McKay, Donald. "Front matter" Multimedia Environmental Models ...

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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 x i activity coefficient g i and reference fugacity f R on a Raoult’s law basis. ©2001 CRC Press LLC f i = x ig if R Now, x i, the mole fraction of solute, can be converted to concentration C mol/m 3 using molar volumes v (m 3 /mol), amounts n (mol), and volumes V (m 3 ) of solute (subscript i) and solution (subscript w for water as an example). Assuming that the solute concentration is small, i.e., V i
1.0. This, then, is the fugacity or vapor pressure of pure liquid solute at the temperature (and strictly the pressure) of the system. The activity coefficient g is defined here on a “Raoult’s law” basis such that g is 1.0 when x is 1.0. In most cases, g values exceed 1.0 and, for hydrophobic chemicals, values may be in the millions. An alternative convention, which we do not use here, is to define g on a Henry’s law basis such that g is 1.0 when x is zero. The activity coefficient is thus a very important quantity. It can be viewed as the ratio of the activity or fugacity of the solute to the activity or fugacity that the solute would have if it were in a solution consisting entirely of its own kind. It depends on the concentration of the solute with a dependence of the type ©2001 CRC Press LLC log g = log g O (1 – x) 2 where g O is the activity coefficient at infinite dilution, i.e., when x the mole fraction approaches zero. Another useful way of viewing activity coefficients is that they can be regarded as an inverse expression of solubility, i.e., an insolubility. A solute that is sparingly soluble in a solvent will have a high activity coefficient, an example being hexane in water. For a liquid solute such as hexane, at the solubility limit, when excess pure hexane is present, the fugacity equals the reference fugacity f R and Therefore, f i = f R = x ig if R x i = 1/g i or g i = 1/x i The activity coefficient is thus the reciprocal of the solubility when expressed as a mole fraction. For solids at saturation, f i is the fugacity of the pure solid f S. Thus, and f S = x ig if R x i = (f S/f R)/g i = F/g i where F is the fugacity ratio discussed earlier. Solid solutes of high melting point thus tend to have low solubilities, because F is small. It is more common to express solubilities in units such as g/m 3 . Under dilute conditions, the solubility S i mol/m 3 is x i/v S, where v S is the molar volume of the solution (m 3 /mol) and approaches the molar volume of the solvent. S i is thus 1/g iv S for liquids and F /g iv S for solids. In the gas phase, the solubility is essentially the vapor pressure in disguise, i.e.,
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McKay, Donald. "Front matter" Multi
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Multimedia Environmental Models The
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hensive, and reliable, and they hav
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Chapter 1 Introduction Chapter 2 So
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McKay, Donald. "Introduction" Multi
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It is now evident that our task is
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McKay, Donald. "Some Basic Concepts
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give the derived units directly wit
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Energy (joule, J) The joule, which
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particles (aerosols), or biota in w
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Worked Example 2.1 A three-phase sy
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(i) What is the concentration (C) i
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Answer ©2001 CRC Press LLC 5.1 kg,
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or or When t is zero, C is zero, th
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What is the absolute minimum piscic
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©2001 CRC Press LLC C 1 = C O/(1 +
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containing nonequilibrium quantitie
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1. Fallout of chemical from air to
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validated using real environments.
Page 39 and 40: ©2001 CRC Press LLC CHAPTER 3 Envi
Page 41 and 42: of other, somewhat similar or homol
Page 43 and 44: Table 3.2 List of Chemicals Commonl
Page 45 and 46: elatively high concentrations. This
Page 47 and 48: exists between toxicologists and ch
Page 49 and 50: determine priority. This is a subje
Page 51 and 52: Another important classification of
Page 53 and 54: Figure 3.1 (continued) ©2001 CRC P
Page 55 and 56: Table 3.5 (continued) dichlorometha
Page 57 and 58: Table 3.5 (continued) total PCB 326
Page 59 and 60: Figure 3.2 Plot of log K AW vs. log
Page 61 and 62: chlorofluoro compounds are very sta
Page 63 and 64: 3.3.2.7 Arsenic Compounds Arsenic,
Page 65 and 66: McKay, Donald. "The Nature of Envir
Page 67 and 68: Figure 4.1 Evaluative environments.
