7. TOXIC ORGANIC CHEMICALS

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.

2

• There are 4 million organic chemicals (IUPAC).
• 1000 new organic chemicals are synthesized
  each year.
• A fraction of these is toxic or
  carcinogenic, and the vast majority of them break
  down in the environment.
• If organics 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.
• Organic chemistry is the chemistry of compounds
  of carbon. Organic chemicals are obtained from
  material produced originally by living organisms
  (petroleum, coal, and plant residues) or they are
  synthesized from other organic compounds or
  inorganics (carbonates or cyanides).

3
7.1 NOMENCLATURE

• 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.

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

• In the environment, alkanes ? alcohol.
• 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.
• 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.

5

• Figure 7.2 shows some examples of cyclic organic
  chemicals that are sometimes difficult to degrade
  in the environment.

• 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.

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

• Drinking water standards. Organic chemicals for
  which maximum allowable drinking water standards
  have been established are shown in Figure 7.3.

• 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.

7
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.
• Biological transformations - 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. It does not have to be an oxidation
  reaction, nor does it have to yield carbon or
  energy for microbial growth or maintenance.

7.2.1 Biological Transformations
8

• The term "secondary substrate utilization" - the
  utilization of organic chemicals at low
  concentrations in the presence of one or more
  primary substrates that are used as carbon and
  energy sources.
• "Co-metabolism" - 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 wide variety of pesticides.
  Dehalogenation, dealkylation, hydrolysis,
  oxidation, reduction, ring cleavage, and
  condensation reactions are all known to occur
  either metabolically or via co-metabolism (see
  Table 7.1). In co-metabolism, the microbe does
  not even derive carbon or net energy from the
  degradation rather, the pesticide is caught up
  in the overall metabolic reactions as a
  detoxification or other enzymatic reaction.
• 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.

9
Table 7.1 Biological Transformations Common in
the Aquatic/Terrestrial Environment
10

• 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
• (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
  concentration yield/ organic concentration
  utilized
• KM Michaelis half saturation
  constant, M L-3.
• Typical cell concentrations in surface waters
  would be 106 107 cells mL-1 and less in
  groundwater

11
Table 7.2 Selected Biotransformation Rate
Constants.
12

• Under typical environmental conditions, the
  concentration of dissolved organics (C lt 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.
• 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 gtgt KM , 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.

13

• 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 for each of the
  congeners.

14

• 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.

15

• 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).

16
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, hydroxyl
  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.

17

• 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 110-12 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.

18
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
19

• 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.

20

• 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 azo 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.

21

• 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)

22

• 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.

23
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.

24

• 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.
25

• 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.
  Nitroreduction is a two-electron, two-proton
  transfer reaction.
• 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.

26
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..
27

• 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.

28
Table 7.5 Redox Half-Reactions Pertinent in
Wastewater, Groundwater, and Sediment Reactions
29
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
• - it loses its "extra" energy through energy
  emission, that is, fluorescence or
  phosphorescence
• - 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.

30

• 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
• f quantum yield
• I? sunlight intensity at wavelength ?,
  photons cm-2 s-1
• e? molar absorbtivity or molar extinction
  coefficient at wavelength ?,
• 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.

31

• The quantum yield is defined by
• (14)
• An einstein is the unit of light 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).

32

• 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.

33

• 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.

34
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.

35

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

36

• 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 ka and 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.

37
Table 7.7Selected Chemical Hydrolysis Rate
Constants, at 298 K and pH 7.
38
Figure 7.5Effect of pH on hydrolysis rate
constants.
39
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.

40

• Volatilization, as described by two-film theory,
  is a function of Henrys 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 ratio 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
• 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.
41

• 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/?z in which ?z 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)

42

• 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)

43

• We may think of the first 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.

44

• 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/Kd predominates.
• (34), (35)
• where CD is the dimensionless drag coefficient,
  W is the wind speed, and v is the kinematic
  viscosity.

45

• 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 a 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)

46

• 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-1 kgi 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.

