecular and easily soluble substances.

3.4.3 Polarity of Maxima of the First Kind In cases where the mercury surface bears a positive charge, the maximum is described as a positive maximum. This takes place if the half-wave potential of the depolarizer, the maximum for which is being investigated, lies on the positive side of the electrocapillary curve. If on the other hand, during the formation of the maximum, the electrode is negatively charged with respect to the solution, it is reported as negative maximum [Fig. 3.5]. No maxima of the first kind are formed at the potential of electrocapillary zero. The reduction of cadmium ions [12] can be taken as an example. At about –0.60 V (vs NCE) is the half-wave potential of free cadmium ions and no maximum is formed on the wave. On adding a trace of iodide the maximum on the electrocapillary parabola shifts to a more negative potential and a positive maximum appears on the cadmium wave. In the presence of ammonia or cyanides, both of which form stable complexes with cadmium ions, the reduction potential of cadmium shifts to negative potentials and a negative maximum occurs on the reduction wave.

The Technique

33

The polar character of maxima becomes evident from the way in – which they are suppressed [Fig. 3.6]. The negative maxima are – suppressed by polyvalent cations at sufficiently lower concentration + by di- or monovalent cations. The Mn suppression occurs in this case regardless of the anion of the –1.6V added salt. On the other hand the Ni positive maxima are not sensitive Tl to the valency of the cations. They –1.0V are more easily suppressed by S = 3:1000 –0.3V electrolytes with divalent than with monovalent anions. Other properties of ions are effective Fig. 3.5 : Positive maximum on the reduction wave for besides the charge. Thus heavy thallus ions and negative maxima for nickel (II) and cations suppress maxima more manganese (II) ions readily than those of the light elements. The polarity of positive and negative maxima also appears when dyes and colloids are added. Positive maxima are suppressed by anionic dyes, but negative maxima by cationic dyes or alkaloids. Similarly positive colloids easily suppress negative maxima and negative colloids are more powerful in suppressing positive maxima. Apart from the different behaviour of suppression, the positive and negative maxima differ somewhat in their shapes. The positive maxima exhibits a relatively broad rising portion, rounded peaks too and fall directly to the limiting current. The 1 negative maxima on the other hand 2 are on the lower side, more acute 3 and often decrease below the 4 5 limiting current. Fig. 3.6 : Influence of Ba2+ on positive and negative maxima. To 25 ml of 5.10–3 N TlCl and NiCl2 the following volumes were added: 1 0; 2 0.05 ml; 3 0.1 ml; 4 0.2 ml; 5 0.4 ml of 1 N BaCl2.

34

Introduction to Polarography and Allied Techniques

3.4.4 Streaming of Electrolyte and Maxima of the First Kind Bruns and his co-workers [13] observed a streaming accompanying the maxima at a mercury cathode of 5 m diameter during the reduction of mercurous nitrate (in nitric acid with 70% ethanol) at low temperatures. The streaming occurs both at room temperature and at –37°C. At –38°C, when mercury solidifies, the streaming and the maximum disappears. Examples of streaming and maxima do not appear with solid electrodes except during the reduction of mercurous ions at a platinum electrode when a film of metallic mercury [14] forms on the platinum surface. Popova and Kryukova [15] demonstrated that the stirring at the surface of a dropping mercury electrode and the corresponding polarographic maximum can be evoked by placing the dropping electrode in an electric field between two platinum electrodes. In cases where, the surface active agents are added to the solution they are adsorbed on the electrode surface and are carried away by the motion of the mercury and of the electrolyte to the place of greatest surface tension. They accumulate there and decrease the surface tension and thus a force against the streaming arises. The iR drop increase with the growth of the mercury drop provided the resistance of the circuit is sufficiently large and the potential of the drop becomes more positive. Thus streaming may start suddenly on a drop through which a diffusion current passed at the beginning and on the current-time curve a jump up to the maximum current appears. This mechanism may explain the current-time curves observed by Bridi•cka [16] and the hysteresis of the polarographic maxima. If a polarographic cathodic curve is recorded with decreasing voltage then the iR drop in the diffusion current is smaller than that at the maximum and the zero potential is reached, i.e., the maximum appears at the lower applied voltage than with polarization in the reverse direction. Maxima of the second kind may be suppressed by reducing the flow rate, e.g., by lowering the height of the mercury head. In accordance with this dependence on the flow rate, no maximum of this kind has been observed with stationary mercury or other electrodes. It occurs with a rotating mercury electrode, but not with a streaming mercury electrode because of its specific hydrodynamic properties. At constant flow-rate and constant drop-time, a maximum of the second kind increases as a linear function of the depolarizer concentration. With increasing concentration of the supporting electrolyte, the decrease in current in the direction from the potential of electrocapillary zero becomes less steep. An external resistance in the polarizing circuit does not affect the height of a maximum of the second kind. No hysteresis has been observed with maxima of this kind. The temperature coefficient is greater than with diffusion currents.

3.4.5 Maxima of the Second Kind Maxima of the second kind occurs on both cathodic and anodic polarographic diffusion currents [17]. These occur usually in concentrated solutions of supporting electrolyte, above 0.1 N. They appear on the limiting current and may, depend on the purity of the

The Technique

35

solution, exceed it five times. In contrast to the maxima of the first kind, the current for these maxima does not fall back abruptly to the limiting current. It only decrease slowly and the greater the distance from the electrocapillary zero the slower the decrease. Exceptionally, a maximum of the second kind may occur with an extremely pure solution of 0.01 N –0.1 N supporting electrolyte at the potential of the electrocapillary zero. Its form then resemble a maximum of the first kind [Fig. 3.7]. The flow rate of the mercury is a decisive factor for the occurrence of maxima of the second kind. They appear as curves as soon as the linear speed of flow exceeds 2 cm / sec, this corresponds to m = 2.14 mg sec for a capillary with a diameter of 0.1 mm. The maximum grows approximately linearly with increasing flow-rate. Above the rate 8 cm/sec further growth of the maximum is retarded.

3.4.6 Suppression of Maxima of the Second Kind

μA

Maxima of the second kind are also sensitive to the presence of surface active agents like those of the first kind. They reflect better the adsorption of substance of widely differing character, since they are drawn out over a broader range of potentials than those of the first kind. A decrease in the maximum on a polarographic curve occurs in the presence of a surface active substance at the potential, at which the 40 substance is adsorbed. At the adsorption potential, the current attains the original value associated with the absence of 30 adsorption. The sensitivity of a maximum of the second kind to adsorption is some one hundred times greater than the 20 sensitivity of the shape of electrocapillary curves to adsorption, with increasing id concentration of adsorptive substance, the 10 decrease on the curve becomes more pronounced until the current falls finally to the normal limiting values and the 0 –0.5 –1.0 –1.5 V maximum of the second kind remains suppressed until the desorption potential Fig. 3.7 : A maxima of the second kind is reached. The plot of the maximum current against the logarithm of the concentration of the surface active substance is S-shaped curve, i.e., the maximum is most sensitive to the addition of a surface-active substance when the maximum has been suppressed to one-half of its original height. The maximum to the suppressive action of surface-active substance rises with increasing drop-time. The adsorption of a number of normal aliphatic alcohols were investigated by Kryukova and Frumkin [18] who suppressed the maxima on the Hg 2Cl2 wave in 3 N

36

Introduction to Polarography and Allied Techniques

KCl. The adsorption of the alcohol on the electrode rises with increasing chain length. With easily soluble alcohols like ethanol, propanol or butanol, they observed increasing suppressive activity upto a certain concentration. On further addition, the maximum increased again. While preparing solution for studying adsorption by means of a maxima of the second kind, the utmost purity must be secured. Micka [19] recommended the purification of solutions by means of active carbon. The shape of a polarographic wave with a maximum of the second kind depends on the purity of the solution as regards surface-active agents.

3.4.7 Streaming of Electrolyte with Maxima of the Second Kind The increase of current above the limiting value due to a maximum of second kind is accompanied by streaming of the solution around the dropping electrode [20]. The direction of this streaming is always the same from the bulk of the solution to the bottom of the drop, over the mercury surface to the neck of the drop and there horizontally along the tip of capillary into the solution (Fig. 3.8). The intensity of this motion attains its maximum at the potential of the electrocapillary zero and slowly decreases with the distance from this potential. The velocity of this streaming exceeds for that for maxima of the first kind by about one order. There is a linear dependence between the flow rate of the mercury and the speed of motion of the solution.

Fig. 3.8 : Direction of stirring action in mercury and in a solution with a maximum of the second kind

3.4.8 Interpretation of Maxima of the Second Kind As maxima of the second kind have a purely hydrodynamic origin, as compared with the maxima of the first kind, and are not caused by any process at the electrode. As with the maxima of the first kind, the relative motion of the mercury and of the solution or maxima of the second kind is analogous to the fall of a mercury drop in the solution. The fall in the maximum with potential on either side of the electrocapillary zero is caused by increasing inhibition of the motion of the surface due to electric charge of the double layer, which because of streaming accumulates at the neck of the drop. Thus, an electric field is formed which decreases the surface tension and counteracts the motion of the mercury. If a surface-active substance is present in solution it is adsorbed at the electrode surface and the motion of mercury carries it to the neck of the drop where it accumulates. The mechanism of suppression is the same as that for maxima of the first kind, because of increased adsorption the surface tension at the neck decreases as compared with that at the bottom. The difference in surface tension gives rise to force opposing the direction of the motion. When the drop-time is lowered, there is not enough time for

The Technique

37

the accumulation of a sufficient amount of suppressing agent. At this stage, the “false waves” disappear and pure maxima occur. A sufficient decrease in the flow-rate removes the “false waves” by stopping the motion of the mercury surface. It often happens in practical polarography that the experimental conditions favour the formation of maxima of both the first and second kind as a single curve. The fundamental requirement is a sufficiently high flow rate of mercury. Also curves with different shapes are encountered that at first sight could be ascribed to maxima of either the first or the second kind, but are due to catalytic origin only.

3.4.9

Practical Applications of Polarographic Maxima

Since the maxima are sensitive to the presence of surface-active agents, maxima that interfere with the accurate evolution of polarographic curves in normal polarographic measurements sometimes permit the detection and the determination of substances that are neither oxidizable nor reducible, but are only absorbed on the electrode surface. Thus, the so called polarographic adsorption analysis is not specific, but it proved to be useful in determining the purity of various substances which contain impurities of colloidal character mostly of organic. The methods making use of a maximum of the first kind are on an average sensitive to 0.0001% of impurities. Those based on suppression of a maximum of the second kind are more exacting as regards the purity of the solutions and chemicals used, but they are by about two orders more sensitive. Polarographic adsorption analysis is used extensively: (i) In the control water purity, (ii) In sugar industry for refining sugars, (iii) The chemistry of polymers, oils and photographic gelatins, (iv) In food analysis, analysis of industrial products, (v) Soil analysis and plant physiology.

3.5

POLAROGRAPHY IN NON-AQUEOUS SOLVENTS

The polarographic investigations of chemical substances to measurements in aqueous solutions only. The search for suitable solvents was initiated to investigate great number of water-insoluble organic compounds. Not only the pure solvents but also the mixture of solvents was found to be suitable for quantitative analysis. The magnitude of diffusion current and, sometimes, the shape of the wave so also the half-wave potential are influenced by using non-aqueous solvents. These effects are chiefly due to change in solvation and in the diffusion coefficients. Well defined waves can be obtained in non-aqueous solvents for substances that give curves with ill-defined limiting currents in water. We can take for example, Ca2+ and Mg2+ give easily measurable waves in acetonitrile in contrast to their behaviour in water. The theoretical investigation of substances in non-aqueous/solvents e.g., in the determination of diffusion coefficients and standard potentials, to the reversibility of the electrode process and complex equilibria has been drawn in the polarographic studies. Thus for solvents with a low dielectric constant, Schaap [21] derived an equation for the reversible wave of a cation, the reduced form of which yields an amalgam with

38

Introduction to Polarography and Allied Techniques

mercury. The formation of ionic pairs is operative in this case and the derivation is similar to that for consecutive complex formation.

3.5.1

Solvents that are Frequently Used

(i) Acetic Acid : The possibility of polarographic analysis in acetic acid was first mentioned by MacGillavry [22]. More detailed investigation since then were given by many workers. The diffusion currents for cations, e.g., Cd2+, Pb2+ and Zn2+ are about two-thirds of those is water. This is due to the greater viscosity of glacial acetic acid. Ions, such as Cu2+, which are reduced at very positive potential form acute maxima. This could be suppressed by Puchsin as shown by previous workers. Not only this there were several other substances found suitable for suppressing maxima in glacial acetic acid. (ii) Acetonitrile : Among other solvent acetonitrile proved very convenient and useful. Previous workers, e.g., Kolthoff and Coetzee [23] and many others have given quite useful information on such investigations. The energies of solvation of the cations and the anions are smaller than in water and most cations are reduced at more positive potentials than in water. In addition to this, more negative potentials can be attained than in water, and well-defined waves for ions like calcium and magnesium can be obtained using tetraethyl ammonium perchlorate or tetra butyl-ammonium iodide as supporting electrolyte. Normally an aqueous saturated calomel electrode is employed as reference electrode with an Ag/Ag+ or Ag/AgCl electrode as already pointed out by previous workers. The potentials, referred to an aqueous SSE for the Ag/Ag+ couple in acetonitrile in the presence of different supporting electrolytes have also been compared. Inorganic ions have been divided into two groups by Kolthoff and Coetzee [24]. The first group includes cations with similar behaviour in acetonitrile and in water. The half-wave potentials become more positive in sequence Li+, Rb+, K+, Na+, NH4+, Ca+, Sr2+, Ba2+, Zn2+, Cd2+, whereas in water the following sequence holds: Li+, Ca2+, K+, Na+, Sr2+, Rb+, Ba2+, Zn2+, Cd2+. The reduction of nNa+, K+, Rb+ and Zn2+ proceeds reversibly, and that of other ions irreversibly. The influence of anions on the electrode process is peculiar. Zinc nitrate in tetraethyl ammonium perchlorate gives a reversible wave at –0.70 V vs. NCE, while zinc chloride in tetraammonium bromide gives an irreversible wave at almost –2.0 V. The horizontal portion of the diffusion current cannot be obtained in the presence of tetraethyl ammonium iodide. According to Kolthoff and Coetzee [24] the second group involves cations whose polarographic behaviour in acetonitrile differs considerably from that in water. In contrast to their behaviour in water, these cations are mostly reversibly reduced or at least approach a reversible behaviour in acetonitrile. The following reductions take place reversibly : AgI/Ag0, CuI/Cu0, MNII/Mn0...well defined waves, although not fully reversible, are obtained with FeII, CrII, BeII...Eu0 and YbII → Yb0.

The Technique

39

When small amounts of water is added to acetonitrile formation of hydrated cations take place. The waves which in acetonitrile were reversible and appeared at positive potential, become irreversible and are shifted to more negative potentials. Changes in diffusion coefficients of Ag+, Tl+ and Cu2+ were investigated by Tachi and Takahashi [25] in mixtures of acetonitrile and water. The hydrogen overvoltage in anhydrous acetonitrile is considerably lowered. Vl•cek [26] found E ½ = –0.60 V (vs NCE) for the half-wave potential of hydrogen reduced from perchloric acid in Acetonitrile saturated with tetra methyl ammonium iodide and the over voltage η1/2 = –0.56 V as compared with η1/2= –1.34 V in water. Coetzee and Kolthoff investigated a large number of acids in acetonitrile and found a far greates dispersion of half-wave potentials than in water. But due to the irreversibility of the process, the strength of acids in acetonitrile cannot be compared on the basis of their half-wave potentials. (iii) Alcohols : Alcohols, e.g., ethanol, methanol and their mixtures with water are most frequently used as solvents. The diffusion currents are usually smaller than those in water. According to Vl•cek[27] anodic waves for alkali metals are obtained in absolute ethanol. Also, the amalgam of alkali metals are relatively stable so that oxidation reduction waves for the system ion amalgam of the alkali metals can be obtained. As such these waves provide a proof of the reversibility of alkali metals at the DME. Properties of complexes also change considerably in alcoholic solution as shown by previous workers. Also the formation of cadmium complexes with chlorides, bromides and thiocyanates take place at much lower concentration than in water. Most organic substance are readily soluble in mixtures of ethanol or methanol with benzene in water permiting polarographic estimations. The reversible organic substances which consume protons during the electrode process, the addition of organic solvents only produces a change in half-wave potential. This was described as a change in the activity of the hydrogenious, Schwabe [28] also determined pH value from change in half-wave potential while with irreversible processes the influence of solvent on E ½ is more complicated. It was also evident that the rate constant for the electrode process measured at constant potential decreases exponentially with increasing concentration of ethanol. (iv) Ethylenediamine : Ethylenediamine is also suitable for polarographic analysis since a number of salts dissolve in it. In reversible electrode process, an estimate of the magnitude of stability constant [29] for the corresponding ethylenediamine complex in water can be determined from the difference between the half-wave potentials of the cations in water and in ethylenediamine. The potential of the anode could be determined from the activity of mercuric ions in liquid ammonia while working with a mercury pool anode. (v) Sulphuric Acid : For studying the property like dehydration of the depolarizer, the acid is useful. Concentration up to a 92 vol. % or 17 M has been used which

40

Introduction to Polarography and Allied Techniques

displays minimum viscosity and maximum conductivity which is quite comparable to that of 1 N KCl. In sulphuric acid Tl+ [30] form a complex which is reduced reversibly and has a half wave potential 0.5 V. This is more negative than that in water (–1.01 V vs NCE). The behaviour of Tl+ is worth mentioning because it rarely forms complexes in aqueous solution (e.g., with EDTA) and has a half-wave potential that is taken as reference in aqueous solutions. (vi) Formic Acid : In formic acid solution [31] the half-wave potentials of cations are more positive than those in water. The maxima of the first kind are also suppressed to a large extent by the surface-active molecules of formic acid. (vii) Liquid Ammonia : Alkali metals are reduced reversibly giving valuable results. The limiting currents follow Ilkovi•c equation. The temperature was kept constant at –36°C ± 0.2°C. The diffusion currents for alkali metals in the solvent at this temperature are 2–3 times higher than those in water at 25°C. The migration, is not fully suppressed, because tetrabutyl ammonium iodide, used as supporting electrolyte, is only soluble up to 5.7, 10–3 M. The sequence of ions of the alkaline earths is the same as in water. Thallium [32] is reduced almost reversibly. Cu2+ give two waves of equal height. The first one is reversible. The diffusion coefficients for thallium and copper agree with those determined from the conductivity data obtained at infinite dilution. Aluminium also gives a measurable wave in liquid ammonia. Mercurous ions, Hg 22+ are unstable in liquid ammonia. Mercuric ion, Hg2+, are reversibly reduced to Hg. As a consequence, the Hg2+/Hg electrode functions reversibly. The potential of a mercury pool anode does not depend on the concentration of nitrate, chloride, iodide or ammonium ions, but only on the concentration of mercuric ions. The half-wave potential of Thallium was taken as reference for determining the half-wave potentials. Polarization is repeated two or three times in usual practice. This results in anodic dissolution of small quantity of mercuric ions, which control the electrode potential. (viii) Other Solvents : The polarographic behaviour of several cations and also oxygen in anhydrous ethylene glycol has also been studied [33]. Well defined waves with half-wave potentials almost the same as those in water were obtained. Other solvents like acetone [34], acetic anhydride [35], aniline [36], benzoyl chloride [37], butanol, dimethyl formamide [38], dimethyl sulphoxide [39], and dioxan [40]–[50] also the mixtures with water have also been used. Research in this area also continues.

References 1. 2. 3. 4.

Graham, D.C.J. Am. Chem. Soc. 68:301 (1946). Ilkovi•c D. : J. Chem. Phys. 35, 129 (1938). Ku•cera G. : Ann. Physik IV. Folge 11, 529, 698 (1903). Kalousek M. : Collection Czechoslov. Chem. Communs. 11, 592 (1939).

The Technique

41

5. Vl•cek A.A. : Chem. Listy 48, 1485 (1954); Collection Czechoslov, Chem. Communs. 20 413 (1955). 6. Hans W., Sturm V.F. : Angew Chem. 65, 393 (1953). 7. Christie J.H., Oster Young R.A. : J. Ann. Chem. Soc. 82, 1841 (1960). 8. Stackelberg V.M., Doppelfeld; Advances in Polarography, p. 68 I.S. Longmuir, Ed. Pergmon Press, London 1960. 9. Hassel bach H., Jahn D., Schwabe K. : Z. Physik, Chem. (Leipzig), Sonderheft (1958), 17. 10. Heyrovsk•y J., Simunek R. : Philos, Mag. 7,951 (1929). 11. Heyrovsk•y J. : Chim Listy 36, 267 (1942). 12. Heyrovsk•y J. Vascautzanu E. : Collection Czechoslov. Chem. Communs. 3, 418 (1931). 13. Bruns B., Frumkin A., Iofas, Vanyukova L., Zolot arev Skaya S. : Acta Physicochem. URSS 9, 359 (1938): Zh. Fig. 13, 786 (1939). 14. Rodeburg : Thesis, Bonn (1942). 15. Popova T.I., Kryukova T.A. : Zh. Fig. Khim 25, 283 (1951). 16. Bridi•cka R. : Collection Czechoslov. Chem. Communs. 8, 419 (1936). 17. Dvo•ra•k J. : Chem. Listy 47, 969 (1953): Collection Czechoslov. Chem. Communs. 19, 39 (1954). 18. Kryukova T.A., : Frumkin A.N.: Zh. Fig. Khim. 23, 819 (1949). 19. Micka K. : Chem. Listy 49, 1148 (1955). 20. Kryukova T.A. Zavodskaya Lab. 9, 691, 699 (1940). 21. Schapp W.B. : J. Am. Chem. Soc. 82, 1837 (1960). 22. Mac Gillavry D. : Trans. Faraday Soc. 32, 1447 (1936). 23. Kolthoff I.M., Coetzee J.F. : J. Am. Chem. Soc. 79, 870 (1957). 24. Kolthoff I.M., Coetzee J.F. : J. Am. Chem. Soc. 79, 1852 (1957). 25. Tachi I., Takahashi R. : Collection Czechoslov. Chem. Communs. 25, 3111 (1960). 26. Vl•cek A.A. : Chem. Listy 48, 1741 (1954); Collection Czechoslov. Chem. Communs. 20, 636, (1955). 27. Vl•cek A.A. Chem. Listy 48, 1485 (1954); Collection Czechoslov. Chem. Communs. 20, 413 (1955). 28. Schwabe K. C : Z. Elektrochem. 61, 484 (1957), z. Physik. Chem. (Leipzig); Sonderheft 1958, 289. 29. Shaap W.B., Messner A.E., Schmidt F.C.: J. Am. Chem. Soc. 77, 2683 (1955). 30. Vl•cek A.A. : Chem. Listy 45, 297, 377 (1951); 46, 258 (1952); Collection Czechoslov. Chem. Communs. 16, 230, 465 (1951). 31. Pinfold T.A. Seba F.: J. Am. Chem. Soc., 78, 2095, 5193 (1956). 32. Mc Elroy A.D.; Lattinen H.A. : J. Am. Chem. Soc. 57, 564 (1953). 33. Gentry C. H.R. : Nature 157, 479 (1946). 34. Arther P., Lyons H.: Anal. Chem. 24, 1422 (1952). 35. Gutmann W., Nedbalek E. : Monatsch, 89, 203 (1958). 36. Novak J.V.A. : Collection Czechoslov. Chem. Communs. 11, 573 (1939). 37. Gutmann W., Sch•ober G.: Monatsh. 88, 404 (1957). 38. Given P.H., Poever M.E.: J. Chem. Soc. 1960, 385, 465. 39. Sch•ober G.; Gutmann W.: Advances in Polarography I.S. Longmair, Ed. p. 940. Pergmon Press, London 1960. 40. Stackelberg M.V., Stracke W. : Z. Elektrochem. 53, 118 (1949).

