Multimedia Environmental Models The Fugacity Approach

McKay, Donald. "Front matter" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC,2001

Multimedia Environmental Models The Fugacity Approach Second Edition

Multimedia Environmental Models The Fugacity Approach Second Edition

Donald Mackay

LEWIS PUBLISHERS Boca Raton London New York Washington, D.C.

Preface This book is about the behavior of organic chemicals in our multimedia environment or biosphere of air, water, soil, and sediments, and the diversity of biota that reside in these media. It is a response to the concern that we have unwisely contaminated our environment with a large number of chemicals in the mistaken belief that the environment’s enormous capacity to dilute and degrade will reduce concentrations to negligible levels. We now know that the environment has only a finite capacity to dilute and degrade. Certain chemicals have persisted and accumulated to levels that have caused adverse effects on wildlife and even humans. Some chemicals have the potential to migrate from medium to medium, reaching unexpected destinations in unexpectedly high concentrations. We need to understand these processes, not only qualitatively in the form of assertions that DDT evaporates and bioaccumulates, but quantitatively as statements that DDT in a particular region evaporates at a rate of 100 kg per year and bioaccumulates from water at a concentration of 1 ng/L to fish at levels of 1 mg/g. We have learned that chemical behavior in the complex assembly of environmental media is not a random process like leaves blowing in the wind. The chemicals behave in accordance with the laws of nature, which dictate chemical partitioning and rates of transport and transformation. Most fundamentally, the chemicals are subject to the law of conservation of mass, i.e., a mass balance exists for the chemical that is a powerful constraint on quantities, concentrations, and fluxes. By coupling the mass balance principle with expressions based on our understanding of the laws of nature, we can formulate a quantitative accounting of chemical inputs and outputs. This book is concerned with developing and applying these expressions in the form of mathematical statements or “models” of chemical fate. These accounts or models are invaluable summaries of chemical behavior. They can form the basis of remedial and proactive strategies. Such models can confirm (or deny) that we really understand chemical fate in the environment. Since many environmental calculations are complex and repetitive, they are particularly suitable for implementation on computers. Accordingly, for many of the calculations described in this book, computer programs are described and made available on the Internet with which a variety of chemicals can be readily assessed in a multitude of environmental situations. The models are formulated using the concept of fugacity, which was introduced by G.N. Lewis in 1901 as a criterion of equilibrium and has proved to be a very convenient and elegant method of calculating multimedia equilibrium partitioning. It has been widely and successfully used in chemical processing calculations. In this book, we exploit it as a convenient and elegant method of explaining and deducing the environmental fate of chemicals. Since publication of the first edition of this book ten years ago, there has been increased acceptance of the benefits of using fugacity to formulate models and interpret environmental fate. Multimedia fugacity models are now routinely used for evaluating chemicals before and after production. Much of the experience gained in these ten years is incorporated in this second edition. Mathematical simulations of chemical fate are now more accurate, compre-

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hensive, and reliable, and they have gained greater credibility as decision-support tools. No doubt this trend will continue, especially as young environmental scientists and engineers take over the reins of environmental science and continue to develop new fugacity models. This book has been written as a result of the author teaching graduate-level courses at the University of Toronto and Trent University. It is hoped that it will be suitable for other graduate courses and for practitioners of the environmental science of chemical fate in government, industry, and the private consulting sector. The simpler concepts are entirely appropriate for undergraduate courses, especially as a means of promoting sensitivity to the concept that chemicals, which provide modern society with so many benefits, must also be more carefully managed from their cradle, in the chemical synthesis plant, to their grave of ultimate destruction. At the end of most chapters is a “Concluding Example” in which a student may be asked to apply the principles discussed in that chapter to one or more chemicals of their choice. Necessary data are given in Table 3.5 in Chapter 3. I have found this useful as a method of assigning different problems to a large number of students, while allowing them to explore the properties and fate of substances of particular interest to them. We no longer regard the environment as a convenient, low-cost dumping ground for unwanted chemicals. When we discharge chemicals into the environment, it must be with a full appreciation of their ultimate fate and possible effects. We must ensure that mistakes of the past with PCBs, mercury, and DDT are not repeated. This is best guaranteed by building up a quantitative understanding of chemical fate in our total multimedia environment, how chemicals will be transported and transformed, and where, and to what extent they may accumulate. It is hoped that this book is one step toward this goal and will be of interest and use to all those who value the environment and seek its more enlightened stewardship. Donald Mackay

©2001 CRC Press LLC

Acknowledgments It is a pleasure to acknowledge the contribution of many colleagues. Much of the credit for the approaches devised in this book is due to the pioneering work by George Baughman, who saw most clearly the evolution of multimedia environmental modeling as a coherent and structured branch of environmental science amid the often frightening complexity of the environment and the formidable number of chemicals with which it is contaminated. Brock Neely, Russ Christman, and Don Crosby were instrumental in encouraging me to apply the fugacity concept to environmental calculations. I am indebted to my former colleagues at the University of Toronto, especially Wan Ying Shiu and Sally Paterson, whose collaboration has been crucial in developing the fugacity approach. I am grateful to my more recent colleagues at Trent University, and our industrial and government partners who have made the Canadian Environmental Modelling Centre a successful focus for the development, validation, and dissemination of mass balance models. This second edition was written in part when on research leave at the Department of Environmental Toxicology at U.C. Davis, where Marion Miller, Don Crosby, and their colleagues were characteristically generous and supportive. At Trent, I was greatly assisted by David Woodfine, Rajesh Seth, Merike Perem, Lynne Milford, Angela McLeod, Adrienne Holstead, Todd Gouin, Alison Fraser, Ian Cousins, Tom Cahill, Jenn Brimecombe, and Andreas Beyer. I am particularly grateful to Steve Sharpe for the figures, to Matt MacLeod and Christopher Warren for their critical review and comments, and to Eva Webster for her outstanding scientific and editorial contributions. Without the support and diligent typing of my wife, Ness, this book would not have been possible. Thank you. I dedicate this book to Ness, Neil, Ian, Julia, and Gwen, and especially to Beth, who was born as this edition neared completion. I hope it will help to ensure that her life is spent in a cleaner, more healthful environment.

©2001 CRC Press LLC

Contents Chapter 1 Introduction Chapter 2 Some Basic Concepts 2.1 Introduction 2.2 Units 2.3 The Environment as Compartments 2.4 Mass Balances 2.5 Eulerian and Lagrangian Coordinate Systems 2.6 Steady State and Equilibrium 2.7 Diffusive and Nondiffusive Environmental Transport Processes 2.8 Residence Times and Persistence 2.9 Real and Evaluative Environments 2.10 Summary Chapter 3 Environmental Chemicals and Their Properties 3.1 Introduction and Data Sources 3.2 Identifying Priority Chemicals 3.3 Key Chemical Properties and Classes 3.4 Concluding Example Chapter 4 The Nature of Environmental Media 4.1 Introduction 4.2 The Atmosphere 4.3 The Hydrosphere or Water 4.4 Bottom Sediments 4.5 Soils 4.6 Summary 4.7 Concluding Example Chapter 5 Phase Equilibrium 5.1 Introduction 5.2 Properties of Pure Substances 5.3 Properties of Solutes in Solution 5.4 Partition Coefficients 5.5 Environmental Partition Coefficients and Z Values 5.6 Multimedia Partitioning Calculations 5.7 Level I Calculations 5.8 Concluding Examples Chapter 6 Advection and Reactions 6.1 Introduction

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6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

Advection Degrading Reactions Combined Advection and Reaction Unsteady-State Calculations The Nature of Environmental Reactions Level II Computer Calculations Summary Concluding Example

Chapter 7 Intermedia Transport 7.1 Introduction 7.2 Diffusive and Nondiffusive Processes 7.3 Molecular Diffusion within a Phase 7.4 Turbulent or Eddy Diffusion within a Phase 7.5 Unsteady-State Diffusion 7.6 Diffusion in Porous Media 7.7 Diffusion between Phases: The Two-Resistance Concept 7.8 Measuring Transport D Values 7.9 Combining Series and Parallel D Values 7.10 Level III Calculations 7.11 Level IV Calculations 7.12 Concluding Examples Chapter 8 Applications of Fugacity Models 8.1 Introduction, Scope, and Strategies 8.2 Level I, II, and III Models 8.3 An Air-Water Exchange Model 8.4 A Surface Soil Model 8.5 A Sediment-Water Exchange Model 8.6 QWASI Model of Chemical Fate in a Lake 8.7 QWASI Model of Chemical Fate in Rivers 8.8 QWASI Multi-segment Models 8.9 A Fish Bioaccumulation Model 8.10 Sewage Treatment Plants 8.11 Indoor Air Models 8.12 Uptake by Plants 8.13 Pharmacokinetic Models 8.14 Human Exposure to Chemicals 8.15 The PBT–LRT Attributes 8.16 Global Models 8.17 Closure Appendix Fugacity Forms References and Bibliography

©2001 CRC Press LLC

McKay, Donald. "Introduction" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC,2001

CHAPTER 1 Introduction

Since the Second World War, and especially since the publication of Rachel Carson’s Silent Spring in 1962, there has been growing concern about contamination of the environment by “man-made” chemicals. These chemicals may be present in industrial and municipal effluents, in consumer or commercial products, in mine tailings, in petroleum products, and in gaseous emissions. Some chemicals such as pesticides may be specifically designed to kill biota present in natural or agricultural ecosystems. They may be organic, inorganic, metallic, or radioactive in nature. Many are present naturally, but usually at much lower concentrations than have been established by human activity. Most of these chemicals cause toxic effects in organisms, including humans, if applied in sufficiently large doses or exposures. They may therefore be designated as “toxic substances.” There is a common public perception and concern that when these substances are present in air, water, or food, there is a risk of adverse effects to human health. Assessment of this risk is difficult (a) because the exposure is usually (fortunately) well below levels at which lethal toxic effects and even sub-lethal effects can be measured with statistical significance against the “noise” of natural population variation, and (b) because of the simultaneous multiple toxic influences of other substances, some taken voluntarily and others involuntarily. There is a growing belief that it is prudent to ensure that the functioning of natural ecosystems is unimpaired by these chemicals, not only because ecosystems have inherent value, but because they can act as sensing sites or early indicators of possible impact on human well-being. Accordingly, there has developed a branch of environmental science concerned with describing, first qualitatively and then quantitatively, the behavior of chemicals in the environment. This science is founded on earlier scientific studies of the condition of the natural environment—meteorology, oceanography, limnology, hydrology, and geomorphology and their physical, energetic, biological, and chemical sub-sciences. This newer branch of environmental science has been variously termed environmental chemistry, environmental toxicology, or chemodynamics. ©2001 CRC Press LLC

It is now evident that our task is to design a society in which the benefits of chemicals are enjoyed while the risk of adverse effects from them is virtually eliminated. To do this, we must exert effective and cost-effective controls over the use of such chemicals, and we must have available methods of calculating their environmental behavior in terms of concentration, persistence, reactivity, and partitioning tendencies between air, water, soils, sediments, and biota. Such calculations are useful when assessing or implementing remedial measures to treat alreadycontaminated environments. They become essential as the only available method for predicting the likely behavior of chemicals that (a) may be newly introduced into commerce or that (b) may be subject to production increases or introduction into new environments. In response to this societal need, this book develops, describes, and illustrates a framework and procedures for calculating the behavior of chemicals in the environment. It employs both conventional procedures that are based on manipulations of concentrations and procedures that use the concepts of activity and fugacity to characterize the equilibrium that exists between environmental phases such as air, water, and soil. Most of the emphasis is placed on organic chemicals, which are fortunately more susceptible to generalization than metals and other inorganic chemicals when assessing environmental behavior. The concept of fugacity, which was introduced by G.N. Lewis in 1901 as a more convenient thermodynamic equilibrium criterion than chemical potential, has been widely used in chemical process calculations. Its convenience in environmental chemical equilibrium or partitioning calculations has become apparent only in the last two decades. It transpires that fugacity is also a convenient quantity for describing mathematically the rates at which chemicals diffuse, or are transported, between phases; for example, volatilization of pesticides from soil to air. The transfer rate can be expressed as being driven by, or proportional to, the fugacity difference that exists between the source and destination phases. It is also relatively easy to transform chemical reaction, advective flow, and nondiffusive transport rate equations into fugacity expressions and build up sets of fugacity equations describing the quite complex behavior of chemicals in multiphase, nonequilibrium environments. These equations adopt a relatively simple form, which facilitates their formulation, solution, and interpretation to determine the dominant environmental phenomena. We develop these mathematical procedures from a foundation of thermodynamics, transport phenomena, and reaction kinetics. Examples are presented of chemical fate assessments in both real and evaluative multimedia environments at various levels of complexity and in more localized situations such as at the surface of a lake. These calculations of environmental fate can be tedious and repetitive, thus there is an incentive to use the computer as a calculating aid. Accordingly, computer programs are made available for many of the calculations described later in the text. It is important that the computer be viewed and used as merely a rather fast and smart adding machine and not as a substitute for understanding. The reader is encouraged to write his or her own programs and modify those provided. The author was “brought up” to write computer programs in languages such as FORTRAN, BASIC, and C. The first edition of this book was regarded as very advanced by including a diskette of programs in BASIC. Such programs have the ©2001 CRC Press LLC

immense benefit that the sequence and details of calculations are totally transparent. Executable versions can be run on any computer. Unfortunately, it is not always easy to change input parameters or equations, and the output is usually printed tables. The modern trend is to use spreadsheets, such as Microsoft EXCEL®, which have improved input and output features, including the ability to draw graphs and charts. Spreadsheets have the disadvantages that calculations are less transparent, there may be problems when changing versions of the spreadsheet program, and not everyone has the same spreadsheet. Sufficient information is given on each mass balance model that readers can write their own programs using the system of their choice. Microsoft Windows® software for performing model calculations is available from the Internet site www.trentu.ca/envmodel. Older DOS-based models are also available. They are updated regularly and are subject to revision. In all cases, the equations correspond closely to those in this book (unless otherwise stated), and they are totally transparent. Some are used in a regulatory context, thus the user is prevented from changing the coding, although all code can be viewed. Preparing a second edition of this book has enabled me to update, expand, and reorganize much of the material presented in the first (1991) edition. I have benefited greatly from the efforts of those who have sought to understand environmental phenomena and who have applied the fugacity approach when deducing the fate of chemicals in the environment. There is no doubt that, as we enter the new millennium, environmental science is becoming more quantitative. It is my hope that this book will contribute to that trend.

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McKay, Donald. "Some Basic Concepts" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC, 2001

CHAPTER

2

Some Basic Concepts 2.1

INTRODUCTION

Much of the scientific fascination with the environment lies in its incredible complexity. It consists of a large number of phases such as air, soil, and water, which vary in properties and composition from place to place (spatially) and with time (temporally). It is very difficult to assemble a complete, detailed description of the condition (temperature, pressure, and composition) of even a small environmental system or microcosm consisting, for example, of a pond with sediment below and air above. It is thus necessary to make numerous simplifying assumptions or statements about the condition of the environment. For example, we may assume that a phase is homogeneous, or it may be in equilibrium with another phase, or it may be unchanging with time. The art of successful environmental modeling lies in the selection of the best, or “least-worst,” set of assumptions that yields a model that is not so complex as to be excessively difficult to understand yet is sufficiently detailed to be useful and faithful to reality. The excessively simple model may be misleading. The excessively detailed model is unlikely to be useful, trusted, or even understandable. The aim is to suppress the less necessary detail in favor of the important processes that control chemical fate. In this chapter, several concepts are introduced that are used when we seek to compile quantitative descriptions of chemical behavior in the environment. But first, it is essential to define the system of units and dimensions that forms the foundation of all calculations.

2.2

UNITS

The introduction of the “SI” or “Système International d’Unités” or International System of Units in 1960 has greatly simplified scientific calculations and communication. With few exceptions, we adopt the SI system. The system is particularly convenient, because it is “coherent” in that the basic units combine one-to-one to ©2001 CRC Press LLC

give the derived units directly with no conversion factors. For example, energy (joules) is variously the product of force (newtons) and distance (metres), or pressure (pascals) and volume (cubic metres), or power (watts) and time (seconds). Thus, the foot-pound, the litre-atmosphere, and the kilowatt-hour become obsolete in favor of the single joule. Some key aspects of the SI system are discussed below. Conversion tables from obsolete or obsolescent unit systems are available in scientific handbooks. Length (metre, m) This base unit is defined as the specified number of wavelengths of a krypton light emission. Area Square metre (m2). Occasionally, the hectare (ha) (an area 100 ¥ 100 m or 104 m2) or the square kilometre (km2) is used. For example, pesticide dosages to soils are often given in kg/ha. Volume (cubic metre, m3) The litre (L) (0.001 m3) is also used because of its convenience in analysis, but it should be avoided in environmental calculations. In the United States, the spellings “meter” and “liter” are often used. Mass (kilogram, kg) Kilogram (kg). The base unit is the kilogram (kg), but it is often more convenient to use the gram (g), especially for concentrations. For large masses, the megagram (Mg) or the equivalent metric tonne (t) may be used. Amount (mole abbreviated to mol) This unit, which is of fundamental importance in environmental chemistry, is really a number of constituent entities or particles such as atoms, ions, or molecules. It is the actual number of particles divided by Avogadro’s number (6.0 ¥ 1023), which is defined as the number of atoms in 12 g of the carbon-12 isotope. When reactions occur, the amounts of substances reacting and forming are best expressed in moles rather than mass, since atoms or molecules combine in simple stoichiometric ratios. The need to involve atomic or molecular masses is thus avoided. Molar Mass or Molecular Mass (or Weight) (g/mol) This is the mass of 1 mole of matter and is sometimes (wrongly) referred to as molecular weight or molecular mass. Strictly, the correct unit is kg/mol, but it is often more convenient to use g/mol, which is obtained by adding the atomic masses (weights). Benzene (C6H6) is thus approximately 78 g/mol or 0.078 kg/mol. ©2001 CRC Press LLC

Time (second or hour, s or h) The standard unit of a second (s) is inconveniently short when considering environmental processes such as flows in large lakes when residence times may be many years. The use of hours, days, and years is thus acceptable. We generally use hours as a compromise. Concentration The preferred unit is the mole per cubic metre (mol/m3) or the gram per cubic metre (g/m3). Most analytical data are reported in amount or mass per litre (L), because a litre is a convenient volume for the analytical chemist to handle and measure. Complications arise if the litre is used in environmental calculations, because it is not coherent with area or length. The common mg/L, which is often ambiguously termed the “part per million,” is equivalent to g/m3. In some circumstances, the use of mass fraction, volume fraction, or mole fraction as concentrations is desirable. It is acceptable, and common, to report concentrations in units such as mol/L or mg/L but, prior to any calculation, they should be converted to a coherent unit of amount of substance per cubic metre. Concentrations such as parts per thousand (ppt), parts per million (ppm), parts per billion (ppb), and parts per trillion (also ppt) should not be used. There can be confusion between parts per thousand and per trillion. The billion is 109 in North America and 1012 in Europe. The air ppm is usually on a volume/volume basis, whereas the water ppm is usually on a mass/volume basis. The mixing ratio used for air is the ratio of numbers of molecules or volumes and is often given in ppm. Concentrations must be presented with no possible ambiguity. Density (kg/m3) This has identical units to mass concentrations, but the use of kg/m3 is preferred, water having a density of 1000 kg/m3 and air a density of approximately 1.2 kg/m3. Force (newton, N) The newton is the force that causes a mass of 1 kg to accelerate at 1 m/s2. It is 10 dynes and is approximately the gravitational force operating on a mass of 102 g at the Earth’s surface. 5

Pressure (pascal, Pa) The pascal or newton per square metre (N/m2) is inconveniently small, since it corresponds to only 102 grams force over one square metre, but it is the standard unit, and it is used here. The atmosphere (atm) is 101325 Pa or 101.325 kPa. The torr or mm of mercury (mmHg) is 133 Pa and, although still widely used, should be regarded as obsolescent. ©2001 CRC Press LLC

Energy (joule, J) The joule, which is one N-m or Pa-m3, is also a small quantity. It replaces the obsolete units of calorie (which is 4.184 J) and Btu (1055 J). Temperature (K) The kelvin is preferred, although environmental temperatures may be expressed in degrees Celsius, °C, and not centigrade, where 0°C is 273.15 K. There is no degree symbol prior to K. Frequency (hertz, Hz) The hertz is one event per second (s–1). It is used in descriptions of acoustic and electromagnetic waves, stirring, and in nuclear decay processes where the quantity of a radioactive material may be described in becquerels (Bq), where 1 Bq corresponds to the amount that has a disintegration rate of 1 Hz. The curie (Ci), which corresponds to 3.7 ¥ 1010 disintegrations per second (and thus 3.7 ¥ 1010 Bq), was formerly used. Gas Constant (R) This constant, which derives from the gas law, is 8.314 J/mol K or Pa-m3/mol K. An advantage of the SI system is that R values in diverse units such as cal/mol K and cm3·atm/mol K become obsolete and a single universal value now applies. 2.2.1

Prefices

The following prefices are used: Factor

Prefix

Factor

Prefix

101

deka da

10–1

deci d

hecto h

–2

centi c

10

2

10

103

kilo k

10–3

milli m

106

mega M

10–6

micro m

109

giga G

10–9

nano n

12

1015 1018

10

tera T

–12

10

pico p

peta P

10–15

femto f

exa E

10–18

atto a

Note that these prefices precede the unit. It is inadvisable to include more than one prefix in a unit, e.g., ng/mg, although mg/kg may be acceptable, because the base unit of mass is the kg. The equivalent µg/g is clearer. The use of expressions such as an aerial pesticide spray rate of 900 g/km2 can be ambiguous, since a kilo(metre2) is not equal to a square kilometre, i.e., a (km)2. The former style is not permissible. ©2001 CRC Press LLC

Expressing the rate as 9 g/ha or 0.9 mg/m2 removes all ambiguity. The prefices deka, hecto, deci, and centi are restricted to lengths, areas, and volumes. A common (and disastrous) mistake is to confuse milli, micro, and nano. We use the convention J/mol-K meaning J mol–1 K–1. Strictly, J/(mol-K) is correct but, in the interests of brevity, the parentheses are omitted. 2.2.2

Dimensional Strategy and Consistency

When undertaking calculations of environmental fate, it is highly desirable to adopt the practice of first converting all the supplied input data, in its diversity of units, into the SI units described above and eliminate the prefices, e.g., 10 kPa should become 104 Pa. Calculations should be done using only these SI units. If necessary, the final results can then be converted to other units for the convenience of the user. When assembling quantities in expressions or equations, it is critically important that the dimensions be correct and consistent. It is always advisable to write down the units on each side of the equation, cancel where appropriate, and check that terms that add or subtract have identical units. For example, a lake may have an inflow or reaction rate of a chemical expressed as follows: A flow rate: (water flow rate G m3/h) ¥ (concentration C g/m3) = GC g/h A reaction rate: (volume V m3) ¥ (rate constant k h–1) ¥ (concentration C mol/m3) = VkC mol/h Obviously, it is erroneous to express the above concentration in mol/L or the volume in cm3. When checking units it may be necessary to allow for changes in the prefices (e.g. kg to g), and for unit conversions (e.g., h to s). 2.2.3

Logarithms

The preferred logarithmic quantity is the natural logarithm to the base e or 2.7183, designated as ln. Base 10 logarithms are still used for certain quantities such as the octanol-water partition coefficient and for plotting on log-log or log-linear graph paper. The natural antilog or exponential of x is written either ex or exp(x). The base 10 log of a quantity is the natural log divided by 2.303 or ln10.