47
Table 7.8 Kinematic Viscosity of Air
48
Table 7.9 Summary Table of Volatilization Data at
20 ºC
49
Table 7.9 (continued)
50

• Lyman et al. compiled solubility data on 78
  organic compounds and presented estimation
  methods based on Kow for different classes of
  compounds. They also included a method based on
  the molecular structure.
• Mackay measured Henry's constant for 22 organic
  chemicals as part of a study of volatilization
  characteristics.
• Transfer coefficients for the gas and liquid
  phases were correlated for environmental
  conditions as
• (42)
• (43)
• Where U10 is the 10-m wind velocity (m s-1), ScL
  and ScG are the dimensionless liquid and gas
  Schmidt numbers.
• Volatile compounds such as those shown in Figure
  7.3a are easily removed from water and wastewater
  by purging with air or by passing them through an
  air stripping tower. In natural waters, they are
  removed by stripping from the atmosphere.
• The overall mass transfer coefficient KL can be
  related to that of oxygen (Table 7.10) because so
  much information exists for oxygen transfer in
  natural waters.

51
Table 7.10 Estimated Henrys Constant and Mass
Transfer Coefficients for Selected Organics at 20
ºC
52
7.2.7 Sorption Reaction

• Soluble organics in natural waters can sorb onto
  particulate suspended material or bed sediments.
  The mechanism and the processes by which this
  occurs include
• - physical adsorption due to van der Waals
  forces
• - chemisorption due to a chemical bonding or
  surface coordination reaction
• - partitioning of the organic chemical into the
  organic carbon phase of the particulates.
• Physical adsorption is purely a surface
  electrostatic phenomenon. Partitioning refers to
  the dissolution of hydrophobic organic chemicals
  into the organic phase of the particulate matter
  it is an absorption phenomenon rather than a
  surface reaction, and it may occur slowly over
  time scales of minutes to days.
• Adsorption isotherms refer to the equilibrium
  relationship of sorption between organics and
  particulates at constant temperature. The
  chemical is dissolved in water in the presence of
  various concentrations of suspended solids. After
  an initial kinetic reaction, a dynamic
  equilibrium is established in which the rate of
  the forward reaction (sorption) is exactly equal
  to the rate of the reverse reaction (desorption).

53

• The sorption of toxicants to suspended
  particulates and bed sediments is a significant
  transfer mechanism. Partitioning of a chemical
  between particulate matter and the dissolved
  phase is not a transformation pathway it only
  relates the concentration of dissolved and sorbed
  states of the chemical.
• The octanol/water partition coefficient, Kow, is
  related to the solubility of a chemical in water.
  
• Tables 7.9 and 7.11 provide log Kow values for a
  number of organic chemicals of environmental
  interest.

Table 7.11 Octanol/Water Partition Coefficients
of Selected Organics, 298 K
54

• The laboratory procedure for measuring Kow is
  given by Lyman.
• 1. Chemical is added to a mixture of pure
  octanol (a nonpolar solvent) and - pure water (a
  polar solvent). The volume ratio of octanol and
  water is set at the estimated Kow.
• 2. Mixture is agitated until equilibrium is
  reached.
• 3. Mixture is centrifuged to separate the two
  phases. The phases are analyzed for the chemical.
• 4. Kow is the ratio of the chemical
  concentration in the octanol phase to chemical
  concentration in the water phase, and has no
  units. The logarithm of Kow has been measured
  from -3 to 7.
• If the octanol/water partition coefficient cannot
  be reliably measured or is not available in
  databases, it can be estimated from solubility
  and molecular weight information,
• (44)
• where MW is the molecular weight of the pollutant
  (g mol-1) and S is in units of ppm for organics
  that are liquid in their pure state at 25 ºC.

55

• For organics that are solid in their pure state
  at 25 ºC,
• (45)
• where MP is the melting point of the pollutant
  (ºC) and ?Sf is the entropy of fusion of the
  pollutant (cal mol-1 deg-1).
• The octanol/water partition coefficient is
  dimensionless, but it derives from the
  partitioning that occurs in the extraction
  between the chemical in octanol and water.
• Octanol was chosen as a reference because it is a
  model solvent with some properties that make it
  similar to organic matter and lipids in nature.
• For a wide variety of organic chemicals, the
  octanol water partition coefficient is a good
  estimator of the organic carbon normalized
  partition coefficient (Koc).