CHAPTER 4

THEORY OF CURRENT POTENTIAL CURVES 4.1 THE ILKOVI•C EQUATION The direct proportionality between the limiting diffusion current and depolarizer concentration is expressed in an equation derived by Ilkovi•c. Due to the growth of each drop of mercury, the observed diffusion current varies with the variation of the surface area of each drop. Thus, at a particular applied potential the current will be observed to oscillate between well-defined upper and lower limits. For an instantaneous current at any time during the drop-life, the Ilkovi•c equation may be expressed in the form: id = 706n D1/2 m2/3 t11 6 C

...(1)

Here, n is the number of electrons transferred in the reduction process [the ions designated as Mn+ which begin to be discharged owing to their reduction by the process: Mn+ + ne M (Hg)(1´) and the ions Mn+ arrive at DME by the relatively slow process of natural diffusion m is the rate of mercury flow expressed in mgs–1, D is the diffusion coefficient of the depolarizer in cm2.5–1, t1 is the drop-time expressed in seconds and C is the depolarizer concentration given in m moles per liter. With these units and the numerical constant 706, the observed current is given in microamperes. It is more usual to consider mean currents. It is observed that the instantaneous current at the end of the drop-life, imax, is related to the mean current during the drop-life, i, by the 6 i . Thus, the form of the Ilkovi•c equation for the mean diffusion 7 max current is expressed as:

relation, τ =

id = 607n D1/2 m2/3 t1/6 C

...(2)

The Ilkovi•c equation is alternatively used in the following form, for the mean diffusion current id = 0.627n D1/2 m2/3 t11 6 C

...(3)

which, for D in cm2s–1, m in gs–1, t1 in seconds and C in mole cm–3, gives the current in amperes. For most work the Ilkovi•c equation in the above forms has proved to be satisfactory, the linear relation between id and C being maintained to within ± 1%. However, the diffusion current constant I, defined by

Theory of Current Potential Curves

43

I = 0.627n FD1/2 =

id 23 16 cm t1

...(4)

only maintains constancy within ± 5%. A typical calibration curve is shown in Fig. 4.1. 5

(μ A )

4 3 2 1 0

0.3

0.4

0.5

0.6

0.7

0.8

Fig. 4.1 : Polarogram showing current oscillations. Working composition : 5 × 10–4 M Cd4, 0.1 M KNO3, 0.001% gelatin

Many corrected forms of the equation have been derived by several workers. The final forms of which essentially identify with the equation and differ only in the value given to numerical constant, A. Equation (2) may be written in the form id = 0.627n FD1/2 C : m2/3 t11 6

...(5)

id μA

15.0

10.0

5.0

0.0 0.5

1.0 .5 C(mM/L)

Fig. 4.2 : Mean diffusion current versus millimolar concentration for Cd2+ in the range 0.163 mM to 1.22 mM, 0.1 M KNO3 as supporting electrolyte with 0.001% gelatin

44

Introduction to Polarography and Allied Techniques

Solution factors : electrode factors If the solution factors are maintained constant, then id = const. m2/3 t11 6

...(6)

By Poiseuille’s equation the rate of flow of liquid through a capillary under a head of the liquid is directly proportioned to the height of the column, h. Thus the rate of flow, v is the proportional to m which is porportional to h. Also v is proportional to 1/t1. ...(7) Therefore, id = const. h 2/3 . h –1/6 = const. h 1/2 The proportionality which is being observed between id and h 1/2 is an acceptable criterion of a diffusion controlled process. See for example the Fig. 4.2.

4.1.1 Consequences of Ilkovi•c Equation The following consequences can be drawn from the Ilkovi•c equation. 1. The diffusion current is directly proportional to the analytical concentration of depolarizer in the solution, e.g., id = •kc ...(8) This is followed from the Ilkovi•c equation and the conditions being that for a given value of m and t1, i.e., when the same capillary is used with a constant height, where k is the Ilkovi•c constant, e.g., • = 0.627 FD1/2 m2/3 t1/6 ...(9) k n

This equation forms the basis of quantitative determination in polarographic analysis. If the limiting diffusion current values or wave heights is mm are plotted against the concentration of a given compound, a straight line passing through the origin is obtained. See Fig. 4.3. This may be used as a calibration curve for determining the concentration of the compound in unknown samples. 40

Zn2+

id (arb.)

30

Cd2+

20

10

0

1

2

3

4

5

6

7

8

9

h(cm½)

Fig. 4.3 : id versus

–4 2+ h plots for a solution containing 5 × 10 M Cd and

9.8 × 10–4 M Zn2+; 0.1 M KNO3 as supporting electrolyte with 0.001% gelatin.

Theory of Current Potential Curves

45

The linear dependence of diffusion current on cencentration does not bold exactly with short drop-times as was first shown by Mass [2] and other workers too. As a result the drop-time should not be less than two sec. The reason being that under these conditions whirling occurs and destroys the diffusion layer and the currents gets increased. The most suitable drop-time is from 3 to 5 sec. It further follows from equation (8) that equivalent concentrations of substances with equal diffusion coefficients give equal currents, since a large number of cations have similar diffusion coefficients and since small differences have only a small effect. The reason being that square root of D is used in the calculation, diffusion currents for the same equivalent concentrations are roughly equal (Table 4.1). TABLE 4.1 Comparison of percentage differences between observed and calculated mean diffusion currents Ion

Δid Ilkovi•c equation %

Δid correct equation %

Tl+ Pb2+ Cd2+ Zn2+ Cu2+

–0.8 +1.0 +7.8 +4.9 –1.3

–13.7 –8.7 0 –3.7 –10.7

IO − 3

+0.4

–9.3

3– Fe ( CN )6

+8.1

–16.9

2– CrO4

–3.6

–15.2

If the diffusion coefficient is known the number of electrons ‘n’ participating in the electrode process may be calculated from the Ilkovi•c equation. Actually comparison can be made under the same condition the diffusion current of substances to be investigated with the diffusion current of a substance taking up a known number of electrons, i.e., with the same capillary, concentration, height of mercury head and temperature. From the ratio of the diffusion currents, the value of n can be determined. 2. Dependence on the Height of Mercury Head, Capillary Characteristics and Potential : If the height of the mercury head is changed at constant concentration of the substance, the flow-rate m and drop-time t charge simultaneously. According to the following equations: m = k' h = k' (h a – h b) t1 = k n

1 h

...(10) ...(11)

46

Introduction to Polarography and Allied Techniques

m is directly proportional and t1 inversely proportional to the corrected height of h of the mercury head: 1 m = k' h; t1 = k" ...(12) h Substituting in the Ilkovi•c equation it takes the form:

⎛ k" ⎞ id = Km2/3 t11 6 = K (k' h)2/3 ⎜⎝ ⎟⎠ h

16

...(13)

and on combining all constants ...(14) id = k h i.e., the diffusion current is directly proportional to the square-root of the corrected height of the mercury head (reservoir). This linear dependence provides an easily accessible experimental test for diffusion controlled currents. The corrected height of the mercury head may be calculated from the above equation (10). In quite some investigations into the character of limiting currents it is sufficient to plot the limiting current against the square-root of the actual height of the mercury head. In case of diffusion controlled current the plot gives a straight line, but this line does not pass through the origin, it only cuts a small intercept on the current axis.

4.2 REVERSIBLE AND IRREVERSIBLE ELECTRODE PROCESSES It is quite possible to control the rates of most electrode processes with some precision, which is quite unlike the case for normal chemical reactions. Control of the applied potential controls the current flow by controlling the height of the activation energy barrier for the process. A simple electrochemical reduction process is considered here, e.g., A + ne

B

...(15)

which is occurring at an inert electrode and also that both oxidant and reductant are soluble in the solvent medium used. A simple view of the effect of an applied potential, E, assumes it to cause a decrease in the reaction energy barrier in one direction and an increase in the reverse direction. An increase of negative potential increases the forward rate of reaction Eq. (15), the energy barrier to its progress being reduced by an amount α (E – E 0) nF. The energy barrier of the reverse reaction is correspondingly increased by an amount β (E – E0) nF. Here the expressions E and E 0 are the applied and standard potentials respectively, while α and β are termed the “transfer coefficients” related through the expression α + β = 1. A transfer coefficient may thus be regarded as the fraction of the applied potential which either assists or hinders the process under consideration. Observing the diagram below, the significance of α and β can be seen in Fig. 4.4.

Theory of Current Potential Curves

47

Forward (reduction) process

α (E–E 0)nF

β (E–E 0)nF

Backward (oxidation) process

Fig. 4.4 : Diagram showing effect on forward and backward reaction activation energy barriers of an applied potential in excess of E 0.

In terms of current densities, the rates of forward (reduction) and backward (oxidation) processes for the reaction* (15) may be expressed as follows: r1 =

and

r2 =

Icath = kcath [A]e nF

...(16)

I an = kan [B]e nF

...(17)

In these equations r1 and r2 represent the two rates, Icath and Ian, i.e., the cathodic and anodic current densities respectively. The terms kcath and kan and the appropriate rate constants. [A]e and [B]e refer to concentrations of oxidized and reduced forms of the depolarizer at the electrode surface. If the applied potential is E 0, with forward and backward rates being equal, the every barrier to either process is the activation energy, Q. That is to say, Q is the activation energy of the electron transfer from electrode to depolarizer particle A, at the surface, at zero applied potential between the electrode and the solution. At an applied potential difference, E, this energy is reduced by an amount α ne E, e being the unit electronic charge. Thus, for the rate of electro-reduction we have

⎡ Q + αne E ⎤ r 1 = k′ [A]e exp ⎢ − ⎥ kT ⎣ ⎦

...(18)

⎡ αn FE ⎤ = k′′ [A]e exp ⎢ − ⎣ RT ⎥⎦ where k′ and k′′ are constants for the particular process and k is the Boltzmann constant. k′′ includes the term e–Q. A analogous expression may be had for the rate of electro-oxidation.

48

Introduction to Polarography and Allied Techniques

Cathodic and anodic rate constants may be expressed as:

(

)

⎡ α nF ⎤ E − E0 ⎥ kcath = k0 exp ⎢ − RT ⎣ ⎦

...(19)

⎡ (1 − α ) n F ⎤ E − E0 ⎥ kan = k0 exp ⎢ RT ...(20) ⎥⎦ ⎣⎢ In the above equations, k0 represents the heterogeneous rate constant of the electrode process at the standard potential, E 0, and includes the term e–Q. These expressions may be inserted in the equations (15) and (17) to give:

(

and

)

(

)

⎡ α nF ⎤ E − E0 ⎥ Icath = nFk0 [A]e exp ⎢ − ⎣ RT ⎦ and

(

...(21)

)

⎡ βnF ⎤ E − E0 ⎥ Ian = – nF k0 [B]e exp ⎢ ⎣ RT ⎦

...(22)

In these latter two equations, the convention that has been adopted as regard to a cathodic current as positive and an anodic current as negative. The algebraic sum of the cathodic and anodic contribution, as observed by the current density I, are represented as:

(

)

(

)

⎧ ⎡ α nF ⎤ ⎡β F ⎤⎫ E − E 0 ⎥ − [ B ]e exp ⎢ n E − E0 ⎥ ⎬ I = nF k0 ⎨[ A ]e exp ⎢ − ⎣ RT ⎦ ⎣ RT ⎦⎭ ⎩ or

(

)

(

⎧ ⎡ α F ⎤ ⎡β F I = I 0 ⎨[ A ]e exp ⎢ − n E − E 0 ⎥ − [ B ]e exp ⎢ n E − E0 RT ⎣ ⎦ ⎣ RT ⎩

) ⎤⎥⎦⎫⎬⎭

...(23)

...(24)

where I0 = nF k0 and is termed the “exchange current density” i.e., the condition when E = E 0 at which no net current is observed, the cathodic and anodic components being of equal magnitude but flowing in opposite directions. For small values of Q, k0 is very large; such a condition is found in “reversible” systems where the electrochemical processes are considered to be very rapid. For considering the essential differences between reversible and irreversible electrode processes, the form taken in the above equation I and E under such conditions that k0 is very large or very small.

4.3 REVERSIBLE POLAROGRAPHIC WAVE A system consisting of a perfectly polarizable dropping mercury electrode and a nonpolarizable stationary electrode. If an external voltage is applied to such a system, the entire potential drop is concentrated at the interface between the dropping electrode and the solution under investigation. Due to this reason the polarographic curves are determined solely by the processes occurring at the DME. The dependence of the current on the potential of the mercury electrode, the polarographic curve gives a particular shape. This concludes the character of the electrode process arising out of the current voltage curves.

Theory of Current Potential Curves

49

The particles of depolarizer subject to electrochemical change i.e., reduction or oxidation at the electrode reach the electrode by diffusion only. The equation derived for this kind of current, the diffusion current, requires a constant concentration of depolarizer at the surface of the electrode for a given potential. If the shape of the current potential curve is to be derived, the relationship between the concentration at the electrode surface and the potential must be taken into account. For reversible processes, this relationship is obtained from the Nernst equation. By a reversible process is meant one in which the ratio of the concentrations of oxidized reduced form at the electrode surface is given by the Nernst equation: E = E0–

RT [Red]0 ln nF [OX ]0

...(25)

In this equation [Red]0 and [OX]0 denote the concentrations of the reduced and oxidized form of the depolarizer at the electrode surface respectively. E 0, the standard oxidation reduction potential of the system and E the potential of the dropping mercury electrode as determined by the applied e.m.f. It is convenient to refer both potentials to the potential of the non-polarizable electrode rather than to the standard hydrogen electrode, E is then numerically equal to the applied e.m.f. Emphasis is laid on the fact that Nernst equation which holds for reversible thermodynamic equilibria, i.e., under conditions when no current is flowing. The use of the Nernst equation is justified if the equilibrium rate of electron exchange between electrode and reactants is so great that it can easily accommodate the small net current flow without a significant departure from the equilibrium concentration.

4.3.1 Cathodic Wave On considering a cathodic reduction the oxidized form of the depolarizer (e.g., Tl+, Cd2+ or reducible molecules) alone is present in the solution. It accepts electrons from the dropping electrode and so electrons flow from the non-polarizable electrode i.e., anode to the DME via the external circuit. This is the so called cathodic current. The polarograph is conventionally connected in such a way that on polarograms this current appears above the galvanometer zero-line. According to the Ilkovi•c equation, the mean current supplied by diffusion of a depolarizer to the electrode surface is given by:

in which

i = k [OX] – [OX]0

...(26)

k = 0.627nF D1/2 m2/3 t11 6

...(27)

is the Ilkovi•c constant. The particles reduced at the surface thereupon diffuse away. In cases where amalgam formation takes place, e.g., in metals like Tl, Pb, Cd, Zn and alkali metals, these are transported by diffusion into the mercury drop. If no amalgam is formed, e.g., in reductions of Fe3+ → Fe2+, Sn4+ → Sn2+ and in some organic systems like quinone → quinol, the reduced particles diffuse back into the bulk of the solution. The equation governing this diffusion away from the surface in either direction is:

50

Introduction to Polarography and Allied Techniques

i = k' [Red]0 – [Red]

...(27a)

in which •k' = 0.627nF D1/2 m2/3 t11 6 differs form k only in the value of diffusion coefficient for the reduced particle D′ . As already stated above, it is assumed that only the oxidized form is present in the bulk of the solution, i.e., [Red] = 0, and so the preceding equation now takes the form: i = •k' [Red]0

...(27b)

If the concentrations of the reduced and oxidized forms at the surface of the electrode are eliminated from equations (27, 27a, 27b). The following equation is obtained: E = E0 –

RT i k ln · nF k '[OX ] − i k '

...(28)

Heyrovsky and Ilkovi•c first derived this equation for a cathodic wave [4].

Fig. 4.5 : Reversible cathodic wave. 5. 10–3 M Tl2SO4, 1 M Li2SO4, 0.04% gelatin; sens. 1 : 150, 208 mV/scale unit

Since

k [OX ] = id ,

...(29)

where id is the mean limiting cathodic diffusion current, equation (28) is readily transformed into the Tomes form [5]

Theory of Current Potential Curves

51

0

E =E −

RT i ln nT id − i

D ; D′

...(30)

D D′ Since for many depolarisers the diffusion

the ratio of the Ilkovi•c constant •k/•k' is

coefficient of the oxidized and the reduced forms are nearly equal and, in their square root form, the expression

D D′ may be set equal to unity. The forgoing equation then

finally takes the form: 0

E=E −

RT i ln nF id − i

...(31)

This equation is the simplest mathematical expression for the shape of a reversible cathodic wave. Experimental reversible cathodic waves accord perfectly with the derived equations. The point on the polarographic curve corresponding to one-half of the limiting diffusion current represent the inflexion point of the curve. It is termed the half-wave point or correspondingly the half-wave potential, E ½. The expression for the half-wave potential may readily be derived from the equation for the polarographic wave introducing i = id /2. Thus is obtained: E ½ = E0 –

RT D ln nF D′

...(32)

from the equation (22) or E ½ = E 0 from equation (23) The half-wave potential is a constant that is independent of the concentration of the depolarizer, of the capillary characteristics and of the galvanometer sensitivity and has a value characteristic of the given depolarizer. If the reduction product does not form an amalgam with mercury, the half-wave potential is virtually identical with the standard oxidation-reduction potential (Eq. 23). If an amalgam is formed, the halfwave potential corresponds to the standard potential of the amalgam electrode (see half-wave potential and its significance). When the depolarizer concentration is varied, the height and the target-potential of the wave change, the half-wave potential for a reversible wave remains constant. Not only this but the relative height i/id of the wave at a given potential is independent of depolarizer concentration. An important property of a reversible polarographic curves is its symmetry with respect to E ½. Thus the distance between E ¼ and E ½ is the same as that between E ½ and E ¾. If an amalgam is formed the half-wave potential corresponds to the standard potential of the amalgam electrode as given in Chapter 1. When the depolarizer concentration is varied, the height and the tangent potential of the wave change, but the half-wave potential for a reversible wave remains constant (see Fig. 4.6). Furthermore, the relative height i/id, of the wave at a given potential is independent of depolarizer concentration. From the equations derived for the polarographic wave, the final equation is:

52

Introduction to Polarography and Allied Techniques

E =E ½ –

4.3.2

RT i ln nF id − i

...(33)

Anodic Wave

Anodic oxidations are of two kinds: (i) The reduced form is in mercury drop so that instead of pure mercury an amalgam flows out of the capillary [3– 6]. This reduced form in which the metal is oxidized at the surface of the DME and the cations thus formed are transported by diffusion into the bulk of the solution, and (ii) The reduced form of the depolarizer is present in the solution and is transported by diffusion to the DME, where it is oxidized and then returned to the bulk of the solution. Here the example of Fe2+ and quinol is workable. In both oxidations, the direction of diffusion of the oxidized and reduced forms is the reverse of that in a cathodic reduction. The electrons flow from the DME through the external circuit to the non-polarizable +∞ –∞ E electrode. The resulting anodic current (negative sign) is recorded beneath the galvanometer zone-line (exceptions are Fig. 4.6 : Independence of half-wave potential from concentration. The concentration of Cd2+ of mixed currents). –3 Considering the diffusion of the increases up to 10 N reduced form the following relationship must hold: –i = •k ([Red] – [Red]0)

...(1)

The oxidized form diffuses from the surface of the electrode back into the bulk of the solution, where its concentration is zero. The current can, therefore, be rewritten as –i = •k [OX]

...(2)

On substituting these diffusion relationships (foregoing equations) in the equation: E = E0 –

RT ln nF

[ Red] 0

[OX 0 ]

...(3)

Theory of Current Potential Curves

53

the equation of the current-potential curve for anodic oxidations at DME is obtained as follows: RT k'Red k ln +i· ...(4) nF k' −i The anodic diffusion current [Red]0 = 0, is attained when [Red]0 = 0, hence on substituting this relationship in the foregoing equation we obtain: E = E 0–

RT i −i D ln d ...(5) nF i D′ The whole anodic curve appears beneath the galvanometer zero line as is shown in the Fig. 4.7. If, as in the cathodic reduction, i is made equal to id /2, and expression identical with equation is obtained e.g., E = E0 –

RT D ln = E0 ...(6) nF D′ when i can be neglected compared with id = k′ [Red] in equation (7) we obtain the exponential form of the anodic curve without concentration polarization i.e., the +i concentration of the depolarizer at the electrode surface was the same as that in the –E +E body of the solution, even with a current passing through the system: E ½ = E0–

E = E0–

RT k' Red + i k ln · nF k' −i

–id

...(7) –i

4.3.3

Cathodic-Anodic Waves

While considering an oxidation-reduction Fig. 4.7 : A Typical Anodic wave system, where both forms are available for electrolysis, it is observed that two diffusion currents are resulting. With increasing negative potentials, the dropping mercury electrode becomes depleted of the oxidized form and the cathodic diffusion current id appears. And an depletion of the reduced form with increasing positive potentials the anodic diffusion current (see Fig. 4.8) appears. Two situations are observed: (a) The oxidized form is in solution (e.g., cations of metals such as Tl+ and Cd2+) and the reduced form in the mercury (i.e., the metals that form amalgam). (b) Both the oxidized and reduced form are in the solution Fe2+ and Fe3+ in oxalate. In both the situations the current is given by the equations: ...(8) i = •k [OX] – [OX ] 0

i.e., diffusion of the oxidized form to the electrode surface.

CHAPTER 5

TYPES OF CURRENTS 5.1 MASS TRANSFER AND ELECTROCHEMICAL PROCESSES Two main types of processes are involved in any electrolysis. These are : transference of matter through a solution towards and away from the electrodes, and the other is in which the electrochemical process involves the exchange of electrons at the electrode surface as an essential part. During an electrolysis three mass transfer processes are of importance, e.g., migration, diffusion and convection. The first of these i.e., migration is an essential effect depending upon the charge carried by an electroactive species and upon its transference number. Thus, the effect is encountered only with charged species. Since the processes of natural diffusion are non-electrical in origin, these are observed for all species in solution whether they are charged or not. Convection effects include the motion of small particles under the influence of stirring, mechanical agitation, and temperature gradients. In polarographic work the migration effect is usually eliminated. The convection effects are eliminated by carrying out any electrolysis in an controlled thermostat and also by protecting the apparatus from all forms of vibrations and shocks.

5.2 DIFFUSION CURRENT The most important component of the wave height is the diffusion current, which reflects the rate at which the ions or molecules of the substance responsible for the wave reach the electrode surface under the sole influence of a diffusive force. On the plateau of the wave these ions or molecules get reduced of oxidized as rapidly as they reach the electrode surface, and their concentration in the layer of solution immediately adjacent to the electrode surface in therefore virtually zero. Hence there is a concentration gradient between the bulk of the solution and the layer at the electrode surface, and it is this concentration gradient which is responsible for the existence of the diffusive force. The diffusion current is very important in polarographic analysis because most practical methods are based on its measurements. The rate at which the electroactive material can reach the electrode surface may however be affected by many other phenomena. The original species or another electroactive one, may be regenerated by a reaction between the product of the electrode reaction and some other constituent of the solution, and in such a case, the current due to the reduction of the regenerated substance will then also be included in the wave height.