2.3

THE ENVIRONMENT AS COMPARTMENTS

It is useful to view the environment as consisting of a number of connected phases or compartments. Examples are the atmosphere, terrestrial soil, a lake, the bottom sediment under the lake, suspended sediment in the lake, and biota in soil or water. The phase may be continuous (e.g., water) or consist of a number of particles that are not in contact, but all of which reside in one phase [e.g., atmospheric ©2001 CRC Press LLC

particles (aerosols), or biota in water]. In some cases, the phases may be similar chemically but different physically, e.g., the troposphere or lower atmosphere, and the stratosphere or upper atmosphere. It may be convenient to lump all biota together as one phase or consider them as two or more classes each with a separate phase. Some compartments are in contact, thus a chemical may migrate between them (e.g., air and water), while others are not in contact, thus direct transfer is impossible (e.g., air and bottom sediment). Some phases are accessible in a short time to migrating chemicals (e.g., surface waters), but others are only accessible slowly (e.g., deep lake or ocean waters), or effectively not at all (e.g., deep soil or rock). Some confusion is possible when expressing concentrations for mixed phases such as water containing suspended solids (SS). An analysis may give a total or bulk concentration expressed as amount of chemical per m3 of mixed water and particles. Alternatively, the water may be filtered to give the concentration or amount of chemical that is dissolved in water per m3 of water. The difference between these is the amount of chemical in the SS phase per m3 of water. This is different from the concentration in the SS phase expressed as amount of chemical per m3 of particle. Concentrations in soils, sediments, and biota can be expressed on a dry or wet weight basis. Occasionally, concentrations in biota are expressed on a lipid or fat content basis. Concentrations must be expressed unambiguously. 2.3.1 Homogeneity and Heterogeneity A key modeling concept is that of phase homogeneity and heterogeneity. Well mixed phases such as shallow pond waters tend to be homogeneous, and gradients in chemical concentration or temperature are negligible. Poorly mixed phases such as soils and bottom sediments are usually heterogeneous, and concentrations vary with depth. Situations in which chemical concentrations are heterogeneous are difficult to describe mathematically, thus there is a compelling incentive to assume homogeneity wherever possible. A sediment in which a chemical is present at a concentration of 1 g/m3 at the surface, dropping linearly to zero at a depth of 10 cm, can be described approximately as a well mixed phase with a concentration of 1 g/m3 and 5 cm deep, or 0.5 g/m3 and 10 cm deep. In all three cases, the amount of chemical present is the same, namely 0.05 g per square metre of sediment horizontal area. Even if a phase is not homogeneous, it may be nearly homogeneous in one or two of the three dimensions. For example, lakes may be well mixed horizontally but not vertically, thus it is possible to describe concentrations as varying only in one dimension (the vertical). A wide, shallow river may be well mixed vertically but not horizontally in the cross-flow or down-flow directions. 2.3.2 Steady- and Unsteady-State Conditions If conditions change relatively slowly with time, there is an incentive to assume “steady-state” behavior, i.e., that properties are independent of time. A severe mathematical penalty is incurred when time dependence has to be characterized, and “unsteady-state,” dynamic, or time-varying conditions apply. We discuss this issue in more detail later. ©2001 CRC Press LLC

2.3.3

Summary

In summary, our simplest view of the environment is that of a small number of phases, each of which is homogeneous or well mixed and unchanging with time. When this is inadequate, the number of phases may be increased; heterogeneity may be permitted in one, two, or three dimensions; and variation with time may be included. The modeler’s philosophy should be to concede each increase in complexity reluctantly, and only when necessary. Each concession results in more mathematical complexity and the need for more data in the form of kinetic or equilibrium parameters. The model becomes more difficult to understand and thus less likely to be used, especially by others. This is not a new idea. William of Occam expressed the same sentiment about 650 years ago, when he formulated his principle of parsimony or “Occam’s Razor,” stating Essentia non sunt multiplicanda praeter necessitatem which can be translated as, “What can be done with fewer (assumptions) is done in vain with more,” or more colloquially, “Don’t make models more complicated than is necessary.”

2.4

MASS BALANCES

When describing a volume of the environment, it is obviously essential to define its limits in space. This may simply be the boundaries of water in a pond or the air over a city to a height of 1000 m. The volume is presumably defined exactly, as are the areas in contact with adjoining phases. Having established this control “envelope” or “volume” or “parcel,” we can write equations describing the processes by which a mass of chemical enters and leaves this envelope. The fundamental and now axiomatic law of conservation of mass, which was first stated clearly by Antoine Lavoisier, provides the basis for all mass balance equations. Rarely do we encounter situations in which nuclear processes violate this law. Mass balance equations are so important as foundations of all environmental calculations that it is essential to define them unambiguously. Three types can be formulated and are illustrated below. We do not treat energy balances, but they are set up similarly. 2.4.1

Closed System, Steady-State Equations

This is the simplest class of equation. It describes how a given mass of chemical will partition between various phases of fixed volume. The basic equation simply expresses the obvious statement that the total amount of chemical present equals the sum of the amounts in each phase, each of these amounts usually being a product of a concentration and a volume. The system is closed or “sealed” in that no entry or exit of chemical is permitted. In environmental calculations, the concentrations are usually so low that the presence of the chemical does not affect the phase volumes. ©2001 CRC Press LLC

Worked Example 2.1 A three-phase system consists of air (100 m3), water (60 m3), and sediment (3 m ). To this is added 2 mol of a hydrocarbon such as benzene. The phase volumes are not affected by this addition, because the volume of hydrocarbon is small. Subscripting air, water, and sediment symbols with A, W, and S, respectively, and designating volume as V (m3) and concentration as C (mol/m3), we can write the mass balance equation. 3

total amount = sum of amounts in each phase mol 2 = VACA + VWCW + VSCS = 100 CA + 60 CW + 3 CS mol To proceed further, we must have information about the relationships between CA, CW , and CS. This could take the form of phase equilibrium equations such as CA/CW = 0.4 and CS/CW = 100 These ratios are usually referred to as partition coefficients or distribution coefficients and are designated KAW and KSW , respectively. We discuss them in more detail later. We can now eliminate CA and CS by substitution to give 2 = 100 (0.4 CW) + 60 CW + 3(100CW) = 400 CW mol Thus, CW = 2/400 = 0.005 mol/m3 It follows that CA = 0.4 CW = 0.002 mol/m3 CS = 100 CW = 0.5 mol/m3 The amounts in each phase (mi) mol are the VC products as follows: mW = VWCW = 0.30 mol

(15%)

mA = VACA = 0.20 mol

(10%)

mS = VSCS = 1.50 mol

(75%)

Total

2.00 mol

This simple algebraic procedure has established the concentrations and amounts in each phase using a closed system, steady-state, mass balance equation and equilibrium relationships. The essential concept is that the total amount of chemical present ©2001 CRC Press LLC

must equal the sum of the individual amounts in each compartment. We later refer to this as a Level I calculation. It is useful because it is not always obvious where concentrations are high, as distinct from amounts. Example 2.2 In this example, 0.04 mol of a pesticide of molar mass 200 g/mol is applied to a closed system consisting of 20 m3 of water, 90 m3 of air, 1 m3 of sediment, and 2 L of biota (fish). If the concentration ratios are air/water 0.1, sediment/water 50, and biota/water 500, what are the concentrations and amounts in each phase in both gram and mole units? Answer The fish contains 0.1 g or 0.0005 mol at a concentration of 50 g/m3 or 0.25 mol/m3. Example 2.3 A circular lake of diameter 2 km and depth 10 m contains suspended solids (SS) with a volume fraction of 10–5, i.e., 1 m3 of SS per 105 m3 water, and biota (such as fish) at a concentration of 1 mg/L. Assuming a density of biota of 1.0 g/cm3, a SS/water partition coefficient of 104, and a biota/water partition coefficient of 105. Calculate the disposition and concentrations of 1.5 kg of a PCB in this system. Answer In this case, 8.3% is present in each of SS and biota and 83% in water with a concentration in water of 39.8 µg/m3. 2.4.2

Open System, Steady-State Equations

In this class of mass balance equation, we introduce the possibility of the chemical flowing into and out of the system and possibly reacting or being formed. The conditions within the system do not change with time, i.e., its condition looks the same now as in the past and in the future. The basic mass balance assertion is that the total rate of input equals the total rate of output, these rates being expressed in moles or grams per unit time. Whereas the basic unit in the closed system balance was mol or g, it is now mol/h or g/h. Worked Example 2.4 A 104 m3 thoroughly mixed pond has a water inflow and outflow of 5 m3/h. The inflow water contains 0.01 mol/m3 of chemical. Chemical is also discharged directly into the pond at a rate of 0.1 mol/h. There is no reaction, volatilization, or other losses of the chemical; it all leaves in the outflow water. ©2001 CRC Press LLC

(i) What is the concentration (C) in the outflow water? We designate this as an unknown C mol/m3. total input rate = total output rate 5 m3/h ¥ 0.01 mol/m3 + 0.1 mol/h = 0.15 mol/h = 5 m3/h ¥ C mol/m3 = 5 C mol/h Thus, C = 0.03 mol/m3 The total inflow and outflow rates of chemical are 0.15 mol/h. (ii) If the chemical also reacts in a first-order manner such that the rate is VCk mol/h where V is the water volume, C is the chemical concentration in the well mixed water of the pond, and k is a first-order rate constant of 10–3 h–1, what will be the new concentration? The output by reaction is VCk or 104 ¥ 10–3 C or 10 C mol/h, thus we rewrite the equation as: 0.05 + 0.1 = 5 C + 10 C = 15 C mol/h Thus, C = 0.01 mol/m3 The total input of 0.15 mol/h is thus equal to the total output of 0.15 mol/h, consisting of 0.05 mol/h outflow and 0.10 mol/h reaction. An inherent assumption is that the prevailing concentration in the pond is constant and equal to the outflow concentration. This is the “well mixed” or “continuously stirred tank” assumption. It may not always apply, but it greatly simplifies calculations when it does. The key step is to equate the sum of the input rates to the sum of the output rates, ensuring that the units are equivalent in all the terms. This often requires some unit-to-unit conversions. Worked Example 2.5 A lake of area (A) 106 m2 and depth 10 m (volume V 107 m3) receives an input of 400 mol/day of chemical in an effluent discharge. Chemical is also present in the inflow water of 104 m3/day at a concentration of 0.01 mol/m3. The chemical reacts with a first-order rate constant k of 10–3 h–1, and it volatilizes at a rate of (10–5 C) mol/m2s, where C is the water concentration and m2 refers to the air-water area. The outflow is 8000 m3/day, there being some loss of water by evaporation. Assuming that the lake water is well mixed, calculate the concentration and all the inputs and outputs in mol/day. Use a time unit of days in this case. ©2001 CRC Press LLC

Discharge Inflow Total input Reaction rate

= = = =

400 mol/day 104 m3/day ¥ 0.01 mol/m3 = 100 mol/day 500 mol/day VCk = 107 m3 ¥ C mol/m3 ¥ 10–3 h–1 ¥ 24 h/day = 24 ¥ 104C mol/day Volatilization rate = 106 m2 ¥ 10–5 C mol/m2 s ¥ 3600 s/h ¥ 24 h/day = 86.4 ¥ 104C mol/day Outflow = 8000 m3/day ¥ C mol/m3 = 0.8 ¥ 104C mol/day

Thus, 500 C Reaction rate Volatilization rate Outflow Total rate of loss

= = = = = =

24 ¥ 104C + 86.4 ¥ 104C + 0.8 ¥ 104C = 111.2 ¥ 104C 4.5 ¥ 10–4 mol/m3 107.9 mol/day (i.e., 108 mol/day) 388.5 mol/day (i.e., 390 mol/day) 3.6 mol/day 500 mol/day = input rate

Until proficiency is gained in manipulating these multi-unit equations, it is best to write out all quantities and units and check that the units are consistent. Judgement should be exercised when selecting the number of significant figures to be carried through the calculation. It is preferable to carry more than is needed, then go back and truncate. Remember that environmental quantities are rarely known with better than 5% accuracy. Avoid conveying an erroneous impression of accuracy by using too many significant figures. Example 2.6 A building, 20 m wide ¥ 25 m long ¥ 5 m high is ventilated at a rate of 200 m3/h. The inflow air contains CO2 at a concentration of 0.6 g/m3. There is an internal source of CO2 in the building of 500 g/h. What is the mass of CO2 in the building and the exit CO2 concentration? Answer 7.75 kg and 3.1 g/m3 Example 2.7 A pesticide is applied to a 10 ha field at an average rate of 1 kg/ha every 4 weeks. The soil is regarded as being 20 cm deep and well mixed. The pesticide evaporates at a rate of 2% of the amount present per day, and it degrades microbially with a rate constant of 0.05 days–1. What is the average standing mass of pesticide present at steady state? What will be the steady-state average concentration of pesticide (g/m3), and in units of mg/g assuming a soil solids density of 2500 kg/m3? ©2001 CRC Press LLC

Answer 5.1 kg, 0.255 g/m3, 0.102 mg/g In all these examples, chemical is flowing or reacting, but observed conditions in the envelope are not changing with time, thus the steady-state condition applies. In Example 2.7, the concentration will change in a “sawtooth” manner but, over the long term, it is constant. 2.4.3

Unsteady-State Equations

Whereas the first two types of mass balances lead to simple algebraic equations, unsteady-state conditions give differential equations in time. The simplest method of setting up the equation is to write d(contents)/dt = total input rate – total output rate The input and output rates should be in units of amount/time, e.g., mol/h or g/h. The “contents” must be in consistent units, e.g., in mol or g, and dt, the time increment, in units consistent with the time unit in the input and output terms, (e.g., h). The differential equation can then be solved along with an appropriate initial or boundary condition to give an algebraic expression for concentration as a function of time. The simplest example is the first-order decay equation. Worked Example 2.8 A lake of 106 m3 with no inflow or outflow is treated with 10 mol of piscicide (a chemical that kills fish), which has a first-order reaction (degradation or decay) rate constant k of 10–2 h–1. What will the concentration be after 1 and 10 days, assuming no further input, and when will half the chemical have been degraded? The contents are VC or 106C mol. The output is only by reaction at a rate of VCk or 106 ¥ 10–2C or 104C mol/h. There is zero input, thus, d (106C)/dt = 106dC/dt = 0 – 104 C mol/h Thus, dC/dt = –10–2C mol/h This differential equation is easily solved by separating the variables C and t to give dC/C = –10–2 dt Integrating gives lnC = –10–2t + IC ©2001 CRC Press LLC

where IC is an integration constant that is usually evaluated from an initial condition, i.e., C = Co when t = 0; thus, IC is lnCo and ln(C/Co) = –10–2 t or C = Co exp (–10–2t) Now, Co is (10 mol)/106m3 or 10–5 mol/m3 Thus, C = 10–5 exp (–10–2t) mol/m3 After 1 day (24 h), C will be 0.79 ¥ 10–5 mol/m3, i.e., 79% remains After 10 days (240 h), C will be 0.091 ¥ 10–5 mol/m3, i.e., 9.1% remains Half the chemical will have degraded when C/Co is 0.5; or 10–2 t is –ln 0.5 or 0.693; or t is 69.3 h Note that the half-time t is 0.693/k. This relationship, that the half-time is 0.693 divided by the rate constant, is very important and is used extensively. It is also possible to have inflow and outflow as well as reaction, as shown in the next example. Worked Example 2.9 A well mixed lake of volume V 106 m3 containing no chemical starts to receive an inflow of 10 m3/s containing chemical at a concentration of 0.2 mol/m3. The chemical reacts with a first-order rate constant of 10–2 h–1, and it also leaves with the outflow of 10 m3/s. By “first-order,” we specify that the rate is proportional to C raised to the power one. What will be the concentration of chemical in the lake one day after the start of the input of chemical? Input rate = 10 ¥ 0.2 = 2 mol/s (we choose a time unit of seconds here) Output by reaction = (106 m3)(10–2 h–1)(1 h/3600s)C mol/m3 = 2.78 C mol/s Output by flow = 10 C mol/s Thus, ©2001 CRC Press LLC

Input – Output = d(contents)/dt 2 – 2.78C – 10C = d(106 C)/dt or dC/(2 – 12.78C) = 10–6 dt or ln(2 – 12.78C)/(–12.78) = 10–6 t + IC When t is zero, C is zero, thus, IC = –ln(2)/12.78 and ln[(2 – 12.78C)/2] = –12.78 ¥ 10–6 t or (2 – 12.78 C) = 2 exp(–12.78 ¥ 10–6 t) or C = (2/12.78)[1 – exp(–12.78 ¥ 10–6 t)] Note that when t is zero, exp(0) is unity and C is zero, as dictated by the initial condition. When t is very large, the exponential group becomes zero, and C approaches (2/12.78) or 0.157 mol/m3. At such times, the input of 2 mol/s is equal to the total of the output by flow of 10 ¥ 0.157 or 1.57 mol/s plus the output by reaction of 2.78 ¥ 0.157 or 0.44 mol/s. This is the steady-state solution, which the lake eventually approaches after a long period of time. When t is 1 day or 86400s, C will be 0.105 mol/m3 or 67% of the way to its final value. C will be halfway to its final value when 12.78 ¥ 10–6 t is 0.693 or t is 54200 s or 15 h. This time is largely controlled by the residence time of the water in the lake, which is (106 m3)/(10 m3/s) or 105 s or 27.8 h Worked Example 2.10 A well mixed lake of 105 m3 is initially contaminated with chemical at a concentration of 1 mol/m3. The chemical leaves by the outflow of 0.5 m3/s, and it reacts with a rate constant of 10–2 h–1. What will be the chemical concentration after 1 and 10 days, and when will 90% of the chemical have left the lake? ©2001 CRC Press LLC

Input = 0 Output by flow = 0.5C Output by reaction = VCk = 105 · C · 10–2h–1(1/3600) = 0.278C Thus, 0 – 0.5C – 0.278C = 105dC/dt dC/C = –0.778 ¥ 10–5dt C = Co exp(–0.778 ¥ 10–5 t) Since CO is 1.0 mol/m3, after 1 day or 864000 s, C will be 0.51 mol/m3. t C

= 10 days = 86400s; C = 0.0012 mol/m3 = 0.1 when 0.778 ¥ 10–5 t = –ln 0.1 or 2.3 or when t is 296000 s or 3.4 days

Example 2.11 If the concentration of CO2 in Example 2.6 has reached steady state of 3.1 g/m3, and then the internal source is reduced to 100 g/h, deduce the equation expressing the time course of CO2 concentration decay and the new steady-state value. Answer New steady-state 1.1 g/m3 and C = 1.1 + 2.0 exp(–0.08 t) Example 2.12 A lake of volume 106 m3 has an outflow of 500 m3/h. It is to be treated with a piscicide, the concentration of which must be kept above 1 mg/m3. It is decided to add 3 kg, thus achieving a concentration of 3 mg/m3, and to allow the concentration to decay to 1 mg/m3 before adding another 2 kg to bring the concentration back to 3 mg/m3. If the piscicide has a degradation half-life of 693 hours (29 days), what will be the interval before the second (and subsequent) applications are required? Answer 30 days Mr. MacLeod, being economically and ecologically perceptive, claims that if he is allowed to make applications every 10 days instead of 30 days, he can maintain the concentration above 1 mg/m3 but reduce the piscicide usage by 35%. Is he correct? Answer Yes ©2001 CRC Press LLC

What is the absolute minimum piscicide usage every 30 days to maintain 1 mg/m3? Answer A total of 1.08 kg added continuously over a 30 day period These unsteady-state solutions usually contain exponential terms such as exp(–kt). The term k is a characteristic rate constant with units of reciprocal time. It is thus somewhat difficult to grasp and remember. A quantity of 0.01 h–1 does not convey an impression of rapidity. It is convenient to calculate its reciprocal 1/k or 100 h, which is a characteristic time. This is the time required for the process to move exp(–1) or to within 37% of the final value, i.e., it is 63% completed. Those working with radioisotopes prefer to use half-lives rather than k, i.e., the time for half completion. This occurs when the term exp(–kt) is 0.5 or kt is ln2 or 0.693, thus the half-time t is 0.693/k. Another useful time is the 90% completion value, which is 2.303/k. Two common mistakes are made if rate constants are manipulated as times rather than frequencies. A rate constant of 1 day–1 is 0.042 h–1, not 24 h–1—a common mistake. If there are two first-order reactions, the total rate constant is the sum of the individual rate constants. This has the effect of giving a total half-time or halflife that is less than either individual half-time. It is a disastrous mistake to add halflives. Their reciprocals add. In some cases, the differential equation can become quite complex, and there may be several of them applying simultaneously. Setting up these equations requires practice and care. There is a common misconception that solving the equations is the difficult task. On the contrary, it is setting them up that is most difficult and requires the most skill. If the equation is difficult to solve, tables of integrals can be consulted, computer programs such as Mathematica or Matlabs can be used, or an obliging mathematician can be sought. For many differential equations, an analytical solution is not feasible, and numerical methods must be used to generate a solution. We discuss techniques for doing this later.

