Calculating fugacity This approach helps, with great accuracy, to elucidate chemical behavior profiles, determine dominant fate processes, and establish which emironmental data are required
Donald Mackay
Sally Paterson Department of Chemical Engineering and Applied Chemistry University of Toronto Toronto, Ontario M5S 1A4 Canada Reasons for developing and improving the capability of estimating the behavior of chemical substances in the environment are obvious. There have been numerous cases in which the health of humans and other organisms has been adversely affected by the indiscriminate emission or formation of chemicals that are biologically active. Chemicals that are persistent, are subject to accumulation in biota, and that move through the environment by unexpected pathways are of particular concern. The general issue has been reviewed in recent texts by Haque (I), Neely (Z), and Thibodeaux (3). A detailed calculation procedure will be presented for predicting mass and concentration distributions, reaction characteristics, and persistence
of a chemical released into a model or evaluative environment. This approach, described previously by Mackay ( 4 ) , has undergone some recent modification and may be useful for elucidating the likely behavior of new, commercial chemicals. I t is important to define the limitations and objectives of such a model. The real environment is very complex, and only small sections of it, such as a pond or a stretch of river, can be modeled adequately. Complex models are unlikely to play a significant r e g ulatory role, since considerable effort must be devoted to understanding the calculations. Moreover, there is an increased probability of undetected error. Baughman and Lassiter ( 5 ) introduced the concept of the evaluative model, in which no attempt is made to simulate the real environment. The aim is, rather, to provide behavioral information characteristic of the substance: for example, the relative amounts of substance that will partition into each environmental medium, the relative concentrations in these media, the dominant reactions, the
overall persistence, and the principal intermedia transport processes. Smith et al. (6) illustrated this approach for I 1 substances of environmental interest. It is rarely possible to calculate actual environmental concentrations since these vary spatially and temporally. A typical behavior profile is that, when emitted into water, the substance tends to partition between water, sediment, atmosphere, and biota in the approximate proportions 20, 20, 60, and 0.1, respectively; the concentrations in sediment and biota are approximately 500 and 1000 times those in the water column; the dominant degradation processes are atmospheric photolysis (about 70%) and aquatic photolysis (about 20%), with other reactions contributing around 10%; and the overall half-life of the substance is 10 days. Fate information in such simple terms is invaluable for regulatory purposes: indeed, it is difficult to conceive how regulation can be effective in its absence. The model calculation is merely a stepping stone to stateme+ ;* which the available data are
Calculations, some concepts “escaping tendency” of a chemical substance from a Dhase. It has units of
2 depends on temperature. pressure. the nature of the substance, and the medium in which it is oresent. Its COnCenkatim dependencb is us slight at high dikrtions.
Physical slgnlficance OIL It quantifies the capacity of t phase fafugacity.At a given fugacity. if 2 is low, Cis low, end only a srnali amount of substance is necessary to
1006 Environmental Science &Technology
in water i t room i e k a t u r e 15-1.5 mol/& a m (i.e.. O.WO.2). In air it is 40 &/in3 atm (i.e.. 8/0.2), a ratio of about 27. Oxygen then adopts a con-
Conclusion: if we can find ?, fa a substance for each environmental
0013-936X/81/0915-1006$01.25/0
@ 1981 American Chemical Society