56

• Karickhoff et al. and Schwarzenbach and Westall
  have published useful empirical equations for
  predicting Koc as a function of Kow
• (46)
• (47)
• Once an estimate of Koc is obtained, the
  calculation of a sediment/water partition
  coefficient suitable for natural waters is
  straightforward because the
• (48)
• where foc is the decimal fraction of organic
  carbon present in the particulate matter
  (mass/mass).
• Figure 7.7 is a schematic of how Kp, Koc, and Kow
  are interrelated. Figure 7.7 is the Langmuir
  adsorption isotherm for sorption of one chemical
  on particulate matter.

57
Figure 7.7Relationship between the
sediment/water partition coefficient Kp, the
organic carbon partition coefficient Koc, and the
octanol/water partition coefficient Kow.Plot (a)
and (b) are for only one chemical and (c) is for
many chemicals.
58

• Kp is a measure of the actual partitioning in
  natural waters.
• The linear portion of the adsorption isotherm
  (Figure 7.7a) can be expressed by equation
• (49)
• The Langmuir isotherm in Figure 7.7a is derived
  from the kinetic eqn for sorption-desorption
• (50), (51)
• where C is the concentration of dissolved
  toxicant, Cp is the concentration of particulate
  toxicant, Cpc is the maximum adsorptive
  concentration of the solids, and k1 and k2 are
  the adsorption and desorption rate constants,
  respectively.

59

• At steady-state, eqn (51) reduces to a Langmuir
  isotherm in which the amount adsorbed is linear
  at low dissolved toxicant concentrations but
  gradually becomes saturated at the maximum value
  (rc) at high dissolved concentrations.
• (52)
• Generally, the adsorption capacity of sediments
  is inversely related to particle size clays gt
  silts gt sands. Sorption of organic chemicals is
  also a function of the organic content of the
  sediment, as measured by Koc, and silts are most
  likely to have the highest organic content.
• Sometimes a Freundlich isotherm is inferred from
  empirical data. The function is of the form
• (53)
• where n is usually greater than 1. In dilute
  solutions, when n approaches 1, the Freundlich
  coefficient, K, is equal to the partition
  coefficient, Kp.

60

• The partition coefficient is derived from
  simplification of the kinetic eqns (50) and (51)
  if rc gtgt r (the linear portion of the Langmuir
  isotherm). In this case, we may write
• (54a), (54b)
• Where kf is the adsorption rate constant and kr
  is the desorption rate constant.
• The total concentration of toxicant
• (55)
• Where fd and fp are the dissolved and particulate
  fractions, respectively
• and the ratio of the reaction rate constants is
  related by
• (58)
• Where the 8 subscripts indicate chemical
  equilibrium.

(56), (57)
61

• From kinetics experiments where dissolved and
  particulate concentrations are monitored over
  time, the ratio of steady-state concentrations
  can be read from the graph (Figure 7.8).
• Sorption reactions usually reach chemical
  equilibrium quickly, and the kinetic
  relationships can often be assumed to be at
  steady-state. This is sometimes referred to as
  the "local equilibrium" assumption, when the
  kinetics of adsorption and desorption are rapid
  relative to other kinetic and transport processes
  in the system.
• O'Conner and Connolly first reported that, for
  organics and metals alike, the sediment/water
  partition coefficient Kp declines as sediment
  (solids) concentrations increase. It is a
  consistent phenomenon in natural waters that is
  particularly important for hydrophobic organic
  chemicals. For example, the Kp for a chemical in
  sediments is much lower than that observed in the
  water column. Most researchers attribute this
  fact to artifacts in the way that one attempts to
  measure Kp, including complexation of a chemical
  by colloids and dissolved organic carbon that
  pass a membrane filter.

