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

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access to information about the stability of the crystalline state, i.e., does not “know” its melting point. As a result, it behaves in a manner corresponding to the liquid vapor pressure. A similar phenomenon occurs above the critical point where a gas such as oxygen, when in solution in water, behaves as if it were a liquid at 25°C, not a gas. No liquid vapor pressure can be measured for either naphthalene or oxygen at 25°C; it can only be calculated. Later, we term this liquid vapor pressure the reference fugacity. We may need to know this fictitious vapor pressure for several reasons. The ratio of the solid vapor pressure to the supercooled liquid vapor pressure is termed the fugacity ratio, F. To estimate F, we need to know how much energy is involved in the solid-liquid transition, i.e., the enthalpy of melting or fusion. The rigorous equation for estimating F at temperature T(K) is (Prausnitz et al., 1986) ©2001 CRC Press LLC ln F = – DS(TM – T)/RT + DCP(TM – T)/RT – DCP ln(TM/T)/R where DS (J/mol K) is the entropy of fusion at the melting point TM (K), DCP (J/mol K) is the difference in heat capacities between the solid and liquid substances, and R is the gas constant. The heat capacity terms are usually small, and they tend to cancel, so the equation can be simplified to ln F = – DS(TM – T)/RT = –( DH/TM)(TM – T)/RT = –( DH/R)(1/T – 1/TM) where DH (J/mol) is the enthalpy of fusion and equals TMDS. Note that, since TM is greater than T, the right-hand side is negative, and F is less than one, except at the melting point, when it is 1.0. F can never exceed 1.0. A convenient method of estimating DH is to exploit Walden’s rule that the entropy of fusion at the melting point DS, which is DH/TM, is often about 56.5 J/mol K. It follows that The group mated as ln F = –(DS/R)(TM/T – 1) DS/R is often assigned a value of 56/8.314 or 6.79. Thus, F is approxi- F = exp[–6.79(TM/T – 1)] If base 10 logs are used and T is 298 K, this equation becomes log F = –6.79(TM/298 – 1)/2.303 = –0.01(TM – 298) This is useful as a quick and easily remembered method of estimating F. If more accurate data are available for DH or DS, they should be used, and if the substance is a high melting point solid, it may be advisable to include the heat capacity terms.
©2001 CRC Press LLC 5.3 PROPERTIES OF SOLUTES IN SOLUTION 5.3.1 Solution in the Gas Phase Equations are needed to deduce the fugacity of a solute in solution from its concentration. We first treat nonionizing substances that retain their structure when in solution. It transpires that, at low concentrations, a substance’s fugacity and concentration are linearly related, i.e., fugacity is proportional to concentration. This suggests using a relationship of the following form: C = Zf where C is concentration (mol/m3), f is fugacity (Pa), and Z, the proportionality constant (termed the fugacity capacity) has units of mol/m3Pa. The aim is then to deduce Z for the substance in air, water, and other phases. Later, we examine the significance of Z in more detail, because it becomes a key quantity when assessing environmental partitioning. The easiest case is a solution in a gas phase (air) in which there are usually no interactions between molecules other than collisions. The basic fugacity equation as presented in thermodynamics texts (Prausnitz et al., 1986) is f = y f PT where y is mole fraction, f is a fugacity coefficient, PT is total (atmospheric) pressure, and P is yPT, the partial pressure. If the gas law applies, P TV = nRT or PV = ynRT Here, n is the total number of moles present, R is the gas constant, V is volume (m 3 ), and T is absolute temperature (K). Now the concentration of the solute in the gas phase C A will be yn/V or P/RT mol/m 3 . C A = yP T/RT = (1/ fRT) f = Z Af Fortunately, the fugacity coefficient f rarely deviates appreciably from unity under environmental conditions. The exceptions occur at low temperatures, high pressures, or when the solute molecules interact chemically with each other in the gas phase. Only this last class is important environmentally. Carboxylic acids such as formic and acetic acid tend to dimerize, as do certain gases such as NO 2. The constant Z A is thus usually (1/RT) or about 4 ¥ 10 –4 mol/m 3 Pa and is the same for all noninteracting substances. The fugacity is thus numerically equal to the partial pressure of the solute P or yP T. This raises a question as to why we use the term fugacity in preference to partial pressure. The answers are that (1) under conditions when f is not unity, fugacity
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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
Page 37 and 38: 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,
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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
Page 83 and 84: likely using an equilibrium criteri
Page 85 and 86: Another useful quantity is the rati
Page 87: experimentally, but not directly, u
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 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
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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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