Types of Currents

59

If the solution contains a species that is not electroactive is in slow equilibrium with one that is, the wave height will include not only the diffusion current of the electroactive species but also a current due to the reduction of additional electroactive materials formed from the non-electroactive species as equilibrium between them is displaced at the drop surface. In some cases excess of the electroactive substance to the electrode surface may be barred by a film of adsorbed material, or the electroactive substance or its reduction (or oxidation) product may undergo adsorption on the drop surface and the current may then be limited by the number of ions or molecules which can be adsorbed on each drop. As already described a current whose magnitude is controlled by the rate of diffusion is called a diffusion current. In polarographic measurements an excess of supporting electrolyte is used for several reasons. It not only eliminates the effects of migration, instead it also greatly diminishes the potential drop iR, thus transforming the current voltage curves at DME into current potential curves. The supporting electrolyte also signifies great practical influence in analytical polarography. A general relationship may be written for the electrolytic current at DME, according to Faraday’s law: i = nF

dN dt

...(1)

where dN/dt denote the number of mole of the depolarizer that reaches the electrode in unit time and is subject to electrochemical change. [F is the Faraday (96500 cont.) and n is the number of electrons taken up or derived by a single molecule of depolarizer during the electrode process]. If the depolarizer is transported to the electrode by diffusion alone, the value dN/dt can be calculated from Fick’s Second Law. In this way, the equation for the diffusion current can be derived.

5.2.1 Diffusion to Stationary Electrodes Linear Diffusion : Diffusion may be described as a spontaneous process leading to equilibration of concentration differences in concentration gradients. If a concentration gradient arises in solution, the solute starts to move from areas of high to those of lower concentration. The rate of diffusion is proportional to the concentration gradient, but also depends on the properties of the diffusing particles. If diffusion occurs in one direction only, the process is termed linear diffusion. Considering linear diffusion to a plane electrode (cross section q), the concentration of depolarizer decreases in the direction perpendicular to the electrode E owing to an electrochemical change at the electrode (Eq. 2). The number of moles dN of the substance that diffuses across the area q at a distance x is proportional to the area q, to the concentration gradient de/dx and to the time interval [Fick’s first law]. dN = Dq

dc dt dx

...(2)

60

Introduction to Polarography and Allied Techniques

In this expression the proportionality constant is the diffusion coefficient D, indicating the number of moles of the substance that passes by diffusion through unit area at a concentration gradient of one in unit time.

5.2.2 Diffusion-Controlled Current Fick’s Law : Diffusion may be described as a spontaneous process leading to equilibration of concentration differences in concentration gradient. If a concentration gradient arises in solution, the solute starts to move from areas to high to those of lower concentration. The rate of diffusion is proportional to the concentration gradient, but also depends on the properties of the diffusing particles. If diffusion occurs in one direction only the process is termed linear diffusion. Consider a cylinder with a cross section q. Fig. 5.1. The concentration of depolarizer decreases in the direction perpendicular to the electrode E owing to an electrochemical change at the electrode. The number of moles dN of the substance that diffuses across the area q at distance x is proportional to the area q, to the concentration gradient dc/dx to the time interval dt dN = Dq

dc dt dx

...(3)

(Fick’s First Law derived in 1855). In this expression the proportionality constant is the diffusion coefficient D, indicating the number of moles of the substance that passes by diffusion through unit area at concentration gradient of one in unit time. Diffusion coefficients are normally of the order, 10–6 – 10–5 cm2. sec–1. The diffusion current is determined by the concentration gradient at the surface of the electrode, i.e., ( ∂c/∂ x) x=0, which is time-dependent (as are the concentration gradients at all other distances). Thus i = nF

dN ⎛ dc ⎞ = nFq D ⎜ ⎟ ⎝ dx ⎠ x = 0 dt

...(4)

E x=0

X X

x + dx

c c + dc

qx qx + dx

Fig. 5.1 : Linear diffusion to Plane Electrode

This concentration gradient may be calculated from Fick’s Second Law: 2

∂c ∂ c =D ∂t ∂x 2

...(5)

Spherical diffusion : When determining the concentration gradient towards a stationary spherical electrode the derivation must be based an Fick’s Second Law, which in spherical co-ordinates has the form;

⎡ ∂2 2 2 ∂c ⎤ ∂c =D⎢ + ⎥ 2 ∂t r ∂r ⎦⎥ ⎣⎢ ∂r Note : For details more books be consulted.

...(6)

Types of Currents

61

If the depolarizer is transported to the electrode by diffusion alone, the value dN/dt can be calculated from Fick’s Second Law and the equation for diffusion current can be derived.

5.2.3 Linear Diffusion to a Growing Dropping Electrode The Ilkovi•c Equation : Calculation of the concentration gradient towards a growing dropping electrode is quite complicated. In 1934, Ilkovi•c [1] solved this problem. He assumed that the dropping electrode behaves as a plane electrode with an area equal to that of the surface of the drop, i.e., area increasing with time. Considering the growth of the drop by the decrease in thickness of the diffusion layer as it spreads out over the growing surface of the drop. Experimental findings of Kemula [2] helped Ilkovi•c in deriving the diffusion current equation that capillaries with equal flow-rates give approximately equal limiting currents and that the dependence of the diffusion current on the height of the mercury column is parabolic.

5.2.4 Diffusion Coefficient The values of the diffusion coefficients for the depolarizers must be known in order to calculate the magnitude of diffusion currents: Nernst [3] Nernst W.; Z. Physik, Chem., 2, 613 (1988) derived the formula: D∞ =

RT

A ...(7) 2 ∞ nF Substituting R = 8.317 V, Coul., deg.–1 and F = 96500 coul., then at 25°C : −7

2.6 7 .1 0 Λ∞ ...(8) n The following Table 5.1 as taken from the following books give some values of diffusion coefficients: [Table 5.1 from Principles of Polarography by Heyrovsky & K•uta, p. 105] D∞ =

TABLE 5.1 Diffusion Coefficients for Ions at Infinite Dilution at 25°C Ion

Λ∞ Ω–1 . cm2

H+ Li+

350 39

9.34 1.04

OH– Cl–

196 76

5.23 2.03

K+

74

1.98

NO3−

72

1.92

Na+

50.5

1.35

IO3−

41

1.09

+ NH 4

73.4

1.96

IO4−

54.4

1.45

D∞ . 105 cm2 . sec–1

Ion

Λ∞ Ω–1 . cm2

D∞ . 105 cm2 . sec–1

62

Introduction to Polarography and Allied Techniques Cs+

79

2.11

BrO3−

54

1.44

Ag+

61.9

1.65

2− SO4

81

1.08

75

2.00

2− CrO4

80

1.07

Mg2+

53.06

0.71

− CH3CO2

41

1.09

Ca2+

59.5

0.79

C6H5CO− 2

32.3

0.86

Sr2+

59.46

0.79

HC 2O−4

40.2

1.07

Ba2+

63.64

0.85

2− C2O4

74.1

0.99

Cd2+

54

0.72

− Fe (CN )3 6

100

0.89

Zn2+

54

0.72

Fe( CN)64 −

110.5

0.74

2+

54 52 73

0.72 0.69 0.95

Tl+

Cu Ni2+ Pb2+

As a matter of fact diffusion coefficients are normally of the order, 10–6–10–5 cm2 . sec . The diffusion current is determined by the concentration gradient at the surface of the electrode, i.e., (∂c/∂x)x=0, which is time dependent (as are the concentration gradients at all other distances). Thus –1

i =nF

dN ⎛ ∂c ⎞ = nFqD ⎜ ⎟ ⎝ ∂x ⎠ x = 0 dt

...(9)

This concentration gradient may be calculated from Fick’s Second Law; (already given) ∂c ∂ 2c =D 2 ∂t ∂x

...(10)

From equation (9) current is obtained towards a planar stationary electrode: i = nFq D

C* −C 0

...(11)

( πDt )

For the limiting diffusion current C*

(C0 = 0); i1 = nFq D

( πDt )

...(12)

According to this equation the current decreases with time as required by the relationship i = kt–1/2. The expression

( πDt ) is the so called differential thickness of

the diffusion layer and is a function of time.

Types of Currents

63

5.2.5 Spherical Diffusion When determining the concentration gradient towards a stationary spherical electrode the derivation must be based on Fick’s Second Law, which in spherical coordinates has the form ⎡∂ 2c 2∂ ⎤ ∂c =D ⎢ 2 + c ⎥ ∂t ⎣⎢ ∂r r ∂r ⎦⎥

...(13)

The solution of this equation is carried out for the appropriate initial and boundry conditions: for t = 0, c = c*, i.e., at the beginning of the electrolysis the same initial concentration of depolarizer is present both is the bulk of the solution and at the electrode. During electrolysis (for limiting diffusion current, i.e., for t = 0 and for r = r0, where r0 is the radius of the spherical electrode). The concentration in zero, c = 0. The differential equations when simplified, the solution leads to the relation for the original variable: c = f (r, t) = c* .

1

2

3

r02 ⎛ r −r0 erf ⎜ ⎝ 2 Df r π

⎛ r0 ⎞ ⎞ ⎟⎠ +c* ⎜1− r ⎟ ⎝ ⎠

...(14)

4

Fig. 5.2 : Polarogram illustrating the dependence of the diffusion current on the mercury head. Zn2+ in 1 M NH3, 1 M NH4Cl (gelatin + Sulphite). Mercury head : 1h = 90, 2 58, 3 40, 4 27 cm

It follows from this equation that when r approaches r0, the solution of the equation resembles that for diffusion towards a plane electrode. Thus diffusion within a short distance from the surface of a spherical electrode may be regarded as linear.

64

Introduction to Polarography and Allied Techniques

5.3 INFLUENCE OF VISCOSITY AND OF COMPLEX FORMATION ON DIFFUSION CURRENT Referring to the quantities in Ilkovi•c equation it is to be noted that the drop-time, the diffusion coefficient and to a large extent the rate of mercury flow (through the change is back-pressure) may be affected by a change in composition of the solution. Moreover, the drop-time may vary considerably is different media, but since only 6th root appears in the equation its influence on the observed phenomena is negligible. Further, the drops-time is easily measured. However, the charge in diffusion coefficient is given by Stokes-Einstein law, which states that the diffusion coefficient is inversely proportional to the viscosity of the solution: D =

k η

...(15)

The relation for dependence of diffusion current on viscosity id η = const.

...(16)

The validity of this relation is limited by that of Stokes-Einstein law, which assumes a satisfactory state that the diffusing particles are spherical and are considerably larger than the solvent particles.

5.4 FACTORS AFFECTING THE DIFFUSION CURRENT The Concentration of the Electroactive Substance : The rate at which the electroactive substance reaches the electrode surface, and consequently the current resulting from its reduction or oxidation as rapidly as it arrives there is proportional to its concentration in the bulk of the solution. The shape of the electrode does not matter. It may be plane, spherical, cylindrical or some other. It may be stationary or moving. Its area may be or may not be constant, or, the mass transfer of the electroactive substance occurs by diffusion, Laminar flow or convection. Two things are generally required: (i) the supply of electroactive substance at the electrode surface must not be affected by any chemical or physical process. This includes kinds of slow chemical reactions, or adsorption on the electrode surface, and (ii) is that the thermodynamics and mechanism of the mass-transfer process must be independent of the concentration of electroactive substance. In all voltammetric techniques, this proportionality between the mass-transfer controlled current and concentration is observed and is the basis of the vast majority of the practical analytical methods and physico chemical application which are based on these techniques. From the Ilkovi•c equation, it follows that for given values of m and t1 i.e., if the some capillary is used with a constant height of the mercury head, the diffusion current is directly proportional to the analytical concentration of depolarizer in the solution : id = k c

...(17)

12 16 k = 0.627 nFD m 2 3t 1

...(18)

where k is the Ilkovi•c constant;

Types of Currents

65

This equation forms the basis of quantitative determinations in polarographic analysis. If the limiting diffusion current values or wave heights in mm are plotted against concentration of a given compound, a straight line passing through the origin is obtained. This could be used as a calibration curve for determining the concentration of the compound in unknown samples. It has been repeatedly verified that the diffusion current is proportional to the concentration of electroactive substance. The linear dependence of diffusion current on concentration does not hold exactly when the drop-time is short. The most suitable drop-time is from 3 to 5 sec (as already stated). Dependence on the Height of the Mercury Head, Capillary Characteristics and Potential: The diffusion current depends on the capillary characteristics m and t, and is therefore affected by varying them and thus how the numerous factors influence them [m is the average rate of flow of mercury in milligrams per second and t is the droptime in seconds]. If the height of mercury head is changed at constant concentration of the substance, the flow rate m and drop-time t changes simultaneously. According to the equation m is directly proportional and t1 inversely proportional to the corrected height h of the mercury head: 1 m = k' h; t1 = k" ...(19) h substituting in Ilkovi•c equation 2/3

id = K m

16

t1

= K (k ' h )

2 3 ⎛ k" ⎞

⎜⎝ h ⎟⎠

16

...(20)

and combining all constants: ...(21) id = k h I i.e., the diffusion current is directly d proportional to the square root of the corrected height of the mercury head (reservoir) Fig. 5.2 and 5.3. The linear dependence as shown in the figures not only represents a further verification of the validity of the Ilkovi•c equation but it also provides an easy test for veryfying diffusion controlled currents. For majority of investigations into the character of limiting currents it is sufficient to plot the limiting current against the square root of the actual height h of mercury head, i.e., the distance from Fig. 5.3 : Dependence of diffusion current the capillary orifice to the mercury level on the square-root of the mercury head.

66

Introduction to Polarography and Allied Techniques

in the reservoir. When the current is diffusion controlled, the plot gives a straight line (Fig. 5.3) but this line will not pass through the origin. It cuts a small intercept on the current axis. Since diffusion currents depend on m2/3 t1/6, further caution is necessary in practical quantitative determinations. When the diffusion currents for the same substance are recorded with two different capillaries the diffusion currents are in the ratio:

( m1 )2 3 (t1 )11 6 ( m2 ) 2 3 (t1 ) 21 6

...(22)

Thus, when concentrations obtained with different capillaries are to be compared the flow rates and drop-times for the capillaries must be known. Consequently, it is desirable for the comparison of results to include m and t1 values characterising the capillary in an account of the experimental data. As already given earlier, flow rate is independent of potential except in the correction term for back pressure, where its influence is negligible, but drop-time depends on potential in the same way as does surface tension. For this reason it is expected that at potentials more negative than the maximum of the electrocapillary parabola–0.56 V vs NCE in chlorides a decrease in the diffusion current with increasing negative potential will occur since the surface tension and also the drop-time decrease. The maximum value of the diffusion current is attained at the potential of the electrocapillary zero then it decreases at more positive potentials. Except at rather negative potentials a change of drop-time with potential, exerts but a small influence on the diffusion current

(

16

(since the diffusion current is a function of the sixth root of drop-time id = kt1

) . If the

diffusion current is recorded in the potential region from –0.56 to –2.0 V (vs NCE) and the drop-time decreases to one half, the diffusion current will fall to (1/2)1/6 i.e., by about 11%. The decrease in the diffusion current with increasing negative potentials must be taken into account specially when comparing the diffusion currents of two different substances of equal concentrations but having different half-wave potentials. Influence of Temperature on the Diffusion Current : An increase in temperature causes an increase in the diffusion coefficient. The effect of temperature on the diffusion current may be derived theoretically as shown by Ilkovi•c [4]. Among the quantities in the Ilkovi•c equation: id = 0.627n Fc D1/2 m2/3 m 2 3t 11 6

...(23)

only D, m and t1 depend on temperature. Further details can be obtained by differentiating Ilkovi•c equation and the above factors into account. On varying various factors it is concluded that the temperature must be kept constant within at least ± 0.5°C in order to keep the error in the determination of diffusion current below 1%. If the temperature coefficient is much larger than about 2% deg., the current is probably at least partly kinetic or catalytic, for the rates of most chemical reaction increase much more rapidly with temperature than rates of diffusion do. This may or may not be always true.

Types of Currents

67

5.4.1 The Limiting Current The total or limiting current that flows on the plateau of a wave includes contributions from several different process. It includes the current that would flow under the same conditions but in the absence of the substance responsible for the wave is called the residual current. The wave height is defined as the difference between the current and the residual current, and is the current due to the presence of the substance of interest. If the substance is ionic, there will be an electrostatic force between its ions and the electrode. The force may be either attraction or repulsion and in either case it affects the rate at which the ion, reaches the electrode surface and undergoes reduction or oxidation. The difference between the limiting current actually obtained and the limiting current that would be obtained in the absence of any electrostatic force is called the migration current. For all polarographic experiments the migration current is rendered negligible by the presence of a relatively large concentration of an indifferent electrolyte, supporting electrolyte, whose ions serve to conduct current through the solution and thus dissipate the electrostatic force but are not reduced or oxidized over the range of potentials that is being studied. Galvanometer G

–

+

– Mercury reservoir oxygen free nitrogen

solution of unknown subs. with excess inert salt +

Fig. 5.4 : The Polarographic set up.

5.4.2 The Residual Current The nature of the layer of an electrolyte solution immediately adjacent to the surface of a mercury drop depends on the potential applied to the drop. If a dropping mercury electrode disconnected from the external circuit is immersed in a pure solution of say potassium chloride, the chloride ions will be preferentially adsorbed on the surface of

68

Introduction to Polarography and Allied Techniques

the drop, and as a result the mercury in the reservoir will acquire a negative charge. This, in turn, will be imparted to the succeeding drops, which will, therefore, adsorb fewer and fewer chloride ions until equilibrium is attained. The negative charge accumulated by the mercury will then be just great enough to counter-balance the tendency for adsorption of excess chloride ions to occur on the surface of the drop. Considering the equation ic = 0.008532 (Emax – E) m2/3 t1/3 ...it is given that the equation describes several important properties of the charging current. It is approximately linearly depended on potential, both at potentials more positive than Emax and at potentials more negative than Emax. With a typical capillary, which has the characteristics m and t 2 mg/sec and 4 sec, respectively, the charging current curve would have a slope of about 0.35μ amp./V in the first of these region and a slope of about 0.15μ amp./V in the second. These values are different because the values of x are different. The majority of practical polarographic analyses are performed by recording a polarogram of the solution being analysed, and extrapolating the portion of the residual current curve that precedes the wave of interest, thus measuring the vertical distance from the plateau to the extrapolated line. The plateau could be extrapolated backwards and the height measured at the half-wave potential. It is to be noted that neither m2/ 3 1/3 t nor x is quite independent of potential, the linear extrapolation is not perfectly accurate, even though the error is negligibly small unless the solution being investigated in extremely dilute or unless the extrapolation crosses Emax. The above equation as well be written as: ic = (kt1/2) m2/3 t1/6 for a particular solution and a particular applied potential. It will be shown in the section of diffusion current that the average diffusion current during the life of a drop, id, is proportional to m2/3 t1/6. Hence the ratio i d /ic is proportional to t1/2. Decreasing the drop-time by increasing the height of the column of mercury above the capillary, therefore decreases this ratio because it causes the charging current to increase more rapidly than the diffusion current, and so attainable sensitivity becomes poorer even though the diffusion current increases.

5.4.3 Migration Current If a dropping electrode is immersed in pure dilute solution of a salt like lead perchlorate, and if a potential on the plateau of the lead wave is applied to it, lead ions will be reduced as fast as they reach the surface of the drop. A current will therefore flow through the cell. Some anodic reaction will occur at which ever reference electrode is being used, and the ions will move through the solution to conduct the current from one electrode through the other. Lead ions will move toward the dropping electrode and the perchlorate ions will move towards the reference electrode. This motion of lead ions causes them to arrive at the drop surface more rapidly than they would if electrical migration did not occur, and this is the cause of the migration current. The value of migration current depends on the transference number of the ions being reduced or oxidised at the drop surface. The larger this transference number, the greater the fraction of the current carried by the motion of that ion. The addition of

Types of Currents

69

supporting electrolyte, whose ions contribute to the conductance but do not contribute to the current because they cannot be oxidized or reduced to any significant extent when they arrive at the drop surface, causes the transference number of the electroactive ion to decrease. If the concentration of the supporting electrolyte is very high, the transference number of the electroactive ion becomes practically zero. Current is then carried across the drop solution interface by the reduction or oxidation of the electroactive ion. It is thus carried through the solution by the motion of the ions of the supporting electrolyte. In such a solution when the transference number is small, the electroactive ion plays only a negligible part in electrolytic conduction through the solution and its motion is affected by the diffusive force alone. The sign of the migration current depends on the sign of the charge on the electroactive ion. Cations are attracted to a cathode, and therefore the migration current increases the wave height when a cation is reduced at the dropping mercury electrode. Anions migrate away from the cathode and therefore the migration current decreases the wave height when anion like iodate or chromate is reduced at the dropping electrode. On examining the figures from literature it can be observed that the addition of supporting electrolyte decreases the wave height of cadmium ion while it increases that of iodate ion. It is assumed that the mechanism of diffusion is the same in a pure salt solution as in the presence of excess of supporting electrolyte, so that the diffusion current is the same in the two cases and that the migration current is given by the product of the total limiting current by the transference number of the electroactive ion [5, 2] il = id + im = id + il t+ = id/(1 – t+) ...(1) for the reduction of a cation, and for the reduction il = id – im = id – il t– = id /(1 + t–)

...(2)

of an anion. Equivalent expression are easily written for the oxidation of cations and anions, for which the migration currents are opposite in sign to those for cathodic waves. Thus, for example, the height of the anodic wave of a cation would increase as supporting electrolyte was added. All practical polarographic work is done under conditions that serve to render the migration current negligible. There are several reasons for this. One of the most important one is that it would be quite undesirable to calculate the concentration of the substance (one which is of interest) a wave height that depended not only on that concentration but also on the concentration and nature of every one of the other ions present. It is plain that the wave heights of lead ions would be quite different in solutions of lead chloride and had perchlorate even though the concentration of the two salts were the same, for the equivalent conductances of the chloride and perchlorate ions are sufficiently different to change the transference number of lead ion by about 3% even if complextion with chloride ion is neglected. It is observed that traces of sodium nitrate or potassium nitrate would affect the limiting current obtained with any given concentration of lead ion, and would do so to different extents because the equivalent conductance of these salts are not at all the same.

70

Introduction to Polarography and Allied Techniques

Another reason for using a considerable excess of supporting electrolyte in practical polarographic work is directly related to these considerations. It is to be noted that the addition of supporting electrolyte produces smaller variations of the limiting currents than it should according to the above equations. This is because a few tenths of a millimole per liter of electrolyte entered the solution from the salt bridge during the preparation and deaeration of the solutions. This would be immaterial if a large excess of electrolyte were already present. Also, the slopes of the waves increase and that the half-wave potentials becomes less negative as the electrolyte concentration rises. This is because the resistance of the solution is fairly high in the absence of added electrolyte and so an appreciable fraction of the voltage applied by the polarograph is dissipated as iR drop through the cell. It is certainly easy to decrease the resistance by adding electrolyte whenever it is possible. A useful rule in order to suppress the migration current to nearly completely, that further variations of the electrolyte concentration will have no effect, the concentration of the supporting electrolyte should be at least 50 times that of the electroactive ion. This is based on the conductance equation. The transference number: t j = c j λ j / ∑ c i λi i

of the jth ion in a solution is also given by the equation. Where in conductance equation, the c’s are the concentrations in equivalents per liter and the λ’s are the equivalent ionic conductances. The concentrations must be expressed in equivalents per liter. This will decrease the transference number of the electroactive ion to about 0.01. A higher concentration of supporting electrolyte is needed if the electroactive ion has an unusually high equivalent conductance (as does hydrogen ion). A lower one will suffice if it has an unusually lower one will suffice if it has an unusually low equivalent conductance (as in large organic ions). Most polarographic work can be carried out with the concentration of supporting electrolyte between 0.1 M and 1 M. In some cases of inorganic polarography even much higher concentrations are often useful. These are other cases where the use of a very concentrated medium may serve to mask an interfering ion. Take for example, thallus ion which yields a wave in almost every known supporing electrolyte but is masked in concentrated hydrochloric acid because of the formation of a chloro complex. Non-ionic substances should not give migration currents. Supporting electrolytes are still used for two reasons. One is to decrease the iR drop through the cell; and the other is to buffer the solution. The resistance of the solution is fairly in the absence of added electrolyte and so an appreciable fraction of the voltage applied by the polarograph is dissipated as iR drop through the cell. It is certainly easy to decrease the resistance by adding electrolyte whenever it is possible. The sign of the migration current depends on the sign of the charge on the electroactive ion. Cations are attracted to a cathode, and therefore the migration current increases the wave height when a cation is reduced at the dropping mercury electrode.

