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  1. 7. TOXIC ORGANIC CHEMICALS If we live as if it matters and it doesn't master, it doesn't matter. If we live as if it doesn't matter, and it matters, then it matters. - The Precautionary Principle, International Conference on an Agenda of Science for Environment and Development Into the 21 st Century, Vienna, Austria (1991)

  2. There are 4 million organic chemicals with names given by the International Union of Pure and Applied Chemistry (IUPAC). Approximately 1000 new organic chemicals are synthesized and used commercially each year. Only a fraction of these prove to be toxic or carcinogenic, and the vast majority of them break down in the environment. • If they do not, if they are persistent as wel1 as toxic, we may need to use mathematical models to determine if they pose an unreasonable risk to humans or the environment. We estimate their fate and transport in the environment, their exposure concentration to humans and wildlife, and perform waste load allocations to meet water quality standards. • Organic chemistry is the chemistry of compounds of carbon. Organic chemicals are obtained from material produced originally by living organisms (such as petroleum, coal, and plant residues) or they are synthesized from other organic compounds or inorganics (e.g., carbonates or cyanides).

  3. 7.1 NOMENCLATURE • There are many different ways to name organic compounds including common names, lUPAC names, and trade names. Figure 7.1 shows some classes of organic compounds that are widely used. The left-hand side of the figure gives some general classes of compounds and the right-hand side is a specific example of each. • In the environment, alkanes are slowly oxidized to form an alcohol, beginning a chain of reactions. • These reactions are usually microbially mediated (enzymes catalyze the reactions), but other abiotic processes such as photolysis, hydrolysis, chemical oxidation or reduction may also be important. • Microbial "infallibility" would state that all organic chemicals that are synthesized can be mineralized all the way to carbon dioxide and water as shown above. But many synthetic compounds have not been shown to degrade in the environment, or they might degrade extremely slowly, or only under special conditions.

  4. Figure 7.1 Some common classes of organic compounds (left) and examples (right). R and R` indicate different alkyl group.

  5. Microbes are not infallible, although given the proper conditions, enough time, and in concert with other physical and chemical reactions, they can often help to break down most organic chemicals. On the other hand, microbes and plants can sometimes synthesize chemicals in nature that are quite toxic and rather slow to degrade. • Chlorinated organic chemicals are not purely man-made (xenobiotics), but now we know that some chlorinated organic chemicals are synthesized by plants and quite common in nature. • To oxidize benzene to carbon dioxide and water requires that the very stable benzene ring must be cleaved. Under anaerobic conditions this can be a difficult task. • There are many toxic organic chemicals that cause problems in the environment and comprise various "priority pollutant" lists. One of the most important lists is that for drinking water standards. Organic chemicals for which maximum allowable drinking water standards have been established are shown in Figure 7.3.

  6. Figure 7.2 Examples of cyclic organic compounds (including alicyclic, aromatic, and heterocyclic compounds).

  7. Figure 7.3 (a) Volatile organic compounds that have maximum contaminant level (MCL) drinking water standards. (b) Some synthetic organic chemicals for which maximum contaminant levels (MCLs) have been established.

  8. Figure 7.3 (continued).

  9. 7.2 ORGANICS REACTIONS • The types of reactions: biological transformations, chemical hydrolysis, oxidation/reduction, photodegradation, volatilization. sorption, and bioconcentration are among the important reactions that organic chemicals undergo in natural waters. 7.2.1 Biological Transformations • Biological transformations refer to the microbially mediated transformation of organic chemicals, often the predominant decay pathway in natural waters. It may occur under aerobic or anaerobic conditions, by bacteria, algae, or fungi, and by an array of mechanisms (dealkylation, ring cleavage, dehalogenation, etc.). It can be an intracellular or extracellunar enzyme transformation. • The term "biodegradation" is used synonymously with "biotransformation," but some researchers reserve "biodegradation" only for oxidation reactions that break down the chemical. Reactions that go all the way to CO2 and H2O are referred to as "mineralization." In the broadest sense, "biotransformation" refers to any microbially mediated reaction that changes the organic chemical.