systematically processed by the use o equations that have inherent physica. validity. Equilibrium criteria A substance such as benzene, when at equilibrium, adopts different concentrations in air, water, sediment, and other phases or media. The ratio of these concentrations-for example, the air-water partition coefficient -can be expressed in various forms, the most convenient being Henry’s law constant, H (in [Pa.m3]/mol), which is the ratio of partial pressure in the atmosphere, P (in Pa), to concentration in water, C (in mol/m3). For sorption on sediments, the partition coefficient K , is used. Other examples of coefficients in environmental studies are bioconcentration factors between water and aquatic biota, and octanol-water partition coefficients. For each substance or solute, a partition coefficient can be defined for each pair of environmental phases. It is more illuminating to express these equilibrium partitioning situations in terms of the fundamental quantity that controls the differing concentrations. Gibbs showed that diffusive equilibrium of a solute between two phases occurs when the chemical potentials of the solute in the phases are equal. This topic is discussed fully in texts on thermodynamics-for example, that by Praucnitz (7). Lewis (8) introduced fugacity as more convenient criterion for equilibrium between phases. Whereas chemical potential has units of energy per mole, which is conceptually difficult to grasp, fugacity has units of pressure (Pa) and can be viewed as the “escaping tendency” that a substance exerts from any given phase. In the atmosphere, fugacity is usually equal to the partial pressure of the substance. Equilibrium is achieved between two phases when the “escaping tendency” from one phase exactly matches that from the other. There may be transfer or exchange of solute between the two phases but the net rate of exchange is zero. A convenient property of fugacity is that it is usually linearly related to concentration at the low concentrations that normally apply to environmental contaminants. It is thus possible to write a fugacity-concentration relationship:
Eaulllbrium Before the model is examined, usefulto clarify the concepts of e librium and steady state as they a to me calculations. This is iiiustr
and steady state
is at a rate exactly balanced by an inflow (emission). The tanks (media) are in equilia*m (equal fuoacb),but their contents are changing. the levels
(fugacities)adjusticg to values such
that there is no net change of amount
an average residence time (perSl5
cificcase
1 c C
C=fZ where C i s concentration (mol/m3);f is fugacity (Pa); and Z is a “fugacity capacity” ([molm3]/Pa). For conceptual purposes, it may be Volume 15, Number 9, September 1981
1007
helpful to consider the analogous situation of equilibrium of heat between two phases. Heat achieves equilibrium between two phases at different heat concentrations, expressed as J/m3. The criterion of equilibrium is that the temperatures of the two phases are equal. Temperature, like fugacity, is a “potential” quantity that determines the relative state of the phases with respect to equilibrium. The relationship between heat concentration and temperature is the simple volumetric heat-capacity relationship: CH = TZH where CH is heat concentration (J/ m3); 2, is a volumetric heat capacity (J/[m3.K]) (which is actually the product of the more commonly used mass heat capacity and the phase density); and T is temperature (K). Whereas heat tends to accumulate in the phases where heat capacity is largest, mass tends to accumulate in phases where fugacity capacity is largest. Apparently, hydrophobic organics tend to partition into lipid phases because that is where their 2 value is largest. If there are two phases, then equilibrium of a substance will be reached when the fugacities are equal, that is: fl = f 2
Thus:
CdZ1 = C2P2 or CdC2 = 2 1 / 2 2 = K12 The dimensionless partition coefficient controlling the distribution of the substance between the two phases ( K I ~is)merely the ratio of the fugacity capacities. The elegance of this approach is apparent if one considers a 10-phase system in which there are potentially 90 definable partition coefficients that are constrained in value with respect to each other such that only nine can be defined independently. There are only 10 fugacity capacities, and the 90 partition coefficients are merely all possible ratios of those 10 values. Expressing equilibrium in terms of fugacity capacities is more convenient because it separates the escaping tendencies of the chemical from each phase and facilitates the calculation of these quantities from other related thermodynamic data.