2.5

EULERIAN AND LAGRANGIAN COORDINATE SYSTEMS

It is usually best to define the mass balance envelope as being fixed in space. This can be called the Eulerian coordinate system. When there is appreciable flow through the envelope, it may be better to define the envelope as being around a certain amount of material and allow that envelope of material to change position. This “fix a parcel of material then follow it in time as it moves” approach is often applied to rivers when we wish to examine the changing condition of a volume of water as it flows downstream and undergoes various reactions. This can be called the Lagrangian coordinate system. It is also applied to “parcels” of air emitted from a stack and subject to wind drift. Both systems must give the same results, but it may be easier to write the equations in one system than the other. The following example is an illustration. It also demonstrates the need to convert units to the SI system. ©2001 CRC Press LLC

Worked Example 2.13 Consider a river into which the 1.8 million population of a city discharges a detergent at a rate of 1 pound per capita per year, i.e., the discharge is 1.8 million pounds per year. The aim is to calculate the concentrations at distances of 1 and 10 miles downstream from a knowledge of the degradation rate of the detergent and the constant downstream flow conditions, which are given below. This can be done in Eulerian or Lagrangian coordinate systems. The input data are first converted to SI units. Discharge rate River flow velocity

1.8 ¥ 106 lb per year

93300 g/h

(E)

1 ft/s

1097 m/h

(U)

River depth

3 ft

0.91 m

(h)

River width

20 yards

18.3 m

(w)

Degradation half-life

0.3 days

7.2 h

(t1/2)

The river flow rate is Uhw, i.e., 18270 m3/h. The rate constant k is 0.693/t1/2, i.e. 0.096 h–1. When the detergent mixes into the river, the concentration will be CO or E/(Uhw) or 5.1 g/m3. Lagrangian Solution A parcel of water that maintains its integrity, i.e., it does not diffuse or disperse, will decay according to the equation C = CO exp(–kt) where t is the time from discharge. At 1 mile (1609 m), the time t will be 1609/U or 1.47 h, and at 10 miles, it will be 14.7 h. Substituting shows that, after 1 and 10 miles, the concentrations will be 4.4 and 1.24 g/m3. The chemical will reach half its input concentration when t is 0.693/k or 7.2 h, which corresponds to 7900 m or 4.92 miles. This Lagrangian solution is straightforward, but it is valid only if conditions in the river remain constant and negligible upstream-downstream dispersion occurs. Eulerian Solution We now simulate the river as a series of connected reaches or segments or well mixed lakes, each being L or 200 m long. Each reach thus has a volume V of Lhw or 3330 m3. A steady-state mass balance on the first reach gives input rate = UhwCO = output rate = UhwC1 + VkC1 where CO and C1 are the input and output concentrations. C1 is also the concentration in the segment. It follows that ©2001 CRC Press LLC

C1 = CO/(1 + Vk/(Uhw)) = CO/(1 + kL/U) Note the consistency of the dimensions, kL/U being dimensionless. The group (1 + kL/U) has a value of 1.0175, thus C1 is 0.983CO. 1.7% of the chemical is lost in each segment. The same equation applies to the second reach, thus C2 is 0.983C1 or 0.9832CO. In general, for the nth reach, Cn is (0.983)nCO or CO/(1 + kL/U)n. One mile is reached when n is 8, and 10 miles corresponds to n of 80, thus C8 is 0.9838CO or 4.45, and C8 is 1.29. The half distance will occur when 0.983n is 0.5, i.e., when n is log 0.5/log 0.983 or 40, corresponding to 8000 m or 5 miles. The Eulerian answer is thus slightly different. It could be made closer to the Lagrangian result by carrying more significant figures or by decreasing L and increasing n. An advantage of the Eulerian system is that it is possible to have segments with different properties such as depth, width, velocity, volume, and temperature. There can be additional inputs. The general equation employing the group (1 + kL/U)n will not then apply, each segment having a specific value of this factor. The mathematical enthusiast will note that L/U is t/n, where t is the flow time to a distance nL m. The Lagrangian factor is thus also (1 + kt/n)n, which approaches exp(kt) when n is large. It is good practice to do the calculation in both systems (even approximately) and check that the results are reasonable. Some water quality models of rivers and estuaries can have several hundred segments, thus it is difficult to grasp the entirety of the results, and mistakes can go undetected.

2.6

STEADY STATE AND EQUILIBRIUM

In the previous section, we introduced the concept of “steady state” as implying unchanging with time, i.e., all time derivatives are zero. There is frequent confusion between this concept and that of “equilibrium,” which can also be regarded as a situation in which no change occurs with time. The difference is very important and, regrettably, the terms are often used synonymously. This is entirely wrong and is best illustrated by an example. Consider the vessel in Figure 2.1A, which contains 100 m3 of water and 100 m3 of air. It also contains a small amount of benzene, say 1000 g. If this is allowed to stand at constant conditions for a long time, the benzene present will equilibrate between the water and the air and will reach unchanging but different concentrations, possibly 8 g/m3 in the water and 2 g/m3 in the air, i.e., a factor of 4 difference in favor of the water. There is thus 800 g in the water and 200 g in the air. In this condition, the system is at equilibrium and at a steady state. If, somehow, the air and its benzene were quickly removed and replaced by clean air, leaving a total of 800 g in the water, and the volumes remained constant, the concentrations would adjust (some benzene transferring from water to air) to give a new equilibrium (and steady state) of 6.4 g/m3 in the water (total 640 g) and 1.6 g/m3 in the air (total 160 g), again with a factor of 4 difference. This factor is a partition coefficient or distribution coefficient or, as is discussed later, a form of Henry’s law constant. During the adjustment period (for example, immediately after removal of the air when the benzene concentration in air is near zero and the water is still near 8 g/m3), ©2001 CRC Press LLC

Figure 2.1

Illustration of the difference between equilibrium and steady-state conditions. Equilibrium implies that the oxygen concentrations in the air and water achieve a ratio or partition coefficient of 20. Steady state implies unchanging with time, even if flow occurs and regardless of whether equilibrium applies.

the concentrations are not at a ratio of 4, the conditions are nonequilibrium, and, since the concentrations are changing with time, they are also of unsteady-state in nature. This correspondence between equilibrium and steady state does not, however, necessarily apply when flow conditions prevail. It is possible for air and water ©2001 CRC Press LLC

containing nonequilibrium quantities of benzene to flow into and out of the tank at constant rates as shown in Figure 2.1B. But equilibrium and a steady-state condition are maintained, since the concentrations in the tank and in the outflows are at a ratio of 1:4. It is possible for near equilibrium to apply in the vessel, even when the inflow concentrations are not in equilibrium, if benzene transfer between air and water is very rapid. Figure 2.1B thus illustrates a flow, equilibrium, and steadystate conditions, whereas Figure 2.1A is a nonflow, equilibrium, and steady-state situation. In Figure 2.1C, there is a deficiency of benzene in the inflow water (or excess in the air) and, although in the time available some benzene transfers from air to water, there is insufficient time for equilibrium to be reached. Steady state applies, because all concentrations are constant with time. This is a flow, nonequilibrium, steady-state condition in which the continuous flow causes a constant displacement from equilibrium. In Figure 2.1D, the inflow water and/or air concentration or rates change with time, but there is sufficient time for the air and water to reach equilibrium in the vessel, thus equilibrium applies (the concentration ratio is always 4), but unsteadystate conditions prevail. Similar behavior could occur if the tank temperature changes with time. This represents a flow, equilibrium, and unsteady-state condition. Finally, in Figure 2.1E, the concentrations change with time, and they are not in equilibrium; thus, a flow, nonequilibrium, unsteady-state condition applies, which is obviously quite complex. The important point is that equilibrium and steady state are not synonymous; neither, either, or both can apply. Equilibrium implies that phases have concentrations (or temperatures or pressures) such that they experience no tendency for net transfer of mass. Steady state merely implies constancy with time. In the real environment, we observe a complex assembly of phases in which some are (approximately) in steady state, others in equilibrium, and still others in both steady state and equilibrium. By carefully determining which applies, we can greatly simplify the mathematics used to describe chemical fate in the environment. A couple of complications are worthy of note. Chemical reactions also tend to proceed to equilibrium but may be prevented from doing so by kinetic or activation considerations. An unlit candle seems to be in equilibrium with air, but in reality it is in a metastable equilibrium state. If lit, it proceeds toward a “burned” state. Thus, some reaction equilibria are not achieved easily, or not at all. Second, “steady state” depends on the time frame of interest. Blood circulation in a sleeping child is nearly in steady state; the flow rates are fairly constant, and no change is discernible over several hours. But, over a period of years, the child grows, and the circulation rate changes; thus, it is not a true steady state when viewed in the long term. The child is in a “pseudo” or “short-term” steady state. In many cases, it is useful to assume steady state to apply for short periods, knowing that it is not valid over long periods. Mathematically, a differential equation that truly describes the system is approximated by an algebraic equation by setting the differential or the d(contents)/dt term to zero. This can be justified by examining the relative magnitude of the input, output, and inventory change terms. ©2001 CRC Press LLC

2.7

DIFFUSIVE AND NONDIFFUSIVE ENVIRONMENTAL TRANSPORT PROCESSES

In the air-water example, it was argued that equilibrium occurs when the ratio of the benzene concentrations in water and air is 4. Thus, if the concentration in water is 4 mol/m3, equilibrium conditions exist when the concentration in air is 1 mol/m3. If the air concentration rises to 2 mol/m3, we expect benzene to transfer by diffusion from air to water until the concentration in air falls, concentration in water rises, and a new equilibrium is reached. This is easily calculated if the total amount of benzene is known. In a nonflow system, if the initial concentrations in air and water are CAO and CWO mol/m3, respectively, and the volumes are VA and VW , then the total amount M is, as shown earlier, M = CAOVA + CWOVW mol Here, CAO is 2, and CWO is 4 mol/m3, and since the volumes are both 100 m3, M is 600 mols. This will distribute such that CW is 4CA or M = 600 = CAVA + CWVW = CAVA + 4CAVW = CA(VA + 4VW) = CA 500 Thus, CA is 1.2 mol/m3, and CW is 4.8 mol/m3. Thus, the water concentration rises from 4.0 to 4.8, while that of the air drops from 2.0 to 1.2 mol/m3. Conversely, if the concentration in water is increased to 10 mol/m3, there will be transfer from water to air until a new equilibrium state is reached. A worrisome dilemma is, “How does the benzene in the water know the concentration in the air so that it can decide to start or stop diffusing?” In fact, it does not know or care. It diffuses regardless of the condition at the destination. Equilibrium merely implies that there is no net diffusion, the water-to-air and air-to-water diffusion rates being equal and opposite. Chemicals in the environment are always striving to reach equilibrium. They may not always achieve this goal, but it is useful to know the direction in which they are heading. Other transport mechanisms occur that are not driven by diffusion. For example, we could take 1 m3 of the water with its associated 1 mol of benzene and physically convey it into the air, forcing it to evaporate, thus causing the concentration of benzene in the air to increase. This nondiffusive, or “bulk,” or “piggyback” transfer occurs at a rate that depends on the rate of removal of the water phase and is not influenced by diffusion. Indeed, it may be in a direction opposite to that of diffusion. In the environment, it transpires that there are many diffusive and nondiffusive processes operating simultaneously. Examples of diffusive transfer processes include 1. 2. 3. 4.

Volatilization from soil to air Volatilization from water to air Absorption or adsorption by sediments from water Diffusive uptake from water by fish during respiration

Some nondiffusive processes are ©2001 CRC Press LLC

1. Fallout of chemical from air to water or soil in dustfall, rain, or snow 2. Deposition of chemical from water to sediments in association with suspended matter which deposits on the bed of sediment 3. The reverse process of resuspension 4. Ingestion and egestion of food containing chemical by biota

The mathematical expressions for these rates are quite different. For diffusion, the net rate of transfer or flux is written as the product of the departure from equilibrium and a kinetic quantity, and the net flux becomes zero when the phases are in equilibrium. We examine these diffusive processes in Chapter 7. For nondiffusive processes, the flux is the product of the volume of the phase transferred (e.g., quantity of sediment or rain) and the concentration. We treat nondiffusive processes in Chapter 6. We use the word flux as short form for transport rate. It has units such as mol/h or g/h. Purists insist that flux should have units of mol/h·m2, i.e., it should be area specific. We will apply it to both. It is erroneous to use the term flux rate since flux, like velocity, already contains the “per time” term.

2.8

RESIDENCE TIMES AND PERSISTENCE

In some environments, such as lakes, it is convenient to define a residence time or detention time. If a pond has a volume of 1000 m3 and experiences inflow and outflow of 2 m3/h, it is apparent that, on average, the water spends 500 h (20.8 days) (i.e., 1000 m3/2 m3/h) in the lake. This residence or detention time may not bear much relationship to the actual time that a particular parcel of water spends in the pond, since some water may bypass most of the pond and reside for only a short time, and some may be trapped for years. The quantity is very useful, however, because it gives immediate insight into the time required to flush out the contents. Obviously, a large lake with a long residence time will be very slow to recover from contamination. Comparison of the residence time with a chemical reaction time (e.g., a half-life) indicates whether a chemical is removed from a lake predominantly by flow or by reaction. If a well mixed lake has a volume V m3 and equal inflow and outflow rates G m3/h, then the flow residence time tF is V/G (h). If it is contaminated by a nonreacting (conservative) chemical at a concentration CO mol/m3 at zero time and there is no new emission, a mass balance gives, as was shown earlier, C = C0 exp(–Gt/V) = C0 exp (–t/tF) = CO exp(–kF t) The residence time is thus the reciprocal of a rate constant kF with units of h–1. The half-time for recovery occurs when t/tF or kFt is ln 2 or 0.693, i.e., when t is 0.693t or 0.693/k. If the chemical also undergoes a reaction with a rate constant kR h–1, it can be shown that C = C0 exp[–(kF + kR)t] = C0 exp(–kTt) ©2001 CRC Press LLC

Thus, the larger (faster) rate constant dominates. The characteristic times tF and tR (i.e., 1/kF and 1/kR) combine as reciprocals to give the total time tT , as do electrical resistances in parallel, i.e., 1/tF + 1/tR = 1/tT = kT + kR Thus, the smaller (shorter) t dominates. The term tR can be viewed as a reaction persistence. Characteristic times such as tR and tF are conceptually easy to grasp and are very convenient quantities to deduce when interpreting the relative importance of environmental processes. For example, if tF is 30 years and tR is 3 years, tT is 2.73 years; thus, reaction dominates the chemical’s fate. Ten out of every 11 molecules react, and only one leaves the lake by flow.

2.9

REAL AND EVALUATIVE ENVIRONMENTS

The environmental scientist who is attempting to describe the behavior of a pesticide in a system such as a lake soon discovers that real lakes are very complex. Considerable effort is required to measure, analyze, and describe the lake, with the result that little energy (or research money) remains with which to describe the behavior of the pesticide. This is an annoying problem, because it diverts attention from the pesticide (which is important) to the condition of the lake (which may be relatively unimportant). A related problem also arises when a new chemical is being considered. Into which lake should it be placed (hypothetically) for evaluation? A significant advance in environmental science was made in 1978, when Baughman and Lassiter (1978) proposed that chemicals may be assessed in “evaluative environments” that have fictitious but realistic properties such as volume, composition, and temperature. Evaluative environments can be decreed to consist of a few homogeneous phases of specified dimensions with constant temperature and composition. Essentially, the environmental scientist designs a “world” to desired specifications, then explores mathematically the likely behavior of chemicals in that world. No claim is made that the evaluative world is identical to any real environment, although broad similarities in chemical behavior are expected. There are good precedents for this approach. In 1824, Carnot devised an evaluative steam engine, now termed the Carnot cycle, which leads to a satisfying explanation of entropy and the second law of thermodynamics. The kinetic theory of gases uses an evaluative assumption of gas molecule behavior. The principal advantage of evaluative environments is that they act as an intellectual stepping stone when tackling the difficult task of describing both chemical behavior and an environment. The task is simplified by sidestepping the effort needed to describe a real environment. The disadvantage is that results of evaluative environment calculations cannot be validated directly, so they are suspect and possibly quite wrong. Some validation can be sought by making the evaluative environment similar to a simple real environment, such as a small pond or a laboratory microcosm. Later, we construct evaluative environments or “unit worlds” and use them to explore the likely behavior of chemicals. In doing so, we use equations that can be ©2001 CRC Press LLC

validated using real environments. A somewhat different assembly of equations proves to be convenient for real environments, but the underlying principles are the same.

2.10

SUMMARY

In this chapter, we have introduced the system of units and dimensions. A view of the environment has been presented as an assembly of phases or compartments that are (we hope) mostly homogeneous rather than heterogeneous in properties, and that vary greatly in volume and composition. We can define these phases or parts of them as “envelopes” about which we can write mass, mole, and, if necessary, energy balance equations. Steady-state conditions will yield algebraic equations, and unsteady-state conditions will yield differential equations. These equations may contain terms for discharges, flow (diffusive and nondiffusive) of material between phases, and for reaction or formation of a chemical. We have discriminated between equilibrium and steady state and introduced the concepts of residence time and persistence. Finally, the use of both real and evaluative environments has been suggested. Having established these basic concepts, or working tools, our next task is to develop the capability of quantifying the rates of the various flow, transport, and reaction processes.