72

Introduction to Polarography and Allied Techniques

Y is CY0 , this rate is equal to kf CY0 . Very little Y will be consumed since the reaction is very slow. So CY0 will be virtually identical with CY, the concentration of Y in the bulk of the solution. Additionally, the current at any instant will be proportional to the area of the electrode at that instant. It will also be affected by the rate of the backward reaction because this competes with reduction of O. Considering the derivation

(

12

ik = 493n D1/2 CY m2/3 t2/3 k f /k b

)

(3)

where ik is the average kinetic current during the life of the drop and D is the diffusion coefficient of Y or O. It is reasonably assumed that these are equal because molecules of these substances will probably have nearly equal sizes. The value of ik will be given in microampere of CY is expressed in millimoles per liter. It is easy to recognize a kinetic current with the help of the Eq. (3) since m2/3 t2/3 does not vary with the height of the column of mercury above the capillary. If all other condition are kept constant, the height of kinetic wave is independent of h corr. This

(

12

)

behaviour is quite different from the behaviour of a diffusion current id /hcorr = k1 . It constitutes the fundamental test for kinetic control of the wave height. There are a number of differences between the kinetic and diffusion-controlled waves giving supporting evidence. However, no conclusive evidence is obtained about the nature of the unknown wave which is suspected to be kinetic. The height of the kinetic wave is larger than the diffusion current that would correspond to the equilibrium concentration of O in the solution. But is smaller than the diffusion current that would correspond to the reduction of the O and Y together. In case n is known, Y can be approximated by applying Ilkovi•c equation. It is not safe to conclude that a wave is kinetic due to its unexpectedly small height, because it also happens with those of adsorption waves. The height of a kinetic wave is influenced by the experimental condition that affect the reaction rates. These include pH, temperature, and ionic strength. The effect of ionic strength depends on the charges borne by the species involved. By changing the composition of the supporting electrolyte in order to displace the equilibrium in favour of O a solution can be obtained in which the concentration of Y is negligible and in which O gives a diffusion controlled wave. When Y is reducible at a more negative potential than O, the total current on the plateau of the wave of Y can be measured. When the equation (3) applicable, the variation of kinetic current with the composition of the solution can be used to elucidate the stoichiometry of the ratedetermining chemical step. Various other kinds of behaviours are possible which have also been observed by many workers. If the pseudo-first order rate constant kf is extremely small, then only little Y will be transformed into O during the life of the drop and as such the kinetic current will be too small to detect. In such a case the wave height of O will be diffusion

Types of Currents

73

controlled and proportional to the concentration of O in the bulk of the solution. On the other hand, if kf is extremely large the wave height will again be diffusion-controlled but will be proportional to the sum of the concentrations of O and Y because actually all of the Y reaching the drop surface will be transformed into O and reduced. In case, where bulk of the solution contains appreciable concentration of both O and Y and where the transformation of Y into O is neither + instantaneous nor slow, the wave height will be the sum of the diffusion current of the O already present. A kinetic current reflecting the formation of additional O at the expense of part of the Y at the drop surface as the equilibrium between them is displaced by reduction. The diffusion current will be proportional to m2/3 t1/6 within the limits of error. The wave height may slow any behaviour intermediate between that of a pure diffusion current at one extreme and that of a pure kinetic current at the other. This depends on the position of the equilibrium between Y and O in any particular solution and on the rate at which it is attained. It is not advisable to use kinetic waves in practical analysis for two reasons: (i) They afford poorer sensitivities than diffusion-controlled waves, and (ii) an impurity may alter the height of the kinetic wave by catalysing the rate-determining step. It is better to explore conditions to obtain diffusion-controlled wave. These can be obtained by investigating the effects of variables such as pH and temperature.

5.4.5 Catalytic Currents Catalytic waves arise from mechanisms like O + ne ⎯⎯→ R

...(1)

kt R + Z ⎯⎯⎯ ...(2) → O in which a substance Z, which would not be reducible at a certain potential if it were present alone, causes the current obtained from the reduction of an electroactive substance O at that potential to increase by reacting with the product R to regenerate O or to form some other substance that is reducible. Catalytic waves are obtained in many mixtures of transition metal ions, such as tangstates, vanadate, molybdate and titanium (v), with oxidizing agents like nitrate, hydrogen peroxide, chlorate. The behaviour of the limiting current in any particular case depends on the relative magnitudes of the diffusion and catalytic currents. The heights of catalytic waves are as sensitive to variations of pH, temperature, and other experimental conditions as those of kinetic ones. The use of a catalytic wave for analytical purposes may often be advantageous because of high sensitivity that may be attained. For examining the catalytic current of nitrate take for example nitrate ion (= Z) does not give a wave in a supporting electrolyte contain 0.1 F sulphuric acid and 0.2 F sodium sulphate. Molybdenum (vi) gives a double wave. The first wave representing reduction to molybdenum (v), and the second represents reduction to molybdenum (iii). Molybdenum (iii) reacts fairly rapidly with nitrate in an acidic solution. At a potential on the plateau of the second wave of molybdenum (vi) in a solution containing nitrate, the molybdenum (iii) formed by the electrode reaction is particularly reoxidized by nitrate and the oxidized molybdenum species is then reduced with more nitrate and so on. The increase of current resulting from the presence of the nitrate that is the

74

Introduction to Polarography and Allied Techniques

difference between the total height of the wave and the diffusion current obtained in the absence of nitrate is the catalytic current of nitrate. In cases where the diffusion current of O is appreciable it may be measured separately in the absence of Z and the catalytic current can then be obtained by difference. Like kinetic currents, catalytic currents can be identified by the fact that they do not vary with h corr. In general these two kinds of currents behave very similarly, but they are easily distinguished because of the peculiar chemical circumstances in which catalytic waves appear. Another important type of catalytic current is observed in solutions containing a base B that is not reducible but that can catalyze the reduction of protons by the following mechanism: B + HA HB+ + C 2HB

HB+ + A–

...(3)

HB

...(4)

H2 + 2B

...(5)

where HA may be hydronium ion or another proton doner. Such catalytic waves are obtained with many organic compounds, including amines, amino acids, proteins, alkaloids. These display complex behaviour. At very low concentrations of catalyst B, the bi-molecular reaction represented by Eq. (5) may be rate determining on the plateau of the wave, where the electron transfer reaction (4) is very fast and then the wave height will increase very rapidly than CB, the bulk concentration of B. But as CB is increased the proton transfer reaction (3) tends to become rate determining. Thus the observed behaviour depends on whether this reaction occurs at the surface of the drop or is the bulk of the solution and this in turn depends largely on the extent to which B can be adsorbed on the drop surface. Most often the ratio of wave height to the concentration of B decreases in the manner of an adsorption isotherm. The dependence on acidity is quite complex. At moderate acidities the wave height may be proportional to the concentration of acid because the proton-transfer reaction is rate-determining, but at high acidities the regeneration of the catalyst, e.g., 2HB

H2 + 2B

may become rate determining step. Then the wave height increases less rapidly than the concentration of acid. Catalytic hydrogen waves are also observed with some inorganic substances. In cases as with the ions of several of the platinum metals they are probably due to the effects of the deposited metals on the over potential for hydrogen evolution.

5.5 ADSORPTION WAVES An adsorption wave may be observed in case either the electroactive species or the product of the electrode reaction is adsorbed onto the surface of the drop. Suppose that the product R of the electrode reaction O + ne → R is adsorbed, its activity is lower in the adsorbed state than in solution which facilitates the reduction of O. There is only a single wave at a very low concentratic of O representing the reduction of O to adsorbed

Types of Currents

75

R. The height of this will be diffusion-controlled, which will be proportional to the 1 2 . In case as the concentration of O is increased, a concentration of O and also to hcorr point is reached at which sufficient R is formed during the life of the drop cover the entire surface. More than this amount of R can be formed only if excess remains in solution. The reduction of the excess O will produce a second wave at a more negative potential because it is more difficult to reduce O to dissolved R than to reduce it to adsorbed R. The original wave is the adsorption wave, whose height will be constant and independent of any further increase in the concentration of O. The second wave which represents the reduction of O to dissolved R is the “normal” wave. The total height of the double wave corresponds to the reduction of all of the O diffusing to the surface of the drop, and is therefore diffusion-controlled and proportional to both the concentration 1 2 . Individually these waves do not follow exactly. of O and hcorr A single wave is obtained at very low concentrations of O represents the reduction of adsorbed O. This is the case when O is adsorbed and R is not. This will reach a limiting height when the amount of O diffusing up to the surface of each drop is just sufficient to cover the drop surface. This happens on increasing the concentration of O. At a still higher concentration, the excess of O remaining dissolved at the drop surface produce a “normal” wave at a less positive potential. The adsorption is due to surface forces. The range of which usually does not exceed molecular dimensions, so that as a rule the adsorbed particles form a monomolecular layer. The particles of the dissolved substances may be bound to the surface by physical, chemical or electrical for a capillary forces causing adsorption in solutions are regarded as physical forces. Adsorption at a DME causes charges in the capacity current and may also influence the faradaic currents. The polarographic currents may be influenced by adsorption by two mechanisms: (i) The depolarizer or its electrode reaction product is adsorbed. In such a case, a separate wave, the so-called adsorption wave is formed. (ii) When some other component of the solution is adsorbed and by its presence at the electrode surface influence the depolarization process splitting the wave for the depolarizer. (iii) Polarographic Currents Influenced by Adsorption of Electroactive Substances. (a) Reversible Processes : Adsorption currents of this type were first observed by Brdi•cka and Knobloch [6] in the reduction of riboflavin and methylene blue respectively. Both compounds formed reversible oxidationreduction systems. At very low concentration of methylene blue (less than 6.10–6 M) only a single reduction wave is observed. At higher concentrations a more negative wave appears which increases linearly with concentration. Whereas the height of the original positive wave remains constant after attaining a certain limiting value. [7] Considering the adsorption of depolarizer, it is assumed that the oxidized form which is subject to a reversible reduction is adsorbed at the dropping mercury electrode whereas the reduced form is not. The reduction of

76

Introduction to Polarography and Allied Techniques

adsorbed molecules requires more energy than that of free molecules because the energy of adsorption has to be overcome. The result is that the reduction of adsorbed molecules must take place at a more negative potentials. (b) Irreversible Processes : In some irreversible reduction two waves are observed. The first one is which is concentration independent above a certain limiting concentration. The shape of the current-time curve may resemble the adsorption pre-wave for the adsorption of the reduction product in reversible systems. In an irreversible reduction, however, it is not expected that the adsorption of the reduction product will facilitate the reduction process. The double-wave may be due to the inhibition of the electrode process by a film of the reduction product and the second which is more negative may correspond to reduction with a higher overvoltage at the covered electrode surface. Such process resembles the inhibition by adsorption of electro-inactive substances. The effect of surface-active substances on the electrode processes also plays a sufficient role. The surface active substances that effect the electrode process are classified according to their charge. Non-ionic more commonly in these are camphor, thymol, gelatine charge depending on the pH values of the solution. Among cationic compounds are the tetra-alkyl ammonium, and tribenzyl ammonium cations which have been specially investigated. A current which at a free surface is controlled by diffusion, may be retarded by a surface-active substance to such an extent that the electrode process becomes ratecontrolling. Sometimes, the electrode process is only accelerated sufficiently at much more negative potentials (considering reduction case) for diffusion to become again, the controlling process. In this way, the increased “irreversibility” in the presence of a film is explainable as evidenced by the decrease in limiting current. The shift of the wave, or the formation of a new diffusion-controlled wave at a more negative potential, though before the desorption potential of the surface-active substance takes place. On the other hand, it also sometime happens that the electrode process takes place at a greater rate when a film is present than when the surface is free. The absorbed substances facilitate the electron transfer, specially with surface active substances of the ionic types.

References 1. 2. 3. 4. 5. 6.

Ilkovi•c, D. : Collection Czechoslov. Chem. Communs. 6, 498 (1934). Kemula W. : Trabojos IX Congr. inter. quim. puray aplicada; Tomo II 297 Madrid (1934). Nernst, W. : Z Physik Chem. 2, 613 (1888). Ilkovi•c D. : Collection Czechoslov. Chem. Communs. 10, 249 (1938). Heyrovsky J. : Arhiv. Hemi Farm, 8, 11 (1934). Bridi•cka R., Knobloch E. Z. Electrochem. 47, 721 (1941).

CHAPTER 6

POLARIZATION 6.1 POLARIZATION OF THE DROPPING MERCURY ELECTRODE AND DEPOLARIZATION PROCESSES When a current passes through an electrode system immersed in a solution containing a common electrolyte, the following relation holds : Eυ − P ...(1) R where Eυ denotes the applied voltage, R the resistance of the polarographic cell and P the polarization, i.e., the electroactive force acting against the electromotive force of the source. Polarization is caused by chemical or physical changes at the electrodes due to the passage of current. In the example given above, it is defined as the difference between the potentials of the two electrodes : P = Ea – Ek ...(2) i=

where ka is the potential of the stationary mercury electrode (mercury pool on the bottom of the cell) and Ek the potential of the dropping mercury electrode regardless of whether it functions as a cathode or as an anode. The relation (3) given in the equation ahead is not as the simple Ohm’s law i.e., Eυ ...(3) R Polarization refers only to the dropping mercury electrode, since the potential of the stationary mercury electrode (i.e., the non-polarizable reference electrode) is constant. This means that the total polarization of the cell can be observed only with a dropping mercury electrode, which is regarded as perfectly polarizable. From the above equation (2) it follows that : i=

P = Eυ – iR

...(4)

This formula shows that the polarization ‘P ’ is smaller than the applied voltage by a value that is given by the potential drop, i.e., iR. While working with more concentrated electrolytes (so called indifferent or supporting electrolytes) the resistance of the electrolyte may be as low as 100Ω . Unless the current exceeds 10–5 A, the product iR is about 1 mV and may be neglected. P

Eυ

On combining this relation with equation (6) we obtain

...(5)

78

Introduction to Polarography and Allied Techniques

Ek = –Eυ + Ea

...(6)

which shows that an external voltage when applied to both electrodes operates only at the dropping mercury electrode. To which it imparts a potential that equals the difference between the potential of the reference electrode and that of the applied voltage. In cases where the current voltage curves are referred to the same reference electrode, the constant Ea may be by convention made equal to zero and hence we get Ek = –Eυ ...(7) i.e., except for its sign, the potential of a completely polarized dropping mercury electrode equals the external applied voltage. A separate reference electrode is usually taken. This is for more accurate determination of potentials on current-potential curves. Secondary electrodes, e.g., calomel, silver chloride are the ones normally used as non-polarizable reference electrodes. Other successful electrodes which have been used at higher current densities are amalgam electrodes, e.g., 1% cadmium amalgam in a cadmium sulphate solution, or oxidation-reduction electrodes like platinum electrode in a mixture of ferric and ferrous ions in 1 : 1 ratio have also been used. The surface area of mercury pool must be sufficiently large to the extent of several square cms in order that it remains non-polarized. Its potential depends on the kind and the concentration of anions in the solution to be electrolized. In such cases, the potential of the mercury pool can be estimated from the composition of the solution.

6.2 REDUCTION OF HYDROGEN IONS AND HYDROGEN OVER VOLTAGE Among the most typical and most frequently studied examples of an irreversible process is the reduction of hydrogen ions. The over voltage of this process varies greatly with the nature of the electrode. The difference between the half-wave potential of the irreversible wave and the standard potential E 0 (virtually equal to the half-wave potential of a reversible wave) is the polarographic over potential (over voltage) η1/2 i.e., η1/2 = (E1/2)irrev – E 0

...(8)

Hydrogen over voltage is usually investigated at constant current density j and is defined as the difference between the electrode potential E, at which hydrogen is reduced at this current density, and the potential Er of a reversible hydrogen electrode in the same solution, i.e.,

η = E – Er

...(9)

Heyrovsky [3] suggested the following reaction mechanism : ...(10) H+ + e → H + + where H is written instead of H3O , for the sake of simplicity. It is supposed that the uptake of a single electron by a hydrogen ion occurs very rapidly and that the rate determining step is the reaction : H+2 + e → H2

...(11)

This mechanism is in accordance with the discharge of hydrogen on some electrodes. In order to explain the shape of the current voltage curve at a dropping mercury

Polarization

79

electrode, Heyrovsky assumed (Ref. as above) that the surface of the electrode is occupied by the evolved molecules of hydrogen, which reduce at the free surface on which the following reaction takes place : ...(12) H + H+ → H+2 K•u ta [4], derived an equation for the polarographic wave of hydrogen ions based on this assumption. K•u ta’s experiments with a streaming mercury electrode [K•uta] [4] collection Czechoslov. Chem. Communs 23, 383 (1958) showed that the concept of surface coverage by hydrogen molecules was not justified. The best agreement with polarographic results is obtained by assuming the reaction: H+ + e → H ...(13) This is supposed to be the slowest step in the proposed mechanism. In fact the influence of the electrode double layer on the discharge of hydrogen ions must also be taken into account. A brief survey of the experiments on the discharge of hydrogen ions at the dropping mercury and the streaming mercury electrode is described below : (i) Current-voltage curves for hydrogen ions without concentration polarization. Workers at about the same period found that in more concentrated solutions of strong acids (e.g., 0.01–0.1 N HCl) and in the absence of neutral salts the above defined reduction potential of hydrogen shifts in accord with the relationship : RT ln ⎡ H+ ⎤ ...(14) ⎣ ⎦ F whereas, with an excess of an indifferent electrolyte the dependence is given by E = const +

2RT ln [H+] ...(15) F In buffer solutions, with one unit increase in the buffer pH shifts the reduction potential of hydrogen by 116 mV to more negative potential. On adding small amounts of neutral salts, the over-voltage is markedly increased. In other words the reduction potential is displaced to more negative potentials, whereas, with increasing concentration of the neutral salt, the reduction potential approaches a constant value that depends on the hydrogen ion concentration. The valency of the neutral salt is also to be taken into account. (ii) Polarographic Waves for Hydrogen Ions Given by Strong Acids : Examining the shape the current-voltage curve and its dependence on the hydrogen ion concentration, it had been inferred that these are the two fundamental quantities in the theory of hydrogen over voltage. It has been stated that the hydrogen wave is asymmetric (Tomes [6],) and that its half-wave potential depends on the hydrogen ion concentration (Tamamushi [5]). (iii) The behaviour of weak non-reducible acids which give reduction waves for hydrogen ions is quite complicated. The limiting current is diffusion controlled for acids with pKa 2–5. The half-wave potential is displaced to more negative E = const +

80

Introduction to Polarography and Allied Techniques

values with increasing concentration of the acid and, particularly of its anions. At the same time, the slope of the wave decreases. Only with very weak boric acid a kinetic limiting current controlled by dissociation rate was observed by past workers.

6.3 DOUBLE LAYER The layer of negative charge at the surface of the electrode and the layer of positively charged solution adjacent to it constitute the so-called double layer. To charge the double layer upto any potential E, a certain quantity of electricity is required. For an electrode of constant area A (in cm2) this is given by q = xA (Emax – E)

...(16)

where q is the quantity of electricity in microcoulombs, x is the differential capacity of the double layer in microfarads/square centimeter, and Emax is the potential of the electrocapillary maximum. The value of x is not independent of potential. In dilute solutions of hydrochloric acid or alkali metal halides it is approximately 40µf/cm2 at potentials more positive than Emax but only about 18 µf/cm2 at potentials more negative than Emax and in each of these regions there are definite further variations with potential [1]. It is evident that the quantity of electricity described by the above equation is positive when E is more negative than Emax, zero when E and Emax are equal, and negative when E is more positive than Emax. The reversal of sign occurs because of the polarity of the double layer is reversed in going from one side of the electrocapillary maximum to the other, and the signs are so chosen as to accord with the customary polarographic convention, in which the flow of electrons into the dropping electrode is taken to constitute a positive current. It can as well be said that the curent is taken to be positive when the dropping electrode is the cathode, and negative when it is the anode. When a reaction is said to take place at the surface of an electrode, it is not implied that the electroactive species must come into actual physical contact with the electrode. There is a potential gradient around an electrode immersed in an electrolyte solution. The potential difference between the electrode and the bulk of the solution may be represented by (E – Emax) where E is the potential of the electrode and Emax is the electrocapillary maximum potential or potential of zero charge. If this is negative, then any surface near the electrode will be at a more negative potential than the bulk of the solution and the potential will become more and more negative as the electrode surface more closely approached. An ion a molecule diffusing toward the electrode will reach a point (whose distance from the electrode surface is always negligible compared with the thickness of the diffusion layer under polarographic condition) at which the potential is sufficiently negative to bring about its reduction. All these points will lie on a spherical surface with a dropping electrode at any instant. There is a simple case in which there is no specific adsorption at the electrode surface and in which the potential varies montonically with distance from the electrode. In more complicated cases specific adsorption does occur and in which the dependence of potential on distance from the

Polarization

81

– + + – – – – + electrode is no monotonic. + – – – – – – + These are depicted schemati– – – – – – + – + + cally in the Figure 6.1. Electrode – + – + + Electrode – – – + + Fig. 6.1 schematic diagrams + + – + + – – – + of the electrical double layer at – – – – – – – – + an electrode whose potential is – – + – – + – – + + – + more negative than the – – + – – – + – potential of the electrocapillary – – ++ – – – + + maximum. (a) No specific – – + – – – + – adsorption, and (b) when the – – – – – – – – + specifically adsorbed cations Helmholtz Diffuse Helmholtz Diffuse are present in the inner layer layer double double Helmholtz plane. layer layer (a) (b) On the basis of the polarographic observations it Fig. 6.1 can be qualitatively described that the surface at which the reaction occurs coincides with the boundary between the Helmholtz layer and the diffuse double layer. Influence of structure of the electrode double layer on the rate of on irreversible process. The double layer affects the rates of electrode processes by its influences on the surface concentration of the depolarizer and on the kinetics of the electrode reaction. This effect was first considered by Frumkin [1] in the case of hydrogen ions. According to Frumkin [1], the electrode process involves only ions in direct contact with the electrode and that electron transfer to more distant ions is not likely. Thus, the electrochemical reaction occurs only in that part of the double layer, which does not exceed the effective ionic radius. Several examples of irreversible processes in which the double layer plays an important role are being described on time to time.

6.4 REDUCTION OF CATIONS (a) Reduction of Hydrogen Ions and Hydrogen Over Voltage : Among the most typical and most frequently studied examples of an irreversible process is the reduction of hydrogen ions [4]. The over voltage of this process varies greatly with the nature of the electrode. The difference between tha half-wave potential of the irreversible wave and the standard potenital E 0 (which is virtually equal to the half-wave potential of a reversible wave) is the polarographic over potential (over voltage) η1/2, η1/2 = (E1/2)irrev – E 0 ...(17) i.e., Hydrogen overvoltage is usually investigated at constant current density j and is defined as the difference between the electrode potential E, at which hydrogen is reduced at this current density, and the potential Er of a reversible hydrogen electrode in the same solution, i.e., η = E – Er .