  10. The term "secondary substrate utilization" refers to the utilization of organic chemicals at low concentrations (less than the concentration required for growth) in the presence of one or more primary substrates that are used as carbon and energy sources. "Co-metabolism" refers to the transformation of a substrate that cannot be used as a sole carbon or energy source but can be degraded in the presence of other substrates. • Many toxic organic reactions in natural waters are microbially mediated with both bacteria and fungi degrading a wade variety of pesticides. Dehalogenation, dealkylation, hydrolysis, oxidation, reduction, tong cleavage, and condensation reactions are all known to occur either metabolically or via co-metabolism (see Table 7.1). • Several bacterial genera are known that are capable of utilizing certain organics as the sole carbon, energy, or nitrogen source. Pseudomonas (with 2,4-D and paraquat), Nocardia (with dalapon and propanil), and Aspergillus species (with trifluralin and picloram) are poignant examples.

  11. Table 7.1 Biological Transformations Common in the Aquatic/Terrestrial Environment

  12. It is convenient when possible to express rate expressions for organic transformations as pseudo-first-order-reactions, such as equation (1) below. The reaction rate expression is then (1) • where C is the toxic organic concentration in solution and kb is the pseudo-first-order biotransformation rate constant. • Table 7.2 is a summary of pseudo-first-order and second-order rate constants kb for the disappearance of toxic organics from natural waters and groundwater via biotransformation. • The actual microbial biotransformation rate follows the Monod or Michaelis-Menton enzyme kinetics expression, where (2) • Where: kb = pseudo-first-order biological transformation rate constant,T-1; μ = maximum growth rate, T-1; X = viable microbial biomass concentration, M L-3; Y = cell yield, microbial cell conc yield/ organic conc utilized; KM = Michaelis half saturation constant, M L-3.

  13. Table 7.2 Selected Biotransfor-mation Rate Constants.

  14. Under typical environmental conditions, the concentration of dissolved organics (C < 10 μg L-1) is less than that of the Michaelis half-saturation constant (KM ≈ 0.1-10 mg L-1). Therefore the equation becomes (3a) • where kb`= μ/YKM. This is essentially second-order biotransformation kinetics. It is first order in bacteria biomass (X) and first order in chemical concentration (C). • Sometimes organic chemicals that are adsorbed to suspended particulate matter are biodegraded in addition to soluble chemical. Equation (3a) must be rewritten in terms of both dissolved and adsorbed chemical concentrations (3b) • where CT is the total whole water chemical concentration, C is the dissolved phase concentration. and Cp is the particulate adsorbed concentration. • If the substrate concentration C is very large such that C >> KM (not likely in natural waters), then the microorganisms are growing exponentially, and the rate expression in equation (2) reduces to (4) • which is a zero-order rate expression in C and first-order in X.

  15. Biotransformation experiments are conducted by batch, column, and chemostat experimental methods. Other fate pathways (photolysis, hydrolysis, volatilization) must be accounted for in order to correctly evaluate the effects of biodegradation. • It is incumbent on the fate modeler to understand the range of breakdown products (metabolites) in biological transformation reactions. Metabolites can be as toxic (or more toxic) than the parent compound. • Following all the metabolites and pathways in the biological degradation of organic chemicals can be complicated. Polychlorinated biphenyls (PCBs) are mixtures of many isomers - the total number of different organic chemicals is 209 congeners. • Figure 7.3b shows the structures, where x and y represent the combinations of chlorine atoms (one to five) at different positions on the biphenyl rings. Each congener has distinct properties that result in a different reactivity than the others. Both the rate of the biological transformation and the pathway can be different far each of the congeners.