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McKay, Donald. "Environmental Chemicals and Their Properties" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC,2001

CHAPTER

3

Environmental Chemicals and Their Properties 3.1 INTRODUCTION AND DATA SOURCES In this book, we focus on techniques for building mass balance models of chemical fate in the environment, rather than on the detailed chemistry that controls transport and transformation, as well as toxic interactions. For a fuller account of the basic chemistry, the reader is referred to the excellent texts by Crosby (1988), Tinsley (1979), Stumm and Morgan (1981), Pankow (1991), Schwarzenbach et al. (1993), Seinfeld and Pandis (1997), Findlayson-Pitts and Pitts (1986), Thibodeaux (1996), and Valsaraj (1995). There is a formidable and growing literature on the nature and properties of chemicals of environmental concern. Numerous handbooks list relevant physicalchemical and toxicological properties. Especially extensive are compilations on pesticides, chemicals of potential occupational exposure, and carcinogens. Government agencies such as the U.S. Environmental Protection Agency (EPA), Environment Canada, scientific organizations such as the Society of Environmental Toxicology and Chemistry (SETAC), industry groups, and individual authors have published numerous reports and books on specific chemicals or classes of chemicals. Conferences are regularly held and proceedings published on specific chemicals such as the “dioxins.” Computer-accessible databases are now widely available for consultation. Table 3.1 lists some of the more widely used texts and scientific journals. Most are available in good reference libraries. Most of the chemicals that we treat in this book are organic, but the mass balancing principles also apply to metals, organometallic chemicals, gases such as oxygen and freons, inorganic compounds, and ions containing elements such as phosphorus and arsenic. Metals and other inorganic compounds tend to require individual treatment, because they usually possess a unique set of properties. Organic compounds, on the other hand, tend to fall into certain well defined classes. We are often able to estimate the properties and behavior of one organic chemical from that ©2001 CRC Press LLC

Table 3.1 Sources of information on chemical properties and estimation methods (See Chapter 1.5 of Mackay, et al., Illustrated Handbooks of Physical Chemical Properties and Environmental Fate for Organic Chemicals, cited below, for more details) The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals (Annual), S. Budavarie, ed. Whitehouse Station, NJ: Merck & Co., 1996. Handbook of Chemistry and Physics, D. R. Lide, ed., 81/e. Boca Raton, FL: CRC Press. Verschueren’s Handbook of Environmental Data on Organic Chemicals. New York: John Wiley & Sons, 1997. Illustrated Handbook of Physical Chemical Properties and Environmental Fate for Organic Chemicals (in 5 volumes). D. Mackay, W. Y Shiu, and K. C. Ma. Boca Raton, FL: CRC Press, 1991–1997. Also available as a CD ROM. Handbook of Environmental Fate and Exposure Data for Organic Chemicals (several volumes), P. H. Howard, ed. Boca Raton, FL: Lewis Publications. Handbook of Environmental Degradation Rates, P. H. Howard et al. Boca Raton, FL: Lewis Publications. Lange’s Handbook of Chemistry, 15/e, J. A. Dean, ed. New York: McGraw-Hill, 1998. Dreisbach’s Physical Properties of Chemical Compounds, Vol I to III. Washington, DC, Amer. Chem. Soc. Technical Reports, European Chemical Industry Ecology and Toxicology Centre (ECETOC). Brussels, Belgium. Sax’s Dangerous Properties of Industrial Materials, 10/e. R. J. Lewis, ed. New York: John Wiley & Sons. Groundwater Chemicals Desk Reference, J. J. Montgomery. Boca Raton, FL: Lewis Publications, 1996. Genium Materials Safety Data Sheets Collection. Amsterdam, NY: Genium Publishing Corp. The Properties of Gases and Liquids, R. C. Reid, J. M. Prausnitz, and B. E. Poling. New York: McGraw-Hill, 1987. NIOSH/OSHA Occupational Health Guidelines for Chemical Hazards. Washington, DC: U.S. Government Printing Office. The Pesticide Manual, 12/e. C. D. S. Tomlin, ed. Loughborough, UK: British Crop Protection Council. The Agrochemicals Handbook, H. Kidd and D. R. James, eds. London: Royal Society of Chemistry. Agrochemicals Desk Reference, 2/e, J. H. Montgomery. Boca Raton, FL: Lewis Publications. ARS Pesticide Properties Database, R. Nash, A. Herner, and D. Wauchope. Beltsville, MD: U.S. Department of Agriculture, www.arsusda.gov/rsml/ppdb.html. Substitution Constants for Correlation Analysis in Chemistry and Biology, C. H. Hansch (currently out of print). New York: Wiley-Interscience. Handbook of Chemical Property Estimation Methods, W. J. Lyman, W. F. Reehl, D. H. Rosenblatt (currently out of print). New York: McGraw-Hill. Handbook of Property Estimation Methods for Chemicals, R. S. Boethling and D. Mackay. Boca Raton, FL: CRC Press, 2000. Chemical Property Estimation: Theory and Practice, E. J. Baum. Boca Raton, FL: Lewis Publications, 1997. Toolkit for Estimating Physiochemical Properties of Organic Compounds, M. Reinhard and A. Drefahl. New York: John Wiley & Sons, 1999. IUPAC Handbook. Research Triangle Park, NC: International Union of Pure and Applied Chemistry. Website for database and EPIWIN estimation methods, Syracuse, NY: Syracuse Research Corporation (http://www.syrres.com).

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of other, somewhat similar or homologous chemicals. An example is the series of chlorinated benzenes that vary systematically in properties from benzene to hexachlorobenzene. It is believed that some 50,000 to 80,000 chemicals are used in commerce. The number of chemicals of environmental concern runs to a few thousand. There are now numerous lists of “priority” chemicals of concern, but there is considerable variation between lists. It is not possible, or even useful, to specify an exact number of chemicals. Some inorganic chemicals ionize in contact with water and thus lose their initial identity. Some lists name PCBs (polychlorinated biphenyls) as one chemical and others as six groups of chemicals whereas, in reality, the PCBs consist of 209 possible individual congeners. Many chemicals, such as surfactants and solvents, are complex mixtures that are difficult to identify and analyze. One designation, such as naphtha, may represent 1000 chemicals. There is a multitude of pesticides, dyes, pigments, polymeric substances, drugs, and silicones that have valuable social and commercial applications. These are in addition to the numerous “natural” chemicals, many of which are very toxic. For legislative purposes, most jurisdictions have compiled lists of chemicals that are, or may be, encountered in the environment, and from these “raw” lists of chemicals of potential concern they have established smaller lists of “priority” chemicals. These chemicals, which are usually observed in the environment, are known to have the potential to cause adverse ecological and/or biological effects and are thus believed to be worthy of control and regulation. In practice, a chemical that fails to reach the “priority” list is usually ignored and receives no priority rather than less priority. These lists should be regarded as dynamic. New chemicals are being added as enthusiastic analytical chemists detect them in unexpected locations or toxicologists discover subtle new effects. Examples are brominated flame retardants, chlorinated alkanes, and certain very stable fluorinated substances (e.g., trifluoroacetic acid) that have only recently been detected and identified. In recent years, concern has grown about the presence of endocrine modulating substances such as nonylphenol, which can disrupt sex ratios and generally interfere with reproductive processes. The popular book Our Stolen Future, by Colborn et al. (1996) brought this issue to public attention. Some of these have industrial or domestic sources, but there is increasing concern about the general contamination by drugs used by humans or in agriculture. Table 3.2 lists about 200 chemicals by class and contains many of the chemicals of current concern.

3.2

IDENTIFYING PRIORITY CHEMICALS

It is a challenging task to identify from “raw lists” of chemicals a smaller, more manageable number of “priority” chemicals. Such chemicals receive intense scrutiny, analytical protocols are developed, properties and toxicity are measured, and reviews are conducted of sources, fate, and effects. This selection contains an element of judgement and is approached by different groups in different ways. A common thread among many of the selection processes is the consideration of six factors: quantity, ©2001 CRC Press LLC

Table 3.2 List of Chemicals Commonly Found on Priority Chemical Lists Volatile Halogentated Hydrocarbons Chloromethane Methylene chloride Chloroform Carbontetrachloride Chloroethane 1,1-Dichloroethane 1,2-Dichloroethane cis-1,2-Dichloroethene trans-1,2-Dichloroethene Vinyl chloride 1,1,1-Trichloroethane 1,1,2-Trichloroethane Trichloroethylene Tetrachloroethylene Hexachloroethane 1,2-Dichloropropane 1,3-Dichloropropane cis-1,3-Dichloropropylene trans-1,3-Dichloropropylene Chloroprene Bromomethane Bromoform Ethylenedibromide Chlorodibromomethane Dichlorobromomethane Dichlorodibromomethane Freons (chlorofluoro-hydrocarbons) Dichlorodifluoromethane Trichlorofluoromethane Halogenated Monoaromatics Chlorobenzene 1,2-Dichlorobenzene 1,3-Dichlorobenzene 1,4-Dichlorobenzene 1,2,3-Trichlorobenzene 1,2,4-Trichlorobenzene 1,2,3,4-Tetrachlorobenzene 1,2,3,5-Tetrachlorobenzene

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Monoaromatic Hydrocarbons Benzene Toluene o-Xylene m-Xylene p-Xylene Ethylbenzene Styrene Polycyclic Aromatic Hydrocarbons Naphthalene 1-Methylnaphthalene 2-Methylnaphthalene Trimethylnaphthalene Biphenyl Acenaphthene Acenaphthylene Fluorene Anthracene Fluoranthene Phenanthrene Pyrene Chrysene Benzo(a)anthracene Dibenz(a,h)anthracene Benzo(b)fluoranthene Benzo(k)fluoranthene Benzo(a)pyrene Perylene Benzo(g,h,i)perylene Indeno(1,2,3)pyrene

Dienes 1,3-Butadiene Cyclopentadiene Hexachlorobutadiene Hexachlorocyclopentadiene Alcohols and Phenols Benzyl alcohol Phenol o-Cresol m-Cresol p-Cresol 2-Hydroxybiphenyl 4-Hydroxybiphenyl Eugenol

Table 3.2 List of Chemicals Commonly Found on Priority Chemical Lists 1,2,4,5-Tetrachlorobenzene Pentachlorobenzene Hexachlorobenzene 2,4,5-Trichlorotoluene Octachlorostyrene Halogenated Biphenyls and Naphthalenes Polychlorinated Biphenyls (PCBs) Polybrominated Biphenyls (PBBs) 1-Chloronaphthalene 2-Chloronaphthalene Polychlorinated Naphthalenes (PCNs) Aroclor Aroclor Aroclor Aroclor Aroclor Aroclor Aroclor Aroclor

Mixtures (PCBs) 1016 1221 1232 1242 1248 1254 1260

Chlorinated Dibenzo-p-dioxins 2,3,7,8-Tetrachlorodibenzo-p-dioxin Tetrachlorinated dibenzo-p-dioxins Pentachlorinated dibenzo-p-dioxins Hexachlorinated dibenzo-p-dioxins Heptachlorinated dibenzo-p-dioxins Octachlorinated dibenzo-p-dioxin Brominated dibenzo-p-dioxins Chlorinated Dibenzofurans Tetrachlorinated dibenzofurans Pentachlorinated dibenzofurans Hexachlorinated dibenzofurans Heptachlorinated dibenzofurans Octachlorodibenzofuran

Halogenated Phenols 2-Chlorophenol 2,4-Dichlorophenol 2,6-Dichlorophenol 2,3,4-Trichlorophenol 2,3,5-Trichlorophenol 2,4,5-Trichlorophenol 2,4,6-Trichlorophenol 2,3,4,5-Tetrachlorophenol 2,3,4,6-Tetrachlorophenol 2,3,5,6-Tetrachlorophenol Pentachlorophenol 4-Chloro-3-methylphenol 2,4-Dimethylphenol 2,6-Di-t-butyl-4-methylphenol Tetrachloroguaiacol Nitrophenols, Nitrotoluenes and Related Compounds 2-Nitrophenol 4-Nitrophenol 2,4-Dinitrophenol 4,6-Dinitro-o-cresol Nitrobenzene 2,4-Dinitrotoluene 2,6-Dinitrotoluene 1-Nitronaphthalene 2-Nitronaphthalene 5-Nitroacenaphthalene Fluorinated Compounds Polyfluorinated alkanes Trifluoroacetic acid Fluoro-chloro acids Polyfluorinated chemicals

Phthalate Esters Nitrosamines and Other Nitrogen Compounds Dimethylphthalate N-Nitrosodimethylamine Diethylphthalate N-Nitrosodiethylamine Di-n-butylphthalate N-Nitrosodiphenylamine Di-n-octylphthalate N-Nitrosodi-n-propylamine Di(2-ethylhexyl) phthalate Diphenylamine Benzylbutylphthalate Indole 4-aminoazobenzene Chlorinated longer chain alkanes Pesticides, including biocides, fungicides, rodenticides, insecticides and herbicides

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persistence, bioaccumulation, potential for transport to distant locations, toxicity, and a miscellaneous group of other adverse effects. 3.2.1

Quantity

The first factor is the quantity produced, used, formed or transported, including consideration of the fraction of the chemical that may be discharged to the environment during use. Some chemicals, such as benzene, are used in very large quantities in fuels, but only a small fraction (possibly less than a fraction of a percent) is emitted into the environment through incomplete combustion or leakage during storage. Other chemicals, such as pesticides, are used in much smaller quantities but are discharged completely and directly into the environment; i.e., 100% is emitted. At the other extreme, there are chemical intermediates that may be produced in large quantities but are emitted in only minuscule amounts (except during an industrial accident). It is difficult to compare the amounts emitted from these various categories, because they are highly variable and episodic. It is essential, however, to consider this factor; many toxic chemicals have no significant adverse impact, because they enter the environment in negligible quantities. Central to the importance of quantity is the adage first stated by Paracelsus, nearly five centuries ago, that the dose makes the poison. This can be restated in the form that all chemicals are toxic if administered to the victim in sufficient quantities. A corollary is that, in sufficiently small doses, all chemicals are safe. Indeed, certain metals and vitamins are essential to survival. The general objective of environmental regulation or “management” must therefore be to ensure that the quantity of a specific substance entering the environment is not excessive. It need not be zero; indeed, it is impossible to achieve zero. Apart from cleaning up past mistakes, the most useful regulatory action is to reduce emissions to acceptable levels and thus ensure that concentrations and exposures are tolerable. Not even the EPA can reduce the toxicity of benzene. It can only reduce emissions. This implies knowing what the emissions are and where they come from. This is the focus of programs such as the Toxics Release Inventory (TRI) in the U.S.A. or the National Pollutant Release Inventory (NPRI) system in Canada. There are similar programs in Europe, Australia, and Japan. Regrettably, the data are often incomplete. A major purpose of this book is to give the reader the ability to translate emission rates into environmental concentrations so that the risk resulting from exposure to these concentrations can be assessed. When this can be done, it provides an incentive to improve release inventories. 3.2.2

Persistence

The second factor is the chemical’s environmental persistence, which may also be expressed as a lifetime, half-life, or residence time. Some chemicals, such as DDT or the PCBs, may persist in the environment for several years by virtue of their resistance to transformation by degrading processes of biological and physical origin. They may have the opportunity to migrate widely throughout the environment and reach vulnerable organisms. Their persistence results in the possibility of establishing ©2001 CRC Press LLC

relatively high concentrations. This arises because, in principle, the amount in the environment (kilograms) can be expressed as the product of the emission rate into the environment (kilograms per year) and the residence time of the chemical in the environment (years). Persistence also retards removal from the environment once emissions are stopped. A legacy of “in place” contamination remains. This is the same equation that controls a human population. For example, the number of Canadians (about 30 million) is determined by the product or the rate at which Canadians are born (about 0.4 million per year) and the lifetime of Canadians (about 75 years). If Canadians were less persistent and lived for only 30 years, the population would drop to 12 million. Intuitively, the amount (and hence the concentration) of a chemical in the environment must control the exposure and effects of that chemical on ecosystems, because toxic and other adverse effects, such as ozone depletion, are generally a response to concentration. Unfortunately, it is difficult to estimate the environmental persistence of a chemical. This is because the rate at which chemicals degrade depends on which environmental media they reside in, on temperature (which varies diurnally and seasonally), on incidence of sunlight (which varies similarly), on the nature and number of degrading microorganisms that may be present, and on other factors such as acidity and the presence of reactants and catalysts. This variable persistence contrasts with radioisotopes, which have a half-life that is fixed and unaffected by the media in which they reside. In reality, a substance experiences a distribution of half-lives, not a single value, and this distribution varies spatially and temporally. Obviously, long-lived chemicals, such as PCBs, are of much greater concern than those, such as phenol, that may persist in the aquatic environment for only a few days as a result of susceptibility to biodegradation. Some estimate of persistence or residence time is thus necessary for priority setting purposes. Organo-halogen chemicals tend to be persistent and are therefore frequently found on priority lists. Later in this book, we develop methods of calculating persistence. 3.2.3

Bioaccumulation

The third factor is potential for bioaccumulation (i.e., uptake of the chemical by organisms). This is a phenomenon, not an effect; thus bioaccumulation per se is not necessarily of concern. It is of concern that bioaccumulation may cause toxicity to the affected organism or to a predator or consumer of that organism. Historically, it was the observation of pesticide bioaccumulation in birds that prompted Rachel Carson to write Silent Spring in 1962, thus greatly increasing public awareness of environmental contamination. As we discuss later, some chemicals, notably the hydrophobic or “water-hating” organic chemicals, partition appreciably into organic media and establish high concentrations in fatty tissue. PCBs may achieve concentrations (i.e., they bioconcentrate) in fish at factors of 100,000 times the concentrations that exist in the water in which the fish dwell. For some chemicals (notably PCBs, mercury, and DDT), there is also a food chain effect. Small fish are consumed by larger fish, at higher trophic levels, and by other animals such as gulls, otters, mink, and humans. These chemicals ©2001 CRC Press LLC

may be transmitted up the food chain, and this may result in a further increase in concentration such that they are biomagnified. Bioaccumulation tendency is normally estimated using an organic phase-water partition coefficient and, more specifically, the octanol-water partition coefficient. This, in turn, can be related to the solubility of the chemical in the water. Clearly, chemicals that bioaccumulate, bioconcentrate, and biomagnify have the potential to travel down unexpected pathways, and they can exert severe toxic effects, especially on organisms at higher trophic levels. The importance of bioaccumulation may be illustrated by noting that, in water containing 1 ng/L of PCB, the fish may contain 105 ng/kg. A human may consume 1000 L of water annually (containing 1000 ng of PCB) and 10 kg of fish (containing 106 ng of PCB), thus exposure from fish consumption is 1000 times greater than that from water. Particularly vulnerable are organisms such as certain birds and mammals that rely heavily on fish as a food source. 3.2.4

Toxicity

The fourth factor is the toxicity of the chemical. The simplest manifestation of toxicity is acute toxicity. This is most easily measured as a concentration that will kill 50% of a population of an aquatic organism, such as fish or an invertebrate (e.g., Daphnia magna), in a period of 24–96 hours, depending on test conditions. When the concentration that kills (or is lethal to) 50% (the LC50) is small, this corresponds to high toxicity. The toxic chemical may also be administered to laboratory animals such as mice or rats, orally or dermally. The results are then expressed as a lethal dose to kill 50% (LD50) in units of mg chemical/kg body weight of the animal. Again, a low LD50 corresponds to high toxicity. More difficult, expensive, and contentious are chronic, or sublethal, tests that assess the susceptibility of the organism to adverse effects from concentrations or doses of chemicals that do not cause immediate death but ultimately may lead to death. For example, the animal may cease to feed, grow more slowly, be unable to reproduce, become more susceptible to predation, or display some abnormal behavior that ultimately affects its life span or performance. The concentrations or doses at which these effects occur are often about 1/10th to 1/100th of those that cause acute effects. Ironically, in many cases, the toxic agent is also an essential nutrient, so too much or too little may cause adverse effects. Although most toxicology is applied to animals, there is also a body of knowledge on phytotoxicity, i.e., toxicity to plants. Plants are much easier to manage, and killing them is less controversial. Tests also exist for assessing toxicity to microorganisms. It is important to emphasise that toxicity alone is not a sufficient cause for concern about a chemical. Arsenic in a bottle is harmless. Disinfectants, biocides, and pesticides are inherently useful because they are toxic. The extent to which the organism is injured depends on the inherent properties of the chemical, the condition of the organism, and the dose or amount that the organism experiences. It is thus misleading to classify or prioritize chemicals solely on the basis of their inherent toxicity, or on the basis of the concentrations in the environment or exposures. Both must be considered. A major task of this book is to estimate exposure. A healthy tension often ©2001 CRC Press LLC

exists between toxicologists and chemists about the relative importance of toxicity and exposure, but fundamentally this argument is about as purposeful as squabbling over whether tea leaves or water are the more important constituents of tea. Most difficult is the issue of genotoxicity, including carcinogenicity, and teratogenicity. In recent years, a battery of tests has been developed in which organisms ranging from microorganisms to mammals are exposed to chemicals in an attempt to determine if they can influence genetic structure or cause cancer. A major difficulty is that these effects may have long latent periods, perhaps 20 to 30 years in humans. The adverse effect may be a result of a series of biochemical events in which the toxic chemical plays only one role. It is difficult to use the results of short-term laboratory experiments to deduce reliably the presence and magnitude of hazard to humans. There may be suspicions that a chemical is producing cancer in perhaps 0.1% of a large human population over a period of perhaps 30 years, an effect that is very difficult (or probably impossible) to detect in epidemiological studies. But this 0.1% translates into the premature death of 30,000 Canadians per year from such a cancer, and is cause for considerable concern. Another difficulty is that humans are voluntarily and involuntarily exposed to many toxic chemicals, including those derived from smoking, legal and illicit drugs, domestic and occupational exposure, as well as environmental exposure. Although research indicates that multiple toxicants act additively when they have similar modes of action, there are cases of synergism and antagonism. Despite these difficulties, a considerable number of chemicals have been assessed as being carcinogenic, mutagenic, or teratogenic, and it is even possible to assign some degree of potency to each chemical. Such chemicals usually rank high on priority lists. As was discussed earlier, endocrine modulating substances are of more recent concern. It seems likely that ingenious toxicologists will find other subtle toxic effects in the future. 3.2.5