82

Introduction to Polarography and Allied Techniques

The sequence of reaction could be 2H+ + 2e → 2H

...(i)

2H → H2

...(ii)

Heyrovsky [3] suggested the following reaction mechanism. For the sake of simplicity, H+ is written instead of H3O+. H+ e → H

...(18)

H + H+ → H+2

...(19)

H+2 + e → H2

...(20)

It is supposed that the update of a single electron by a hydrogen ion occurs very rapidly and that the rate determining step is reaction (19). This mechanism is in accordance with the discharge of hydrogen on some electrodes. (b) Polarographic Waves for Hydrogen Ions as given by Strong Acids : As regards the shape of the current-voltage curve and its dependence on the hydrogen ion concentration. These two are very important and fundamental quantities in the theory of hydrogen over voltage. It has been stated, for example, that the hydrogen wave is asymmetric [1] and its half-wave potential depends on the hydrogen ion concentration [6]. (c) Polarographic Waves for Hydrogen Ions Given by Weak Non-Reducible Acids: The behaviour of weak non-reducible acids that give reduction waves for hydrogen ions is quite complicated. For acids which have ka between 2–5, the resulting limiting current is diffusion controlled. The half-wave potential is displaced to more negative values with increasing concentration of the acid and particularly of its anions and at the same time, the slope of the wave decreases. A further example characterized by the strong influence of the double layer on polarographic behaviour could be represented by the system Eu 3++e

Eu2 +

...(21)

The standard oxidation reduction potential for this system is –0.601 V (in 1 M NaClO4) so that the influence of the double layer may be studied on either side of the electro-capillary zero.

References 1. Frumkin A. N. : 2, Physik. Chem. 164 A, 121 (1933). 2. Graham, D.C., J. Electrochem. Soc., 98, 343 (1951) and J. Am. Chem. Soc., 71, 2975 (1949). 3. Heyrovsky, J., Chem. Listy 31, 440 (1937). 4. K•uta J., Chem. Listy 50, 991 (1956). 5. Tamamushi R. : Bull Chem. Soc., Japan 25, 287, 293 (1952) : 26, 56 (1953). 6. Tomes J., Collection Czechoslov. Chem. Communs. 9, 1950 (1937).

CHAPTER 7

AMPEROMETRIC TITRATIONS A conventional amperometric titration is one whose course is followed by measuring a current—almost always a limiting current at a voltammetric indicator electrode. Depending on the potential of the electrode and the voltammetric characteristics of the chemical substances involved, the current may be proportional to the concentration of the substances being titrated, to the concentration of the excess of reagent, or to the concentration of one of the products of the reaction, or it may depend on two of these concentrations. The titration curve is a plot of the limiting current against the volume of the reagent added. If necessary it may be corrected for the residual current and for dilution by the reagent. Ideally it consists of two straight lines intersecting at the equivalence point. Amperometric titrations can be used to determine many substances, such as phosphate and sulphate that are not electroactive besides amperometric titrations are usually less tedious and more precise.

7.1 TYPES OF AMPEROMETRIC TITRATIONS 7.1.1 Theory of Amperometric Titration Curves The shape of an amperometric titration curve depends on the substance being titrated, the reagent used, and the potential applied to the indicator electrode. Many different combinations are possible but the features common to most titrations curves can be explained by taking the titration of lead ion in weakly acidic supporting electrolyte with standard potassium chromate, using dropping electrode at a potential where both lead ion and chromium (vi) yield their diffusion currents. For the sake of simplicity it is assumed that the solubility of lead chromate is negligibly small in the medium employed and that the concentration of supporting electrolyte is so high that the migration current can be ignored. The chemical equilibrium is attained between the addition of each aliquot of reagent and the measurement of the current, and that the diffusion current of each ion is proportional to its concentration. An amperometric titration curve is a plot (i – ir) [V 0 + v] against v, where V 0 is the volume of solution titrated and υ the volume of reagent added. The factor (V 0 + v)/V 0 serves as a correction for dilution by the reagent. In case the reaction proceeds virtually to completion at every point during titration, the plot consists of two straight lines which intersect the equivalence point. The slope of the line preceding the equivalence point depends on the value of k′ i.e., the ratio of diffusion current to concentration for the substance being titrated; that of the line following the equivalence point depends on the value of k for the reagent.

84

Introduction to Polarography and Allied Techniques

The example of lead being titrated with chromate (that has been taken) (i) both k’s are positive at potentials where both ions can be reduced and in this case the plot is V shaped. (ii) In the same titration when it is performed at a potential where chromate ion is reduced but lead ion is not. In this case kcr would be positive while kpb would be zero. Then the current would remain equal to residual current until the equivalence point is reached, the titration curve would be _/-shaped. (iii) If the chromate ion would be titrated with lead ion at the latter potential, the current would decrease until equivalence point is reached and remain zero after it had been passed. The curve would be\_-shaped. On titrating lead ion with sulphide at a potential where lead ion gives a cathodic current while sulphide gives anodic one so that kPb would be positive while ks negative. The cathodic current would decrease to zero at the equivalence point, and the anodic current would increase thereafter if the two ks ′ were numerically equal. A single straight line intersecting the zero current axis at the equivalence point would be obtained. There is a probability that their values would differ slightly. In such a case the curve would consist of two straight lines intersecting each other (at a very obtuse angle) and the zero current line at the equivalence point. For the titration of lead ion with chromate, the point of intersection of the two line segments is described by the rearranged equation: v cr =

0 0 V ib CPb C cr

...(1)

which is exactly the volume of the reagent required to reach the equivalence point. This is true of all amperometric titrations. No matter what kind of chemical reaction may be involved, or what shape of the titration curve is attained and no matter what values of ks ′ may be there. The line segment should always intersect at the equivalence point. Sources of error do remain in amperometric titration as well. Amperometric titrations are useful in cases where potentiometric titrations fail. There are two kinds of interferences in amperometric titration. (i) substances that consume the reagent, that co-precipitates, (ii) that take part in induced reactions with the substance being determined. Interference in amperometric titrations takes place as is there in any other technique. Amperometric titrations have often been employed to evaluate solubility products and other equilibrium constants. For example, if a reducible ion Mn+ is titrated with an inert one Xn– to give the precipitate Mx, and if the concentration of both solutions are known the value of kt under conditions of the titration is easily obtained by appropriate use of the equations. The equilibrium-constant expression would be : ...(2) [Mn+] [Xn–] = 1/kt The apparatus and technique are described ahead.

7.2 KINDS OF AMPEROMETRIC TITRATIONS (i) (a) Redox Titrations, (b) Complexometric and Chelometric Titrations, (c) Compensation and Diffusion-Layer Titrations. (ii) Amperometric Titrations with Two Polarized Electrodes.

Amperometric Titrations

85

7.2.1 Redox Titrations The titration curve obtained in an amperometric redox titration may have any of a fairly large number of shapes. The possibilities are more numerous than in a precipitation titration because there are four substances—the oxidized and reduced forms of each of the two couples involved which may contribute to the current. Each of the four may give a cathodic current (k > 0) or an anodic one (k < 0), or may be electrolytically inert (k = 0), at the potential selected. (k denotes the ratio of diffusion current to concentration). However, two cases are more common than others. In one of them, only one of these four substances yields a current, which may be either cathodic or anodic. In the other, the oxidized form of one couple yields a cathodic current while the reduced form of the yields an anodic one. For the first case example which can be furnished is the titration of vanadium (iv) with vanadium (ii) in 1 F sulphuric acid, using the dropping mercury electrode as the indicator electrode. The following equation describes the reaction : VO++ + V++ + 2H+ = 2V+++ + H2O

...(3)

The second kind of redox titration curve could be exemplified in a titration of iron (111) with vanadium (11) in a neutral citrate medium. At – 0.8V vs SCE iron (111) is reduced to iron (11) giving a cathodic current while vanadium (11) is oxidized to vanadium (111) giving an anodic current. Mercury electrodes are specially advantages in titrations with strong reducing agents because very negative potentials can be attained and because the electrode surface does not catalyze the oxidation of the reagent by water or hydrogen ion. The rotating platinum wire electrode in particular has been very widely used in amperometric titrations.

7.2.2 Complexometric and Chelometric Titrations Amperometric techniques cna be used to find the end point of a complexometric or chelometric titration in several ways. If the metal ion is electroactive and the complex or chelonate is fairly stable, it may be possible to find a potential at which the unreacted metal ion yields its limiting current while the reaction product is inert [6]. The titration of cupric ion with ethylene diamine tetra acetate may be performed with a dropping electrode at a potential where cupric ion is reduced but the chelonate is not can be taken as an example. The current due to the reduction of unreacted cupric ion decreases as the equivalence point is approached and becomes very small after it has been passed. In a redox titration, e.g., O x1 + Red2 = Red1 + O x 2 ; the measurement of the diffusion current of O x1 appreciable kinetic currents will be obtained near the equivalence point unless the reverse reaction is quite slow, although such a situation is quite rare. One can titrate an ion giving a chelonate more stable than that of the indicator in the presence of other giving less stable ones by appropriate selection of the indicator.

86

Introduction to Polarography and Allied Techniques

7.2.3 Compensation and Diffusion-Layer Titrations Compensation titrations are those titrations in which the “reagent” and the “substance being titrated” give currents of opposite signs at some potential, but ideally do not react with each other at all. The end point of such a titration is the point where the cathodic current due to the reduction of one of them is just equal to the anodic current due to the oxidation of the other. In such a case the measured current is just equal to the residual current. This occurs when the electrode itself is oxidized in the anodic half-reaction. This is quite likely to be possible if the electrode is made of mercury, aluminium, silver, or some other relatively base metal [4] the titration of oxygen with sulphide at a mercury electrode [3] is a typical example. In principle, a compensation titration could be performed even if no net chemical reaction could occur at all. Example could be iron (iii)–iron (ii). The couple behaves reversibly at a dropping mercury electrode in a weakly acidic solution containing citrate, ethylene diamine tetra acetate, oxalate or tartrate. In any of these media ferric iron could be titrated with ferrous iron at any potential on the rising part of their waves, where ferric iron would give a cathodic current and ferrous iron an anodic one. Diffusion-layer titrations can be exemplified by the titration of oxygen with a strong acid [2]. The titration can be performed with a dropping mercury electrode at a potential (– 1.8 V vs SCE) where both oxygen and hydrogen are reducible. A neutral but unbuffered supporting electrolyte should be used to suppress the migration current of hydrogen ion. When oxygen is reduced, hydroxyl ions are formed at the electrode surface by the half reaction O2 + 2H2O + 4e = 4OH– As these diffuse away from the electrode surface they react with hydrogen ions diffusing towards it. Hydrogen ions are thus prevented from reacting the electrode surface until their flux equals that of hydroxyl ion, when D1/2 H + C+H = 4D1 2O2 CO2 . Upto this point the value (i – ir ) remains constant after correction is made for dilution. After this it increases linearly with the volume of the acid added in excess.

7.3 AMPEROMETRIC TITRATIONS WITH TWO POLARIZED ELECTRODES In such a case qualitatively different curves are obtained with two polarized electrodes, also known as dual-electrode amperometric titrations. These are titrations in which the current-potential curve for each of the two electrodes changes as the composition of the titration mixture changes. Case is easy to discuss in which two electrodes are identical, because then the behaviour of both can be explained with the aid of a single currentpotential curve. It is not necessary for these to be identical, they may have different areas, the efficiencies of stirring at their surfaces may differ, and they may even be made from different materials. In such an arrangement the difference between the potentials of the two indicator electrodes must be equal to the applied potential (neglecting iR drop through the cell), and the current flowing through the indicator cathode must be equal to (but have the opposite sign from) that flowing through the indicator anode.

Amperometric Titrations

87

The current varies as the titration proceeds and the shape of the titration curve depends on the reversibilities of the couples involved and on the magnitude of the potential difference applied. In principle these titrations can be made with electrodes of any kind, but stationary platinum wire electrode in stirred solutions are much the most commonly used. Amperometric titration with two polarized electrodes have sometimes been claimed to be more sensitive than those employing one polarized electrode. For this reason they have been widely used in coulometric and other titrations in which high sensitivity is needed. The principles and applications of these titrations have been reviewed by Stock [7], Delahay [10] and Lingane [5].

7.4 APPARATUS AND TECHNIQUES Experimentally, amperometric titrations are much simpler than other polarographic or voltammetric techniques. Since the current has to be measured at only a single potential, simple apparatus is needed. Fewer variables need to be controlled because the exact value of the current at any point is not important : all that matters is, how it varies as the reagent is added. The temperature, the composition of the supporting electrolyte, the height of the mercury column above a dropping mercury electrode or the rate of rotation or stirring of another electrode is used. Other factors which are very important in other voltammetric technique are, therefore, of little concern in amperometric titrations, what is necessary to avoid significant variations during the course of any one titration. All amperometic titrations are performed by measuring the current after the addition of each of a fairly small number of aliquots of the reagent. In order to avoid reduction wave of dissolved oxygen, inert gas is bubbled for sufficient time after each addition. More useful would be to use a microburette equipped with a three-ways stopcock. If the solution is sensitive to air precautions must be taken. Mixing after each addition is necessary even when deaeration is not. A stream of inert gas can be used for stirring even if it is not required for deaeration. Stirring must be stopped before the current is measured except in the case of rotating wire and stirred pool electrodes. Amperometric titration can be performed with any voltammetric indicator electrode. Widely used are rotating platinum wire electrodes. In amperometric titrations concentrated reagents are to be employed. There are two reasons for it. One, as is already indicated is to minimize the importance of the theoretically necessary correction for dilution. The other is to minimize variations in the concentrations of the supporting electrolyte, which would affect the diffusion current constants of the substances that contribute to the measured current. Regardless of the shape of the titration curve, failure to correct for dilution always causes the end point found by the usual extrapolative procedure to occur a little earlier than it should changes in the concentration of the supporting electrolyte may displace the end point in either direction. The simplest example could be of a solution containing high concentration of sodium perchlorate as supporting electrolyte which is being titrated with a very dilute reagent.

Introduction to Polarography and Allied Techniques

Most amperometric titrations are performed with reagents having normalities at least 10 or 20 times as large as those of the solutions titrated. Comprehensive reviews of the applications of amperometric titrations in practical analysis have been given in the literature cited. As already stated that an amperometric titration is one in which the end point is determined by the current resulting from a potential applied across the two electrodes.

ic

current

88

0

100

200

%c.p.

ia

7.4.1 The Working Electrode : Reference Electrode

Fig. 7.1 : Amperometric titration curve for applied potential at E1 and E2

In the case in which the potential of a working electrode is controlled relative to a reference electrode, the potential is applied so that a limiting current which is proportional to the concentration of one or more of the reactants or products of the titration is measured. As a result a titration curve is obtained by plotting the limiting current as a function of volume of titrant added. The shape of the titration curve can be predicted from hydrodynamic voltammograms of the solution obtained at various M stages of the titration. The Fig. 7.1, shows resulting amperometric titration curves for two values of applied potential. Their shapes are determined by the behaviour of the limiting current of the voltammogram at the – particular potential during the titration. Fig. 7.2, described the experimental set up of titration assembly.

7.5 TWO WORKING ELECTRODES +

In brief, a useful variation of the amperometric Fig. 7.2 : Wiring diagram for a titration involves meaning the current resulting titration assembly without an from a small fixed potential applied across two external applied voltage (with a working electrodes. One of these electrodes rotating electrode) functions as an anode and the other as a cathode. The expected current behaviour during a titration can be explained by means of hydrodynamic voltammograms. The advantage of the two working electrode variation is the elimination of a reference electrode, which can be troublesome in non-aqueous solvents. One advantage of amperometric titration is it ease of automation. A titrator can be signaled to shut off when a specified current level is reached.

Amperometric Titrations

89

7.6 CHRONOAMPEROMETRY

P o tential

C urr ent

The excitation signal in chronoamperometry is a square-wave voltage signal. This is shown in Fig. 7.3 (a) which steps the potential of the working electrode from a value at which no faradaic current occurs, Ei, to a potential, Es , at which the surface concentration of the electroactive τ Es species is effectively zero. The 0 potential can either be maintained τ at Es until the end of the experiment or be stepped to a final Ei potential Ef after some interest of Ef time T has passed. The latter experiment is termed doubleTime Time potential-step chronoamperometry. Current as a function of time (a) Potential excitation (b) Current-time response signal for double signal (chronoamperois the system response as well as potential step gram) the monitored response in chronoampe-rometry. A typical Fig. 7.3 : Chronoamperometry. double potential-step chronoamperogram is shown by the solid line in Fig. 7.3 (b) (the dashed line shows the background response to the excitation signal for a solution containing supporting electrolyte only. This current decays rapidly when the electrode has been charged to the applied potential). The potential step initiates an instantaneous current as a result of the reduction of O to R. The current then drops as the electrolysis proceeds. It is important to note that the charge Q passed across the interface is related to the amount of material that has been converted, and the current i is related to the instantaneous rate at which this conversion occurs. Current is physically defined as the rate of charge flow. Therefore, Q = nFN

...(1)

where N is the number of moles converted, and the instantaneous current at time t is

⎛ dQ ⎞ ⎛ dN ⎞ = nF ⎜ it = ⎜ ⎟ ⎝ dt ⎠ t ⎝ dt ⎟⎠ t

...(2)

The rate of conversion, dN/dt, is directly proportional to the electrode area and to the flux of material to the electrode as described by the following equation (which is derived from Fick’s first law) :

⎛ ∂C 0 ⎞ it = nF AD0 ⎜⎝ ∂X ⎟⎠ X =0, t

...(3)

90

Introduction to Polarography and Allied Techniques

where

it = current at time t, A n = number of electrons, eq/mol F = Faraday’s constant, 96,485 C/eq A = electrode area, cm2 C = concentration of O, mol/cm3 (mol/L!) D = Diffusion coefficient of O, cm2/s t = time’ s X = distance from the electrode, cm Chronoamperometry has proven useful for the measurement of diffusion coefficient of electroactive species. An average value of it1 2 over a range of time is determined at an electrode the area of which is accurately known and with a solution of known concentration. The diffusion coefficient can then be calculated from it1 2 via the Cattrell equation [8]. The electrode area can be physically measured, but the common practice is to measure it electrochemically by performing the chronoamperometric experiment as a redox species whose diffusion coefficient is known [1]. The value of A is then calculated from it1 2 . If the heterogeneous electron transfer of the redox species with the electrode itself is slow, the current after the potential step in necessarily less than in a system in which the electron transfer is rapid. This aspect of chronoamperometry has been used for the measurement of heterogeneous rate constants [9] [7]. The behaviour of it1 2 as a function of time can be influenced substantially by the presence of chemical reactions that are coupled to the electrode process. Consequently, characteristic variations of it1 2 vs t have been effectively utilized for the quantitative study of such homogeneous chemical reactions. The ECE reaction in which a chemical step exists between two electron transfer steps is one mechanism that has been investigated by means of chronoamperometry : E : O + e ⎯⎯→ R k

C : R ⎯⎯→ X E : X + e ⎯⎯→ P. As shown in the reaction sequence above, a rate determining chemical step in interposed between the two electrode reactions. The two dashed lines in Fig. 7.3 (a) show hypothetical chronoamperograms for the 1e reduction of O to R and for direct 2e reduction of O to P with no kinetic complications. The solid line shows a typical chronoamperogram for an ECE mechanism. The current is intermediate between the 1e and 2e reductions, since the reduction of X to P is controlled by the rate of the chemical reaction of R to generate X. The exact position of the solid line is determined by the value of the rate constant k. Chronoamperometry has been applied to the study of several electrode mechanisms [12,13]. In such studies different mechanisms may exhibit similar responses [1, 6]. Double-potential step chronoamperometry is particularly suited for studying systems that follow EC [12] or dimerization [16] mechanism.

Amperometric Titrations

91

References 1. Delahay, P., New Instrumental Methods in Electrochemistry, Interscience, N7. 1954. pp. 258–264. 2. Kemula, W., and Siekierski, S., Collection Czechoslov. Chem. Communs. 15, 1069 (1950). 3. Kolthoff, I.M., and Miller, C.S., J. Am. Chem. Soc. 62, 2171 (1940). 4. Kolthoff, I.M., and Sambyctti, C.J., Anal Chem. Acta, 21 71 (1959); 22, 253, 351 (1960). 5. Lingane, J.J., Electroanalytical Chemistry, Interscience., N.Y., 2nd ed., 1958, pp. 280– 295. 6. Pribil, R., and Matyska, B., Collection Czechoslov. Chem. Communs., 16, 139 (1951). 7. Stock, J.T., Anal. Chem., 36, 355 R (1964). 8. Cottrell eq. p. 58 Kissinger Peter T., Heinman W.R., Laboratory Technique Marcel Dekker Inc. N.Y. 9. William R. Heinman, Dept. of Chemistry University of Cincinnati, Ohio Kissinger Peter T., Dept. of Chem. Purdue University, Inc., West Lafayette, Indiana. 10. Adams, R.N., Electrochemistry at Solid Electrodes, Marcel Dekker, New York, 1969. 11. Bard, A.J, and Faulkner, L.R., Electrochemical Methods : Fundamentals and Applications, Wiley, New York, 1980. 12. Albert, G.S., and Shain I., Anal. Chem. 35 : 1859 (1963). 13. Hawley, M.D., and Feldberg, S.W., J. Phys. Chem. 70 : 3459 (1966). 14. Feldberg, S.J., Phys. Chem., 73 : 1238 (1969). 15. Schwaz, W.M., and Shain I., J. Phys. Chem. 69 : 30 (1965). 16. Olmstead, M.L., and Nicholson, R.S., Anal. Chem. 41 : 851 (1969).

CHAPTER 8

POLAROGRAPHY OF METAL COMPLEXES 8.1 REVERSIBLE, DIFFUSION-CONTROLLED SYSTEMS DETERMINATION OF FORMULAE AND STABILITY CONSTANTS OF COMPLEXED METAL IONS

id(μ A)

Effects of Ligands on Polarographic Waves : When metal ions in solution undergo complexation with ligands other than water molecules, their polarographic reduction waves appear in two quite distinct ways. Firstly, the half-wave potential is shifted to more negative potential. This happens almost invariably. Secondly, the diffusion current charges and usually becomes 6 smaller (Fig. 8.1). 5 Studies of the stabilities of metal 4 complexes polarographically, involve the 3 determination of shifts in half-wave 2 potentials or limiting currents of metal ions 1 in the presence of increasing amounts of 0.3 0.4 0.5 0.6 0.7 0.8 complexing ligands. The shift of half wave potential of the reduction of a metal ion Fig 8.1 : Effect of complexation on taking place reversibly, both in the absence reduction wave of a metallic ion and presence of complexing agents, shifts towards cathodic direction. The shift increases with increasing ligand concentration. The rate of the electron exchange process remains relatively fast with respect to that of diffusion so that the latter is still rate determining. It is also to be noted that in the presence of the ligands, the reduction wave has a shape indicative of a greater degree of reversibility than that observed for the reduction of the aquo ion, which is attenuated and of lower slope than expected for a 2-electron reversible reduction. The decrease of diffusion current with increasing ligand concentration is to be expected owing to the increased bulk of the complexed ions relative to that of aquo ions. Such variations of diffusion coefficient have been used as the basis of methods of determining stability constants of complexes in solution. Methods for determining stability constants of metal complexes by polarographic method are being divided into three categories : (i) Methods which are applicable to reversible reductions only.