Fugacity capacities In what follows, fugacities will be developed for the atmosphere, water, sorbed phases, biotic phases, an octano1 phase, and pure solid and liquid 1008 Environmental Science & Technology
phases. If the chemical is at equilibrium between all phases, then: fa = f w = f s
=fB
=f
The atmosphere. In the vapor phase, the fugacity is rigorously expressed by: f = y$PT P where y is the substance’s (solute’s) mole fraction; PT is the total pressure (Pa) (here atmospheric pressure); and 4 is the fugacity coefficient, which is dimehsionless and is introduced to account for nonideal behavior. Fortunately, at atmospheric pressure, $ is usually close to unity and can thus be ignored. The exceptions are solutes, such as carboxylic acids, that associate in the vapor phase. The fugacity is thus equivalent, in most cases, to the partial pressure, P. It should be noted that this equation assumes the solute to be in truly gaseous form, not associated with particles. Concentration C is related to partial pressure through the gas law: C=n/V=P/RT=fIRT=fZ Thus, Za for vapors is simply 1 / R T and has a value of 4.04 X lod4 mol/ (m3.Pa), corresponding to R of 8.31 (Pa.m3)/(mol.K) (or J/ [mol-K]), and a temperature of 25 OC (298 K). Za is independent of the nature of the solute or the composition of the vapor (for nonassociating solutes and low- or atmospheric-pressure conditions) and has an obvious temperature dependence. Water. In aqueous solution, the fugacity is given by: f = xyPS where x is the mole fraction; Ps is the vapor pressure of the pure liquid solute at the system temperature; and y is the liquid-phase activity coefficient on a Raoult’s law convention (not a Henry’s law convention). By this convention, when x is unity, y is also unity, and f becomes the pure liquid state component vapor pressure. Generally, for nonionizing substances, y increases to an “infinite dilution” value as x tends to zero. This relationship between x and y is often of the form: In y = K(l - x ) ~ In most environmental situations, x is quite small; thus, In y can be equated to K without serious error. This nearconstancy in y leads to the very convenient near-linear relationship between C and f,reflected as a constant value in Z . The relationship betweenf and C to give Z for infinite dilution conditions can be obtained by writing:
Z = C / f = C/P = 1/H = x/vwf = 1/ V W Y P S where v, is the molar volume (m3/ mol) of the solution, which is approximately that of water (1.8 X m3/mol). For water, Z , is simply the reciprocal of Henry’s law constant, H . This is in accord with the definition of H , which is the constant by which liquid concentration is multiplied to give partial pressure, P, which is here equated to fugacity: P=HC Since H is important in fugacity calculations, it is desirable to elucidate certain conditions under which this simple approach may be applied incorrectly . First, these equations are applicable only if the solute is in truly dissolved forms at a concentration less than or equal to saturation. Often, the solute is present environmentally in solution in a sorbed form associated with suspended mineral or organic matter. Very hydrophobic compounds, such as polychlorinated biphenyls (PCBs) or polynuclear aromatic hydrocarbons (PAHs), may be present in colloidal form at a total concentration in excess of their solubility. Such forms of solute are effectively in another phase and do not contribute to the solution fugacity. It is thus essential to ensure that a measured concentration is truly dissolved; if this is not the case, the fraction which is dissolved must be calculated. Second, there are several methods of measuring or estimating H . In principle, these reduce to the direct or indirect measurement of P and C at equilibrium, or to the separate calculation of H , using the saturation vapor pressure (Ps) as P and the solubility of the solute (Cs) as C. The assumption is usually, and correctly, made that H calculated as Ps/Cs is constant at lower P and C values. This latter method is very convenient, since solubilities and vapor pressures are widely available in the literature. Unfortunately, the pure solute may undergo a phase transition (melting, boiling, or crystalline) near environmental temperatures. Thus, the published Ps and Cs data may refer to different phases. For example, published PCB solubilities are usually of the pure isomers (most of which are solid), whereas the vapor pressures may be those of the liquid mixtures, which are essentially subcooled. To calculate H , both measurements must refer to the same phase or erroneous results will be obtained. One can use PS/Cs/solid or Ps/Cs/liquid.