  16. There are several basic types of biodegradation experiments. Natural water samples from lakes or rivers can have organic toxicant added to them in batch experiments. Disappearance of toxicant is monitored. • Organic xenobiotic chemicals can be added to a water-sediment sample to simulate in situ conditions, or a contaminated sediment sample alone may be used with or without a spiked addition. Primary sewage, activated sludge, or digester sludge may be used as a seed to test degradability and measure xenobiotic disappearance. • Radiolabeled organic chemicals can be used to estimate metabolic degradation (mineralization) by measuring CO2 off-gas and synthesis into biomass. These experiments are called heterotrophic uptake experiments. • The organic chemical may be added in minute concentrations to simulate exposure in natural conditions, or it may be the sole carbon source to the culture to determine whether transformation reactions are possible.

  17. Biodegradation is affected by numerous factors that influence biological growth: • Temperature: effects on biodegradation of toxics are similar to those on biochemical oxygen demand (BOD) using an Arrhenius-type relationship. • Nutrients: are necessary for growth and often limit growth rate. Other organic compounds may serve as a primary substrate so that the chemical of interest is utilized via co-metabolism or as a secondary substrate. • Acclimation: is necessary for expressing repressed (induced) enzymes or fostering those organisms that can degrade the toxicant through gradual exposure to the toxicant over time. A shock load of toxicant may kill a culture that would otherwise adapt if gradually exposed. • Population density or biomass concentration: organisms must be present in large enough numbers to significantly degrade the toxicant (a lag often occurs if the organisms are too few).

  18. 7.2.2 Chemical Oxidation • Chemical oxidation takes place in the presence of dissolved oxygen in natural waters. Oxygen is reduced and the organic chemical is oxidized, but the reaction can be slow. Alternatively, chemical oxidation can be triggered by photochemical transients that may have considerable oxidizing power but low concentrations. • Oxidants such as peroxyl radicals ROO·, alkoxy radicals RO·, hydrogen peroxide H2O2, hydrokyl radicals ·OH, singlet oxygen O2, and solvated electrons are produced in low concentrations and react quickly in natural waters. Because of their large oxidizing power, they may react with a variety of trace organics in solution, but each transient reacts rather specifically with certain trace organic moieties. • It is better to determine the relevant oxidant chemistry and to measure the oxidant concentration when possible. Since the transient chemical oxidants are often generated photochemically, light-absorbing chromophores, such as humic and fulvic acids and algal pigments, and sunlight intensity will influence oxidation rates.

  19. Alkyl peroxyl radicals (∼1 × 10-9 M in sunlit natural waters) react rapidly with phenols and amines in natural waters to form acids and aromatic radicals: • Singlet oxygen reacts specifically with olefins: • Singlet oxygen concentrations in sunlit natural waters are on the order of 1×10-12 M. All of these oxidation reactions may be assumed to be second-order reactions: (5) • where C is the organic concentration and Ox is the oxidant concentration. • Table 7.3: the second-order rate constants for chemical oxidation of selected priority organic chemicals with singlet oxygen and alkyl peroxyl radicals.

  20. Table 7.3 Second-Order Reaction Rate Constants for Chemical Oxidation: Summary Table of Oxidation Data with Singlet Oxygen O2 and Alkyl Peroxyl Radicals ROO∙

  21. Free radical oxidation requires a chain or series of reactions involving an initiation step, propagation, and subsequent termination. We will illustrate the free radical reaction using the alkyl peroxyl radical ROO· as an example.