Page 69 and 70: are subject to two important deposi
Page 71 and 72: metals and organic chemicals from w
Page 73 and 74: carbon figure for deeper sediments
Page 75 and 76: flows. The quality of this groundwa
Page 77 and 78: Table 4.2 Evaluative Environments A
Page 79 and 80: McKay, Donald. "Phase Equilibrium"
Page 81 and 82: Figure 5.1 Some principles and conc
Page 83 and 84: likely using an equilibrium criteri
Page 85 and 86: Another useful quantity is the rati
Page 87 and 88: experimentally, but not directly, u
Page 89: ©2001 CRC Press LLC 5.3 PROPERTIES
Page 93 and 94: where ©2001 CRC Press LLC pH is -l
Page 95 and 96: In terms of solubilities, S iA and
Page 97 and 98: The temperature coefficient is the
Page 99 and 100: (1982), Baum (1997) and Leo (2000).
Page 101 and 102: Although it may appear environmenta
Page 103 and 104: Figure 5.4 Illustration of quantita
Page 105 and 106: 5.5 ENVIRONMENTAL PARTITION COEFFIC
Page 107 and 108: C S = K PC W benzene = 1.1 ¥ 0.001
Page 109 and 110: Mackay (1986), in an attempt to sim
Page 111 and 112: Compartment Definition of Fugacity
Page 113 and 114: high concentration in the fish, but
Page 115 and 116: heat capacity of 0.38 J/g°C requir
Page 117 and 118: Therefore, ©2001 CRC Press LLC f =
Page 119 and 120: ©2001 CRC Press LLC Z T = S(V i/V
Page 121 and 122: ©2001 CRC Press LLC air Z = P S /R
Page 123 and 124: Table 5.1 Table 5.1 Summary of Defi
Page 125 and 126: Figure 5.7 Fugacity form 1 for dedu
Page 127 and 128: Calculate the following physical-ch
Page 129 and 130: ©2001 CRC Press LLC CHAPTER 6 Adve
Page 131 and 132: that all water will spend 100 days
Page 133 and 134: This enables us to conceive of, and
Page 135 and 136: ©2001 CRC Press LLC f = 15/0.5 = 3
Page 137 and 138: D AS dominates. A residence time of
Page 139 and 140: and Therefore, ©2001 CRC Press LLC
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eaction situation in which there is
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The rate constants in each case are
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©2001 CRC Press LLC 1/t O = SD Ai/
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e achieved in 10 days. Detractors o
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sulfate to sulfide or by dechlorina
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to Zepp and Cline (1977) for the or
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©2001 CRC Press LLC 6.7 LEVEL II C
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Figure 6.3 Fugacity Level II calcul
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McKay, Donald. "Intermedia Transpor
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Figure 7.1 Illustration of nonequil
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5. Diffusion within soils, and from
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sionally, the term flux rate is use
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©2001 CRC Press LLC N = ABDC/ Dy m
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no currents or eddies. In practice,
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diffusivity, and some unknown layer
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where ©2001 CRC Press LLC X = y/ U
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fraction of the total volume that i
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Figure 7.6 Mass transfer at the int
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partition coefficient. The signific
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and the series retains a similar ra
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ments of resuspension rates are par
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Figure 7.8 Movement of air phase (k
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ates can thus be used to estimate m
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Figure 7.9 Combination of D values
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Figure 7.10 Four-compartment Level
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Table 7.2 Order of Magnitude Values
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Unlike the Level II calculation, it
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Figure 7.12 Sample Level III output
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McKay, Donald. "Applications of Fug
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applications. Citations are given t
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Another approach is to employ Monte
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LEVEL1B A six-compartment Level I p
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Figure 8.1 Air-water exchange proce
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The total rates of transfer are thu
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Figure 8.2 Chemical transport and t
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mean. For chemical between depths o
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8.5.2 Process Description The water
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learn the benefits of using fugacit
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where Figure 8.5 QWASI model: stead
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are similar to those described by M
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C F ª Z Ff W ª 1.608 mol/m 3 ª 4
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y Mackay et al. (1983), and an appl
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accordingly, but the final solution
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Figure 8.10 Fish bioaccumulation pr
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The nature of the processes control
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iomagnification is more significant
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An alternative and more elegant met
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8.11.2 Model of a Chemical Evaporat
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Paterson et al. (1991), and Hung an
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8.14.1 Introduction ©2001 CRC Pres
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mated again in mg/day. Food, the ot
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models. Most interest is in LRT in
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available from the University of To
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McKay, Donald. "Appendix" Multimedi
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©2001 CRC Press LLC
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