Techniques are emerging by which
y can be calculated from molecular structure ( 9 ) . If such y data are
At equilibrium, the fugacities of the sorbed and dissolved material must be equal; so if 2, is the sorbed-phase fugacity capacity:
available, H can be deduced as u yPs, provided that data are available for Ps. f = HC = C,/Z, This liquid solute vapor pressure may be experimentally inaccessible if the then 2, = C,/H.C = X p / H ( X / K p )= solute is solid or gas at this tempera- K,p/H. The group K,p is dimensionture, that is, if the system temperature less and is actually the partition coeflies outside the range from triple point ficient expressed as a moles-per-unitto critical point. In such cases, Ps is a volume ratio. If in 1 m3 of solution hypothetical quantity with a value that containing a low concentration of can be inferred by extrapolating the sorbent of volume fraction S , the fuliquid vapor pressure curve below the gacity is f , then the concentration of triple point or above the critical dissolved material is 2, f or f / H point. mol/m3; thus, there aref / H mol disIt is erroneous to use a solid vapor solved. pressure in this calculation. Yalkowsky The sorbed concentration is f Z , or (10) has shown that the entropy of C , mol/m3 of sorbent, or a total of fusion of many organic solutes is ap- f Z , S mol or fK,pS/H. The total proximately 13.6 cal/(mol.K). This amount is thus: permits the ratio of the solid and liquid vapor pressures P s s / P s to ~ be esti- f / H +fKpPS/H orf(1 + K ~ P S ) / H ), mated as exp(6.79(1 - T M / ~ ’where and the fraction dissolved becomes: T Mis the melting point (K) and T is the system temperature. This approach C f / H ) / f ( l -k K,PS/H = 1/(1 K,pS) has been used to correlate the solubility of series of organic solutes (1 1, 12). Sorbed phases (sediment or sus- and the fraction sorbed becomes: pended). The importance of calculating CfK,PS/H)/f(l + K,PS)/H Z for sorbed phases lies in the necessity = K,PS/(1 + KpPS) of discriminating between truly dissolved and sorbed materials, as are If the sorbent concentration is exoften measured in total by environ- pressed as S’ g/m3 (or mg/L), this is mental analyses. The approach taken equivalent to 106Sp, and the group below differs from that presented by K,pS in these equations becomes the Mackay ( 4 ) and is believed to be sim- more conventional group 10-6K,S’, For correlating K,, and hence Z,, for pler and more rigorous. Sorption equilibria are usually ex- organic solutes in sediments and soils, pressed as equations or isotherms re- it is very convenient to correlate the lating dissolved to sorbed concentra- organic carbon partition coefficient, tions. Examples are the Freundlich, Koc,of Karickhoff et al. (13) with KO,, BET, Langmuir, or linear equations. the octanol-water partition coeffiFor most hydrophobic compounds at cient. This analysis can also be applied to concentrations well below their solubilities, the linear equation is adequate sorption on atmospheric particles, but caution must be exercised in situations (Karickhoff et al. [13]): in which the sorbed solute is physically X = K,C trapped in or enveloped by the particle. where X is the sorbed concentration, This may occur, for example, with here expressed as mol solute/106 g PAHs formed durihg combustion and sorbent (wet or dry), and K , is a sorp- is associated with (or inside) soot tion coefficient with units of m3 particles. Such materials are unable to water/106 g sorbent. The equation is exert their intrinsic fugacity outside often expressed in mass concentration the limits of the particle, and therefore units ( X in g/106 g or pg/g, and C in are not in a true equilibrium. g/m3 or mg/L), in which case an Biotic phases. For biota, a bioconidentical numerical value is obtained centration factor, K B , is used instead for K,. of the partition coefficient. If it is exIf the sorbent concentration ex- pressed as a ratio of the concentration pressed as volume fraction is S and its in the biota (say, fish) on a wet weight density is p g/cm3 or lo6 g/m3, then its basis, it is identical to K,. If expressed concentration is Sp 106 g/m3 or g/ on a wet volume basis, it is rigorously cm3. This concentration is typically analogous to the group K,p, where p is g/cm3 or 10 mg/L; thus, it is the fish density. However, since p is convenient to record data as g/m3 or near unity, the difference is dimenlo6 Sp. The concentration of sorbed sional, rather than numerical. If a dry weight or lipid content basis material ( C , ) , expressed as m0l/m3 sorbent, is thus X p mol/m3. is used, a modified concentration fac-
+