62
Figure 7.8 Kinetic sorption experiment in a
batch reactor
63
7.2.8 Bioconcentration and Bioaccumulation

• Bioconcentration of toxicants is defined as the
  direct uptake of aqueous toxicant through the
  gills and epithelial tissues of aquatic
  organisms. This fate process is of interest
  because it helps to predict human exposure to the
  toxicant in food items, particularly fish.
• Bioconcentration is part of the greater picture
  of bioaccumulation and biomagnification that
  includes food chain effects. Bioaccumulation
  refers to uptake of the toxicant by the fish from
  a number of different sources including
  bioconcentration from the water and biouptake
  from various food items (prey) or sediment
  ingestion. Biomagnification refers to the process
  whereby bioaccumulation increases with each step
  on the trophic ladder.
• The terms bioconcentration, bioaccumulation, and
  biomagnification are sometimes mistakenly used
  interchangeably. It is useful to accept the
  following definitions for the sake of discussion.

64

• Bioconcentration the uptake of toxic organics
  through the gill membrane and epithelial tissue
  from the dissolved phase.
• Bioaccumulation the total biouptake of toxic
  organics by the organism from food items
  (benthos, fish prey, sediment ingestion, etc.) as
  well as via mass transport of dissolved organics
  through the gill and epithelium.
• Biomagnification that circumstance where
  bioaccumulation causes an increase in total body
  burden as one proceeds up the trophic ladder from
  primary producer to top carnivore.
• Bioconcentration experiments measure the net
  bioconcentration effect after x days, having
  reached equilibrium conditions, by measuring the
  toxicant concentration in the test organism. The
  BCF (bioconcentration factor) is the ratio of the
  concentration in the organism to the
  concentration in the water.

65

• The BCF derives from a kinetic expression
  relating the water toxicant concentration and
  organism mass
• (59)
• where e efficiency of toxic absorption at the
  gill
• k1 (L filtered/kg organism per day)
• k2 depuration rate constant
  including excretion and clearance of metabolites,
  day-1
• C dissolved toxicant, µg L-1
• B organism biomass, kg L-1
• F organism toxicant residue (whole
  body), µg kg-1
• Steady-state solution is
• (60)
• where BCF has units of (µg/kg)/(µg/L).
• Bioconcentration is analogous to sorption of
  hydrophobic organics. Organic chemicals tend to
  partition into the fatty tissue of fish and other
  aquatic organisms, and BCF is analogous to the
  sediment/water partition coefficient, Kp.
• Bioconcentration also can be measured in algae
  and higher plants, where uptake occurs by
  adsorption to the cell surfaces or sorption into
  the tissues.

66

• An empirical relationship for bioconcentration
  (BCF-Kow) in bluegill sunfish in 28 days exposure
  for 84 organic priority pollutants was
• (61)
• and for rainbow trout with ten chlorobenzenes it
  was
• (62)
• for low-level exposures typical of natural
  waters. Fathead minnow, bluegill, rainbow trout,
  brook trout, and mosquito fish are the species
  most frequently involved in bioconcentration
  tests.
• Bioconcentration experiments, per se, do not
  measure the metabolism or detoxification of the
  chemical. Chemicals can be metabolized to more or
  less toxic products that may have different
  depuration characteristics. The bioconcentration
  experiment only measures the final body burden at
  equilibrium (although interim data that were used
  to determine when equilibrium was reached may be
  available).
• The fact that a chemical bioaccumulates at all is
  an indication that it resists biodegradation and
  is somewhat "biologically hard" or "nonlabile."

67

• The kinetics of bioaccumulation are shown
  schematically in Figure 7.9.
• Fish can lose unmetabolized toxics via biliary
  excretion or "desorption" through the gill. On
  the other hand, toxic organics can undergo
  biotransformations and be eliminated as metabolic
  products.
• The rate constant, k2, includes total depuration
  (both excretion of unmetabolized toxics, k2, and
  elimination of metabolites, k2). Only a
  fraction of this elimination is returned to the
  water column as dissolved parent compound,
  designated as k2 in Figure 7.9.
• Hydrophobic organics tend to accumulate in fatty
  tissue of animals. Lipid normalized
  bioconcentration factors both in the laboratory
  and in the field have been correlated
  successfully with the hydrophobicity of toxic
  organics as measured by the octanol/water
  partition coefficient, Kow (Table 7.12).
  Biomagnification occurs in lake trout for PCBs in
  the Great Lakes due to the contribution of
  alewife and small fish to the diet of these top
  carnivores.