  22. The chemical is represented as an arbitrary organic, RH. A-B is the initiator, which is any free radical source including peroxides, H2O2, metal salts, and auto compounds. Investigators have utilized a commercially available azo initiator to estimate the reactivity of pesticides to ROO· in natural waters. • If no initiators are available in the water, then reaction (c) represents the probable oxidation pathway, a slow reaction with dissolved oxygen. Otherwise steps (a) and (b) lead to peroxide formation, step (d). Once the highly reactive peroxide radical is formed, it continues to react with the organic chemical, RH, and regenerates another free radical, R', as given in reaction (e). • This step may be repeated thousands of times for every photon of light absorbed. Chance collisions between free radicals can terminate the reaction, reactions (f), (g), and (h). At the low pollutant concentrations found in natural waters, reaction (f) is the most likely termination step. Hydrogen peroxide may also be formed, especially when natural dissolved organic matter (DOC) and humates are present. H2O2 is a powerful oxidant in natural waters.

  23. If the initiation step is rapid, then the rate-limiting step is the rate of oxidation of the organic in reaction (e): (6) • Provided that reaction (d) is more raped than reaction (e), the rate of peroxide formation is (7) • and assuming steady state, the rate of radical be equal to the rate of termination: (8), (9) • Substituting equation (9) into equation (6), we find the final reaction rate for the oxidation of the organic chemical is (10)

  24. The rate of reaction is a pseudo-first-order reaction, where k3 is the overall reaction rate constant which is a function of rf, the rate of peroxide formation. If the rate of peroxide formation is relatively constant (as expected in natural waters), then the free radical oxidation of the toxic organic can be computed as a pseudo-first-order reaction. • First-order oxidations of pesticides and organic chemicals have been reported in natural waters. However, these oxidations are often microbially mediated. Strictly chemical free radical oxidation of toxic organics in natural waters remains important for a few classes of compounds. Free radical oxidation is often a part of the photolytic cycle of reactions in natural waters and atmospheric waters. • Oxidations of organic chemicals by O2(aq) is generally slow, but it can be mediated by microorganisms. Cytochrome P450 monooxygenase is a well-studied enzyme with an iron porphyrin active site. Methanotrophs and other organisms can use this pathway to oxidize organics in natural waters, a type of biological transformation.

  25. 7.2.3 Redox Reactions • Electron acceptors such as oxygen, nitrate, and sulfate can be reduced in natural waters while oxidizing trace organic contaminants. Oxidation reactions of toxic organic chemicals are especially important in sediments and groundwater, where conditions may be anoxic or anaerobic. The general scheme for utilization of electron acceptors in natural waters fort lows thermodynamics (Table 7.4). • The sequence of electron acceptors is approximately: • The organic chemical in Table 7.4 is represented as a simple carbohydrate (CH2O such as glucose C6H12O6) but other organics may be important reductants in natural waters and groundwaters.

  26. Strict chemical reduction reactions that do not involve a biological catalyst (abiotic reactions) are common in groundwater but less important in natural waters and sediments, where a great complement of enzymes are available for redox transformations. In groundwater, H2S is a common reductant. It can reduce nitrobenzene to aniline in homogeneous reactions. Table 7.4 Redox Reactions in a Closed Oxidant System at 25ºC and pH 7.0 and Their Free Energies of Reaction.

  27. Likewise, humic substances and their decay products (natural organic matter, NOM) are good reductants in homogeneous systems. • Figure 7.4 is a structure-activity relationship demonstrating that, in homogeneous solution, the second-order kinetic rate constant kAB is directly proportional to the one-electron reduction potential of the redox couple. (11) • where H2X is the reductant. • Schwarzenbach et al. have shown that, in the case of juglone, it is not the diprotic dihydroquinone H2JUG that is the reactant with nitroaromatics, but rather the anions HJUG- and JUG2-. Reductants in natural waters include quinone, juglone (oak tree exudate), lawsone, and Fe-porphyrins. • The reduction of nitroaromatic compounds in natural waters and soil water may be viewed as an electron transfer system that is mediated by NOM or its constituents.

  28. Figure 7.4 Liner free-energy relationship between second-order rate constant and the one electron potential for reduction of substituted nitrobenzenes with natural organic matter (Juglone). From Schwarzenbach, et al..