tor must be applied. Several convenient correlations exist for KB,notably those of Neely et al. (14) and Veith et al. (15). Octanol phase. The importance of Z for octanol (Z,) lies in the utility of the octanol-water partition coefficient, KO,, as an indicator of hydrophobicity, as documented in the many studies of Hansch and Leo (16). Following the example of water, it can be shown that Z , is 1/voyZs,where yois the activity coefficient of the solute in octanol; Ps is the vapor pressure of the liquid solute at the system temperature; and uo is the molar volume of octanol saturated with water. Of greatest interest is KO, expressed as a concentration ratio (m0l/m3) or (g/m3), that is, C,jC,, when the fugacities are equal:
KO, = Co/C, = Z,/Zw = uwYw/uoYo
and the vapor pressures cancel. For most hydrophobic organic compounds, yoappears to be fairly constant in the range 1-10; of course, uw and vo are also constant. The value of KO, is thus dominated by y,. Since ywcontrols aqueous solubility, it follows that solubility and KO, are closely related, as has been shown by Mackay et al. (1 7), who developed the correlations: In KO, = 7.494 - In Cs (for liquids) In KO, = 7.494 - In Cs 6.79 ( 1 - T R . I / T(for ) solids)
+
Pure solid and liquid phases. For pure solid or liquid substances, the fugacity is the vapor pressure. The material’s concentration of C is the inverse of the molar volume, us (m3/ mol). 2, is thus given by: z, = C/f = l/PSus Such phases occur environmentally only when the solute solubility in a phase is exceeded and “precipitation” occurs. Interestingly, examination of this definition demonstrates that vapor pressure is essentially the air-pure solute partition coefficient, since: Kap = Za/Zp = PSvS/RT Likewise, water solubility, Cs, is essentially the water-pure solute partition coefficient: Kwp= Z,/Z, = PSv,/H = Csus For liquid solutes, the solubility Cs is 1/uwyw,whereas for solid solutes, the solubility Cs is P S ~ / P S ~ v wwhere y w rPs, and P s are ~ the solid and liquid vapor pressures. (This ratio was discussed earlier.) Figure 2 illustrates the relationships between these partition coefficients
Volume 15, Number 9, September 1981
1009
and fugacity capacities. Requirements that, for a new chemical, data must be obtained for properties such as solubility, vapor pressure, K p ,and the like, can be viewed as establishing a set of Z values for the relevant environmental media. Inert solutes. Some substances, such as ceramic or mineral matter, polymers, metals, and sparingly soluble metal salts do not partition appreciably between environmental media and their a propriate Z values are unavailabre. The thermodynamic explanation is that such substances have near-infinite Z values in their pure solute form because of very low values of Ps.If the presence of a pure solute phase is postulated, virtually all the solute will enter or remain in that phase. This is normally a trivial problem, except when, for example, the environmental aquatic concentrations exceed the solubility and phase separation (precipitation) occurs.
Selection of model volumes In order to calculate environmental partitioning in the form of amounts in each medium, it is necessary to assume volumes for each medium and an amount of solute. Clearly, any concentration can be obtained by the selection of suitable volumes and solute amount; thus, only the relative con-
I
\ 4
centrations have significance. The mass distribution depends on the assumed-phase volumes; therefore, the results are reasonable only to the extent that the volumes are reasonable. Further, selection of suspended matter concentrations and organic carbon contents of soils and sediments affects the results. The model “world” volumes and properties selected here are considered reasonable for evaluation purposes. The “world” consists of a I-km square with a IO-!an-high atmosphere; 30% of the area is covered by soil whose depth is 3 cm; and 70% is water covering an average depth of 10 m, with 3 cm of sediment, 5 ppm by volume of suspended solids, and 0.5 ppm of biota. The densities are 1000 kg/m’ for water and biota, 1500 kg/m3 for solid phases, and 1.19 kg/m3 for air. The organic carbon contents are 2% for soil and 4% for sediment and suspended solids. A temperature of 25 “C is assumed. The total amounts of solute are 100 mol for Level I and I mol/h for Level 11. The organic carbon sorption coefficient, K,, is assumed to be 0.6 (13) and the bioconcentration factor, K B , obtained from the Veith correlation (15) is: log K g = 0.85log Kow - 0.70 The calculation of Z values for a hy-
pothetical solute similar in properties to naphthalene is shown in Table 1.
