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

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1. Heat (moles) in water = 10 ¥ 4.2 ¥ 10 = 420 J (moles) 72% 2. Heat (moles) in copper (air) = 5 ¥ 0.38 ¥ 10 = 19 J (moles) 33% 3. Heat (moles) in hydrogen (sediment) = 1 ¥ 14.3 ¥ 10 = 143 J (moles) 25% The concentrations are ©2001 CRC Press LLC Total = 582 J and 100% The distribution of heat (moles) is influenced by the relative phase masses (volumes) and the heat capacities (Z values). Despite the fact that the third phase is small, its much larger heat capacity (Z) results in accumulation of a substantial fraction of the total (25%), and its concentration is a factor of 3.4 and 38 greater than the other two phases—which is, of course, the ratio of the heat capacities (the ratio of Z values, this ratio being the partition coefficient). This example could have been solved using heat capacity partition coefficients but, of course, no such quantities are tabulated in handbooks. Indeed, any suggestion that heat partition coefficients are useful would be treated with derision. In environmental calculations, on the other hand, the use of Z is less conventional, and the use of partition coefficients is routine. In essence, the use of fugacity capacities is an attempt to bring to environmental calculations some of the procedural benefits that are routinely enjoyed by the use of heat capacities. Worked Example 5.8 Water 4.2 ¥ 10 = 42 J/g (mol/m 3 ) Copper (air) 0.38 ¥ 10 = 3.8 J/g (mol/m 3 ) Hydrogen (sediment) 14.3 ¥ 10 = 143 J/g (mol/m 3 ) A three-phase system has Z values Z 1 = 5 ¥ 10 –4 , Z 2 = 1.0, and Z 3 = 20 (all mol/m 3 Pa), and volumes V 1 = 1000, V 2 = 10, and V 3 = 0.1 (all m 3 ). Calculate the distributions, concentrations, and fugacity when 1 mol of solute is distributed at equilibrium between these phases. It is suggested that the calculations be done in tabular form. Phase Z V VZ C = Zf VC % 1 5 ¥ 10 –4 1000 0.5 4 ¥ 10 –5 0.04 4 2 1.0 10 10 0.08 0.80 80 3 20 0.1 2 1.6 0.16 16 Total 12.5 1.0 100 M = V 1Z 1f + V 2Z 2f + V 3Z 3f = f SV iZ i
Therefore, ©2001 CRC Press LLC f = M/SV iZ i = 1.0/12.5 = 0.08 Again, a large value of Z or C does not necessarily imply a large quantity. Quantity is controlled by VZ. Concentration is controlled by Z. 5.6.4 Sorption by Dispersed Phases A frequently encountered environmental calculation is the estimation of the fraction of a chemical that is present in a fluid that is sorbed to some dispersed sorbing phases within that fluid. This is a special case of multimedia partitioning involving only two phases. Examples are the estimation of the fraction of material attached to aerosols in air or associated with suspended solids or with biotic matter in water. The reason for this calculation is that the measured concentration is often of the total (i.e., dissolved and sorbed) chemical, and it is useful to know what fractions are in each phase. This is particularly useful when subsequently calculating uptake of chemical by fish from water in which the partitioning may be only from the dissolved solute. It is useful to establish the general equations describing sorption in such cases as follows. We designate the continuous phase by subscript A and the dispersed phase by subscript B. The dispersed phase volume is typically a factor of 10 –5 or less, as compared to that of the continuous phase. • The volumes (m 3 ) are denoted V A and V B, and usually V A is much greater than V B. • The equilibrium concentrations are denoted C A and C B mol/m 3 . • The dimensionless partition coefficient K BA is C B/C A. • The total amount of solute M moles is distributed between the two phases. M = V AC A + V BC B = V TC T where C T is the total concentration. It can be assumed that V T, the total volume is approximately V A. Now, Therefore, Therefore, C B = K BAC A M = C A(V A + V BK BA) = C TV A C A = C T/(1 + K BAV B/V A) = C T/(1 + K BAv B) where v B is the volume fraction of phase B and is approximately V B/V A. The fraction dissolved (i.e., in the continuous phase) is
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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.
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©2001 CRC Press LLC CHAPTER 3 Envi
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of other, somewhat similar or homol
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Table 3.2 List of Chemicals Commonl
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elatively high concentrations. This
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exists between toxicologists and ch
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determine priority. This is a subje
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Another important classification of
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Figure 3.1 (continued) ©2001 CRC P
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Table 3.5 (continued) dichlorometha
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Table 3.5 (continued) total PCB 326
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Figure 3.2 Plot of log K AW vs. log
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chlorofluoro compounds are very sta
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3.3.2.7 Arsenic Compounds Arsenic,
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Page 67 and 68: Figure 4.1 Evaluative environments.
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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
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Page 85 and 86: Another useful quantity is the rati
Page 87 and 88: experimentally, but not directly, u
Page 89 and 90: ©2001 CRC Press LLC 5.3 PROPERTIES
Page 91 and 92: 1.0. This, then, is the fugacity or
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: heat capacity of 0.38 J/g°C requir
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
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Page 141 and 142: eaction situation in which there is
Page 143 and 144: The rate constants in each case are
Page 145 and 146: ©2001 CRC Press LLC 1/t O = SD Ai/
Page 147 and 148: e achieved in 10 days. Detractors o
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Page 153 and 154: ©2001 CRC Press LLC 6.7 LEVEL II C
Page 155 and 156: Figure 6.3 Fugacity Level II calcul
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Page 159 and 160: Figure 7.1 Illustration of nonequil
Page 161 and 162: 5. Diffusion within soils, and from
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Page 165 and 166: ©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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