  29. Natural organic matter contains electron transfer mediators such as quinones, hydroquinones, and Fe-porphyrin-like substances. • These mediators are reactants that are regenerated in the process by the bulk reductant, which is in excess. • One can add half-reactions of xenobiotic organic oxidations with standard reductants in sediments and groundwater (H2S, Fe2+, and CH4) to determine if the reaction is favored thermodynamically (Table 7.5). In the absence of bacteria, the reaction may be slow.

  30. Table 7.5 Redox Half-Reactions Pertinent in Wastewater, Groundwater, and Sediment Reactions

  31. Table 7.5 (continued)

  32. 7.2.4 Photochemical Transformation Reactions • Direct photolysis, a light-initiated transformation reaction, is a function of the incident energy on the molecule and the quantum yield of the chemical. • When light strikes the pollutant molecule, the energy content of the molecule is increased and the molecule reaches an excited electron state. This excited state is unstable and the molecule reaches a normal (lower) energy level by one of two paths: - (1) it loses its "extra" energy through energy emission, that is, fluorescence or phosphorescence; - (2) it is converted to a different molecule through the new electron distribution that existed in the excited state. Usually the organic chemical is oxidized. • Photolysis may be direct or indirect. Indirect photolysis occurs when an intermediary molecule becomes energized, which then reacts with the chemical of interest.

  33. The basic equation for direct photolysis is of the form: (12) • Where C is the concentration of organic chemical, and kp is the rate constant for photolysis. Photo1ysis rate constants can be measured in the yield with sunlight or under laboratory conditions. • The first-order rate constant, kp can be estimated directly: (13) • where kp = photolysis rate constant, s-1 J = 6.02 × 1020 = conversion constant φ = quantum yield Iλ = sunlight intensity at wavelength λ, photons cm-2 s-1 ελ = molar absorbtivity or molar extinction coefficient at wavelength λ, molarity-1 cm-1. • The near-surface photolysis rate constants, quantum yields, and wavelengths at which they were measured are presented in Table 7.6. Photolysis will not be an important fate process unless sunlight is absorbed in the visible or near-ultraviolet wavelength ranges (above 290 nm) by either the organic chemical or its sensitizing agent.

  34. The quantum yield is defined by (14) • An einstein is the unit of fight on a molar basis (a quantum or photon is the unit of light on a molecular basis). The quantum yield may be thought of as the efficiency of photoreaction. Incoming radiation is measured in units of energy per unit area per time (e g., cal cm-2 s-1). The incident light in units of einsteins cm-2 s-1 nm-1 can be converted to watts cm-2 nm-1 by multiplying by the wavelength (nm) and 3.03 × 1039. • The intensity of light varies over the depth of the water column and may be related by (15) • where Iz is the intensity at depth z, I0 is the intensity at the surface, and Ke is an extinction coefficient for light disappearance. • Light disappearance is caused by the scattering of light by reflection off particulate matter, and absorption by any molecule. Absorbed energy can be converted to heat or can cause photolysis. Light disappearance is a function of wavelength and water quality (e.g., color, suspended solids, dissolved organic carbon).

  35. Indirect or sensitized photolysis occurs when a nontarget molecule is transformed directly by light, which, in turn, transmits its energy to the pollutant molecule. Changes in the molecule then occur as a result of the increased energy content. • The kinetic equation for indirect photolysis is (16) • where k2 is the indirect photolysis rate constant, X is the concentration of the nontarget intermediary, and kp is the overall pseudo-first-order rate constant for sensitized photolysis. • The important role of inducing agents (e.g., algae exudates and nitrate) has been demonstrated. • Inorganics, especially iron, play an important role in the photochemical cycle in natural waters. Hydrogen peroxide, a common transient oxidant, is a natural source of hydroxyl radicals in rivers, oceans, and atmospheric water droplets.