Illustrative calculation Level I. With the relationships between physicochemical properties and Z values established, it is instructive to demonstrate how these values can be used to calculate partitioning by use of a hypothetical compound with properties and Z values listed in Table 1. If each phase in equilibrium has a volume of V, m3and a fugacity capacity of Zi, then the concentration in each phase, Ci, is f Z i , where f is the prevailing common fugacity. The amount of material in each phase, Mi, is thus V . and the total amount MT isO ZiVi. civi F I ’ Since the total amount is known, the fugacity can thus be calculated as: f =M T / Z Z ~ ~ Hence, the individual values of Ci anb Mi can be deduced. The results are given in Figure 3,which shows that the Pa. prevailing fugacity is 1.36 X There is 32% of the solute in the water, 55% in the air, 11% in the sediment, 2.3% in the soil, 0.018% in suspended solids, and 0.003% in the biota. The latter two media are thus unimportant from a mass balance viewpoint, although biota are the location of the highest concentration. The suspended solids have a concentration 114 times that of the water on a mass/volume basis, or 76 (that is, K P )times on the conventional basis of pg/g or mg/L. The total concentration in the water is 4.54 X mol/m3, of which only 0.06% is sorbed and 0.009% is biosorbed, most being in solution. It is clear that this calculation gives two different classes of information-where most of the solute partitions and where the highest concentrations occur. There may be some confusion between these classes that could lead to erroneous conclusions, such as “PCBs reach high concentrations in fish, thus that is where most PCBs partition.”
Illustrative calculation Level 11. In this level, reactions and advectian are added to the Level I calculation. Possible reactions include photolysis, hydrolysis, biodegradation, and oxidation. By definition, all are expressed in first-order form with a rate constant, k, with units of reciprocal hours. The rate (mol/[m’-h]) is the product of k(h-I) and concentration (mol/m3). Reactions in a phase can be added as follows:
+
+
Rate = klC k2C k3C . . . = C 2 k i = CK mol/(m3-h)
+
I010
Environmental Science 8 Technology
where K is the total first-order rate constant. The solute reaction is balanced by an input ( I mol/h), such that a steady-state concentration is established
mol/h. The total reaction rate can then be obtained and will equal I. It is immaterial in which phase the solute enters, since it is effectively distributed instantaneously throughout the system. I = ViClKi VZCZKZ V ~ C ~ K S It is also possible to calculate an . . = 2VCK overall persistence or average resiin which the subscripts apply to the dence time as the total amount of solute present as X , V ,divided by l. It individual compartments. If we assume a common fugacity to is effectively the reciprocal of a weighted-mean rate constant: prevail, C; can be replaced by ZJand I =f2VZK; hence, f = I/ZVZK. r = 2C,V,/I = ZZ,V,/ZV,Z,K, Individual phase concentrations, C;, Figure 4 gives an output for the hipocan be calculated asfz;, and reaction rates as C;K; mol/(m3-h) or V;CiK; thetical solute and illustrates this approach using assumed rate constants given in Table 2 for emissions of I mol/h. In Figure 4, the fugacity is 1.13 X Pa; the percentage distribution between phases is identical to that in Figure 3; and the total amount is 83 mol. Essentially, this amount is sufficient to establish concentrations that will result in a total reaction rate balancing the emissions of l mol/h. The persistence or residence time is thus 83 h. It is instructive to examine where most of this reaction occurs. Table 2 gives the rate constants-rates in mol/ (m3-h) and in mol/h-and their percentage of the total. This "transformation matrix" shows that the dominant reactions are photolysis and oxidation in air and water, and biodegradation in water and sediment. The highest rate constant is "biodegradation" in biota; but this is unimportant from a mass-balance viewpoint, since so little of the solute is present in the biota. Although the air rate constants are also high and the volume is large,
+
,.
+
+.