Polarography of Metal Complexes

93

(ii) Methods applicable to irreversible reductions. (iii) Methods which may be applicable to both reversible and irreversible systems. The polarographic technique, involving the direct measurement of half-wave potentials of aquo and complexed metal ions may be used to determine the stability constants of metal-ligand systems of a variety of types. Cases where reversible reductions take place, three main types of metal-ligand systems are applicable. (i) Those in which a single complex species is formed to the virtual exclusion of all others over the entire ligand concentration working range. (ii) Those in which several complexes are formed in stepwise manner, but whose stabilities differ sharply from one another between the limits of ligand concentration. (iii) Cases in which a set of mobile equilibria exists between the various complexes and the aquo ion. This is being represented by the following equation : M(H2O)n

MX(H2O)n–1

MX2(H2O)n–2

::: MX4

...(1)

In such systems, several types of complexes are present at every ligand concentration. The proportion of higher species increases with increasing concentration of ligand. Finally, the predominent species is that with the highest possible coordination number. Large number of systems have been studied polarographically in this category by previous authors.

8.2 DETERMINATION OF STABILITY CONSTANTS AND COORDINATION NUMBERS OF METAL COMPLEXES (i) The method of Lingane [3]. (ii) The method of DeFord and Hume [1] for determining consecutive overall stability constants. (iii) The method of Schaap and McMasters [5] Mixed ligand systems. (i) The Method of Lingane : The reduction of a complexed ion to the metallic state (as an amalgam) is being considered at the dropping mercury electrode. The electrode reaction may be expressed as :

( n− jm) + + ne = Hg

MX f

M(Hg) + j (Xm–)

...(2)

where MXf is the complex of metal ion M with ligand X carrying a charge (n – j m). The charge on the metal being n + and on the ligand species as m–. This overall process is represented as being made up of two reactions. The first one involving prior dissociation of the complex ion into aquo ions and ligand. The second one is the electrochemical reaction of the aquo ion itself, thus : MXf (n – j m)+

M n + j X m− 0

...(3)

| ne, E M If these processes take place reversibly and much more rapidly than the rate of natural diffusion of ions to the electrode surface, then the potential of the DME at all points on the polarographic wave may be given by :

94

Introduction to Polarography and Allied Techniques

E = E0A −

0

RT C γ ln 0A A nF C M γM

...(4)

where CA0 is the concentration of amalgam formed on the surface of the DME and γA 0 is the concentration of the metal ion M in the solution at the its activity coefficient C M

drop surface and

0 M its activity coefficient. E A is the standard potential of the amalgam.

The overall thermodynamic stability constant, βM X + , of the complex MXf (omitting the charges) is given by the expression.

βMXf =

[ MX f ] [ M ][ X ]f

...(5)

here the bracketed terms represent activities. The concentration of the complex in the bulk of the solution, for a given concentration of metal ion and ligand may be written as : C MXf =

βMXf CM γ M [ X ]

f

...(6)

γ MX f

At the electrode surface the metal ion will have a concentration given by the expression : 0 C MX f

=

0 βMX f Cm γ M [X ]

f

....(7)

γ MXf

where, as before, the superscript° refers to the values at the surface. This equation is valid if it be assumed that the concentration of the ligand is large and constant throughout the solution with the same value of activity coefficient both in the bulk and at the electrode surface. The shift in the half-wave potential, produced by the presence of an excess of ligand X, is given by :

γ MI MXf βMXf [ X ] . RT . (E1/2)S – (E1/2)C = Δ E1/2 = 2303 log nF IM γ MX f

f

...(8)

If it is assumed that the diffusion current constants IM , IMX are approximately equal. Thus, the equation in its simplified form as was originally used by Lingane [3] is given as :

Δ E1/2 =

2.3 0 3RT 00591 . 00591 . log βMXf C X' = log βMXf + j log c x ( at 25°C) nF n n

The equation :

...(9)

Polarography of Metal Complexes

95

E = (E1/2)c –

00591 . i log at 25°C n id − i

...(10)

is seen to be identical with the Heyrovsky- Ilkovi•c equation for the reduction of an aquo ion. The equation thus holds both for simple and complexed ions provided that the reduction of both proceeds reversibly. A more simplified equation based on the assumption that the half-wave potential is independent of the concentration of the complex species is given below : 00591 . 00591 . log βMXf − j log C X ...(11) n n It is evident that the rate of charge of half-wave potential with ligand concentration may be expressed as, 0 (E1/2)c = E A −

(

d E1 2

)c

d log C X

= −j

. 00591 at 25° C n

...(12)

Thus, a plot of (E1/2)c versus log CX should be linear of slope – j (0.0591/n) from which the coordination number, j, of the complex, M X f , may be found. Once j is found, it is simple to calculate βMx from the equation given below : f

00591 . 00591 . log βMX j − j logCX at 25° C n n This equation was originally used by Lingane.

Δ E1/2 =

...(13)

(ii) The method of DeFord and Hume [1] for determining consecutive overall stability constants DeFord and Hume made the first attempt in polarography, regarding the stepequilibria between successfully formed complexes in solution. The concentration of each complex species, for a given free ligand concentration, is given by the expression of the form of equations (6 and 7) which are already given. The equation 7 on summing up over all possible (mononuclear) species, now takes the form: N

N

0

0

0 0 M∑ = CM ∑ C MX

βMXf [ X ]

f

M Xf

...(14)

where j = 1, 2, 3, ..., N. The shift in half-wave potential is now finally expressed by :

Δ E1/2

⎛ I 2.3 0 3RT log ⎜ γ M C = nF IM ⎜⎝

f βMXf [ X ] ⎞ ⎟ ∑ γ ⎟⎠ MXf 0 N

...(15)

In order to calculate the individual overall constants, it is convenient to rearrange the above equation and finally express in the form :

96

Introduction to Polarography and Allied Techniques

γ (γ ) γ (γ ) γM γ X + β2 [ X ]2 M X + ... + βN [ X ]N M X γ MX γ MX 2 γ MX 2

F0 [X] = β0 + β1 [X]

N

...(16)

N

In the equation (16) the left hand side has been written as F0 [X] which denotes that it is a function of the free ligand concentration. The summation, on the right hand side has been given in the expanded form. The initial term β0, is the stability constant of the “zero complex” which by definition, has the value unity. It is, therefore, possible in principle to calculate the N stability constants form N values of the function F0[X] corresponding to the range of [X] values. In actual practice, it is necessary to use many more values of [X] than the normal value of N.

8.2.1 Calculation of Individual Complex Stability Constants In the equation (16) the function F0[X] expresses in terms of the concentration of free uncomplexed ligand and also a set of activity coefficients. Working in solutions of constant ionic strength, the values of activity coefficients can be maintained constant. Not only so, in condition of constant ionic strength, it is assumed that the activity coefficient in the equation (16) may be dropped and finally the latter takes the form : F0[X] = 1 + β1[X] + β2[X]2 + ... + βN [X]N

...(17)

In normal practice it is desirable to determine the shift in half-wave potential of a given metal ion for about twelve values of ligand concentration in the range of 0.1 to 2.0 M depending upon the ligand’s solubility. The metal ion concentration which is normally to be used is 5 × 10–4M to 10–3M. The choice has a latitude as the half-wave potential shifts are independent of it. It should, however, normally be maintained strictly constant over any particular run of ligand concentration in order to correctly and easily allow for the variation of the limiting current. After making suitable corrections to the observed E1/2 values, the various F0[X] functions are calculated for each value of [X]. To determine β1, ..., βN , the graphical extrapolation method devised by Leden [2] is applied. On plotting the derived F1[X] values against corresponding values of X, a limiting slope is obtained, as [X] tends of zero, of β2 and an intercept, on the F1[X] axis of β1. Thus a confirmative estimation of β1 is possible and in addition, a preliminary value of β2 is obtained. A function F2[X] can thus be defined similarly. In order to account for N complexes, this procedure is continued. As such the FN–1[X] versus [X] plot gives is a straight line and indicating directly, that the penultimate function has been reached. It is a usual practice to attempt measurement of half-wave potentials to the nearest 0.1 mV.

8.3 MIXED LIGAND SYSTEMS–THE METHOD OF SCHAAP AND MCMASTERS The method signifies the logical extension of the DeFord and Hume method. The method was applied in cases where the metal ions complex with two ligand species are simultaneously present in the solution.

Polarography of Metal Complexes

97

Considering a complexing reaction of the type : M + i X + jY

M Xi Y f

...(18)

in which, i, j are stoichiometry numbers and X, Y are two different ligands species. In this method [Y] is regarded as maintained constant while [X] is varied. A relation of identical form holds under such conditions that [X] is constant and [Y] varied. This principle was applied by Schaap and McMasters to the copper and cadmiumethylene diamine-oxalate systems. The oxalate concentration being held constant while that of ethylene diamine was varied. For this system, three mixed complexes are possible, e.g., Cd (en) (OX), Cd (en)2 (OX) and Cd (en) (OX )2− . By using the conventional DeFord2 Hume method values of the two constants could be determined from studies on the simple cadmium-ethylene diamine and cadmium oxalate systems. The other constant could be found from F10 function by obtaining the intercept from a plot of F10 (en, OX) versus [en]. For more details the readers are advised to consult valid literature on the subject. The polarographic technique, involving the direct measurement of half-wave potentials of aquo and complexed metal ions, may be used to determine the stability constants of metal-ligand systems of a variety of types. All these methods are applicable when the electrode process of both simple and complexed species occur reversible. Irreversible reductions have been taken up later on. The method of Schwarzenbach [6] and Ringhbom and Eriksson [4] have been quite popular and useful.

References 1. 2. 3. 4. 5. 6.

Deferd, D.D., Hume, D.N., J. Am. Soc. 73, 5321 (1951). Leden, I., Z. Phys. Chem. 188, 160 (1941). Lingane, J.J., Chem. Rev. 29, 1 (1941). Ringbom, A., and Eriksson, L., Acta. Chem. Scand. 7, 1105 (1953). Schaap, W.B., and McMasters, D.L., J. Am. Soc. 83, 4699 (1961). Schwarzenbech, G., and Akermann, H., Helv. Chim. Acta. 35, 485 (1952).

CHAPTER 9

POLAROGRAPHY OF ORGANIC COMPOUNDS The polarographic activity of organic compounds is due to the presence of one or more functional groups in the molecule. Out of the more important compounds are aldehydes, α−β unsaturated ketones, nitro and nitroso-compounds, disulphides, polymer hydrocarbons, halides, and peroxides. As a rule, the reduction waves of organic substances are governed by the rate of the electrode process and by diffusion. In the reduction of organic substances, the hydrogen ion concentration has a similar significance as the concentration of the complex forming agent in the reduction of complexes. For this reason, the half-wave potential is usually a function of pH, e.g., OX + pH+

HP O P X + ne → H 1 Red.

...(1)

As already described applications of polarography are based on the measurement and interpretation of current voltage curves. In 1922, however. Dr. Jaroslov Heyrovsky of Charles University, Prague, introduced the dropping mercury electrode. This electrode consists of mercury drop, hanging for a few seconds at the orifice of a glass capillary from which the mercury regularly drops out. The electrode and a reference electrode are immersed into the solution to be electrolysed. When an external voltage is applied across these two electrodes controlled potential electrolysis can be carried out (Fig. 9.1). The variation of current with a continuously increasing voltage can be measured by an instrument in the circuit. This measurement gives courrent-voltage curves i.e., i vs E. These curves, obtained with a dropping mercury electrode or even with any other electrode with a periodically renewed surface are completely reproducible and are called polarographic curves. These curves depend only on the composition of the electrolysed solution, with experimental conditions kept constant. In the presence of substances which undergo reduction or oxidation at the surface of the dropping electrode, or substances that catalytically effect the electrode process, or those that form stable compounds with mercury, an increase in cathodic or anodic current on the currentvoltage curve is observed. The current rises in a given potential range and this increase is followed by a region of potential in which the current has reached a limiting value. The S-shaped portion of the current-voltage curve is called a polarographic wave. The shape and position of polarographic waves provides us with information on both the quantitative and qualitative composition of the electrolysed solution. The difference

Polarography of Organic Compounds

99

between the limiting currrent and the current before the waves rise, is called the wave height. This usually depends in the concentration of the electroactive substance in solution. Most analytical applications of both organic and inorganic polarography are based on the increase in wave height with concentration. Another important quantity is known as half-wave potential. This is the point on a polarographic curve at which the current reaches half of its limiting value. The wave height, although, it depends on concentration, the half-wave potential is practically independent of the concentration of the electroactive species. But its value does depends on the kind of organic compound involved. The half-wave potential is a quantity that can be used for qualitative characterization of organic substances because, the half-wave potential depends on the nature of electrolysed solution and also on the composition of the solution. Measurements of both wave heights and half-wave potentials are important in solving problems in fundamental organic chemistry. The measurements of wave heights can be applied to the study of some slowly established equilibria, of reaction kinetics and hence of optimum conditions for any desired syntheses. The half-wave potentials offer information about rapidly established equilibria, reactivity towards nucleophilic attack and similar reactions, and the presence of certain structural groups in the molecule. Commonly used in chemical analysis, the polarographic technique can solve some problems of structure, reactivity, mechanism and synthesis in organic chemistry.

9.1 STRUCTURAL EFFECTS As already indicated in Chapter 1 that for systems in which the equilibrium between the oxidised and reduced forms is rapidly established at the surface of the electrode. These are called reversible systems and the half-wave potentials measured polarographically are practically equal to standard oxidation-reduction potentials measured potentiometrically. In these cases the half-wave potentials are a function of the equilibrium constants of the oxidation-reduction equilibrium. The possibility of characterising oxidation reduction properties of numerous systems is offered by polarography whereas application of potentiometry is not possible. Systems which involve a step with a high activation energy, are called irreversible systems. The half-wave potential is a function of the rate constant of the electrode process involved. It is not surprising to find correlations between the values of half-wave potentials and the structure of organic compounds. This is because of the relationship of half-wave potentials to equilibrium or rate constants. Among structural factors that effect halfwave potentials are : (i) the nature of the electroactive group, i.e., the group where cleavage or formation of bond occurs during electrolysis, (ii) stereochemistry, and (iii) the nature of substituents. In general, the shift towards more positive potentials of a cathodic wave, corresponding to a reduction process, indicates that the reduction is proceedings more readily. A shift toward more negative potential indicates that the reduction is proceeding with greater difficulty. Similarly, for anodic waves, corresponding to an oxidation process, the shift towards more negative values indicate that the oxidation proceeds more readily.

100

Introduction to Polarography and Allied Techniques

9.2 NATURE OF ELECTROACTIVE GROUP The decisive factors for determining the polarographic behaviour of the organic molecule are : the nature of atoms in the electroactive group, their arrangement in space, and the type of bond cleaved or formed. The polarographic behaviour also depends on the molecular frame to which the electroactive group is bound, the substituents present, and in particular on the groups present in the immediate vicinity of the electroactive group. Some such groups are more susceptible to the effects of the molecular framework. Valid quantitative comparison of half-wave potential is possible when the electrode processes follow the same mechanism for all the systems to be composed. It is generally true that reduction proceeds more easily when conjugation of double or triple bonds of the electroactive group with a multiple bond or with an aromatic ring occurs. Taking the example of the reduction observed in Δ 4 – 3 ketosteroids is shifted to more positive potential for Δ 1.4 – 3 ketosteroids by 0.15 to 0.22 volts. But for Δ 4.6 – 3 ketosteroids by 0.29 to 0.45 volt. Similarly as the number of condensed aromatic rings increases, the reduction is made easier. Single C – X bonds are usually reduced at more negative potentials than C = C – CX, but at more positive potentials than C – C = C – X (X is halogen). A rigorous comparison of electroactive groups is restricted to a sequence of closely related groups such as C – F < C – Cl < C – Br < C – I in which the ease of reduction of the C – X bond increases with the increasing polarizability of the halogen X. There are some other examples also. Examples of simplified reduction processes are given in the Table 9.1 and 9.2. TABLE 9.1 These bond types can be reduced at a dropping mercury electrode

C – C C = C C≡ C

C – N C = N C≡ N N – N N = N

Condensed benzenoid rings Carbonium ions Some heterocyclic rings

C–O C = O

C–S C = S

N – O N = O O – O

N – S O – S S – S

C–X

O – X S – X X = Halogen

Polarography of Organic Compounds

101 TABLE 9.2

A system of conjugate multiple bonds represents a single electroactive group

C=C–C ≡C–C=O Electroactive Group


> exp[(1–α )f η] and the equation Fig. 17.8 becomes: i = io e −α f η

...(36)

or

η=

RT RT lnio − lni αF αF

...(37)

A successful model of electrode kinetics must explain the frequent validity of the above equation, known as Tafel equation. The empirical tafel constants : equation η = a + b logi can be identified from theory as

α=

2.3RT log io αF

b=

−2. 3RT αF

...(38)

254

Introduction to Polarography and Allied Techniques

The tafel form can be expected to hold whenever the back reaction (i.e., the anodic process, when a net reduction is considered, and vice versa) contributes less than 1% of the current. Tafel relationships cannot be observed fro such cases, because they require the absence of mass-transfer effects on the current. When electrode kinetics are sluggish and significant activation over potentials are required, good Tafel relationships can be seen. This point explains the fact that Tafel behaviour is an indicator of totally irreversible kinetics. Systems in that category allow no significant current flow except at high overpotentials, where the faradaic process is effectively unidirectional and, therefore, chemically irreversible.

(d) Tafel Plots A plot of log i. vs. η, known as Tafel plot, is a useful device for evaluating kinetic parameters. In general, there is an anodic branch with a slope (1–α )F/2.3RT and a cathodic branch with slope –α F/2.3RT. As shown in Fig. 17.8 both linear segments extrapolate to an intercept of log i0.

(1–α )F Slope = 2.3RT

log |i| –3.5

–αF Slope = 2.3RT

–4.5 log i0 –5.5

–6.5 200

150

100

50

–50

–100

–150

–200

η, mV

Fig. 17.8 : Tafel plots for anodic and cathodic branches of the current-overpotential curve for R with –α = 0.5, T = 298 K, and j0 = 10-6 A/cm2. O+e

Note that for –α = 0.5, b = 0.118 V, a value that is sometimes quoted as ‘typical’ Tafel slope. 9

The plots deviate sharply from linear behaviour as η approches zero, this is because the back reactions can no longer be regarded as negliglible. The transfer co-efficient α and the exchange current, i0 are obviously readily accessible from this kind of presentation when it can be applied.

Exchange Current Plots (Tafel Plots) This kind of plot is useful for obtaining from experiments in which i0 is measured essentially directly. From the equations it recognized that the exchange current can be related as :

Kinetics of Electrode Process

255

log io = log FAk o + log C*o +

αF αF Eo' − Ee q 2.3RT 2.3RT

...(39)

Therefore, a plot of log i0 vs. Eeq at constant C* should be linear with a slope of −αF / 2. 3 RT . The equilibrium potential Eeq can be varied experimentally by changing the bulk concentration of species R, while that of species O is held constant. This kind of plot is useful for obtaining α from experiments in which i0 is measured essentially directly.

17.8 EFFECTS OF MASS TRANSFER A more complete 1-η relation can be obtained from

⎡ Co ( o,t ) −αf η CR ( O,t ) (1 −α )f η ⎤ i = io ⎢ e e − ⎥ * C*R ⎣⎢ Co ⎦⎥

...(40)

(where η = E – Eeq) by substituting for C o (O,t ) C *o and C R (O,t )C *R

(x = 0)R

According to

Co

Co

*

( x = 0)

and

CR

CR* i ⎛ i ⎞ = ⎜1 − io ⎝ il,c ⎟⎠

e −αη

i il

...(41)

i il,a

...(42)

1 –

=1 −

⎛ i ⎞ (1−α ) f η e − ⎜1 − ⎝ il,a ⎟⎠

...(43)

This equation can be rearranged easily to give i as an explicit function of η over the whole range of η. For small overpotentials, a linearized relation can be used. In the Tafel regions, other useful forms of the above equation can be obtained. For the cathodic branch at high η values, the anodic contribution is insignificant and as such this equation becomes i ⎛ i ⎞ −αf η ⎛ i ⎞ = ⎜1 − − ⎜1 − e ⎟ e ( 1 − α) fn ⎟ io ⎝ il ,c ⎠ il,a ⎠ ⎝

...(44)

This equation can be useful for obtaining kinetic parameters for systems in which the normal Tafel plots are complicated by mass-transfer effects.

256

Introduction to Polarography and Allied Techniques

References 1. B.E. Conway, “Theory and Principles of Electrode Processes,” Ronald, New York, 1965, Chap. 6. 2. H.R. Thirsk, “A Guide to the Study of Kinetics,” Academic, New York, 1972, Chap. 1. 3. J. O’m. Bockris and A.K.N. Reddy, “Modern Electrochemistry,” Vol. 2, Plenum, New York, 1970, Chap. 8. 4. K. J. Vetter, “Electrochemical Kinetics,” Academic, New york, 1967, Chap. 2. 5. C.N. Reilley in “Treatise on Analytical Chemistry,” Part I, Vol. 4, I.M. Kolthoff and P.J. Elving Eds., Wiley-Interscience, 1963, Chap. 42. 6. T. Erdey-Gr•uz, “Kinetics of Electrode Processes,” Wiley-Interscience, New York, 1972, Chap.1 & 4. 7. W.J. Albery, “Electrode Kinetics,” Clarendon, Oxford, 1975. J.E.B. Randles, Trans. Faraday Soc., 48,828 (1952). H. Kojima and A.J. Bard, J. Am. Chem. Soc., 97, 6317 (1975). 8. M. E. Peover, Electroanal. Chem., 2, 1 (1967). N. Koizumi and S. Aoyagui, J. Electroanal. Chem., 55,452 (1974).

CHAPTER 18

BIOELECTRODICS INTRODUCTION Electrochemistry as we have come to know it consists in the study of ionic solutions, and electrodes where ions and electrons combine and separate. Galvani from Bologna, Italy, in 1791, put forth that bio electrochemistry has been a part of electrochemistry. It would be not too much to say that there are electrochemical events going on in living systems where ever you pry into them. The nervous system is certainly based on the flow of electric currents and it is not of all fanciful to see nerves as the wires that run between the enzymes, the electrodes of the body. Bodies are full of membranes, 100, and so are electrochemical cells. Some reactions in the body baffle chemists by going up tree energy gradients, but again that is just what happens in electrolysis, in electrochemical reactors. We can study electrochemical phenomena in the immense complexity of living systems when all we know is how to explain simple systems like fuel cells and corrosion seems to be the crassest arrogance. The science of biology is a truly gigantic edifice, so big, in fact, that it includes all of organic chemistry and uses it to explore very very complicated interactions.

USEFUL PRELIMINARIES The aminoacid glycine i.e., NH3+–CH2–COO– would be simplest example excluding of course H3O+, H2O, and O2 of an entity that takes part in bioreactions, A Structural element within the amino acid is the peptide group

− N− C − | | H O which is important because when many of these groups occur in a chain, and such chains form a polymer, one has a protein. Proteins form skin, nails, and skeletal structures. Enzymes biocatalysts are proteins, Hemoglobin, which carries O2 around the body is a protein. Proteins can have molecular weights as law as 10,000 but some are really very large with molecular weights of 50 × 106. The corresponding radii of the larger of these entities (when they get formed spherically), would be in the hundreds of angstorms. Examples of some amino acids are shown in the Fig. 18.1. Structures that

258

Introduction to Polarography and Allied Techniques

H | H2N—C—COOH | H

Glycine (gly)

H | H2N—C—COOH | CH2

CH2CH3

H | H2N—C—COOH | CH2 | OH

Isoleucine(ile)

Serine (ser)

H | H 2N—C—COOH | CH2 | COOH

H | H2N—C—COOH | (CH2)4 | NH2

H | H2 N—C—COOH | CH CH3

N H

Tryptophan (trp)

Aspartic acid (asp)

Lysine (lys)

Fig. 18.1 Examples of some amino acids. (Reprinted with permission from Accounts of Chemical Research 21 copyright 1989, Fig. 1, American Chemical Society)

a protein, for example in glycine. The proteins found in nature are made up of only about 20 different individual amino acids. On the other hand, a typical protein consists of several hundreds of these 20 distinguishable amino acids. These proteins (containing several hundreds of the 20 special amino acids) might be thought at first to be long, long chains containing repeated peptide groups (see last fig.) 18.2 which can be written more R R | | H—N—C—C—N—C—C—OH | | || | | || H H O H H O

Peptide Fig. 18.2 Peptide

explicitly as where the R’s may be hydrocarbon chains on other peptide elements and the shaded area denotes the bond between the two peptides. However these long flexible chains are neither linear nor random in shape. They coil and stretch in a way that greatly affects the properties of the protein i.e., how it does its work. Among the most important of these structures is an arrangement called the α -helix (according to pauling and Corey 1951) but of the elements in cells, the mitochondrion. These mitochondria are the entities in cells where energy is made from the oxidation of organics derived from intake of food and oxygen.