Long-Range Transport

As lakes go, Lake Superior is fairly pristine, since there is relatively little industry on its shores. In the U.S. part of this lake is an island, Isle Royale, which is a protected park and is thus even more pristine. In this island is a lake, Siskiwit Lake, which cannot conceivably be contaminated. No responsible funding agency would waste money on the analysis of fish from that lake for substances such as PCBs. Remarkably, perceptive researchers detected substantial concentrations of PCBs. Similarly, surprisingly high concentrations have been detected in wildlife in the Arctic and Antarctic. Clearly, certain contaminants can travel long distances through the atmosphere and oceans and are deposited in remote regions. This potential for long-range transport (LRT) is of concern for several reasons. There is an ethical issue when the use of a chemical in one nation (which presumably enjoys social or economic benefit from it) results in exposure in other downwind nations that derive no benefit, only adverse effects. This transboundary pollution issue also applies to gases such as SO2, which can cause acidification of poorly buffered lakes at distant locations. A regulatory agency may then be in the position of having little or no control over exposures experienced by its public. The political implications are obvious. ©2001 CRC Press LLC

There is therefore a compelling incentive to identify those chemicals that can undertake long-range transport and implement international agreements to control them. A start on this process has been made recently by the United Nations Environment Program (UNEP), which has identified 12 substances or groups for international regulations or bans. These substances, listed in Table 3.3, are also identified as persistent, bioaccumulative, and toxic. Others are scheduled for restriction or reduction. They may represent merely the first group of chemicals that will be subject to international controls. Most contentious of the 12 is DDT, which is still widely and beneficially used for malaria control. Table 3.3 Substances Scheduled for Elimination, Restriction, or Reduction by UNEP

Scheduled for Elimination

Scheduled for Restriction

Scheduled for Reduction

Aldrin

DDT

PAHs

Chlordane

Hexachlorocyclohexanes

Dioxins/furans

DDT

Polychlorinated biphenyls

Hexachlorobenzene

Dieldrin Endrin Heptachlor Hexabromobiphenyl Hexachlorobenzene Mirex Polychlorinated biphenyls Toxaphene

3.2.6

Other Effects

Finally, there is a variety of other adverse effects that are of concern, including • the ability to influence atmospheric chemistry (e.g., freons) • alteration in pH (e.g., oxides of sulfur and nitrogen causing acid rain) • unusual chemical properties such as chelating capacity, which alters the availability of other chemicals in the environment • interference with visibility • odor (e.g., from organo-sulfur compounds) • color (e.g., from dyes) • the ability to cause foaming in rivers (e.g., detergents or surfactants) • formation of toxic metabolites or degradation products

3.2.7

Selection Procedures

A common selection procedure involves scoring these factors on some numeric hazard scale. The factors then may be combined to give an overall factor and ©2001 CRC Press LLC

determine priority. This is a subjective process, and it becomes difficult for two major reasons. First, chemicals that are subject to quite different patterns of use are difficult to compare. For example, chemical X may be produced in very large quantities, emitted into the environment, and found in substantial concentrations in the environment, but it may not be believed to be particularly toxic. Examples are solvents such as trichloroethylene or plasticizers such as the phthalate esters. On the other hand, chemical Y may be produced in minuscule amounts but be very toxic, an example being the “dioxins.” Which deserves the higher priority? Second, it appears that the adverse effects suffered by aquatic organisms and other animals, including humans, are the result of exposure to a large number of chemicals, not just to one or two chemicals. Thus, assessing chemicals on a caseby-case basis may obscure the cumulative effect of a large number of chemicals. For example, if an organism is exposed to 150 chemicals, each at a concentration that is only 1% of the level that will cause death, then death will very likely occur, but it cannot be attributed to any one of these chemicals. It is the cumulative effect that causes death. The obvious prudent approach is to reduce exposure to all chemicals to the maximum extent possible. The issue is further complicated by the possibility that some chemicals will act synergistically, i.e., they produce an effect that is greater than additive; or they may act antagonistically, i.e., the combined effect is less than additive. As a result, there will be cases in which we are unable to prove that a specific chemical causes a toxic effect but, in reality, it does contribute to an overall toxic effect. Indeed, some believe that this situation will be the rule rather than the exception. A compelling case can be made that the prudent course of action is for society to cast a fairly wide net of suspicion (i.e., assemble a fairly large list of chemicals) then work to elucidate sources, fate, and effects with the aim of reducing overall exposure of humans, and our companion organisms, to a level at which there is assurance that no significant toxic effects can exist from these chemicals. The risk from these chemicals then becomes small as compared to other risks such as accidents, disease, and exposure to natural toxic substances. This approach has been extended and articulated as the “Precautionary Principle,” the “Substitution Principle,” and the “Principle of Prudent Avoidance.” One preferred approach is to undertake a risk assessment for each chemical. Formal procedures for conducting such assessments have been published, notably by the U.S. Environmental Protection Agency (EPA). The process involves identifying the chemical, its sources, the environment in which it is present, and the organisms that may be affected. The toxicity of the substance is evaluated and routes of exposure quantified. Ultimately, the prevailing concentrations or doses are measured or estimated and compared with levels that are known to cause effects, and conclusions are drawn regarding the proximity to levels at which there is a risk of effect. This necessarily involves consideration of the chemical’s behavior in an actual environment. Risk is thus assessed only for that environment. Risk or toxic effects are thus not inherent properties of a chemical; they depend on the extent to which the chemical reaches the organism. ©2001 CRC Press LLC

3.3 3.3.1

KEY CHEMICAL PROPERTIES AND CLASSES

Key Properties

In Chapter 5, we discuss physicochemical properties in more detail and, in Chapter 6, we examine reactivities. It is useful at this stage to introduce some of these properties and identify how they apply to different classes of chemicals. It transpires that we can learn a great deal about how a chemical partitions in the environment from its behavior in an air-water-octanol (strictly 1-octanol) system as shown later in Figure 3.2. There are three partition coefficients, KAW , KOW , and KOA, only two of which are independent, since KOA must equal KOW/KAW. These can be measured directly or estimated from vapor pressure, solubility in water, and solubility in octanol, but not all chemicals have measurable solubilities because of miscibility. Octanol is an excellent surrogate for natural organic matter in soils and sediments, lipids, or fats, and even plant waxes. It has approximately the same C:H:O ratio as lipids. Correlations are thus developed between soil-water and octanol-water partition coefficients, as discussed in more detail later. An important attribute of organic chemicals is the degree to which they are hydrophobic. This implies that the chemical is sparingly soluble in, or “hates,” water and prefers to partition into lipid, organic, or fat phases. A convenient descriptor of this hydrophobic tendency is KOW. A high value of perhaps one million, as applies to DDT, implies that the chemical will achieve a concentration in an organic medium approximately a million times that of water with which it is in contact. In reality, most organic chemicals are approximately equally soluble in lipid or fat phases, but they vary greatly in their solubility in water. Thus, differences in hydrophobicity are largely due to differences of behavior in, or affinity for, the water phase, not differences in solubility in lipids. The word lipophilic is thus unfortunate and is best avoided. The chemical’s tendency to evaporate or partition into the atmosphere is primarily controlled by its vapor pressure, which is essentially the maximum pressure that a pure chemical can exert in the gas phase or atmosphere. It can be viewed as the solubility of the chemical in the gas phase. Indeed, if the vapor pressure in units of Pa is divided by the gas constant, temperature group RT, where R is the gas constant (8.314 Pa m3/mol K), and T is absolute temperature (K), then vapor pressure can be converted into a solubility with units of mol/m3. Organic chemicals vary enormously in their vapor pressure and correspondingly in their boiling point. Some (e.g., the lower alkanes) that are present in gasoline are very volatile, whereas others (e.g., DDT) have exceedingly low vapor pressures. Partitioning from a pure chemical phase to the atmosphere is controlled by vapor pressure. Partitioning from aqueous solution to the atmosphere is controlled by KAW, a joint function of vapor pressure and solubility in water. A substance may have a high KAW , because its solubility in water is low. Partitioning from soils and other organic media to the atmosphere is controlled by KAO (air/octanol), which is conventionally reported as its reciprocal, KOA. Partitioning from water to organic media, including fish, is controlled by KOW . Substances that display a significant tendency to partition into the air phase over other phases are termed volatile organic chemicals or VOCs. They have high vapor pressures. ©2001 CRC Press LLC

Another important classification of organic chemicals is according to their dissociating tendencies in water solution. Some organic acids, notably the phenols, will form ionic species (phenolates) at high pH. The tendency to ionize is characterized by the acid dissociation constant KA, often expressed as pKA, its negative base ten logarithm. In concert with partitioning characteristics, the other set of properties that determine environmental behavior is reactivity or persistence, usually expressed as a halflife. It is misleading to assign a single number to a half-life, because it depends on the intrinsic properties of the chemical and on the nature of the environment. Factors such as sunlight intensity, hydroxyl radical concentration, the nature of the microbial community, as well as temperature vary considerably from place to place and time to time. Here, we use a semiquantitative classification of half-lives into classes, assuming that average environmental conditions apply. Different classes are defined for air, water, soils, and sediments. The classification is that used in a series of “Illustrated Handbooks” by Mackay, Shiu, and Ma is shown below in Table 3.4. Table 3.4 Classes of Chemical Half-Life or Persistence, Adapted from the Handbooks of Mackay et al., 2000 Class 1 2 3 4 5 6 7 8 9

Mean half–life (hours) 5 17 (~ 1 day) 55 (~ 2 day) 170 (~1 week) 550 (~3 weeks) 1700 (~2 months) 5500 (~8 months) 17000 (~2 years) 55000 (~6 years)

Range (hours) 30,000

The half-lives are on a logarithmic scale with a factor of approximately 3 between adjacent classes. It is probably misleading to divide the classes into finer groupings; indeed, a single chemical may experience half-lives ranging over three classes, depending on environmental conditions such as season. We examine, in the following sections, a number of classes of compounds that are of concern environmentally. In doing so, we note their partitioning and persistence properties. The structures of many of these chemicals are given in Figure 3.1. Table 3.5 gives suggested values of these properties for selected chemicals. Figure 3.2 is a plot of log KAW versus log KOW for the chemicals in Table 3.5 on which lines of constant KOA lie on the 45° diagonal. This graph shows the wide variation in properties. Volatile compounds tend to lie to the upper left, water-soluble compounds to the lower left, and hydrophobic compounds to the lower right. Assuming reasonable relative volumes of air (650,000), water (1300), and octanol (1), the percentages in each phase at equilibrium can be calculated. The lines of constant percentages are also shown. Lee and Mackay (1995) have used equilateral triangular diagrams to display the variation in partitioning properties in a format similar to that of Figure 3.2. ©2001 CRC Press LLC

Figure 3.1

Structures of selected chemicals of environmental interest (continues).

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Figure 3.1

(continued)

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Table 3.5 Physical Chemical properties of Selected Organic Chemicals at 25°C Including Estimated Half-Lives Classified as in Table 3.4 and Toxicity Expressed as Oral LD50 to the Rat. These data have been selected from a number of sources, including Mackay et al. (2000), RTECS (2000), and the Hazardous Substances Data Bank (2000). Degradation Half-lives (h)

Chemical Name benzene 1,2,4-trimethylbenzene ethylbenzene n-propylbenzene styrene toluene nitrobenzene 2-nitrotoluene 4-nitrotoluene 2,4-dinitrotoluene chlorobenzene 1,4-dichlorobenzene 1,2,3-trichlorobenzene 1,2,3,4-tetrachlorobenzene pentachlorobenzene hexachlorobenzene fluorobenzene bromobenzene iodobenzene n-pentane n-hexane 1,3-butadiene 1,4-cyclohexadiene

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Molar Vapor Aqueous Melting mass (g/mol) pressure (Pa) solubility (g/m3) Log KOW point ((C) 78.11 12700 1780 2.13 5.53 120.2 270 57 3.6 –43.8 106.2 1270 152 3.13 –95 120.2 450 52 3.69 –101.6 104.14 880 300 3.05 –30.6 92.13 3800 515 2.69 –95 123.11 20 1900 1.85 5.6 137.14 17.9 651.42 2.3 –3.85 137.14 0.653 254.4 2.37 51.7 182.14 0.133 270 2.01 70 112.6 1580 484 2.8 –45.6 147.01 130 83 3.4 53.1 181.45 28 21 4.1 53 215.9 4 7.8 4.5 47.5 250.3 0.22 0.65 5 86 284.8 0.0023 0.005 5.5 230 96.104 10480 1430 2.27 –42.21 157.02 552 410 2.99 –30.8 204.01 130 340 3.28 –31.35 72.15 68400 38.5 3.45 –129.7 86.17 20200 9.5 4.11 –95 54.09 281000 735 1.99 –108.9 80.14 9010 700 2.3 –49.2

Air Water 17 170 17 550 17 550 17 550 5 170 17 550 5 1700 17 55 17 55 17 55 170 1700 550 1700 550 1700 1700 5500 5500 17000 7350 55000 17 170 170 1700 170 1700 17 550 17 550 5 170 5 170

Soil Sediment 550 1700 1700 5500 1700 5500 1700 5500 550 1700 1700 5500 1700 5500 1700 5500 1700 5500 1700 5500 5500 17000 5500 17000 5500 17000 5500 17000 17000 17000 55000 55000 550 1700 5500 17000 5500 17000 1700 5500 1700 5500 550 1700 550 1700

Rat oral LD50 (mg/kg) 930 3550 5460 6040 2650 5000 349 891 1960 268 1110 500 756 1470 11000 3500 4399 2383 1749 90000 30000 5480 130

Table 3.5 (continued) dichloromethane trichloromethane carbon tetrachloride tribromomethane bromochloromethane bromodichloromethane 1,2-dichloroethane 1,1,2,2-tetrachloroethane pentachloroethane hexachloroethane 1,2-dichloropropane 1,2,3-trichloropropane chloroethene (vinyl chloride) trichloroethylene tetrachloroethylene methoxybenzene bis(2-chloroethyl)ether bis(2-chloroisopropyl)ether 2-chloroethyl vinyl ether bis(2-chloroethoxy)methane 1-pentanol 1-hexanol benzyl alcohol cyclohexanol benzaldehyde 3-pentanone 2-heptanone cyclohexanone acetophenone

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84.94 119.38 153.82 252.75 129.384 163.8 98.96 167.85 202.3 236.74 112.99 147.43 62.5 131.39 165.83 108.15 143.02 171.07 106.55 173.1 88.149 102.176 108.14 100.16 106.12 86.135 114.18 98.144 120.15

26222 26244 15250 727 19600 6670 10540 793 625 50 6620 492 354600 9900 2415 472 206 104 3566 21.6 300 110 12 85 174 4700 500 620 45

13200 8200 800 3100 14778 4500 8606 2962 500 50 2800 1896 2763 1100 150 2030 10200 1700 15000 8100 22000 6000 80 38000 3000 34000 4300 23000 5500

1.25 1.97 2.64 2.38 1.41 2.1 1.48 2.39 2.89 3.93 2 2.63 1.38 2.53 2.88 2.11 1.12 2.58 1.28 1.26 1.5 2.03 1.1 1.23 1.48 0.82 2.08 0.81 1.63

–95 –63.5 –22.9 –8.3 –87.95 –57.1 –35.36 –36 –29 186.1 –100.4 –14.7 –153.8 –73 –19 –37.5 –46.8 –97 –69.7 0 –78.2 –44.6 –15.3 25.15 –55.6 –38.97 –35 –32.1 19.62

1700 1700 17000 1700 550 550 1700 17000 17000 17000 550 550 55 170 550 17 17 17 17 17 55 55 55 55 5 55 55 55 550

1700 1700 1700 1700 550 550 1700 1700 1700 1700 5500 5500 550 5500 5500 550 550 550 550 550 55 55 55 55 55 170 170 170 170

5500 5500 5500 5500 1700 1700 5500 5500 5500 5500 5500 5500 1700 1700 1700 550 550 550 550 550 55 55 55 55 55 170 170 170 170

17000 17000 17000 17000 5500 5500 17000 17000 17000 17000 17000 17000 5500 5500 5500 1700 1700 1700 1700 1700 170 170 170 170 170 550 550 550 550

1600 1000 2350 933 5000 430 750 200 920 5000 1947 505 500 4920 2629 3700 75 240 210 65 3030 720 1230 1400 1300 2410 1670 1540 815

Table 3.5 (continued) vinyl acetate propyl acetate methyl methacrylate diphenylamine aniline quinoline thiophene benzoic acid hexanoic acid phenylacetic acid salicylic acid anthracene benzo[a]pyrene chyrsene

86.09 102.13 100.12 169.23 93.12 129.16 84.14 122.13 116.1 136.15 138.12 178.2 252.3 228.3

naphthalene phenanthrene p-xylene pyrene benzo(b)thiophene 1-methylnaphthalene biphenyl PCB-7 PCB-15 PCB-29 PCB-52 PCB-101 PCB-153 PCB-209

128.19 178.2 106.2 202.3 134.19 142.2 154.2 223.1 223.1 257.5 292 326.4 360.9 498.7

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14100 4500 5100 0.0612 65.19 1.21 10620 0.11 5 0.83 0.0208 0.001 7 x 10–7 5.7 x 10–7 10.4 0.02 1170 0.0006 26.66 8.84 1.3 0.254 0.0048 0.0132 0.0049 0.00109 0.000119 5.02x10–8

20000 21000 15600 300 36070 6110 3015 3400 958 16600 2300 0.045 0.0038 0.002

0.73 1.24 1.38 3.45 0.9 2.06 1.81 1.89 1.92 1.41 2.2 4.54 6.04 5.61

–92.8 –95 –42.8 52.8 –6.3 –14.85 –38 122.4 –3.44 77 159 216.2 175 255

55 55 17 5 5 55 55 55 55 55 55 55 170 170

55 55 55 55 170 170 55 55 55 55 55 550 1700 1700

170 170 55 170 170 550 1700 170 170 170 170 5500 17000 17000

550 550 170 550 1700 1700 5500 550 550 550 550 17000 55000 55000

2900 9370 7872 2000 250 331 1400 1700 6400 2250 891 8000 n/a n/a

31 1.1 214.9488 0.132 130 28 7 1.25 0.06 0.14 0.03 0.01 0.001 10–6

3.37 4.57 3.18 5.18 3.12 3.87 3.9 5 5.3 5.6 6.1 6.4 6.9 8.26

80.5 101 13.2 156 30.85 –22 71 24.4 149 78 87 76.5 103 305.9

17 55 17 170 170 17 55 170 170 550 1700 1700 5500 55000

170 550 550 1700 550 170 170 5500 5500 17000 55000 55000 55000 55000

1700 5500 1700 17000 1700 1700 550 17000 17000 55000 55000 55000 55000 55000

5500 17000 5500 55000 5500 5500 1700 17000 17000 55000 55000 55000 55000 55000

2400 n/a 4300 n/a 2200 1840 3280 n/a n/a n/a n/a n/a n/a n/a

Table 3.5 (continued) total PCB dibenzo-p-dioxin 2,3,7,8-tetraCDD 1,2,3,4,7,8-hexaCDD 1,2,3,4,6,7,8-heptaCDD OCDD dibenzofuran 2,8-dichlorodibenzofuran 2,3,7,8-tetrachlorodibenzofuran octachlorodibenzofuran 4-chlorophenol 2,4-dichlorophenol 2,3,4-trichlorophenol 2,4,6-trichlorophenol 2,3,4,6-tetrachlorophenol pentachlorophenol 2,4-dimethylphenol p-cresol dimethylphthalate (DMP) diethylphthalate (DEP) dibutylphthalate (DBP) butyl benzyl phthalate di-(2-ethylhexyl)-phthalate (DEHP) aldicarb aldrin carbaryl carbofuran chloropyrifos

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326 184 322 391 425.2 460 168.2 237.1 306 443.8 128.56 163 197.45 197.45 231.89 266.34 122.17 108.13 194.2 222.26 278.34 312.39 390.54

0.0009 0.055 0.0000002 5.1x10–9 7.5x10–10 1.1x10–10 0.3 0.00039 2x10–6 5x10–10 20 12 1 1.25 0.28 0.00415 13.02 13 0.22 0.22 0.00187 0.00115 1.33x10–5

190.25 364.93 201.22 221.3 350.6

0.004 0.005 0.0000267 0.00008 0.00227

0.024 0.865 1.93x10–5 4.42x10–6 2.4x10–6 7.4x10–8 4.75 0.0145 4.19x10–4 1.16x10–6 27000 4500 500 434 183 14 8795 20000 4000 1080 11.2 2.69 0.285 6000 0.02 120 351 0.73

6.6 4.3 6.8 7.8 8 8.2 4.31 5.44 6.1 8 2.4 3.2 3.8 3.69 4.45 5.05 2.35 1.96 2.12 2.47 4.72 4.68 5.11

0 123 305 273 265 322 86.5 184 227 258 43 44 79 69.5 70 190 26 34.8 5 –40.5 –35 –35 –50

1.1 6.50 2.36 2.32 4.92

99 104 142 151 41

5500 55000 500000 55 55 1700 170 550 17000 550 1700 55000 550 1700 55000 550 5500 55000 55 170 1700 170 550 5500 170 550 17000 550 5500 55000 55 550 550 55 550 550 170 170 1700 170 170 1700 550 550 1700 550 550 1700 17 55 170 5 17 55 170 170 550 170 170 550 55 170 550 55 170 550 55 170 550 5 55 55 5 17

550 5500 170 170 170

1700 17000 550 550 170

500000 5500 55000 55000 55000 55000 5500 17000 55000 55000 1700 1700 5500 5500 5500 5500 550 170 1700 1700 1700 1700 1700

1900 1220 0.02 0.8 6.325 1 n/a n/a n/a n/a 500 2830 2800 2800 140 210 2300 207 2400 8600 8000 13500 25000

17000 55000 1700 1700 1700

0.5 39 230 5 82

Table 3.5 (continued) cis-chlordane p,p’-DDE p,p’-DDT dieldrin diazinon g–HCH (lindane) a–HCH heptachlor malathion methoxychlor mirex parathion methyl parathion atrazine 2-(2,4-dichlorophenoxy) acetic acid dicamba mecoprop metolachlor simazine trifluralin thiram

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409.8 319 354.5 380.93 304.36 290.85 290.85 373.4 330.36 345.7 545.59 291.27 263.5 215.68 221.04

0.0004 0.000866 0.00002 0.0005 0.008 0.00374 0.003 0.053 0.001 0.00013 0.0001 0.0006 0.002 0.00004 0.00008

221.04 214.6 283.8 201.7 335.5 240.4

0.0045 0.00031 0.0042 8.5x10–6 0.015 0.00133

0.056 0.04 0.0055 0.17 60 7.3 1 0.056 145 0.045 0.000065 12.4 25 30 400 4500 620 430 5 0.5 30

6 5.7 6.19 5.2 3.3 3.7 3.81 5.27 2.8 5.08 6.9 3.8 3 2.75 2.81

103 88 108.5 176 0 112 157 95 2.9 86 485 6 37 174 140.5

55 170 170 55 550 1040 1420 55 17 17 170 17 17 5 17

17000 55000 5500 17000 1700 17000 3364 550 55 170 170 550 550 550 55

17000 55000 17000 17000 1700 17000 1687 1700 55 1700 55000 550 550 1700 550

55000 55000 55000 55000 5500 55000 55000 5500 550 5500 55000 1700 1700 1700 1700

500 880 87 38.3 66 76 177 40 290 1855 235 2 6.01 672 375

2.21 3.94 3.13 2.18 5.34 1.73

114 94 0 225 48.5 145

55 17 170 55 170 170

550 170 1700 550 1700 170

550 170 1700 1700 1700 550

1700 1700 5500 5500 5500 1700

1039 650 2200 971 1930 560

Figure 3.2

Plot of log KAW vs. log KOW for the chemicals in Table 3.5 on which dotted lines of constant KOA line on the 45° diagonal. This graph shows the wide variation in properties. Volatile compounds tend to lie to the upper left, water-soluble compounds to the lower left, and hydrophobic compounds to the lower right. The thicker lines represent constant percentages present at equilibrium in air, water, and octanol phases, assuming a volume ratio of 656,000:1300:1, respectively. Modified from Gouin et al. (2000).