68
Figure 7.9 Bioaccumulation kinetics for
hydrophobic organic chemicals in fish
69
Table 7.12Bioconcentration Factor (BCF) for
Selected Organic Chemicals in Fish (Units µg/kg
fish- µg L water)
70
7.2.9 Comparison of Pathway

• Most of the transformations discussed in Section
  7.2 are expressed as second-order reactions. It
  is difficult to compare the magnitudes of these
  reactions-the rate constants all have different
  units. Each of the transformations can be written
  as pseudo-first-order reactions assuming that the
  second concentration in the reaction rate
  expression can be assumed to be relatively
  constant.
• The overall reaction rate
• (63)
• where C dissolved organic concentration, ML-3
• t time, T
• kb biotransformation rate constant,
  T-1
• ko oxidation rate constant, T-1
• kr reduction rate constant, T-1
• kp photolysis rate constant, T-1
• kh hydrolysis rate constant, T-1
• kv volatilization rate constant, T-1

71

• Equation (63) includes an assumption that the
  atmosphere has a neg1igible concentration
  (partial pressure) of the organic, so only
  volatilization occurs (stripping out of the water
  body).
• For first-order reactions in a batch reactor
  without transport, the reaction rate
• (64)
• Solving for the concentration as a function of
  time
• (65), (66)
• Taking the natural logarithm of both sides of
  equation (66) and solving for time (half-life)
  yields the well-known relationship below
• (67)
• where t1/2 overall half-life of the chemical
  due to all transformation reactions
• the sum of all the
  pseudo-first-order reaction rate constants
• Individual half-lives may be compared to
  determine which reaction predominates (gives the
  shortest half-life).

72
7.3 ORGANIC CHEMICALS IN LAKES 7.3.1
Completely Mixed Systems

• As an approximation, lakes can be represented as
  ideal completely mixed flow through reactors (CMF
  systems) or a network of CMF compartments.
• A mass balance system of equations
• Figure 7.10 a schematic of the various reactions
  in the lake water column and sediment.
• An assumption of local equilibrium may be used to
  relate the particulate adsorbed concentration to
  the dissolved concentration through the partition
  coefficient Kp.
• (68)
• where Kp sediment/water partition
  coefficient, L kg-1
• C dissolved organic chemical
  concentration, µg L-1
• r mass sorbed, µg kg-1
• M suspended or bed solids
  concentration, kg L-1
• Cp particulate adsorbed concentration, µg L-1
• CT total (dissolved plus particulate)
  concentration, µg L-1

73
Figure 7.10 Schematic of a fate model for
organic chemicals in water and sediment
74

• Sorptive equilibrium is usually a valid
  assumption in natural waters because the time
  scale for most sorption reactions (minutes to
  hours) is small compared to the time scale for
  reactions and transport (days to years).
• Figure 7.10 indicates a rapid local equilibrium
  assumption for bioconcentration. If uptake and
  depuration kinetics (hours to days) are fast
  relative to other reactions and time scales, this
  is a valid assumption. Use of the
  bioconcentration factor (BCF) helps to simplify
  the equations, and it is another partitioning
  coefficient that we may use similar to Kp.
• (69)
• where BCF bioconcentration factor, L kg-1
• C dissolved chemical
  concentration, µg L-1
• F residue concentration in whole
  fish, µg kg-1
• The total concentration of chemical CT may be
  larger or smaller in the sediment than the
  overlying water depending on whether the water
  column or sediment was contaminated first.
  Partitioning of the chemical between the
  dissolved pore water C2 and adsorbed sediment
  Cp2, may also be different due to the dependence
  of Kp2, on solids concentration. Generally, Kp2 lt
  Kp1, because the sediment has a much higher
  solids concentration.