Bioelectrodics

259

Membrane Potentials The measurement and interpretation of the protentials across biological membranes has been going on for about a century. A remarkable suggestion was put forward by Bois-Raymond in 1868, whose concept was that a cell surface could be well looked at as though it were an electrode. The principal elements in biological cells is shown in Fig. 18.3. A Section of a yeast cell with its membrane is shown in Fig. 18.4.

nucleus nucleolus

mitochondrium

endoplasmatic reticulum

1 μm

Golgi complex

Cytoplasmic membrane

Lysosome approx. 10 μm

Fig. 18.3 : The scheme of an animal cell. reprinted from J. Koryta, Ions, Electrodes And Membranes Fig. 69. Copyright © J. Wiley & Sons, Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

Fig. 18.4 : Electron micrograph of a section from a yeast cell. The outer envelope is the cell wall. The inner double line is the cytoplasmatic membrane. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 70. Copyright © J. Wiley & Sons, Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

From these two figures it is inferred that the animal cells are rather complex, each one containing the heriditary material and in particular the entities known as mitochondria. It is infact the energy producing properties of these are discussed in forthcoming sections. Membranes, the subject of this section, can be relatively thick (0.1mm) of made chemically). Biological membranes are very much thinner (50–100Å) of the same (3–5 nm) range as that of passive oxide. The figure shows the essential constituents of the biological membranes. These are lipids and proteins. In myetin membrane the lipid content is 80% while at the other end the range, in mitochondria there is an inner membrane containing only about 20% lipid. There are many kinds of lipids as well as very many kinds of proteins. In membranes are usually phospholipids Fig 18.5. The

260

Introduction to Polarography and Allied Techniques

IB1

IN

IM

IB2

O || O H2C—O—C—R || | O R—C—O—CH ′ | || H 2C—O—P—O—X | O

Teflon septum window (a)

aqueous solution drop of lipid solution

IC P

Fig. 18.5: Typical biological membrane structures. A liquidmosaic model in the form proposed by A. Kortya with different types of disposition of membrane protein) (phospholipids are shown as dark circles with two wavy tails); IB1, integral, membrane-bridging protein, with a single polypeptide span; IB2, the same with several spans; IN and IC, integral noncytoplasmic and cytoplasmic proteins; IM, integral buried proteins; P, peripheral protein. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 81. Copyright © Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

polar head Hydrophobic end

(b) Plateau-Gibbs boundary

Fig. 18.5(a): A scheme of the bilayer lipid membrane. The black circles indicate the polar heads (the hydrophilic part) consisting of phosphoric acid, ethanol amine, and anlogue derivatives. The wavy lines are the long alkyl chains of fatty acids (the hydrophobic part) (Reprinted from J. Koryta, ions, Electrodes and Membranes, above. Copyright © J. Wiley & Sons Ltd. 1991.

(c)

BLM

Fig. 18.6: Preparation of a bilayer lipid membrane. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 84. Copyright © J. Wiley & Sons Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

structure often contains an H atom and this allows the phosphoric acid element to ionize. In the membrane structure, the alkyl groups R and R′ are directed inward while the popular groups are on the surface. A scheme of bilayer and lipid membrane. The black circles indicate the polar heads (the hydrophilic part) consisting of phosphoric acid, ethanol amine; and analogue derivatives. The wavy lines are the long alkyl chains of fatty acids (the hydrophoblic part). [Taken from J. Koryta, Ions Electrodes and Membranes.] The most common model system to act as a smiplified biological membrane is the “bilayer Lipid membrane” (BLM) which was first prepared Mueller in 1962. It consists of two lipid molecules tail to tail Fig. 18.6 with the polar groups oriented to face the solution. In the basic BLM individual, compounds of a biological system can be built and examined.

Bioelectrodics

261

The BLMs, although very thin exhibit very high resistance, up to 10 10 ohms. Nevertheless, some pores do develop in these membranes and water, followed by ions, enters there and reduces the resistance. Application of a potential increases the flow of ions through the pores and the number of pores. This further reduces the resistance. Teflon septum window (a)

aqueous solution drop of lipid solution

(b) Plateau-Gibbs boundary (c)

BLM

Fig. 18.7 : Preparation of a bilayer lipid membrane [Taken from J. Koryta Ions, Electrodes and Membranes.

The method of measuring a membrane potential is simple. A calomel electrode is placed in a solution (if the solution contains Cl–) on either side of membrane, which usually occupies a hole about 1 mm in diameter in a teflon sheet. Since the potential of the calomel electrode is accurately known and varies accoding to Nernst potential with logdCl-, the difference in potential arising from the two different Cl– concentrations in each side of the membrane is easily known and can be subtracted from the total potential difference registered between the two electrodes to give the value due to the membrane. Most of the membrane potentials recorded in the literature lie within values of tens to hundreds of milli volts.

Simplistic Theory The theory of an equilibrium on one species between each side of the membrane was formulated by Donnan in 1925 until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl–) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane according to Hodg kin and Keynes 1953. Until 1950s Some bio-electrochemists confidently explained membrane potentials by assuming that only one ion like K+ in KCl permeated the membrane. If so, then ui−α = μ + nF ϕ* = ic + RT In aiα + nF ϕ α

(1)

262

Introduction to Polarography and Allied Techniques

would be the expression for electrochemical potential of the permeable ion i, on one side, α , on the other side β, the corresponding expression for electrochemical potential of the same ion, there would be −β

bi

β

β = μ + η F ϕβ = boj σ + RTln α i + nF ϕ

As long as equilibrium can be assumed between permeating ions, i on each side e.g, on the α and the β side respectively −β

bi−α = bi Hence

αΔ R ϕ =

αβ RT ln i ηF ααi

...(2)

Being developed in parallel with the rise and fall of the Donan equilibrium theory of membrane potentials was the application of liquid function. Potential theory to membranes. This was proposed as far back as 1888 by great Nernst himself. The theory grew by application of the Nernst-Planck equation to take into account the driving forces due to concentration and potential gradients.

Modern Approaches to the Theory of Membrane Potentials According to (Jahn, 1962) there is found to be a poor match between theory and experiment. Ionic concentration differences alone, then, do not completely determine membrane potentials in living systems. Membrane Some membrane potentials are affected by light, just as if the membranes were semi-conductors. This is entirely outside the capabilities of A B theories that depend on the interplay of potential and concentration gradients in 1949 Albert Szent-Gyogyi made a EA–A• = E R•1 e Ea' – 2 = E R•3 suggestion that some biomaterials might be regarded as semiconductors. This was criticized and another view was that A• B• biomaterials could be thought of as possible electronic conductors and hence E1 E2 electrodes. This was consistent with the idea that the first step in photosynthesis is the photo-electrochemical decomposition of water, and it would account in Fig. 18.8: Schematic diagram showing the oxidation principle, for the photosensitivity of and reduction reactions occuring at a membrane solution interface on sides 1 and 2 of the membrane. membranes. (Reprinted from M.A. Habibi and O’M. Bockris, In case Szent Gyorgyi’s concept is J. Bioelectricity 2:66 (1984). Reprinted by accepted to interpret the electronic permission of Marcel Dekker.)

Bioelectrodics

263

conduction of some biomaterials, the To To idea that arose was that electronic Instruments Instruments transfer at the solid/solution interface could occur with the solid E A Outer We being a biomaterial. Jahn in 1962 Inner Aqueous Aqueous was the first to come up with Solution (1) Solution different theory of membrane (SCE) (SCE)(2) potentials. Jahn’s concepts pictured AE (SCE) the membrane as a bioelectrode, μ1 , μ1 μ2 , μ2 s s [Red]1 with each side the site 1 differing [Red]2 [Red]1 A– D [Red]2 (but coupled) redox reactions, the membrane itself acting somewhat 0 0 e E1 E2 like the membrane in a fuel cell Fig. A more detailed view, due to Tien is D + [OX]2 [OX]1 A shown in Fig. 18.8. Electron s Conducting s [OX]2 The equations deduced for the [OX]1 BLM s two reactions making up a corrosion ψ1 , ψ ψ2 , ψs 1 2 0 a i couple are specialized in the sense E a Ea E a that the cathodic reaction is taken to be hydrogen evolution and the anodic one, metal dissolution. The α values being assumed to be one half, but one can drop these assumptions Fig. 18.9 : Transmembrane electron movement and and assume that the membrane redox reactions. Also shown schematically are potentials is simply that of a electrodes and circuit diagram for cyclic voltammetry. WE, working electrode; SCE, saturated calomel bioelectrode. Somewhat similar reasoning can electrode; AE, auxiliary electrode. μ, and μ are be applied to the comings and goings chemical and electrochemical potentials, respectively. of the Na+, K+ and Cl– ions which Bulk concentrations of reduced (RED) and oxidized (in this view) determine the (OX) species on either side of the membrane as indicated by subscripts 1 and 2; interface potential of the membrane. Koryta concentrations are designated by a superscripts has for mulated this theory by (Reprinted from H.T. Tien, Aspects of Membrane writing electrode kinetic equation Chemistry, Kluwer Academic Publishers, 1991.) similar to those that lie behind the Butler-Volmer equation. The movement of ions occurs across the membrane of working electrochemical cells and in these cases certainly the ions are driven by two interfacial cooperating processes. Such movements occur as a result of events elsewhere. The differences in concentration in which they originate are not the causes of the potentials with which they are associated. These causes are surface electron-transfer reactions that occur at the interfaces, i.e., at interfaces on either side of the membranes. Such sites of electron transfer are probably at enzymes absorbed at the membrane surfaces. Thus in this view, the actual origin of membrane potentials lies in the free-energy changes in redox reactions occuring respectively, on each of the two membrane surfaces.

264

Introduction to Polarography and Allied Techniques

Electrical Conduction in Biological Organisms Electronic. The initial reaction to the proposition that electronic currents flow in biological organisms understandably negative. In early investigations of this subject, the common view seemed to be justified for proteins that were crystallised out from the dissolved form and thoroughly dried show an extremely high resistivity. In 1960’s, some evidence of a significant 10–4 electrical conductance in biomaterials was Fully Hydrated Hemoglobin available. Significant conductance was found 1.2 eV Fully Hydrated Cholesterol in crustaceans. Indirect support also came from –6 Dry Palmitate 0.9 eV 10 Synthetic mechanisms involving electron flow which Partially Hydrated Melanin Synthetic Melanin 1.5 eV seemed necessary to explain phenomena in 1.2 eV photosynthesis, in enzyme reactivity and in the 10–8 energy producing activities in mitochondria. All Trans βCarotene Rosenberg and Postow realized that 1.5 eV Dry Sheep Root 2.3 eV proteins in the body are far from dry, and a 10–10 nearer approximation to the in vitro situation would be to find out the electronic conductivity Retinal- Aniline Protonated –12 of wet proteins. However, the difficulty that Schiff’s Base 10 Complex 2.1 eV arose was that since protein is wet, the Dry Hemoglobin Dry Cholesterol conductance measured may be partly ionic. 2.4 eV Palmitate 3.6 eV –14 Rosenberg and Postow managed to separate 10 2.7 3.0 3.5 4.0 out the ionic component of conductivity. They 1000 found that the energy of activation for the T°K electronic part of the conductance went linearly downward as the water content of the protein Fig. 18.10 The log of current plotted increased. It appeared as though water, or its against 1/T(K) for a variety of biological ionized constituents acted like doping agent in substances. The activation energies are increasing the electrical conductance of intrinsic calculated from the slopes of the lines. semi-conductors. Thus an increase of ~108 times (Reprinted with permission from B. Rosenbergh and E. Postow, Ann.N.Y. in conductance can arise in this way. Fig. 18.10. Acad. Sci. 158:61, 1969, p. 162, Fig. 1.) However, in respect to the mechanism for the reduction of O2 in biosystems. Szent-Gyorgyi suggested that methyl glyoxal, rather than O2 accepts electrons from enzyme H – C = O | C = O | CH3 surfaces and thereafter reduces O2 homogeneously. This kind of biochemical approach to cancer predated the recognition of DNA, which redirected the attention from biochemistry to genetics. In the account of electrical conductance in biological organisms, it is important to stress: the usefulness of examining semiconduction by means of the Hall effect. Thus,

Bioelectrodics

265

if an electric current flows through a body in the x direction, and a magnetic field is applied normal to the body in the z direction, an extra electric field is caused to exist in the y direction. From measurements made, then, on the effect of applying this magnetic field to a current flowing through a body, it is possible to determine the charge carrier concentration in the body. Moreover, the sign of the charge carriers, whether electrons (negative) or holes, (positive) can be determined. Knowing the conductance, the applied field strength and the concentration and sign of the charge carriers, it is possible to calculate their mobility values range between 0.01 cm 2/V s to 10 cm 2/Vs at room temperature. The carrier concentration varies over a range of 108 – 1018 sec. The biological materials measured (a comprehensive data set was gathered for the first time by Gutmann Lyons and Keyzer in 1983) show a wide variety of behaviours as to conductance in which either electrons or holes predominate. How does electronic conductance occur in biological materials in this respect, the basic mechanism of conductance in an impurity-containing protein is similar to that of a doped semiconductor such as silicon. However, complications occur in respect to the distance between sites from which electrons originate and those in which they may be received. Basically, electrons tend to transfer through energy barriers within the structure by quantum mechanism tunneling. However, a rough rule the maximum jump length for the tunneling electron is about 20Å. If there is no receiver state for an electrons within that distance, the probability of a successful tunnel transfer will be so slow that the dominant mechanisms of transport may change from that of a tunneling to that of electron hopping between neighboring atoms. Systems that allow tunneling will generally show a much higher value of charge-carrier mobility than those in which atom-to-atom electron hopping is the preferred mode. Another factor is crystallographic and concerns the shape and size of ordered areas in the protein in which there are respective groups, giving rise to band formation, which then enhances the concentration of electrons able to travel under a field gradient.

ELECTRICAL CONDUCTION IN BIOLOGICAL ORGANISMS PROTONIC There are possibilities in biological structures in which the charge carrier is neither an electron nor a hole, but a proton as per Nagle and Morowiz in 1978 and Pething in 1998. Because quantum mechanical tunneling is a frequent mode of transport with electrons, it may be asked if it is likely that proteins could also tunnel. Thus, the Gamow factor for the probability of tunneling is given by the equation. PT αe −

4π l 2mE η

...(3)

where m is the mass tunneling particle, l is the transfer distance, and E is the energy of the entity tunneling. The proton is ~ 1840 times heavier than the electron. Assuming that the distance of transfer for the proton is about one tenth that for the electron, and the E value is the same, the tunneling probability for individual proteins will be about e–4 that for electrons. However, in proteins even if they are wet, so that the activation energy for electrical conductance is only ~0.5eV, the probability of activating an electron to the conductance band will be as little as about 10–7 at room temperature. Particularly,

266

Introduction to Polarography and Allied Techniques

it proteins, it may i.e., that the proton concentration exceeds that of conductance-band electrons so that conductance via proton tunneling mechanism becomes likely. Detailed investigation suggests that the rate deterimining step is usually some comformal charge rather than the tunneling step. This would be similar to the situation of protons conducting in aqueous solutions, where the rotation of a water molecule under the field of the approaching proton, is rate determining, not the rate of proton tunneling. Similar conformational changes are necessary in a protein structure, in which electron and proton transfer are the R O C C important steps in electrical | R | H conductance. A possible proton O H O=C C H | N conducting pathway within a H O – H N O N H C H H cytoplasmic membrane is | | H O N C shown in the Fig. 18.11. H H C H R O O Specific conductance in R | C C biological organisms covers the R enormous range of 1015. It is Direction of proton flow possible to understand why the Fig. 18.11 : A series of H bonds (...) serving as a protonrange is so large. The specific conducting pathway within a cytoplasmic or intramemconductance will depend on the brane protein. (Reprinted with permission from J.F. Nagle proteins’ structure. Is it and H.J. Morowitz, proc. Nat. Acad. Sci. U.S.A. 78, 298, suitable for band formation as 1978, p. 299, Fig.3.) it seems to be in many proteins. However, it will also depend on the degree and type of doping, not the intentional addition of trace additives as in the organic semiconductors, but the presence of other entities (water, extra organic substances, fragments etc.) in the structure. Finally, protons may add to the transport because although the probability of tunneling of the individual proton is much smaller than that of an electron, the number of available.

THE ELECTROCHEMICAL MECHANISMS OF THE NERVOUS SYSTEM AN UNFINISHED SECTION Electrical activities are an integrated part of the activity of the brain, but there the amplitude of the encephalographic oscillations is in the microvolt region, whereas tens of millivolts are needed to trigger passage of a pulse through the nervous system. Bernstein, in 1962 first focused attention on the alleged importance of the ratios of the Na+ and K+ concentrations of the intra and extracellular fluids of the nerve axon and related them via a Nernst type equation to the electrical potential measured across it. Thus the theoretical approach to the passage of electricity through nerves become electrochemical. Hodgkin and Huxley, Nobel prize winners published seminal experiments on the current potential relation across the membrane of the nerve sheath during 1952. Attached to the original and elegant expeirments they described was a phenomenological theory of the surprising results were reported the result inferred the interpretation of the variation of potential across the membrane containing the intracellular fluid when the

Bioelectrodics

267

passage of current through a nerve was triggered and this confirmed as to what has been found experimentally and was expressed impressively mathematically also. The Hodgkin-Huxley (H-H) theory of the nervous system was an example of bioeletrochemistry glillering with the virtue, a work truly to be compared in status with the best known piece of electrochemistry the Debye-Hickel theory of ionic solutions. It appeared later that the theory was untestable. The electrophysiologists still use the HH theory.

ENZYMES AS ELECTRODES Enzymes: Enzymes are catalysts for reactions in the body in fact they serve to make the nature of biochemical activities different and faster. Enzymes are proteins and their molecular weight varies greatly, from 103 to 106: Apart from their acceleration of a reaction brought about by enzymes, there is their astounding specificity: They are turned on and of by tiny changes in the structure of the entities taking part in the bioreaction being catalysed. Apart from this there are ‘coenzymes’, by which is meant another substance, mostly a vitamins, that has to be present to make the enzyme work. Enzyme catalysts have yet another, puzzling feature, reactions catalyzed by them do indeed increase in rate, with temperature. However, proteins tend to unfold at certain temperature known as denaturation, when this occurs, the enzyme loses its activity. They still retain their extraordinary activity and specificity for reaction with a substance in solution that it is meant to catalyze.

Electrodes Carrying Enzymes: The 1980s were spent in discovering what not to do if one wished to carry enzymes in electrode and use their powers as electrocatalysts. 1. Single electron tunneling jumps greater than about 20Å do not happen, although much can be alone (Heller and Delgani, 1987) to facilitate successive jumps. 2. Even partial decomposition of an enzyme upon adsorption must be prevented because the fragments produced from a passive layer on the electrode and in activate any enzymatic activity there. 3. Far-reaching decomposition of the enzyme upon adsorption must obviously be avoided, for it occurs, it destroys the enzymes catalytic power. There are only two ways to obtain a successful, adsorbed enzyme acting as an electrocatalyst (Rusling 1997). 1. The enzyme itself and the electrode system upon which it is to adsorb must be highly purified. 2. The most important point (much applied by Eddowes and Hill at the University of Oxford) is to have a suitable promotors as the electrode. It is this prelayer that encourages complicated large bimolecules to adsorb and still retain some of the properties as catalysis that they show in solution. It has been known that one way to make model membranes is to use bilayers of phospholipids placed tail to tail and insert proteins is to them. Fig: 18.12.

Bioelectrodics 10 Current, μA

active in electron exchanges in chlorophyll and bacteria, and resulting in the production of H. Why is it that the pre adsorbed surfactant layer on the electrode (e.g., the DDAB), has such a helpful effect in facilitating the reactions of enzyme electrode? For one thing, the surfactant is a good, adsorber on the metal or graphite electrode. Correspondingly, if, upon adsorption, there is some partial dissociation of the complex enzyme, the pre adsorbed surfactant makes it difficult for such fragments to build up passive layers on the electrode layers that could diminish electron transfer. Another factor that has to be controlled, in case one wishes to obtain the maximum reaction rate, is pH. At a pH 9, the reduction involves protonation. The rates of these reactions are very high, a rate constant of 8000m-1cc-1, equivalent to an i0 of –10–5 A cm–2 if the reactant concentration is 10–3 M.

269

Fe(III)

c

Fe(II) ba

5 0 –5 Fe(II)

–10

0.40

0.20

Fe(III) 0.00 –0.20 –0.40 E, V vs SCE

Fig. 18.14 : Cyclic voltmmograms at 100mVs-1 inpH 5.5 buffer. a, pH 5.5 buffer on bare pyrolytic graphite (PG); b, 0.5 mMMB (horse, from Sigma) in buffer on bare PG; c, MB-DDAB film on PG in buffer, no MB in solution. (reprinted from J.F. Rusling, “Electrochemical Enzyme Catalysis,” Interface, 6(4): 26-312, Fig. 2 1997. Reproduced with permission from the Electrochemical Society, Inc.)

The Electrochemical Enzyme-Catalyzed Oxidation of Styrene Styrene is a phenyl ethylene, C–C6H11 – Ch = CH2, a compound important in a number of polymerization. In the body the cytochrome P450 enzyme in the liver can form styrene oxide, which then may react with organisms’ DNA, i.e., become a carcinogen. The use of MB in lipid films to oxidize styrene has been achieved by Rusting et.al. (1997) in a series of reactions that can be written as follows: X-MB Fe(III) + e– X-MB Fe(II) (at electrode) X-MB Fe(II) + O2 → X – MB Fe(II) – O2 X-MB Fe(II) – O2 + 2e– + 2H+ → X – MB Fe(II) + H2O2 (at electrode) H2O2 + X – MB Fe(III) → X – MB Fe(IV) = O + H2O 2X – MB Fe(IV) = O + H2O2 → 2HX – MB Fe(IV) = O + O2 Styrene + X – MB Fe(IV) = O → X – MB Fe(III) + styrene oxide It can resonably be concluded that the inclusion of enzyme proteins in SAMs provokes fast electrode reactions.