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3.3.2

3.3.2.1

Chemical Classes (see Fig. 3.1 for structures and Table 3.5 for properties) Hydrocarbons

Hydrocarbons are naturally occurring chemicals present in crude oil and natural gas. Some are formed by biogenic processes in vegetation, but most contamination comes from oil spills, effluents from petroleum and petrochemical refineries, and the use of fuels for transportation purposes. The alkanes can be separated into classes of normal, branched (or iso) species and cyclic alkanes, which range in molar mass from methane or natural gas to waxes. They are usually sparingly soluble in water. For example, hexane has a solubility of approximately 10 g/m3. This solubility falls by a factor of about 3 or 4 for every carbon added. The branched and cyclic alkanes tend to be more soluble in water, apparently because they have smaller molecular areas and volumes. Highly branched or cyclic alkanes such as terpenes are produced by vegetation. They are often sweet smelling and tend to be very resistant to biodegradation. The alkenes or olefins are not naturally occurring to any significant extent. They are mainly used as petrochemical intermediates. The alkynes, of which ethyne or acetylene is the first member, are also chemical intermediates that are rarely found in the environment. These unsaturated hydrocarbons tend to be fairly reactive and short-lived in the environment, whereas the alkanes are more stable and persistent. Of particular environmental interest are the aromatics, the simplest of which is benzene. The aromatics are relatively soluble in water, for example, benzene has a solubility of 1780 g/m3. They are regarded as fairly toxic and often troublesome compounds. A variety of substituted aromatics can be obtained by substituting various alkyl groups. For example, methyl benzene is toluene. When two benzene rings are fused, the result is naphthalene, which is also a chemical of considerable environmental interest. Subsequent fusing of benzene rings to naphthalene leads to a variety of chemicals referred to as the polycyclic aromatic hydrocarbons or polynuclear aromatic hydrocarbons (PAHs). These compounds tend to be formed when a fuel is burned with insufficient oxygen. They are thus present in exhaust from engines and are of interest because many are carcinogenic. Biphenyl is a hydrocarbon that is not of much importance as such, but it forms an interesting series of chlorinated compounds, the PCBs or polychlorinated biphenyls, which are discussed later. 3.3.2.2

Halogenated Hydrocarbons

If the hydrogen in a hydrocarbon is substituted by chlorine (or less frequently by bromine, fluorine, or iodine), the resulting compound tends to be less flammable, more stable, more hydrophobic, and more environmentally troublesome. Replacing a hydrogen with a chlorine usually causes an increase in molar volume and area and a corresponding decrease in solubility by a factor of about 3. The stability of many of these compounds makes them invaluable as solvents, examples being methylene chloride and tetrachloroethylene. The fluorinated and ©2001 CRC Press LLC

chlorofluoro compounds are very stable and are used as refrigerants. Because these molecules are quite small, they are fairly soluble in water and are therefore able to penetrate the tissues of organisms quite readily. They are thus used as anaesthetics and narcotic agents. The chlorinated aromatics are a particularly interesting group of chemicals. The chlorobenzenes are biologically active. 1,4 or paradichlorobenzene is widely used as a deodorant and disinfectant. The polychlorinated biphenyls, or PCBs, and their brominated cousins, the PBBs, are notorious environmental contaminants, as are chlorinated terpenes such as toxaphene, which is a very potent and long-lived insecticide. Many of the early pesticides, such as DDT, mirex, and chlordane, are chlorinated hydrocarbons. They possess the desirable properties of stability and a high tendency to partition out of air and water into the target organisms. Thus, application of a pesticide results in protection for a prolonged time. As Rachel Carson demonstrated in Silent Spring, the problem is that these chemicals persist long enough to affect non-target organisms and to drift throughout the environment, causing widespread contamination. Fluorinated chemicals also possess considerable stability and, because the fluorine atom is lighter than chlorine, they are generally more volatile. Polyfluorinated substances are very stable in the environment as a result of the strong C-F bond. Brominated chemicals are also stable, but with reduced volatility. A major use of brominated substances is in fire retardants, specifically polybrominated diphenyl ethers. 3.3.2.3

Oxygenated Compounds

The most common oxygenated organic compounds are the alcohols, ethanol being among the most widely used. Others are octanol, which is a convenient analytical surrogate for fat, and glycerol is of interest because it forms the backbone of fat molecules by esterification with fatty acids to form glycerides. The phenols consist of an aromatic molecule in which a hydrogen is replaced by an OH group. They are acidic and tend to be biologically disruptive. Phenol, or carbolic acid, was the first disinfectant. Substituting chlorines on phenol tends to increase the toxic potency of the substance and its tendency to ionize, i.e., its pKa is reduced. Pentachlorophenol (PCP) is a particularly toxic chemical and has been widely used for wood preservation. The ketones such as acetone, and aldehydes such as formaldehyde, are fairly reactive in the environment and can be of concern as atmospheric contaminants in regions close to sources of emission. Much of the smog problem is attributable to aldehydes formed in combustion processes. Organic acids such as acetic acid are also fairly reactive. They are not usually regarded as an environmental problem, but trifluoroacetic acid, which is formed by combustion of freons and from some pesticides, is very persistent. Some chlorinated organic acids, e.g., 2,4-D, are potent herbicides. Longer-chain acids, such as stearic acid, are mainly of interest because they esterify with glycerol to form fats. Humic and fulvic acids are of considerable environmental importance. These are substances ©2001 CRC Press LLC

of complex and variable structure that are naturally present in soils, water, and sediments. They are the remnants of living organic materials, such as wood, that has been subjected to prolonged microbial conversion. These acids are sparingly soluble in water, but the solubility can be increased at high pH. The esters or “salts” or organic acids and alcohols tend to be relatively innocuous and short-lived in most cases. A notable exception is the phthalate esters, which are very stable oily substances and are invaluable additives (plasticizers) for plastics, rendering them more flexible. Notable among the phthalate esters is diethylhexylphthalate (DEHP), the ester with two molecules of 2 ethylhexanol. The other esters of interest are the glycerides—for example, glyceryl trioleate, the ester of glycerine and oleic acid. This chemical has similar properties to fat and has been suggested as a convenient surrogate for measuring fat to water partitioning. The “dioxins” and “furans” are two series of organic compounds that have become environmentally notorious. The chlorinated dibenzo-p-dioxins were never produced intentionally but are formed under combustion conditions when chlorine is present. They form a series of very toxic chemicals, the most celebrated of which is 2,3,7,8 tetrachlorodibenzo-p-dioxin (TCDD). TCDD is possibly the most toxic chemical to mammals. A dose of 2 mg of TCDD per kg of body weight is sufficient to kill small rodents. A related series of chemicals is the dibenzofurans, which are similar in properties to the dioxins. It appears that molecules that are long and flat, with chlorine atoms strategically located at the ends, are particularly toxic. Examples are the chloronaphthalenes, DDT, the PCBs, and chlorinated dibenzo-p-dioxins and dibenzofurans. Other oxygenated compounds of interest include carbohydrates, cellulose, and lignins, which occur naturally. 3.3.2.4

Nitrogen Compounds

Nitrogen compounds of environmental interest include amines, amides, pyridines, quinolines, and amino acids, and various nitro compounds including nitro polycyclicaromatics and nitroso compounds. Many of these compounds occur naturally, are quite toxic, and are difficult to analyze. 3.3.2.5

Sulfur Compounds

Sulfur compounds, including thiols, thiophenes, and mercaptans, are well known because of their strong odor. One of the most prevalent classes of synthetic organic chemicals is the alkyl benzene sulfonates, which are widely used in detergents. 3.3.2.6

Phosphorus Compounds

Phosphorus compounds play a key role in energy transfer in organisms. Organophosphate compounds have been developed as pesticides (e.g., chloropyrifos), which have the very desirable properties of high biological activity but relatively short environmental persistence. They have therefore largely replaced organo-chlorine compounds in agriculture. ©2001 CRC Press LLC

3.3.2.7

Arsenic Compounds

Arsenic, which behaves somewhat similarly to phosphorus, is inadvertently liberated in mineral processing and has a long and celebrated history as a poison. It usually exists in anionic and organic forms. 3.3.2.8

Metals

Most metals are essential for human life in small quantities but can be toxic if administered in excessive dosages. The metals of primary toxicological interest here are those that form organo-metallic molecules. Notable is mercury, which can exist as the element in various ionic and organometallic forms. Other metals such as lead and tin behave similarly. A formidable literature exists on the behavior, fate, and effects of the “heavy” metals such as lead, copper, and chromium. These metals often have a complex environmental chemistry and toxicology that vary considerably, depending on their ionic state as influenced by acidity and redox status. 3.3.2.9

Pharmaceuticals and Personal Care Products

Considerable quantities of drugs are used by humans and for veterinary purposes on livestock. Antibiotics and steroids are examples. These substances are excreted and may pass through sewage treatment plants or enter soils or groundwater following agricultural use. There is a growing concern that these substances may have adverse effects or may cause an increase in antibiotic resistance in bacteria. Among personal care products of concern are detergents, fabric softeners, fragrances, and certain solvents. They may evaporate or be discharged with sewage, which may or may not be adequately treated. 3.3.2.10

Other Chemicals

Several other chemicals are of environmental concern including ozone, radon, chlorine, organic and inorganic sulfides and cyanides, as well as the indeterminate broad class of “conventional” pollutants or indicators of pollution such as biochemical oxygen demand (BOD) and chemical oxygen demand (COD). Finally, certain mineral substances such as asbestos are of concern, more because of their physical structure than their chemical composition. 3.3.2.11

The Future

It would be unwise to assume that current lists of priority chemicals are complete and will remain static. It may be that the chemicals on the lists reflect our present ability to detect and analyze them rather than their real environmental significance. The prevalence of organo-chlorine chemicals on lists is in part the result of the sensitive electron capture detector. As new analytical methods emerge, new chemicals will presumably be found, and priorities will change. Happy hunting grounds for environmental chemists include combustion gases, dyes, mine tailings, effluents ©2001 CRC Press LLC

from pulp and paper operations (especially those involving chlorine bleaching), landfill leachates, and a vast assortment of products of metabolic conversion in organisms ranging from bacteria to humans.

3.4

CONCLUDING EXAMPLE

Select five substances from Table 3.5 that range in their values of vapor pressure, aqueous solubility, and log KOW. Calculate KAW as vapor pressure (Pa) --------------------------------------------3 solubility (g/m )

( molar mass (g/mol ) ------------------------------------------------RT

where R is 8.314 Pa m3/mol K, and T is absolute temperature (298 K). Calculate how 100 kg of each of these chemicals would partition at equilibrium between three phases namely, 1 m3 octanol (representing perhaps 100 m3 of soil) 5000 m3 water 106 m3 air

Calculate all the concentrations and amounts (which should add to 100 kg!) and discuss briefly how each substance is behaving, i.e., its partitioning preference.

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McKay, Donald. "The Nature of Environmental Media" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC,2001

CHAPTER

4

The Nature of Environmental Media 4.1

INTRODUCTION

The objective of this chapter is to present a qualitative description of environmental media, highlighting some of their more important properties. This is done because the fate of a chemical depends on two groups of properties: those of the chemical and those of the environment in which it resides. We find it useful to assemble “evaluative” environments, which are used in later calculations. We can consider, for example, an area of 1 ¥ 1 km, consisting of some air, water, soil, and sediment. Volumes and properties can be assigned to these media, which are typical but purely illustrative and will, of course, require modification if chemical fate in a specific region is to be treated. The sequence is to treat the atmosphere, the hydrosphere (i.e., water), and then the lithosphere (bottom sediments and terrestrial soils), each with its resident biotic community. It transpires that it is convenient to define two evaluative environments. First is a simple four-compartment system that is easily understood and illustrates the application of the general principles of environmental partitioning. Second is a more complex, eight-compartment system that is more representative of real environments. It is correspondingly more demanding of data and leads to more lengthy calculations. The environments or “unit worlds” are depicted in Figure 4.1. Details are discussed by Neely and Mackay, 1982.

4.2 4.2.1

THE ATMOSPHERE

Air

The layer of the atmosphere that is in most intimate contact with the surface of the Earth is the troposphere, which extends to a height of about 10 km. The temperature, density, and pressure of the atmosphere fall steadily with increasing height, ©2001 CRC Press LLC

Figure 4.1

Evaluative environments.

which is a nuisance in subsequent calculations. If we assume uniform density at a pressure of one atmosphere, then the entire troposphere can be viewed as being compressed into a height of about 6 km. Exchange of matter from the troposphere ©2001 CRC Press LLC

through the tropopause to the stratosphere is a relatively slow process and is rarely important in environmental calculations, except in the case of chemicals such as the freons, which catalyze the destruction of stratospheric ozone, thus facilitating the penetration of UV light to the Earth’s surface. A reasonable atmospheric volume over our 1 km square world is thus 1000 ¥ 1000 ¥ 6000 or 6 ¥ 109 m3. If our environmental model is concerned with a localized situation (e.g., a state, province, or metropolitan region), it is unlikely that most pollutants would manage to penetrate higher than about 500 to 2000 m during the time the air resides over the region. It therefore may be appropriate to reduce the height of the atmosphere to 500 to 2000 m in such cases. In extreme cases (e.g., over small ponds or fields), the accessible mixed height of the atmosphere may be as low as 10 m. The modeler must make a judgement as to the volume of air that is accessible to the chemical during the time that the air resides in the region of interest. 4.2.2

Aerosols

The atmosphere contains a considerable amount of particulate matter or aerosols that are important in determining the fate of certain chemicals. These particles may range in size and composition from water in the form of fog or cloud droplets to dust particles from soil and smoke from combustion. They vary greatly in size, but a diameter of a few mm is typical. Larger particles tend to deposit fairly rapidly. The concentration of these aerosols is normally reported in mg/m3. A rural area may have a concentration of about 5 mg/m3, and a fairly polluted urban area a concentration of 100 mg/m3. For illustrative purposes, we can assume that the particles have a density of 1.5 g/cm3 and are present at a concentration of 30 mg/m3. This corresponds to volume fraction of particles of 2 ¥ 10–11. The density of these particles is usually unknown, thus the volume fractions are only estimates. It is, however, convenient for us to calculate this amount in the form of a volume fraction. In an evaluative air volume of 6 ¥ 109 m3, there is thus 0.12 m3 or 120 L of solid material. These aerosols are derived from numerous sources. Some are mineral dust particles generated from soils by wind or human activity. Some are mainly organic in nature, being derived from combustion sources such as vehicle exhaust or wood fires, i.e., smoke. Some are generated from oxides of sulfur and nitrogen. Some “secondary” aerosols are formed by condensation as a result of oxidation of hydrocarbons in the atmosphere to less volatile species. These hydrocarbons can be generated by human activity such as fuel use, or they can be of natural origin. Forests often generate large quantities of isoprene that oxidize to give a blue haze, hence the terms “smokey” or “blue” mountains. These aerosols also contain quantities of water, the amount of which depends on the prevailing humidity. 4.2.3

Deposition Processes

Aerosol particles have a very high surface area and thus absorb (or adsorb or sorb) many pollutants, especially those of very low vapor pressure, such as the PCBs or polyaromatic hydrocarbons. In the case of benzo(a)pyrene, almost all the chemical present in the atmosphere is associated with particles, and very little exists in the gas phase. This is important, because chemicals associated with aerosol particles ©2001 CRC Press LLC

are subject to two important deposition processes. First is dry deposition, in which the aerosol particle falls under the influence of gravity to the Earth’s surface. This falling velocity, or deposition velocity, is quite slow and depends on the turbulent condition of the atmosphere, the size and properties of the aerosol particle, and the nature of the ground surface, but a typical velocity is about 0.3 cm/s or 10.8 m/h. The result is deposition of 10.8 m/h ¥ 2 ¥ 10–11 (volume fraction) ¥ 106 m2 or 0.000216 m3/h or 1.89 m3/year. Second, the particles may be scavenged or swept out of the air by wet deposition with raindrops. As it falls, each raindrop sweeps through a volume of air about 200,000 times its volume prior to landing on the surface. Thus, it has the potential to remove a considerable quantity of aerosol from the atmosphere. Rain is therefore often highly contaminated with substances such as PCBs and PAHs. There is a common fallacy that rain water is pure. In reality, it is often much more contaminated than surface water. Typical rainfall rates lie in the range 0.3 to 1 m per year but, of course, vary greatly with climate. We adopt a figure of 0.8 m/year for illustrative purposes. This results in the scavenging of 200,000 ¥ 0.8 m/year ¥ 2 ¥ 10–11 ¥ 106 m2 or 3.2 m3/year, about twice the dry deposition. Snow is an even more efficient scavenger of aerosol particles. It appears that one volume of snow (as solid ice) may scavenge about one million volumes of atmosphere, five times more than rain, presumably because of its flaky nature with a high surface area and a slower, more tortuous downward journey. In the four-compartment evaluative environment, we ignore aerosols, but we include them in the eight-compartment version.