-
s
E
. E
70%
+
where C B represents ~ input concentrations. If CB;equals C,, the advection terms cancel. Figure 5 gives an output for such a system, including advection in the air and water
.
VOIUnlO.
2,
Amount,
ma
moU(m3 Pa)
mol
IOTo soil Water Biota Suspended solids Sdment
30%
+
lllustratke Level I calculation
---Air
-.
+
FIGURE 3
Area = 106 m'
E
0
the concentration is small; thus, atmospheric processes account for only 50% of the total. These deductions illustrate the utility of models in bringing together data on partitioning, volumes, and rate constants to elucidate how most degradation occurs. Mathematically, the critical quantity in this regard is the product VCK or VZK. It is not immediately clear where the product, as distinct from the individual terms, is largest. A fast rate constant need not result in a fast reaction rate, environmentally. For regulatory purposes, it is clear that, in this case, reliable data on aquatic photolysis, oxidation, and biodegradation are required. Other processes can be ignored; the only requirement is that the rate constant is of the same order of magnitude, or less, than those assumed. Likewise, only approximate values for K , and KBare necessary, but an accurate value of H is essential. Level 11, with advection. Advection can be introduced as a first-order process that has a rate constant, K,, defined as the phase flow rate out (and in) Gi(m3/h), divided by the phase volume. The reciprocal of K, is then the residence time or space time. K, can be added to the other constants. If there is solute in-flow, the equation becomes more complex: I ZG;CB; I 2Ka;VjC~; = 2V;C;(K; K,;)
9x101 7 x 106 35 35 21x10"
403x 190x10' 0333 628
55 0 2 33 31 B
OW3
379 379
0018 10 9 100 0
Consentrailon
mol/m3
Psis
550x10-0 2 59 x 10-4 454x10-6 856x10-
696x10-4 2 59 x 10-2 682x10.' 128x10-'
5 1 7 ~ 1 0 - ~5 1 7 ~ 1 0 - ~ 517XlO-' 517x10-2
Fugacity = 1.363 x Pa Temperature = 25 "C Media densities (kglm'): Air = 119 so11 = 1500 Water = 1000 Biota = loo0 Suspended solids = 1500 Sediment = 1500 Organic carbon contents: Soil = 2% Suspended solids = 4% Sediment = 4%
Volume 15. Number 9. September 1981
1011
FIGURE 4
IllustratIve Level II calculation with no advection
45.61 Soil Water
1.93
26.38
4.56x
0.502
2.15x IO-'
0.031
3.77x
0.422 0.0002
Biota
0.0025
7.10x
Suspended solids
0.0150
4.29x
Sediment
9 01
4.29 x IO-'
82 95
c
-
'7
Fugaclty = 1.131 x Perslstence = 82.95 h
1012 Environmental Science a Technology
IO-'
0 0.045 __ 1.000
Pa
phases. Inclusion of advection results in net outflow in air and water; therefore, the total amount present drops. It becomes possible to attribute the amount of solute in the system to its source, which is also interesting from a regulatory viewpoint. Here, 52% is advected into the system and 48% arises from local emissions. The regulatory implication is that reducing local omissions by, say, 50% will reduce local concentrations by approximately 25%. Thus, local attempts to improve environmental quality become frustrated by emissions originating elsewhere. Information of this type is invaluable for regulatory purposes. Interestingly, local efforts will be most effective on less persistent pollutants, and, conversely, less effective on persistent pollutants. In the case illustrated in Figure 5, the amount of solute resident in the
1.0 mollh
Advective
=
(IOs mVh x IO-* moVmJ) K. = 0.10lh-'
FIGURE 5
p Advective outflow
inflow
Illustrative Level II calculation with advection
1.614 . molih ~
\
Amowl, mol
0.133 mollh
I:--
0 10 mollh I O 5 m3/h x 10-6 mollm K , = 0 014Ih
Emission 1 mllh
Total input 1.0
I
+ 1.0 + 0.1 = 2.1
l"Lal ""yl",
1.614
system is 29 mol, compared to the 83 mol in Figure 4, which shows the same rate constants. The reason for this difference is the large advective term, especially that in the air, which corresponds to a rate constant of 0.1 h-', Of the total inflow of 2. I mol/h, only 0.35 mol/h is reacted; the remaining 1.75 mol/h is advected out, mostly in the air. The dominance of advection results in a fundamental difficulty in identifying and quantifying environmental processes by measurements of actual environments. Only where advection is slow can these other processes be adequately observed and quantified. The residence time of the solute in the environment of Figure 5 is only 14 h, but its persistence to reaction or the average lifetime of a solute molecule is 83 h. When advection is present, the definitions of persistence and residence time thus become different.