APPENDIX Table 1 : Values of Important Constants (N, F and R for the chemical mole) Avogadro’s Number N = (6.023 0 ± 0.000 2) × 1023 mole–1 Charge on the Electron e = (4.802 94 ± 0.000 08) × 10–10 e.s.u. = (1.602 09 ± 0.000 03) × 10–20 e.m.u. = (1.602 09 ± 0.0003 03) × 10–19 coulomb Faraday Constant F = (9,649.3 ± 0.2) e.m.u. equivalent–1 = (96,493 ± 2) coulomb equivalent–1 Gas Constant R = (8.3147 ± 0.000 05) joule deg.–1 mole–1 = (1.987 2 ± 0.000 01) cal. deg.–1 mole–1 = (0.082 057 ± 0.000 000 5) l.atm.deg.–1 mole–1 Boltzmann’s Constant k = (1.380 49 ± 0.000 05) × 10–16 erg deg.–1 Ice Point T0ºC = (273.150 0 ± 0.000 2) ºK Velocity of Light C = (2.997 928 ± 0.000 004) × 10 10 cm sec–1 Planck’s Constant h = (6.6254 ± 0.000 2) × 10–27 erg sec Standard Atmosphere 1 atm. = 1,013,250 dyne cm–2 Standard Gravitational Acceleration g 0 = 980.665 cm sec–1 Defined Calorie 1 cal. = 4.1840 joules Relation between Chemical and Physical Mole 1 phys. mole = 1.000 275 chem. mole Relation between Litre and Cubic Centimetre 11. = (1,000.028 ± 0.004) cm3

Appendix

271 TABLE 2 Electron Affinities of the Atoms

The electron affinity of an atom or radical is the energy absorbed in converting the particular ion shown into the neutral atom or radical. Values under I are those given by Fritchard (Chem. Rev. 52 (1953) 529); values under II are those given in LandoltBörnstein, I Band, 1 Teil, p. 213. Ion

I kcal/mole

H– Li– Na– K– Hg– C– C4– N–

17.22 12.5 28 16 35.4 48 ± 20 –708 –16

N 3– Bi– O– O2– S–

> 47 ? > 17 ? 53.8 ± 0.8 – 210 > 24

II kcal/mole

II eV

Ion

I kcal/mole

II kcal/mole

16.5 10

0.72 0.5

S2– Se– Se2– Te–

–80 > 40? –97 50?

–90

28

1.2

F– Cl– Br–

83.5 ± 2 88.2 ± 1.5 81.6 ± 1.5

94 87 81

4.1 3.78 3.52

Γ

74.6 ± 1.5

72 70 45 60

3.12 3 2 2.5

53.5 – 150 60

2.34 – 6.5 2.5

CN– OH– HS–

II eV –4

TABLE 3 The Work of Extraction of an Electron from various Metals in Electron Volts Ag Al

4.70 4.20

Cu Fe

4.48 4.63

Nb Nd

3.99 3.3

Si Sm

3.59 3.2

As Au B Ba Be Bi C Ca Cd Ce Co Cr Cs

4.79 4.71 4.6 2.52 3.92 4.34 4.36 3.20 4.04 2.88 4.25 4.45 1.94

Ga Ge Hf Hg Ir K La Li Mg Mn Mo Na

4.16 4.62 3.53 4.53 4.57 2.25 3.3 2.46 3.70 3.95 4.24 2.28

Ni Os Pb Pd Pr Pt Rb Re Rh Ru Sb Se

4.91 4.55 4.04 4.98 2.7 5.36 2.13 4.97 4.65 4.52 4.56 4.87

Sn Sr Ta Te Th Ti Tl U V W Zn Zr

4.39 2.74 4.13 4.73 3.47 4.16 4.05 3.45 4.11 4.53 4.27 3.93

272

Introduction to Polarography and Allied Techniques TABLE 4 Dielectric Constant of Aqueous Solutions at 25°C ε = 78.54 – 2Ac (valid c = 0.5 – 2.0) Solute

A

Solute

A

HCl LiCl NaCl KCl RbCl NaF KF

10 7 5.5 5 5 6 6.5

NaI KI MgCl2 BaCl2 LaCl3 NaOH Na2SO4

7.5 8 15 14 22 10.5 11

TABLE 5 Dielectric Constants (∈ ∈ ) of some Inorganic Solvents

Reproduced from Harned and Owen, Physical Chemistry of Electrolyte Solutions, First Edition, by courtesy of Reinhold Book Division Solvent

∈

tºC

Solvent

∈

tºC

AsCl3

12.8

20

NH3

16.9

25

D2O

77.94

25

N 2H2

51.7

25

HCN

106.8

25

N 2O4

2.4

18

83.6

25

NOCl

18.2

12

HF H2SO4

101

25

POCl3

13.3

22

9.8

240

SO2

14.1

20

I2

11.1

118

SOCl2

09.25

20

IF5

36.2

25

SO2Cl2

09.2

20

SeOCl2

46.2

20

HgBr2

TABLE 6 Dielectric Constants of Mixtures of Water and Organic Solvents at 25ºC Non-aqueous

Weight % of Non-aqueous Component

Component

10

20

30

40

50

60

70

80

90

100

CH3 CH 2OH CH3 CH 2CH 2OH

72.8 71.8

67.0 64.9

61.1 57.7

55.0 50.3

49.0 43.0

43.4 36.4

38.0 30.7

32.8 26.1

28.1 22.7

24.3 20.1

(CH 3) 2CHOH

71.4

64.1

56.9

49.7

42.5

35.3

28.7

23.7

20.3

18.0

(CH3 ) 3COH

70.0

61.3

52.6

43.9

35.4

27.9

21.4

16.5

12.4

9.9

CH 2OH.CH 2OH

75.6

72.8

69.8

66.8

63.2

59.4

54.7

49.3

43.7

37.7

Appendix

273 TABLE 7 Polarographic Half-Wave Potentials (in Volts vs. the normal Calomel Electrode) in Aqueous Solution

Ion

N

+

Li

A

B

– 2.31

– 2.31

Ca

– 2.23

– 2.23

K+

– 2.17

– 2.17

Na+

– 2.15

– 2.15

2+

– 2.13

– 2.13

+

– 2.09

– 2.09

+

Rb

– 2.07

NH+4

– 2.08

NH3CH+3

– 2.8a

NH2(CH3)+2

– 2.09a

NH(CH3)+3

– 2.27

N(CH3)+4

– 2.7

N(C2H5)+4

– 2.71

+ 7 4

– 2.56

+ 9 4

– 2.61

2+

Sr

Cs

N(C3H ) N(C4H )

– 2.07 – 2.15b

Rare Earth Metals – 1.90

– 1.94

2+

– 1.89

– 1.89

Ra Sc

– 1.9 to – 2.0

2+

Ba

– 2.29

3+

– 1.96

– 1.84

Zr4+

– 1.7 TABLE 8 Anodic Depolarization Potentials

Process

Solution

Hg + Cl− → HGCl Hg

+ N −3

E1/2 + 0.21

→ HgN 3

+ 0.21

−

Hg + CNS → HgCNS

+ 0.14

Hg + Br − → HgBr

+ 0.10

Hg + 2OH− → HgO

Anion concentration

+ 0.04

274

Introduction to Polarography and Allied Techniques Process

Solution

E1/2

Hg + 2SO23 − → Hg(SO3 )2

= 0.001 M

– 0.05

Hg + Γ → HgI Hg

+ 2S2O23−

– 0.07

→ Hg(S2O3 ) 22−

– 0.18

Hg + 2CN− → Hg(CN)2

– 0.4

Hg + S2 − → HgS

– 0.6

Fe II → Fe III II

Fe → Fe

III

II

Mn → Mn I

III

II

Re → Re

0.1 N KHF2

+ 0.08

C

– 0.38

2 N KOH, tartrate

– 0.40

1 N HCiO4

– 0.54

II

III

1 N HCiO4

– 0.42

III

V

Re → Re

1 N HCiO4

– 0.26

→

1 N HCiO4

0.0

→

Cr III

0.1 N Na2SO4

– 0.62

ReV CrII

→ Re

ReVII

Re

II

IV

HCl

– 0.06

SnII

→ SnIV

tartrate pH = 2.3

– 0.18

SnII

→ SnIV

tartrate pH =7

– 0.48

SnII

→ SnIV

tartrate pH =13

– 0.75

SnII

→ SnIV

1 N KOH

– 0.77

Sn → Sn

SnII → SnIV

F

– 0.24

SbIII

→ SbV

0.5 N KOH

– 0.34

AsIII

AsV

0.5 N KOH

– 0.25

Ti III → Ti IV

HCl

– 0.18

VIV

pH = 6.8

+ 0.07

C

– 0.36

1 N KOH

– 0.46

IV

V

→

→

VV V

→V

VIV → VV

TABLE 9 Inorganic Oxidation Reduction Potentials Process CuI

CuII

I

II

Cu

Cu

Solution

E1/2

0.1 N Na2SO4

– 0.06

C

– 0.25

Appendix

275

Process CuI

CuII

II

III

Solution

E1/2

Citrate buffer pH = 7.0

– 0.21

Cu

Cu

Saturated CaCl2

– 0.55

CuII

CuIII

D

– 1.42

MnII

MnIII

Triethanolamine, 0.5 N NaOH

– 0.49

Fe

III

1 N Sodium oxalate

– 0.30

Fe

III

Citrate buffer pH = 4.0

– 0.04

Fe II

Fe III

Citrate buffer pH = 7.0

– 0.49

Fe II

Fe III

Tartrate buffer pH = 10.0

– 0.9

II

III

1 N KOH

– 0.9

Tii

Saturated CaCl2

– 0.15

TiIII

TiiIV

0.1 N KCNS

– 0.49

TiIII

TiiIV

Citric or tartaric acid

– 0.48

1 N H2SO4

– 0.55

1 N oxalate, pH = 4.5

– 1.16

1 N HCl

– 0.93

Fe

II

Fe

II

Fe Ti

Fe

III

IV

VII

VIII

II

III

V

U

V

III

U

IV

NpIII

NpIV

1 N HCl

– 0.10

PuIII

PuIV

1 N HClZ

+ 0.65

TABLE 10 Electrode Potentials and Electrical Conductivities Electrode

Electrode reaction

Volts

Li = Li+ + e–

+ 3.045

Acid Solution Li/Li+ +

+

K/K

K=K + e ++

Ba/Ba

++

Ca/Ca

++

++

Ba = Ba

++

Ca = Ca

+

–

+ 2.925

+ 2e

–

+ 2.906

+ 2e

–

+ 2.866

–

Na/Na

Na = Na + e

Mg/Mg++

Mg = Mg++ + 2e–

+ 2.363

Al/Al3+

Al = Al3+ + 3e–

+ 1.662

Mn/Mn++

Mn = Mn++ + 2e–

+ 1.180

+ 2.7142

276

Introduction to Polarography and Allied Techniques Electrode

Electrode reaction

Volts

Zn/Zn++

Zn = Zn++ + 2e–

+ 0.762 8

Cr/Cr

3+

Fe/Fe

++

Cr = Cr

3+

Fe = Fe

++

+ 3e

–

+ 0.744

+ 2e

–

+ 0.440 2

Cd/Cd++

Cd = Cd++ + 2e–

+ 0.440 9

Pb/PbSO4/SO4–

Pb + SO4– = PbSO4 + 2e–

+ 0.358 8

++

Pb/Pb

Pb = Pb +

++

+ 2e

+

–

+ 0.126

–

Pt/H2/H

H2 = 2H + 2e

Ag/AgBr/Br–

Ag + Br– = AgBr + e–

– 0.071 3

Cu/CuCl/Cl

Cu + Cl– = CuCl + e–

– 0.137

+

Pt/Cu , Cu

++

+

++

Cu + Cu + e

–

0.000 0

–

– 0.153

–

–

Ag/AgCl/Cl

Ag + Br = AgBr + e

Pt/Hg/Hg2Cl2/Cl–

2Cl– ± 2Hg = Hg2Cl2 + 2e–

– 0.267 6

Cu/Cu++

Cu = Cu++ + 2e–

– 0.337

Pt/I2/I–

31 = I3– + 2e–

– 0.536

++

Pt/Fe , Fe

3+

Fe

+

++

= Fe

3+

+

+e

–

– 0.771

–

Ag/Ag

Ag = Ag + e

Au/AuCl4–, Cl–

Au + 4Cl– = AuCl4– + 3e–

Pt/Cl2/Cl–

2Cl– = Cl2 + 2e–

++

Pt/Mn , MnO

– 4

++

Mn

–

– 0.799 1 – 1.00 – 1.359 5 – 4

+

+ 4H2O = MnO 8H + 5e

–

Pt/F2/F

– 0.222 5

2F = F2(g) + 2e

–

–

– 1.51 – 2.87

TABLE 11 Ionic Properties of Water Temperature °C

0

10

20

25

Specific conductivity, ohm–1 cm–1 × 108

1.2

2.3

4.2

5.5

Ionic product KW × 1015

1.14

2.92

6.81

10.08

30

50

100

7.0

17

—

14.7

56

513

Appendix

277 TABLE 12 Ionisation Constants of Acids (at 25°C)

Acid

–log K

Acetic Benzoic Boric Bromacetic n-Butyric Carbonic

K1 K2

Chloroacetic Chromic Cinnamic (cis) Cinnamic (trans) Citric

K1 K2 K3

Dichloroacetic Formic Fumaric

K1 K2

Glutaric Glycine Hydrocyanic Hydrofluoric Hydrosulphuric (H2S)

K1

Acid

4.76 4.20 9.24 2.87 4.82 6.37 10.25 2.86 6.49 3.88 4.43 3.06 4.74 5.40 1.30 3.75 3.03 4.47 4.34 9.78 9.14 3.14 7.24

Nitrous Oxalic Phenol Phosphoric

Phosphorus Phenolphthalein o-Phthalic Picric Propionic Salicylic Silicic Succinic Sulfanilic Sulphuric Sulphurous

K2 14.92 K1 2.00 K2 6.26 K1 2.85 K2 6.10

Maleic Malonic

–log K

Tartaric Trichloroacetic Uric

K1 K2 K1 K2 K3 K1 K2 K1 K2

Ca K1 K2 K1 K1 K1 K2 K1 K2

4.47 1.19 4.21 9.89 2.12 7.21 12.32 1.80 6.15 9.70 2.89 5.41 0.38 4.87 2.97 9.7 4.19 5.57 3.19 0.40 1.92 1.76 7.20 3.02 4.54 0.89 3.89

TABLE 13 Buffer Mixtures Buffer Compositions (After Clark and Lubs) 4.85 20.75 8.3 5.3

ml ml ml ml

0.2 0.2 0.2 0.2

N N N N

HCl HCl HCl HCl

+ + + +

25 25 25 25

ml ml ml Ml

0.2 0.2 0.2 0.2

KCl KCl KCl KCl

pH (20°C) diluted diluted diluted diluted

to to to to

100 100 100 100

ml ml ml ml

1.0 1.4 1.8 2.0

278

Introduction to Polarography and Allied Techniques Buffer Compositions (After Clark and Lubs)

pH (20°C)

46.70 32.95 20.32 9.90 10.40 22.15 6.95 43.00

ml ml ml ml ml ml ml ml

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

N N N N N N N N

HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml

2.2 2.6 3.0 3.4 4.0 4.6 5.2 5.8

5.70 17.80 39.50 45.20

ml ml ml ml

0.1 0.1 0.1 0.1

N N N N

NaOH NaOH NaOH NaOH

+ + + +

50 50 50 50

ml ml ml ml

0.1M 0.1M 0.1M 0.1M

KH2PO4 KH2PO4 KH2PO4 KH2PO4

6.0 6.6 7.4 7.8

2.61 8.50 21.30 36.85 43.90

ml ml ml ml ml

0.1 0.1 0.1 0.1 0.1

N N N N N

NaOH NaOH NaOH NaOH NaOH

+ + + + +

50 50 50 50 50

ml ml ml ml ml

0.1M 0.1M 0.1M 0.1M 0.1M

H3BO3 H3BO3 H3BO3 H3BO3 H3BO3

diluted diluted diluted diluted

diluted diluted diluted diluted diluted

to to to to

to to to to to

100 100 100 100

100 100 100 100 100

ml ml ml ml

ml ml ml ml ml

7.8 8.4 9.0 9.6 100

QUESTIONS Chapter 1 1. 2. 3. 4. 5.

Describe Polarography giving applications. What is a Polarographic cell? Describe the experimental set up of Polarographic circuit. Describe the Half-wave potential and its significance. Describe ionic strength and also give the influence of ionic strength on halfwave potentials. 6. What are the factors which affect the half-wave potentials?

Chapter 2 1. 2. 3. 4.

Describe Dropping Mercury Electrode (D.M.E.). What are the advantages of D.M.E.? What particular cell is used in Polarography? What are its advantages? Describe the various electrodes giving their uses. (a) Hanging Mercury Drop Electrodes. (b) Carbon Electrodes. (c) Carbon Paste Electrodes. (d) Glassy Carbon Electrodes. (e) Mercury Pool Electrode. (f) Calomel cell. 5. Which reference electrodes mostly used in Polarography? Why? 6. How would you distinguish between working electrode and a reference electrode?

Chapter 3 1. 2. 3. 4. 5.

Describe the Polarographic circuit. What is the significance of diffusion in classical Polarography? What solvents are mostly used in Polarography? Why supporting electrolytes are used in Polarography? What is Polarographic maxima? What various types of maxima are being observed in Polarography? 6. Innumerate various non-aqueous solvents. 7. Which are useful in Polarography?

280

Introduction to Polarography and Allied Techniques

Chapter 4 1. 2. 3. 4. 5.

Describe the Ilkovic equation? What are its consequences? Describe the cathodic and anodic waves. What are reversible and irreversible electrode processes? What is the significance of reversible polarographic wave? Describe the coupled chemical reactions and chemical reversibility.

Chapter 5 1. 2. 3. 4. 5.

What are the various currents that have some significance in Polarography? Describe the diffusion current and its significance in Polarography. What are diffusion-controlled currents? Describe the diffusion coefficient and its significance. What are the various factors that affect the diffusion current?

Chapter 6 1. What is the Polarization of the D.M.E.? Give an account of the depolarization process. 2. What is hydrogen over voltage and give an account of the reduction of hydrogen ions? 3. Describe double layer. How double layer affects the reduction process? 4. Give a brief account of the reduction of cation giving two examples.

Chapter 7 1. 2. 3. 4. 5. 6. 7.

Describe the theory of amperometry. Describe the types of amperometric titrations. What are redox titrations? What are complexometric and chelometric titrations? Give an account of amperometric titrations with two polarized electrodes. Describe the experimental set up of amperometric titrations. What is chronoamperometry?

Chapter 8 1. How metal complexes are determined by Polarographic method? 2. What is the significance of reversible, diffusion-controlled system in metal complex? 3. How the formulae and stability constants of metal complexes are determined by polarography? 4. What methods are employed in studying mixed ligand complexes? 5. How the co-ordination number of metal complex could be determined?

281

Chapter 9 1. 2. 3. 4.

Which bond types are reducible at D.M.E.? Which functional groups are reducible at D.M.E.? Can Polarography be used to detect and follow intermediates in some reactions? Describe the utility of Polarographic methods in the electrosynthesis of organic compounds. 5. What are the advantages of electro-organic syntheses?

Chapter 10 1. What conditions are required in order to use mathematical analysis to resolve overlapped first derivative D.C. polarograms? 2. What are the advantages of using Non-aqueous solvents or solvent extracts in D.C. Polarography? 3. Describe in brief theory, principles and applications of cyclic and pulse techniques. 4. What is stripping analysis? Describe the electrodes used in these techniques. 5. Give a brief account of voltammetric methods. Also the differential and derivative voltammetry.

Chapter 11 1. Innumerate various types of organic electrode reactions giving examples. 2. What are the various categories of electrolytic reaction pathaways of N-heterocyclic reactions in general? Give examples. 3. Describe the experimental technique for running an electrochemical experiment with an organic system. 4. Give a circuit diagram for galvanostatic method (constant current). 5. Also give circuit for potentiostatic method. 6. What is Polarization study? How is it done?

PART II. ALLIED TECHNIQUES Chapter 10 1. Define Kalousek’s commutator method. How is the method related to the square wave and pulse-polarographic techniques. 2. What are charging currents? 3. Give an account of the sinusoidal A.C. Polarograph? 4. Does the A.C. Polarograph constructed from operational amplifier provide some advantages? 5. What is the disadvantage of operational amplifier employed in most existing electroanalytical instruments?

282

Introduction to Polarography and Allied Techniques

6. What arrangement is named as milli- or microcoulometry? 7. Innumerate the various methods for determining ‘n’ by electrolysis.

Chapter 11 1. Describe chronopotentiometry in brief. What are its analytical applications? 2. What are the advantages of chronopotentiometry over polarography for a particular type of experiment? 3. What type of cells are used for chronopotentiometry? 4. What is the significant use of pulse polarography and differential pulse polarography with D.C. Polarography? 5. Give an account of electrolytic currents and kinetic currents. 6. Give brief account of pulse polarography and oscillographic Polarography.

Chapter 12 1. What is voltammetry? 2. Describe in brief coulometric methods. 3. Distinguish between differential and derivative voltammetry.

Chapter 13 1. 2. 3. 4. 5. 6.

Give a brief account of the technique applied in electro-organic synthesis. What are the main reactions that take place in electro-organic synthesis? What is the main electrochemical activity in heterocyclic systems? Describe the experimental technique. How is the current efficiency determined? What is polarization study?

Chapter 14 1. 2. 3. 4. 5. 6. 7. 8.

What are ion selective electrodes? What part is played by hydrogen in corrosion? How is corrosion controlled? Give an account of potential-pH diagrams applied in corrosion processes. What are electronation reactions in corrosion? What are the factors that affect the rate of corrosion. Give some common examples of corrosion? What is passivation?

Chapter 15 1. 2. 3. 4. 5.

What pollution problems arise from the predominent form of energy conversion? What uncertainties are there in predicting the future pollution of the atmosphere? What is the power output of an electrochemical energy converter? What are fuel cells? Give a brief account of some important fuel cells?

283

Chapter 16 1. 2. 3. 4. 5.

Describe energy density. Electricity storage density. Give an account of some important storage batteries. What are new electricity storers? Describe lead-acid storage battery.

Chapter 17 1. 2. 3. 4. 5.

Distinguish between faradic and non-faradic processes. What is an ideal polarised electrode? Describe briefly the electrical double layer. What are the factors which affect the rates of electrode reactions and current? Give a brief account of the following given one example of each. (i) Formal potential (ii) Electrochemical potentials (iii) Absolute potential (iv) Cell potential (v) Liquid junction potential. 6. Give the current over potential equation. 7. What are the implications of Butler-Volmer equation?

General Question 1. Define Faraday’s laws of electrolysis. 2. Define EMF of a cell. 3. Describe Fick’s laws of diffusion and their use in the study of polarography.

Describe: 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Nern’st equation. Activity and activity coefficient. Ionic strength and ionic equlibrium. Boltzman’s constant. Avogadro’s number. Elcovic equation. Solubility and solubility product. Buffer solutions. Give two examples. Polarity of an electrode. Half wave potential. D.M.E. its advantages and disadvantages. Electrode potential and standard electrode potential. Indicator electrode and reference electrode. Liquid junction. Reversible and irreversible electrode reactions.

284

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

Introduction to Polarography and Allied Techniques

Double layer and its part played during electrolysis. Over voltage. Free energy. Concentration polarization. Hydrogen over-voltage. Current efficiency. How it is determined? Advantages and disadvantages of D.M.E. Dielectric constant. Why there are no standard potentials more negative than about –3 volts and more positive than about +2 volt, in aqueous solution? What is pH? How can one determines pH of solution? How does a three electrode system differs from the two electrode system? What are these named as? Give advantages of choosing the three electrode system. What is the significance for the use of normal hydrogen electrode? Differenciate between D.C. and A.C. polarography. Why in polarographic experiments, it is desirable to remove dissolved oxygen from the electrolyte by bubbling an inert gas through it? Why is it necessary to add an inert electrolyte to the experimental solution of polarography before carrying out the actual experiment? When Ed. vs log iid-i , is plotted, the linear plot for reaction that behaves

reversibly under diffusion controlled conditions. What would be the value of the slope of this linear plot and what would be the expression and its value at the intercept? Explain giving an example. 35. Describe the various types of currents that have some significance in polarography and allied techniques.