4.3 4.3.1

THE HYDROSPHERE OR WATER

Water

Seventy percent of the Earth’s surface is covered by water. In some evaluative models, the area of water is taken as 70% of the 1 million m2 or 700,000 m2. Similarly to the atmosphere, only near-surface water is accessible to pollutants in the short term. In the oceans, this depth is about 100 m but, since most situations of environmental interest involve fresh or estuarine water, it is more appropriate to use a shallower water depth of perhaps 10 m. This yields a water volume of about 7 ¥ 106 m3. If the aim is to mimic the proportions of water and soil in a political jurisdiction, such as a state or province, the area of water will normally be considerably reduced to perhaps 10% of the total, or about 106 m3. We normally regard the water as being pure, i.e., containing no dissolved electrolytes, but we do treat its content of suspended particles. 4.3.2

Particulate Matter

Particulate matter in the water plays a key role in influencing the behavior of chemicals. Again, we do not normally know if the chemical is absorbed or adsorbed to the particles. We play it safe and use the vague term sorbed. A very clear natural water may have a concentration of particles as low as 1 g/m3 or the equivalent 1 mg/L. ©2001 CRC Press LLC

In most cases, however, the concentration is higher, in the range of 5 to 20 g/m3. Very turbid, muddy waters may have concentrations over 100 g/m3. Assuming a concentration of 7.5 g/m3 and a density of 1.5 g/cm3 gives a volume fraction of particles of about 5 ¥ 10-6. Thus, in the 7 ¥ 106 m3 of water, there is 35 m3 of particles. This particulate matter consists of a wide variety of materials. It contains mineral matter, which may be clay or silica in nature. It also contains dead or detrital organic matter, which is often referred to as humin, humic acids, and fulvic acids or, more vaguely, as organic matter. It is relatively easy to measure the total concentration of organic carbon (OC) in water or particles by converting the carbon to carbon dioxide and measuring the amount spectroscopically. Alternatively, the solids can be dried to remove water, then heated to ignition temperatures to burn off organic matter. The loss is referred to as loss on ignition (LOI) or as organic matter (OM). Thus, there are frequent reports of the amount of dissolved organic carbon (DOC) or total organic carbon (TOC) in water. These humic and fulvic acids have been the subject of intense study for many years. They are organic materials of variable composition that probably originate from the ligneous material present in vegetation. They contain a variety of chemical structures including substituted alkane, cycloalkane, and aromatic groups, and they have acidic properties imparted by phenolic or carboxylic acids. They are, therefore, fairly soluble in alkaline solution in which they are present in ionic form, but they may be precipitated under acidic conditions. The operational difference between humic and fulvic acids is the pH at which precipitation occurs. It is important to discriminate between organic matter (OM) and organic carbon (OC). Typically, OM contains 50 to 60% OC, thus an OM analysis of 10% may also be 5% OC. A mass basis, i.e., g/100 g, is commonly used. For convenience in our evaluative calculations, we will treat OM as 50% OC, and we will assume the density of both OM and OC as being equal to that of water. Concentrations of these suspended materials may be defined operationally by using filters of various pore size, for example, 0.45 mm. There is a tendency to describe material that is smaller than this, i.e., that passes through the filter, as being operationally “dissolved.” It is not clear how we can best discriminate between “dissolved” and “particulate” forms of such material, since there is presumably a continuous size spectrum ranging from molecules of a few nanometres to relatively large particles of 100 or 1000 nm. It transpires that the organic material in the suspended phases is of great importance, because it has a high sorptive capacity for organic chemicals. It is therefore common to assign an organic carbon content to these phases. In a fairly productive lake, the OM content may be as high as 50% but, for illustrative purposes, a figure of 33% for OM or 16.7% OC is convenient. In each cubic metre of water, there is thus 2.5 g or cm3 of OM and 5.0 g or 2.5 cm3 of mineral matter, totaling 7.5 g or 5.0 cm3, giving an average particle density of 1.5 g/cm3. 4.3.3

Fish and Aquatic Biota

Fish are of particular interest, because they are of commercial and recreational importance to users of water, and they tend to bioconcentrate or bioaccumulate ©2001 CRC Press LLC

metals and organic chemicals from water. They are thus convenient monitors of the contamination status of lakes. This raises the question, “What is the volume fraction of fish in a lake?” Most anglers and even aquatic biologists greatly overestimate this number. It is probably, in most cases, in the region of 10–8 to 10–9, but this is somewhat misleading, because most of the biotic material in a lake is not fish—it is material of lower trophic levels, on which fish feed. For illustrative purposes, we can assume that all the biotic material in the water is fish, and the total concentration is about 1 part per million, yielding a volume of “fish” of about 7 m3. It proves useful later to define a lipid or fat content of fish, a figure of 5% by volume being typical. In summary, the water thus consists of 7 ¥ 106 m3 of water containing 35 m3 of particulate matter and 7 m3 of “fish” or biota. In shallow or near-shore water, there may be a considerable quantity of aquatic plants or macrophytes. These plants provide a substrate for a thriving microbial community, and they possess inherent sorptive capacity. Their importance is usually underestimated. Because of the present limited ability to quantify their sorptive properties, we ignore them here. 4.3.4

Deposition Processes

The particulate matter in water is important, because, like aerosols in the atmosphere, it serves as a vehicle for the transport of chemical from the bulk of the water to the bottom sediments. Hydrophobic substances tend to partition appreciably on to the particles and are thus subject to fairly rapid deposition. This deposition velocity is typically 0.5 to 2.0 m per day or 0.02 to 0.08 m/h. This velocity is sufficient to cause removal of most of the suspended matter from most lakes during the course of a year. Thus, under ice-covered lakes in the winter, the water may clarify. Some of the deposited particulate matter is resuspended from the bottom sediment through the action of currents, storms, and the disturbances caused by bottom-dwelling fish and invertebrates. During the summer, there is considerable photosynthetic fixation of carbon by algae, resulting in the formation of considerable quantities of organic carbon in the water column. Much of this is destined to fall to the bottom of the lake, but much is degraded by microorganisms within the water column. Assuming, as discussed earlier, 5 ¥ 10–6 m3 of particles per m3 of water and a deposition velocity of 200 m per year, we arrive at a deposition rate of 0.001 m3/m2 of sediment area per year or, for an area of 7 ¥ 105 m2, a flow of 700 m3/year. We examine this rate in more detail in the next section.

4.4 4.4.1

BOTTOM SEDIMENTS

Sediment Solids

Inspection of the state of the bottom of lakes reveals that there is a fairly fluffy or nepheloid active layer at the water–sediment interface. This layer typically consists of 95% water and 5% particles and is often highly organic in nature. It may consist of deposited particles and fecal material from the water column. It is stirred ©2001 CRC Press LLC

by currents and by the action of the various biota present in this benthic region. The sediment becomes more consolidated at greater depths, and the water content tends to drop toward 50%. The top few centimetres of sediment are occupied by burrowing organisms that feed on the organic matter (and on each other) and generally turn over (bioturbate) this entire “active layer” of sediment. Depending on the condition of the water column above, this layer may be oxygenated (aerobic or oxic) or depleted of oxygen (anaerobic or anoxic). This has profound implications for the fate of inorganic substances such as metals and arsenic, but it is relatively unimportant for organic chemicals except in that the oxygen status influences the nature of the microbial community, which in turn influences the availability of metabolic pathways for chemical degradation. The deeper sediments are less accessible, and ultimately the material becomes almost completely buried and inaccessible to the aquatic environment above. Most of the activity occurs in the top 5 cm of the sediment, but it is misleading to assume that sediments deeper than this are not accessible. There remains a possibility of bioturbation or diffusion reintroducing chemical to the water column. Bottom sediments are difficult to investigate, can be unpleasant, and have little or no commercial value. They are therefore often ignored. This is unfortunate, because they serve as the depositories for much of the toxic material discharged into water. They are thus very important, are valuable as a “sink” for contaminants, and merit more sympathy and attention. Fast-flowing rivers are normally sufficiently turbulent that the bottom is scoured, exposing rock or consolidated mineral matter. Thus, their sediments tend to be less important. Sluggish rivers have appreciable sediments. 4.4.2

Deposition, Resuspension, and Burial

It is possible to estimate the rate of deposition, i.e., the amount of material that falls annually to the bottom of the lake and is retained there. This can be done by sediment traps, which are essentially trays that collect falling particles, or by taking a sediment core and assigning dates to it at various depths using concentrations of various radioactive metals such as lead. Nuclear events provide convenient dating markers for sediment depths. The measurement of deposition is complicated by the presence of the reverse process of resuspension caused by currents and biotic activity. It is difficult to measure how much material is rising and falling, since much may be merely cycling up and down in the water column. Burial or net deposition rates vary enormously, but a figure of about 1 mm per year is typical. Much of this is water, which is trapped in the burial process. Chemicals present in sediments are primarily removed by degradation, burial, or resuspension back to the water column. For illustrative purposes we adopt a sediment depth of 3 cm and suggest that it consists of 67% water and 33% solids, and these solids consist of about 10% organic matter or 5% organic carbon. Living creatures are included in this figure. Some of this deposited material is resuspended to the water column, some of the organic matter is degraded (i.e., used as a source of energy by benthic or bottom-living organisms), and some is destined to be permanently buried. The low 5% organic ©2001 CRC Press LLC

carbon figure for deeper sediments compared to high 17% for the depositing material implies that about 75% of the organic carbon is degraded. It is now possible to assemble an approximate mass balance for the sediment mineral matter (MM) and organic matter (OM) and thus the organic carbon (OC). This is given in Table 4.1. Table 4.1 Illustrative Sediment–Water Mass Balance on a 1 m2 Area Basis Mineral matter

Organic matter

cm3

g

Deposition

500

1200

Resuspension

200

480

–

–

233

233

300

720

67

67

OM conversion Burial (solids)

cm3

Organic carbon

Total

g

cm3

g

500

500

1000

1700

250

200

200

400

680

100

233

233

117

367

787

33

g

Total burial is 1000 cm3/year or 1420 g/year, corresponding to a “velocity” of 1 mm/year. The sediment thus has a density of 1.42 g/cm3 or 1420 kg/m3. Assumed densities are: mineral matter 2.4 g/cm3, organic matter 1 g/cm3. Organic matter is 50% (mass) organic carbon.

On a 1 m2 basis, the deposition rate is 0.001 m3 per year or 1000 cm3 per year. With a particle density of 1.7 g/cm3, this corresponds to 1700 g/year of which 500 g is OM, and 1200 g is MM. We assume that 40% of this is resuspended, i.e., 200 g of OM and 480 g of MM. Of the remaining 300 g OM, we assume that 233 g is digested or degraded to CO2, and 67 g is buried along with the remaining 720 g of MM. Total burial is thus 1420 g, which consists of 720 g of MM, 67 g of OM, and 633 g of water. The total volumetric burial rate of solids is 367 cm3/year. Now, associated with these solids is 633 cm3 of pore water; thus, the total volumetric burial rate of solids plus water is approximately 1000 cm3/year, corresponding to a rise in the sediment-water interface of 1 mm/year. The mass percentage of OC in the depositing and resuspending material is 15%, while in the buried material it is 4.2%. The bulk sediment density, including pore water, is 1420 kg/m3. On a 7 ¥ 105 m2 basis, the deposition rate is 700 m3/year, resuspension is 280 m3/year, burial is 257 m3/year, and degradation accounts for the remaining 163 m3/year. The organic and mineral matter balances are thus fairly complicated, but it is important to define them, because they control the fate of many hydrophobic chemicals. It is noteworthy that the burial rate of 1 mm/year coupled with the sediment depth of 3 cm indicates that, on average, it will take 30 years for sediment solids to become buried. During this time, they may continue to release sorbed chemical back to the water column. This is the crux of the “in-place contaminated sediments” problem, which is unfortunately very common, especially in the Great Lakes Basin. In the simple four-compartment environment, we treat only the solids but, in the eight-compartment version, we include the sediment pore water. In the interests of simplicity, we assign a density of 1500 kg/m3 to the sediment in the four-compartment model. ©2001 CRC Press LLC

4.5 4.5.1

SOILS

The Nature of Soil

Soil is a complex organic matrix consisting of air, water, mineral matter (notably clay and silica), and organic matter, which is similar in general nature to the organic matter discussed earlier for the water column. The surface soil is subject to diurnal and seasonal temperature changes and to marked variations in water content, and thus in air content. At times it may be completely flooded, and at other times almost completely dry. The organic matter in the soil plays a crucial role in controlling the retention of the water and thus in ensuring the viability of plants. The organic matter content is typically 1 to 5%, but peat soils and forest soils can have much higher organic matter contents. Depletion of organic matter through excessive agriculture tends to render the soil infertile, which is an issue of great concern in agricultural regions. Soils vary enormously in their composition and texture and consist of various layers, or horizons, of different properties. There is transport vertically and horizontally by diffusion in air and in water, flow, or advection in water and, of course, movement of water and nutrients into plant roots and thence into stems and foliage. Burrowing animals such as worms can also play an important role in mixing and transporting chemicals in soils. A typical soil may consist of 50% solid matter, 20% air, and 30% water, by volume. The dry soil thus has a porosity of 50%. The solid matter may consist of about 2% organic carbon or 4% organic matter. During and after rainfall, water flows vertically downward through the soil and may carry chemicals with it. During periods of dry weather, water tends to return to the surface by capillary action, again moving the chemicals. Later, we set up equations describing the diffusion or permeation of chemicals in soils. When doing so, we treat the soil as having a constant porosity. In reality, there are channels or “macroporous” areas formed by burrowing animals and decayed roots, and these enable water and air to flow rapidly through the soil, bypassing the more tightly packed soil matrix. This phenomenon is very difficult to address when compiling models of transport in soils and is the source of considerable frustration to soil scientists. Most soils are, of course, covered with vegetation, which stabilizes the soil and prevents it from being eroded by wind or water action. Under dry conditions, with poor vegetation cover, considerable quantities of soil can be eroded by wind action, carrying with it sorbed chemicals. Sand dunes are an extreme example. In populated regions, of more concern is the loss of soil in water runoff. This water often contains very high concentrations of soil, perhaps as much as a volume fraction of 1 part per thousand of solid material. This serves as a vehicle for the movement of chemicals, especially agricultural chemicals such as pesticides, from the soils into water bodies such as lakes. 4.5.2

Transport in Soils

In most areas, there is a net movement of water vertically from the surface soil to greater depths into a pervious layer of rock or aquifer through which groundwater ©2001 CRC Press LLC

flows. The quality of this groundwater has become of considerable concern recently, especially to those who rely on wells for their water supply. This water tends to move very slowly (i.e., at a velocity of metres per year) through the porous sub-surface strata. If contaminated, it can take decades or even centuries to recover. Of particular concern are regions in which chemical leachate from dumps or landfills has seeped into the groundwater and has migrated some distance into rivers, wells, or lakes. It is quite difficult and expensive to investigate, sample, and measure contaminant flow in groundwater. It may not even be clear in which direction the water is flowing or how fast it is flowing. Chemicals associated with groundwater generally move more slowly than the velocity of the groundwater. They are retarded by sorption to the soil to an extent expressed as a “retardation factor,” which is essentially the ratio of (a) the amount of chemical that is sorbed to the solid matrix to (b) the amount that is in solution. Sorption of organic chemicals is usually accomplished preferentially to organic matter; however, clays also have considerable sorptive capacity, especially when dry. Polar, and especially ionic, substances may interact strongly with mineral matter. The characterization of migration of chemicals in groundwater is difficult, and especially so when a chemical is present in an non-aqueous phase, for example, as a bulk oil or emulsified oil phase. Considerable effort has been devoted to understanding the fate of nonaqueous phase liquids (NAPLs) such as oils, and dense NAPLs (DNAPLs) such as chlorinated solvents that can sink in the aquifer and are very difficult to recover. For illustrative purposes, we treat the soil as covering an area 1000 m ¥ 300 m ¥ 15 cm deep, which is about the depth to which agricultural soils are plowed. This yields a volume of 45,000 m3. This consists of about 50% solids, of which 4% is organic matter content or 2% by mass organic carbon. The porosity of the soil, or void space, is 50% and consists of 20% air and 30% water. Assuming a density of the soil solids of 2400 kg/m3 and water of 1000 kg/m3 gives masses of 1200 kg solids and 300 kg water per m3 (and a negligible 0.2 kg air), totaling 1500 kg, corresponding to a bulk density of 1500 kg/m3. Rainwater falls on this soil at a rate of 0.8 m per year, i.e., 0.8 m3/m2 year. Of this, perhaps 0.3 m evaporates, 0.3 m runs off, and 0.2 m percolates to depths and contributes to groundwater flow. This results in water flows of 90,000 m3/year by evaporation, 90,000 m3/year by runoff, and 60,000 m3/year by percolation to depths totaling 240,000 m3/year. With the runoff is associated 90 m3/year of solids, i.e., an assumed high concentration of 0.1% by volume. Again, it must be emphasized that these numbers are entirely illustrative. This soil runoff rate of 90 m3/year does not correspond to the deposition rate of 700 m3/year, partly because of the contribution of organic matter generated in the water column, but mainly because of the low ratio of soil area to water area. 4.5.3

Terrestrial Vegetation

Until recently, most environmental models have ignored terrestrial vegetation. The reason for this is not that vegetation is unimportant, but rather that modelers currently have enormous difficulty calculating the partitioning of chemicals into plants. This topic is receiving more attention as a result of the realization that consumption of contaminated vegetation, either by humans, domestic animals, or wildlife, is a major route or vector for the transfer of toxic chemicals from one ©2001 CRC Press LLC

species to another, and ultimately to humans. Plants play a critical role in stabilizing soils and in inducing water movement from soil to the atmosphere, and they may serve as collectors and recipients of toxic chemicals deposited or absorbed from the atmosphere. They can also degrade certain chemicals and increase the level of microbial activity in the root zone, thus increasing the degradation rate in the soil. Amounts of vegetation, in terms of quantity of biomass per square metre, vary enormously from near zero in deserts to massive quantities that greatly exceed accessible soil volumes in tropical rain forests. They also vary seasonally. If it is desired to include vegetation, a typical “depth” of plant biomass might be 1 cm. This, of course, consists mainly of water, cellulose, starch, and ligneous material. There is little doubt that future, more sophisticated models will include chemical partitioning behavior into plants. But at the present state of the art, it is convenient (and rather unsatisfactory) to regard the plants as having a volume of 3000 m3, containing the equivalent of 1% lipid-like material and 50% water. We ignore vegetation in the simple four-compartment model, treating the soil as only a simple solid phase.

4.6

SUMMARY

These evaluative volumes, areas, compositions, and flow rates are summarized in Table 4.2. From them is derived a simple four-compartment version. Also suggested is an alternative environment that is more terrestrial and less aquatic, and it reflects more faithfully a typical political jurisdiction. It is emphasized again that the quantities are purely illustrative, and site-specific values may be quite different. All that is needed at this stage is a reasonable basis for calculation. Scientists who have devoted their lives to studying the intricacies of the structure, composition, and processes of the atmosphere, hydrosphere, or lithosphere will undoubtedly be offended at the simplistic approach taken in this chapter. The environment is very complex, and it is essential to probe the fine detail present in its many compartments. But, if we are to attempt broad calculations of multimedia chemical fate, we must suppress much of the media-specific detail. When the broad patterns of chemical behavior are established, it may be appropriate to revisit the media that are important for that chemical and focus on detailed behavior in a specific medium. At that time, a more detailed and site-specific description of the medium of interest will be justified and required. Our philosophy is that the model should be only as complex as is required to answer the immediate question, not every question that could be asked. As questions are answered, new questions will surface and new, more complex models can be developed to answer these questions.

4.7

CONCLUDING EXAMPLE

Select a region with which you are familiar; for example, a county, watershed, state, or province. Calculate the volumes of air to a height of 1000 m; soil to a depth ©2001 CRC Press LLC

Table 4.2 Evaluative Environments A. Four-compartment, 1 km2 environment Areas (m2)

¥ 105 3 ¥ 105 7 ¥ 105

Air–water

7

Air–soil Water–sediment

Depths (m)

Volumes (m3)

Densities (kg/m3)

6000

¥ 109 7 ¥ 106 4.5 ¥ 104 2.1 ¥ 104

1.2

Air Water

10

Soil

0.15

Sediment

0.03

6

Compositions

1000 1500

2% OC

1500

5% OC

B. Eight-compartment, 1 km2 environment, areas as in A above Volumes (m3) Air

¥ 7¥ 4.5 ¥

Soil (50% solids, 20% air, 30% water) Sediment (30% solids)

1.2

106

1000

Water

104

1500

Soil (50% solids, 20% air, 30% water)

1500

Sediment (30% solids)

35

1500

16.7% OC

0.12

1500

2

7

1000

5% lipid

3000

1000

1% lipid

2.1

Suspended Sediment Aerosols

¥

Aquatic Biota Vegetation

Compositions

109

6

Water

Densities (kg/m3)

104

Air

¥ 10–11 volume fraction or 30 mg/m3

0.8 m/year or 800,000 m3/year 560,000 m3 to water; 240,000 m3 to soil

Rain Rate Aerosol Deposition Rates (total) Dry deposition Wet deposition

¥ 10–6 m3 /h or 1.89 m3 /year 365 ¥ 10–6 m3 /h or 3.2 m3 /year

216

Sediment Deposition Rates Deposition

700 m3 /year solids 17% OC

Resuspension

280 m3 /year solids 17% OC

Net deposition (burial)

257 m3 /year solids 5% OC

Fate of Water in Soil Evaporation

90,000 m3 /year

Runoff to water

90,000 m3 /year

Percolation to groundwater

60,000 m3 /year

Solids runoff

90 m3 /year

©2001 CRC Press LLC

Table 4.2 (continued) C. Regional, 100,000 km2 environment as used in the EQC model of Mackay et al. (1996b) Volume (m3) 14

Air

10

Aerosols

2000

Water

2

Soil

9

¥ 10 ¥ 109

Area (m2) 100

¥

10

(2 ¥ 10–11 vol frn)

– 11

8

¥ ¥ 10 ¥

Composition

9

9

10

10

90

109

2% OC

Sediment

10

Suspended sediment

106

–

20% OC

¥

–

5% lipid

Fish

2

105

10

9

4% OC

For details of other properties see Mackay et al. 1996b.

of 10 cm; water and bottom sediment to a depth of 3 cm, and vegetation. Obtain data on average temperature, rain rate, water flows, and wind velocity, and calculate air and water residence times. Attempt to obtain information on typical concentrations of aerosols, suspended solids in water, and the organic carbon contents of soils, bottom, and suspended sediments. Prepare a summary table of these data similar to Table 4.2. These basic environmental data can be used in subsequent assessments of the fate of chemicals in this region.