  36. Direct photolysis of H2O2 produces ·OH, but this pathway is relatively unimportant because H2O2 does not absorb visible light very strongly. The important source of ·OH involves hydrogen peroxide and iron (II) in a photo-Fenton reaction. • Hydroxyl radicals are a highly reactive and important transient oxidant of a wide range of organic xenobiotics in solution. They can be generated by direct photolysis of nitrate and nitrite in natural waters, or they can be generated from H2O2 in the reaction shown above. Nitrobenzene, anisole, and several pesticides have been shown to be oxidized by hydroxyl radicals in natural waters.

  37. 7.2.5 Chemical Hydrolysis • Chemical hydrolysis is that fate pathway by which an organic chemical reacts with water. Particularly, a nucleophile (hydroxide, water, or hydronium ions), N, displaces a leaving group, X, as shown. • Hydrolysis does not include acid-base, hydration, addition, or elimination reactions. The hydrolysis reaction consists of the cleaving of a molecular bond and the formation of a new bond with components of the water molecule (H+, OH-). It is often a strong function of pH (see Figure 7.5). • Three examples of a hydrolysis reaction are presented below.

  38. Types of compounds that are generally susceptible to hydrolysis are: - Alkyl halides - Amides - Amines - Carbamates - Carboxylic acid esters - Epoxides - Nitriles - Phosphonic acrid esters - Phosphoric acid esters - Sulfonic acid esters - Sulfuric acid esters • The kinetic expression for hydrolysis is

  39. A summary of these data is presented in Table 7.7. • Hydrolysis experiments usually involve fixing the pH at some target value, eliminating other fate processes, and measuring toxicant disappearance over time. A sterile sample in a glass tube, filled to avoid a gas space, and kept in the dark eliminates the other fate pathways. In order to evaluate kaand kb, several non-neutral pH experiments must be conducted as depicted in Figure 7.5. • Often, the hydrolysis reaction rate expression in equation (17) is simplified to a pseudo-first-order reaction rate expression at a given pH and temperature (Table 7.7, 298 K and pH 7). (18) • where kh = kb [OH-] + ka [H+] + kn and kh is the pseudo-first-order hydrolysis rate constant, T-1; kb is the base-catalyzed rate constant, molarity-1 T-1; ka is the acid-catalyzed rate, polarity-1 T-1 ; and kn is the neutral rate constant, T-1.

  40. Table 7.7Selected Chemical Hydrolysis Rate Constants, at 298 K and pH 7.

  41. Figure 7.5Effect of pH on hydrolysis rate constants.

  42. 7.2.6 Volatilization/Gas Transfer • The transfer of pollutants from water to air or from air to water is an important fate process to consider when modeling organic chemicals. Volatilization is a transfer process; it does not result in the breakdown of a substance, only its movement from the liquid to gas phase, or vice versa. • Gas transfer of pollutants is analogous to the reaeration of oxygen in surface waters and will be related to known oxygen transfer rates. The rate of volatilization is related to the site of the molecule (as measured by the molecular weight). • Gas transfer models are often based on two-film theory (figure 7.6). Two-film theory was derived by Lewis and Whitman in 1923. Mass transfer is governed by molecular diffusion through a stagnant liquid and gas film. Mass moves from areas of high concentration to areas of low concentration. Transfer can be limited at the gas film or the liquid film. • Oxygen, for example, is controlled by the liquid-film resistance. Nitrogen gas, although approximately four times more abundant in the atmosphere than oxygen, has a greater liquid-film resistance than oxygen.

  43. Volatilization, as described by two-film theory, is a function of Henry`s constant, the gas-film resistance, and the liquid-film resistance. The film resistance depends on diffusion and mixing. Henry's constant, H, is a ratio of a chemical's vapor pressure to its solubility. It is a thermodynamic radio of the fugacity of the chemical (escaping tendency from air and water). (19) • where pg is the partial pressure of the chemical of interest in the gas phase, and Csl is its saturation solubility. • Henry's constant can be "dimensionless" [mg/L (in air)/mg/L (in water)] or it has units of atm m3 mol-1. Figure 7.6 Two-film theory of gas-liquid interchange.