75

• A framework for a mass balance model for an
  organic chemical in a lake is given by Figure
  7.10. Waste inputs, their fate and effects, can
  be assessed in this context.
• Anthropogenic inputs may also enter the water
  body from the atmosphere via wet precipitation
  and dry deposition. The concentration in rainfall
  is related to the gas phase concentration and
  Henry's constant, so the deposition mass is equal
  to the volume of rainfall times the aqueous phase
  concentration
• (70)
• Where Cprecip is the precipitation
  concentration, Cg is the gas phase concentration,
  and H is Henry's constant with the appropriate
  units.
• The flux of contaminants due to dry deposition is
  related to the depositional velocity and the
  gaseous concentration
• (71)
• where vd is the deposition velocity (LT-1), Cg is
  the gas phase concentration (ML-3) and Jd is the
  areal mass flux due to dry deposition (ML-2T-1).
• Equation (71) is empirical. Both gases and
  aerosol particles may contribute to dry
  deposition but the gas phase concentration should
  be proportional in either case, vd serving as the
  empirical proportionality constant.

76

• The mass balance equation for a lake with toxic
  organic chemical inputs can be written assuming
  complete mixing, steady flow conditions,
  instantaneous local sorption equilibrium, and no
  atmospheric deposition.
• (72)
• Equation (72) has three unknown dependent
  variables CT, and C - but the assumption of
  local equilibrium allows us to write the equation
  entirely in terms of total (whole water,
  unfiltered) concentration.
• (73)
• where CT total concentration C Cp, ML-3
• V volume of the lake, L3
• t time, T
• Q flowrate in and out, L3T-1
• fp particulate fraction of total
  chemical concentration, dimensionless
• Cp/ CT KpM /(1 KpM)
• fd dissolved fraction of total
  chemical concentration, dimensionless
• C/ CT 1 /(1 KpM)
• C dissolved chemical concentration, ML-3
• Cp particulate chemical concentration,
  ML-3
• ks sedimentation rate constant,T-1

77

• Equation (73) is an ordinary differential
  equation with constant coefficients. It is
  solvable by first-order methods such as the
  integration factor method. Dividing through by
  the constant volume and rearranging, we have
• (74)
• The final solution is
• (75)
• where CTo initial total input concentration,
  ML-3
• a integration factor
• t mean hydraulic detention time
  V/Q, T
• We see that the solution to a continuous input of
  organic chemical to a lake is composed of two
  terms in equation (75) the first term is the
  die-away of initial conditions, and the second
  term is the asymptotic "hump" (the shape of a
  Langmuir isotherm), which builds to a
  steady-state concentration as t ? 8.
• (76)
  
  
• The steady-state concentration is directly
  proportional to the total concentration of
  organic inputs to the lake.

78

• Because it takes an infinite amount of time (or
  the lake to reach steady state in the strictest
  sense, we speak of time to 95 of steady state,
  that is, the length of time required for the
  concentration in the lake to reach 95 of the
  value that it will ultimately achieve.
• (77)
• or
• (78)
• By inspection, one can prove that equations (75)
  and (78) are equal when
• (79)
• Equation (79) gives the time to 95 of steady
  state. For the simplest case of a nonadsorbing
  dissolved chemical undergoing first-order
  reaction decay, a k 1/t.
• The greater is the flushing rate ( 1/t) and the
  reaction rate constant, the less is time required
  to achieve steady state. Conservative substances
  (k 0) take the longest time to reach steady
  state after a step function change in inputs.

79
Figure 7.13Schematic of lake recovery from a
persistent hydrophobic pollutant
7.3.2 Dieldrin Case Study in Coralville
Reservoir, Iowa

• The following case study is used to illustrate
  aspects of ecosystem recovery from a persistent
  hydrophobic organic pollutant. It also
  demonstrates the use of compartmentalization
  within a lake to simulate transport.
• Figure 7.13 a schematic of water column,
  sediment, and fish concentrations following a
  period when large discharges of chemical were put
  into the system. Because the contaminant is
  hydrophobic and persistent, it remains in the
  system for a long time, accumulating in fish
  tissue and sediment. It disappears by washout
  (advection), burial into the deep sediment, and
  slow degradation reactions. Depending on the
  sediment dynamics of the system and the rate of
  chemical degradation, these can be slow processes
  taking years to decades.