©2001 CRC Press LLC

McKay, Donald. "Phase Equilibrium" Multimedia Environmental Models Edited by Donald McKay Boca Raton: CRC Press LLC,2001

CHAPTER

5

Phase Equilibrium 5.1 5.1.1

INTRODUCTION

The Nature of Partitioning Phenomena

There are two distinct tasks that must be addressed when predicting equilibrium partitioning of chemicals in the environment. First, we must fully understand how chemicals behave under ideal, laboratory conditions of controlled temperature and well defined, pure phases. This is the task of physical chemistry. Second is the translation of these partitioning data into the more complex and less defined conditions of the environment where phases vary in composition and properties. In both cases, we are concerned with the equilibrium distribution of a chemical between phases as illustrated in the simple two-compartment system of Figure 5.1. A small volume of nonaqueous phase (e.g., a particle of organic or mineral matter, a fish, or an air bubble) is introduced into water that contains a dissolved chemical such as benzene. There is a tendency for some of the benzene to migrate into this new phase and establish a concentration that is some multiple of that in the water. In the case of organic particles, the multiple may be 100 or, if the phase is air, the multiple may be only 0.2. Equilibrium becomes established in hours or days between the benzene dissolved in the water and the benzene in, or on, the nonaqueous phase. Analytical measurements may give the total or average concentration that includes the nonaqueous phase and may differ considerably from the actual dissolved water concentration. The phase may subsequently settle to the lake bottom or rise to the surface, conveying benzene with it. Clearly, it is essential to establish the capability of calculating these concentrations and thus the fractions of the total amount of benzene that remain in the water, and enter the second phase. In some cases, 95% of the benzene may migrate into the phase, and in others only 5%. These systems will behave quite differently. The aim is to answer the question, “Given a concentration in one phase, what will be the concentration in another phase that has been in contact with it long enough to achieve equilibrium?” This task is part of the science of thermodynamics ©2001 CRC Press LLC

Figure 5.1

Some principles and concept in phase equilibrium.

that is fully described in several excellent texts such as those of Denbigh (1966), Van Ness and Abbott (1982), Prausnitz et al. (1969), and for aquatic environmental systems by Stumm and Morgan (1981) and Pankow (1991). It is assumed here that the reader is familiar with the general principles of thermodynamics; therefore, no attempt is made to derive all the equations. The aim is rather to extract from the science of thermodynamics those parts that are pertinent to environmental chemical equilibria and explain their source, significance, and applications. ©2001 CRC Press LLC

Environmental thermodynamics or phase equilibrium physical chemistry applies to a relatively narrow range of conditions. Tropospheric or surface temperatures range only between –40° and +40°C and usually between the narrower limits of 0° and 25°C. Total pressures are almost invariably atmospheric but, of course, with an additional hydrostatic pressure at lake or ocean bottoms. Concentrations of chemical contaminants are (fortunately) usually low. Situations in which the concentration is high (as in spills of oil or chemicals) are best treated separately. These limited ranges are fortunate in that they simplify the equations and permit us to ignore large and complex areas of thermodynamics that deal with high and low pressures and temperatures, and with high concentrations. The presence of a chemical in the environment rarely affects the overall dominant structure, processes, and properties of the environment; therefore, we can take the environment “as is” and explore the behavior of chemicals in it with little fear of the environment being changed in the short term as a result. There are, however, certain notable exceptions, particularly when the biosphere (which can be significantly altered by chemicals) plays an important role in determining the landscape. An example is the stabilizing influence of vegetation on soils. Another is the role of depositing carbon of photosynthetic origin in lakes. A point worth emphasizing is that thermodynamics is based on a few fundamental “laws” or axioms from which an assembly of equations can be derived that relate certain useful properties to each other. Examples are the relationship between vapor pressure and enthalpy of vaporization, or concentration and partial pressure. In some cases, the role of thermodynamics is simply to suggest suitable relationships. Thermodynamics never defines the actual value of a property such as the boiling point of benzene; such data must be obtained experimentally. We thus process experimental data using thermodynamic relationships. Despite its name, thermodynamics is not concerned with process rates; indeed, none of the equations derived in this chapter need contain time as a dimension. It transpires that two approaches can be used to develop equations relating equilibrium concentrations to each other as shown in Figure 5.1. The simpler and most widely used is Nernst’s Distribution law, which postulates that the concentration ratio C1/C2 is relatively constant and is equal to a partition or distribution coefficient K12. Thus, C2 can be calculated as C1K12. K12 presumably can be expressed as a function of temperature and, if necessary, of concentration. Experimentally, mixtures are equilibrated, and concentrations measured and plotted as in Figure 5.1. Linear or nonlinear equations then can be fitted to the data. The second approach involves the introduction of an intermediate quantity, a criterion of equilibrium, which can be related separately to C1 and C2. Chemical potential, fugacity, and activity are suitable criteria, with fugacity being preferred for most organic substances because of the simplicity of the equations that relate fugacity to concentration. The advantage of the equilibrium criterion approach is that properties of each phase are treated separately using a phase-specific equation. Treating phases in pairs, as is done with partition coefficients, can obscure the nature of the underlying phenomena. We may detect a variability in K12 and not know from which phase the variability is derived. Further complications arise if we have 10 phases to consider. There are then 90 possible partition coefficients, of which only 9 are independent. Mistakes are less ©2001 CRC Press LLC

likely using an equilibrium criterion and the 10 equations relating it to concentration, one for each phase. It is useful to discriminate between partition coefficients and distribution coefficients. Although usage varies, a partition coefficient is strictly the ratio of the concentrations of the same chemical species in two phases. A distribution coefficient is a ratio of total concentrations of all species. Thus, if a chemical ionizes, the partition coefficient may apply to the unionized species, while the distribution coefficient applies to ionized and nonionized species in total. 5.1.2

Some Thermodynamic Fundamentals

There are four laws of thermodynamics. They are numbered 0, 1, 2, and 3, because the need for the zeroth was not realized until after the first was postulated. Although these laws cannot be proved mathematically, they are now universally accepted as true, or axiomatic, because they are supported by all available experimental evidence. On consideration, they are intuitively reasonable, and it now seems inconceivable that they are ever disobeyed. The zeroth law introduces the concept of temperature as a criterion of thermal equilibrium by stating that, when bodies are at thermal equilibrium, i.e., there is no net heat flow in either direction, their temperatures are equal. The first law was discovered largely as a result of careful experiments by Joule, and it establishes the concept of energy and its conservation. Energy takes several forms—potential, kinetic, heat, chemical, electrical, nuclear, and electromagnetic. There are fixed conversion rates among these forms. Furthermore, energy can neither be formed nor destroyed; it merely changes its form. Of particular importance are conversions between thermal energy (heat) and mechanical energy (work). The second law is intellectually more demanding and introduces the concept of entropy and a series of useful related properties, including chemical potential and fugacity. It is observed that, whereas there are fixed exchange rates between heat and work energy, it is not always possible to effect the change. The conversion of mechanical energy to heat (as in an automobile brake) is always easy, but the reverse process of converting heat to mechanical energy (as in a thermal power station) proves to be more difficult. If a quantity of heat is available at high temperature, then only a fraction of it, perhaps one third, can be converted into mechanical energy. The remainder is rejected as heat, but at a lower temperature. Most thermodynamics texts introduce hypothetical processes such as the Carnot cycle at this stage to illustrate these conversions. After some manipulation, it can be shown that there is a property of a system, called its entropy, that controls these conversions. Apparently, regardless of how it is arranged to convert heat to work, the overall entropy of the system cannot decrease. It must increase by what is termed an irreversible process, or in the limit, it could remain constant by what is called a reversible process. Although there may be a local entropy decrease, this must be offset by another and greater entropy increase elsewhere. Clausius summarized this law in the statement that the “entropy of the universe increases.” It can be shown that entropy is related to randomness or probability. An increase in entropy corresponds to a change to a more random or disordered or probable condition. The third law is not important for our immediate purposes. ©2001 CRC Press LLC

We are concerned with systems in which a chemical migrates from phase to phase. These phase changes involve input or output of energy, thus this energy exchange can compensate for entropy loss or gain. It can be shown that, whereas entropy maximization is the criterion of equilibrium for a system containing constant energy at constant volume, the criterion at constant temperature and pressure (the environmentally relevant condition) is minimization of the related function, the Gibbs free energy, which serves to combine energy and entropy in a common currency. Return to the example presented in Figure 5.1, of benzene diffusing from water into an air bubble and striving to achieve equilibrium. The basic concept is that, if we start with a benzene concentration in the water and none in air, the free energy of the system will decrease as benzene migrates from water to air, because the increase in free energy associated with the rise in benzene concentration in the air is less that of the decrease associated with benzene loss from the water. The process is thus spontaneous and irreversible. Benzene continues to diffuse from water into the air until it reaches a point at which the free energy increase in the air is exactly matched by the free energy decrease in the water. At this point, the system comes to rest or equilibrium. Likewise, if the system started with a higher benzene concentration in the air phase and approached equilibrium, it would reach exactly the same point of equilibrium with a particular ratio of concentrations in each phase. The system thus seeks a minimum in free energy at which its derivative with respect to moles of benzene is equal in both air and water phases. This derivative is of such importance that it is called the chemical potential. The underlying principle of phase equilibrium thermodynamics is that, when a solute such as benzene achieves equilibrium between phases such as air, water, and fish, it seeks to establish an equal chemical potential in all phases. The net diffusion flux will always be from high to low chemical potential. Thus, we can use chemical potential for deductions of mass diffusion in the same way that we use temperature in heat transfer calculations. 5.1.3

Fugacity

Unfortunately, chemical potential is logarithmically related to concentration, thus doubling the concentration does not double the chemical potential. A further complication is that a chemical potential cannot be measured absolutely, therefore it is necessary to establish some standard state at which it has a reference value. It was when addressing this problem that G.N. Lewis introduced a new equilibrium criterion in 1901, which he termed fugacity, and which has units of pressure and is assigned the symbol f. The term fugacity comes from the Latin root fugere, describing a “fleeing” or “escaping” tendency. It is identical to partial pressure in ideal gases and is logarithmically related to chemical potential. It is thus linearly or nearly linearly related to concentration. Absolute values can be established because, at low partial pressures under ideal conditions, fugacity and partial pressure become equal. Thus, we can replace the equilibrium criterion of chemical potential by that of fugacity. When benzene migrates between water and air, it is seeking to establish an equal fugacity in both phases; its escaping tendency, or pressures, are equal in both phases. ©2001 CRC Press LLC

Another useful quantity is the ratio of fugacity to some reference fugacity such as the vapor pressure of liquid benzene. This is a dimensionless quantity and is termed activity. Activity can also be used as an equilibrium criterion. This proves to be preferable for substances such as ions, metals, or polymers that do not appreciably evaporate and thus cannot establish vapor phase concentrations and partial pressures. Our task, then, is to start with a concentration of solute chemical in one phase, from this deduce the chemical potential, fugacity, or activity, argue that these equilibrium criteria will be equal in the other phase, and then calculate the corresponding concentration in the second phase. We therefore require recipes for deducing C from f and vice versa. This approach is depicted at the bottom of Figure 5.1. The partition coefficient approach contains the inherent assumption that, whatever the factors are that are used to convert C1 to f1 and C2 to f2, the ratio of these factors is constant over the range of concentration of interest. Thus, it is not actually necessary to calculate the fugacities; their use is sidestepped. In the fugacity approach, no such assumption is made, and the individual calculations are undertaken. We can illustrate these approaches with an example. Worked Example 5.1 Benzene is present in water at a specified temperature and a concentration C1 of 1 mol/m3 (78 g/m3). What is the equilibrium concentration in air C2? 1. Partition coefficient approach

K21 is 0.2, i.e., C2/C1 Therefore, C2 = K21C1 = 0.2 ¥ 1 = 0.2 mol/m3 = 15.6 g/m3 1. Fugacity approach

Using techniques devised later, we find that, for water under these conditions, f1

=

C1/Z1

=

C1/0.002 =

500 Pa

=

f2

C2

=

Z2f2

=

0.0004f2

0.2 mol/m3

=

15.6 g/m3

=

Clearly, the problem is to determine the conversion factors Z2 and Z1, or K21, which is their ratio. Care must be taken to avoid confusing K21 with its reciprocal K12 or C1/C2, which in this case has a value of 5. We therefore face the task of developing methods of estimating Z values that relate concentration and fugacity, and partition coefficients that are ratios of Z values. The theoretical foundations are set out in Section 5.3 and result in a set of working equations applicable to the air-water-octanol system. The three solubilities (or ©2001 CRC Press LLC

pseudo-solubilities) in these media and the three partition coefficients are then discussed in more detail in Section 5.4. Armed with this knowledge we then address how this “laboratory” information can be applied to environmental media such as soils and aerosols.

5.2 PROPERTIES OF PURE SUBSTANCES For reasons discussed later, it is important to ascertain if the substance of interest is solid, liquid, or vapor at the environmental temperature. This is obviously done by comparing this temperature with the melting and boiling points. Figure 5.2 is the familiar P-T diagram that enables the state of a substance to be determined. Of particular interest for solids is the supercooled liquid vapor pressure line, shown as a dashed line. This is the vapor pressure that a solid (such as naphthalene, which melts at 80°C) would have if it were liquid at 25°C. The reason it is not liquid at 25°C is that naphthalene is able to achieve a lower free energy state by forming a crystal. Above 80°C, this lower energy state is not available, and the substance remains liquid. Above the boiling point, the liquid state is abandoned in favor of a vapor state. It is not possible to measure the supercooled liquid vapor pressure by direct experiment. It can be calculated as discussed shortly, and it can be measured

Figure 5.2

P-T diagram for a pure substance.

©2001 CRC Press LLC

experimentally, but not directly, using gas chromatographic retention times. It is possible to measure the vapor pressure above the boiling point by operating at high pressures. Beyond the critical point, the vapor pressure cannot be measured, but it can be estimated. The triple-point temperature at which solid, liquid, and vapor phases coexist is usually very close to the melting point at atmospheric pressure, because the solidliquid equilibrium line is nearly vertical; i.e., pressure has a negligible effect on melting point. Melting point is easily measured for stable substances, and estimation methods are available as reviewed by Tesconi and Yalkowsky (2000). High melting points result from strong intermolecular bonds in the solid state and symmetry of the molecule. Ice (H20) has a high melting point compared to H2S because of strong hydrogen bonding. The symmetrical three-ring compound anthracene has a higher melting point (216°C) than the similar but unsymmetrical phenanthrene (101°C). The critical point temperature is of environmental interest only for gases, since it is usually well above environmental temperatures. For example, it is 305 K for ethane and 562 K for benzene. Its principal interest lies in its being the upper limit for measurement of vapor pressure. The location of the liquid-vapor equilibrium or vapor pressure line is very important, since it establishes the volatility of the substances, as does the boiling point, which is the temperature at which the vapor pressure equals 1 atmosphere. Methods of estimating boiling point have been reviewed by Lyman (2000), and methods of using boiling point to estimate vapor pressures at other temperatures have been reviewed by Sage and Sage (2000). For many substances, correlations exist for vapor pressure as a function of temperature. The simplest correlation is the two-parameter Clapeyron equation, ln P = A – B/T A and B are constants, and T is absolute temperature (K). B is DH/R, where DH is the enthalpy of vaporization (J/mol), and R is the gas constant. A better fit is obtained with the three-parameter Antoine equation, lnP = A – B/(T + C) Care must be taken to check the units of P, whether base e or base 10 logs are used, and whether T is K or °C in the Antoine equation. Several other equations are used as reviewed by Reid et al. (1987). Correlations also exist for the vapor pressure of solids and supercooled liquids. Of particular environmental interest is the relationship between these vapor pressures, which can be used to calculate the unmeasurable supercooled liquid vapor pressure from that of the solid. The reason for this is that, when a solid such as naphthalene is present in a dilute, subsaturated, dissolved, or sorbed state at 25°C, the molecules do not encounter each other with sufficient frequency to form a crystal. Thus, the low-energy crystal state is not accessible. The molecule thus behaves as if it were a liquid at 25°C. It “thinks” it is a liquid, because it has no ©2001 CRC Press LLC

access to information about the stability of the crystalline state, i.e., does not “know” its melting point. As a result, it behaves in a manner corresponding to the liquid vapor pressure. A similar phenomenon occurs above the critical point where a gas such as oxygen, when in solution in water, behaves as if it were a liquid at 25°C, not a gas. No liquid vapor pressure can be measured for either naphthalene or oxygen at 25°C; it can only be calculated. Later, we term this liquid vapor pressure the reference fugacity. We may need to know this fictitious vapor pressure for several reasons. The ratio of the solid vapor pressure to the supercooled liquid vapor pressure is termed the fugacity ratio, F. To estimate F, we need to know how much energy is involved in the solid-liquid transition, i.e., the enthalpy of melting or fusion. The rigorous equation for estimating F at temperature T(K) is (Prausnitz et al., 1986) ln F = –DS(TM – T)/RT + DCP(TM – T)/RT – DCP ln(TM/T)/R where DS (J/mol K) is the entropy of fusion at the melting point TM (K), DCP (J/mol K) is the difference in heat capacities between the solid and liquid substances, and R is the gas constant. The heat capacity terms are usually small, and they tend to cancel, so the equation can be simplified to ln F = –DS(TM – T)/RT = –(DH/TM)(TM – T)/RT = –(DH/R)(1/T – 1/TM) where DH (J/mol) is the enthalpy of fusion and equals TMDS. Note that, since TM is greater than T, the right-hand side is negative, and F is less than one, except at the melting point, when it is 1.0. F can never exceed 1.0. A convenient method of estimating DH is to exploit Walden’s rule that the entropy of fusion at the melting point DS, which is DH/TM, is often about 56.5 J/mol K. It follows that ln F = –(DS/R)(TM/T – 1) The group DS/R is often assigned a value of 56/8.314 or 6.79. Thus, F is approximated as F = exp[–6.79(TM/T – 1)] If base 10 logs are used and T is 298 K, this equation becomes log F = –6.79(TM/298 – 1)/2.303 = –0.01(TM – 298) This is useful as a quick and easily remembered method of estimating F. If more accurate data are available for DH or DS, they should be used, and if the substance is a high melting point solid, it may be advisable to include the heat capacity terms. ©2001 CRC Press LLC

5.3 5.3.1

PROPERTIES OF SOLUTES IN SOLUTION

Solution in the Gas Phase

Equations are needed to deduce the fugacity of a solute in solution from its concentration. We first treat nonionizing substances that retain their structure when in solution. It transpires that, at low concentrations, a substance’s fugacity and concentration are linearly related, i.e., fugacity is proportional to concentration. This suggests using a relationship of the following form: C = Zf where C is concentration (mol/m3), f is fugacity (Pa), and Z, the proportionality constant (termed the fugacity capacity) has units of mol/m3Pa. The aim is then to deduce Z for the substance in air, water, and other phases. Later, we examine the significance of Z in more detail, because it becomes a key quantity when assessing environmental partitioning. The easiest case is a solution in a gas phase (air) in which there are usually no interactions between molecules other than collisions. The basic fugacity equation as presented in thermodynamics texts (Prausnitz et al., 1986) is f = y f PT where y is mole fraction, f is a fugacity coefficient, PT is total (atmospheric) pressure, and P is yPT, the partial pressure. If the gas law applies, PTV = nRT or PV = ynRT Here, n is the total number of moles present, R is the gas constant, V is volume (m3), and T is absolute temperature (K). Now the concentration of the solute in the gas phase CA will be yn/V or P/RT mol/m3. CA = yPT/RT = (1/ fRT) f = ZAf Fortunately, the fugacity coefficient f rarely deviates appreciably from unity under environmental conditions. The exceptions occur at low temperatures, high pressures, or when the solute molecules interact chemically with each other in the gas phase. Only this last class is important environmentally. Carboxylic acids such as formic and acetic acid tend to dimerize, as do certain gases such as NO2. The constant ZA is thus usually (1/RT) or about 4 ¥ 10–4 mol/m3Pa and is the same for all noninteracting substances. The fugacity is thus numerically equal to the partial pressure of the solute P or yPT. This raises a question as to why we use the term fugacity in preference to partial pressure. The answers are that (1) under conditions when f is not unity, fugacity ©2001 CRC Press LLC

and partial pressure are not equal, and (2) there is some conceptual difficulty about referring to a “partial pressure of DDT in a fish” when there is no vapor present for a pressure to be present in—even partially. 5.3.2

Solution in Liquid Phases

The fugacity equation (Prausnitz et al., 1986) for solute i in solution is given in terms of mole fraction xi activity coefficient gi and reference fugacity fR on a Raoult’s law basis. fi = xigifR Now, xi, the mole fraction of solute, can be converted to concentration C mol/m3 using molar volumes v (m3/mol), amounts n (mol), and volumes V (m3) of solute (subscript i) and solution (subscript w for water as an example). Assuming that the solute concentration is small, i.e., Vi