  44. The value of H can be used to develop simplifying assumptions for modeling volatilization. If either the liquid-film or the gas-film controls - that is, one resistance is much greater than the other - the lesser resistance can be neglected. • The flux of contaminants across the boundary can be modeled by Fick's first law of diffusion at equilibrium, (20) • where D is the molecular diffusion coefficient and dC/dx is the concentration gradient in either the gas or liquid phase. • If we consider the molecular diffusion to occur through a thin stagnant film, the mass flux is then (21) • where k = D/Δz in which Δz is the film thickness and k is the mass transfer coefficient with units of LT-1. • At steady state, the flux through both films of Figure 7.6 must be equal: (22)

  45. If Henry's law applies exactly at the interface, we can express the concentrations in terms of bulk phase concentrations, which are measurable by substitution below: (23) (24) (25) • By rearranging equation (25), we can solve for N in terms of bulk phase concentration, mass transfer coefficients for each phase, and Henry's constant: (26) • where KL is the overall mass transfer coefficient derived for expression of the gas transfer in terms of a liquid phase concentration. (27)

  46. We may think of the thirst term on the right-hand side of the equation as a liquid-film resistance and the second term as a gas phase resistance using an electrical resistance analogy. • We can compare the two resistances to determine if the (28) • gas phase resistance, rg, or the liquid phase resistance, rl, predominates. • Equivalently, we could choose to write the overall mass transfer in terms of the buck gas phase concentration. (29), (30) • If the gas is soluble, then H is small and the gas-film resistance controls mass transfer. • In terms of a differential equation, the overall gas transfer: (31) • where Csat = pg/H, A is the interfacial surface area, and V is the volume of the liquid.

  47. In streams, A/V is the reciprocal depth of the water and the equation can be expressed as (32) • where Z is the mean depth and kli is termed the volatilization rate constant (T-1). • Equations (31) and (32) apply for either gas absorption or gas stripping from the water body. It is a reversible process. • The mass transfer coefficients are dependent on the hydrodynamic characteristics of the air-water interface and flow regime. For flowing water, we may write (33) • where u is the mean stream velocity and Z is the mean depth. • For smooth flow (no ripples or waves) and wind speed less than 5 ms-1, 1/Kδ predominates. (34), (35) • where CD is the dimensionless drag coefficient, W is the wind speed, and v is the kinematic viscosity.

  48. The transfer term for aerodynamically rough flow with wave is (36) • where d is the diameter or amplitude of the waves, u* is the surface shear velocity and α is a constant dependent on the physics of the wave properties. • The diffusion coefficients in water and air have been related to molecular weight (37) • where Dl is the diffusivity of the chemical in water and MW is the molecular weight, and (38) • where Dg is the diffusivity of the chemical in air. • The mass transfer rate constant, kli, can then be related to the oxygen reaeration rate, ka, by a ratio of the diffusivity of the chemical to that of oxygen in water: (39) • where DO2 is 2.4 × 10-5 cm2 s-1 at 20 ºC.

  49. The reaeration rate, ka, can be calculated from any of the formulas available. In addition, the overall gas-film transfer rate may be calculated from (40) • Where vg is the kinematic viscosity of all (a function of temperature) as presented in Table 7.8, Z is the water depth, and W is the wind speed in m s-1kgi has units of T-1. • Solubility, vapor pressure, and Henry's constant data are presented in Table 7.9. • Dimensionless Henry's constant refer to a concentration ratio of mg/L air per mg/L in the water phase. • Yalkowsky measured the solubility of 26 halogenated benzenes at 25 ºC and developed the following relationship: (41) • Where Sw is solubility (mol L-1), MP is the melting point (ºC), and Kow is the estimated octanol/water partition coefficient.

  50. Table 7.8 Kinematic Viscosity of Air