80
Figure 7.14Selected insecticides used in the
past in the midwestern United States

• Figure 7.14 some persistent insecticides (e.g.
  chlorinated hydrocarbons) used in the Midwest.
  These chemicals were banned in the 1970s and
  early 1980s because of their persistence and
  propensity to bioaccumulate in fish and wildlife.
  Also shown are two replacement insecticides
  (ester compounds), which hydrolyze and break down
  in the environment. They are toxic but much less
  persistent.

81

• Agricultural usage of pesticides in Iowa is
  widespread, particularly grass and broadleaf
  herbicides and row crop soil insecticides. One of
  the insecticides widely used for control of the
  corn rootworm and cutworm from 1960 to 1975 was
  the chlorinated hydrocarbon, aldrin.
• Aldrin is microbially metabolized to its
  persistent epoxide, dieldrin. Dieldrin is itself
  an insecticide of certain toxicity and is also a
  hydrophobic substance of limited solubility in
  water (0.25 ppm) and low vapor pressure (2.7
  10-6 mm Hg at 25 ºC). It is known to
  bioaccumulate to levels as high as 1.6 mg/kg wet
  weight in edible tissue of Iowa catfish.
• Coralville Reservoir is a mainstream impoundment
  of the Iowa River in eastern Iowa. It drains
  approximately 3084 square miles (7978 km2) of
  prime Iowa farmland and receives extensive
  agricultural runoff with 90 of its drainage
  basin in intensive agriculture. It is a
  variable-level, flood control and recreational
  reservoir, which has undergone considerable
  sedimentation since it was created in 1958.
• At conservation pool (680 ft above mean sea
  level, msl), the reservoir has a capacity of
  38,000 acre-ft (4.79 107 m3), a surface area of
  4900 acres (1.98 107m2), a mean depth of
  approximately 8 ft (2.44 m), and a mean detention
  time of 14 days. In 1958, the capacity at
  conservation pool was 53,750 acre-ft (6.63 107
  m3).

82

• The total pesticide concentration is the sum of
  the particulate plus the dissolved
  concentrations, with instantaneous sorptive
  equilibrium assumed
• (80)
• where fd C/ CT 1/(1 KpM) fraction of
  dissolved pesticide
• fp Cp/ CT KpM/(1 KpM) fraction
  of particulate pesticide
• W(t) time-variable loading of
  pesticide, M/T
• CT total concentration in the water
  column, ML-3
• sum of the pseudo-first-order
  degradation rate constants
• t mean hydraulic detention time
• V reservoir volume, L3
• ks sedimentation rate constant, T-1
• The fish residue equation is
• (81)
• where k1 pesticide uptake rate by fish, T-1

83

• Equations (80) and (81) may be solved
  analytically for constant coefficients and simple
  pesticide loading functions, W(t), or they may be
  integrated numerically. In the case of a
  pesticide ban, the W(t) might typically decline
  in an exponential manner due to degradation by
  soil organisms or a ban on application.
• For an exponentially declining loading function
  at rate ?, the analytical solutions to equations
  (80) and (81) are
• (82)
• (83)
• where CTo initial total pesticide
  concentration in lake, ML-3
• CTin,o initial total pesticide inflow
  concentration, ML-3
• ? rate of exponentially declining
  inflow concentration,T-1

84
Figure 7.15Compartmental configuration for a
two-box pond model or an eight-box lake model

• Figure 7.15 is a schematic diagram of
  hypothetical pond or lake configurations that are
  possible for this problem. Each box is assumed to
  be completely mixed with bulk exchange between
  water compartments. There is dispersion in
  Coralville Reservoir that seems to be simulated
  best by the eight-compartment model based on dye
  studies.

85
Figure 7.16Result of model and field data for
dieldrin in Coralville Reservoi