+ 0.133 + 0.353 = 2.1
Reaclion, molih
Air
16.13
1.61 x IO-*
0.177
Soil
0.68
7.59 x 10-5
0.01 1
Water
9.33
1.33~ 10-6
0.149
Biota
0.00088
2.5
0.0053
1 . 5 2 10-4 ~
0
1.52x10-4
0.016
/Sediment
I
Concentralion. mollmJ
29.34 3.18
X
10-4
Fugacity = 4.00 x 10-5 Pa Reaction persistence = 29.3410.353 Residence time = 29.W2.1
A rational mechanism The equilibrium models described here are best regarded merely as tools for facilitating the mental assimilation of physicochemical and reaction data. They do not purport to calculate the actual solute concentrations or their precise behavior in the environment. Since the models are based on valid physical laws, the behavior expressed should be in broad agreement with environmental behavior. It would be worthwhile to test models of substances of established environmental fate. This is done, to a limited extent, in Table 3, which gives Level I data for selected substances and shows the generally expected behavior. lt is expected that the ratios of concentrations in various media should agree broadly with those obtained by environmental monitoring, except in cases in which media conditions are far from equilibrium.
=
8.7~10-5
0.353
= 83 h
14 h
Since the model assumes equilibrium to exist between phases, caution must be exercised when a solute's behavior is influenced by an intermedium transfer resistance. For example, a substance that is emitted into water but reacts in the atmosphere may experience a water-to-air transfer resistance, which will strongly influence the relative concentrations and fugacities in each phase. A Level 111 calculation would be required for such situations. In these calculations, six media have been used-air, water, soil, sediment, aquatic biota, and suspended solids. Others could be added if more detail is required; for example, soil biota, soil pore water, atmospheric particles, or sediment biota. There is no real increase in mathematical complexity. It is interesting to note that the Level I calculation can be undertaken with the use of partition coefficients
Volume 15, Number 9, September
1981
1013
instead of fugacity capacities. The becomes clarified and obvious, and mass balance equation can be: calculations of persistence or concentration can usually be done by hand M = X V = CI V I CtK21 V2 with acceptable accuracy. Essentially, C I K ~ I V ~. . the model screens out the mass of irwhere K Z I = CZ/CI,K ~ =I C ~ / C I ,relevant detail to highlight the domiand so on thus: nant processes. Although evaluative models of this CI = MA V I + K2t V2 type cannot be validated by environK ~V I, . . . mental observation, some validation is from which the other concentrations made possible through controlledcan be calculated. A similar approach microcosm, or pond experiments. The can be used for Level II. in which: role of microcosms may be to validate models experimentally for some I = C K V = ClKiVl members of specific homologous series, i or groups, rather than as a direct regC I K ~ I K ~ VCZI K ~ I K ~.V. .~ ulatory tool. Unfortunately, the expense of microcosm experiments tends Calculations of these types have to be high; thus, the approach is unbeen described by McCall(18). Neely suited for routine use. (19). and Klopffer (20).and will give These models may also serve as a identical results to the fugacity calcu- guide to appropriate environmental lations, since the basic mathematical monitoring strategies. For instance, formulation is identical. The advan- design of monitoring systems is greatly tage of the fugacity approach is that facilitated by advance information on the behavior of each phase is treated likely relative media concentrations. separately. There is no need to infer The primary advantage of this pseudopartition coefficients between modeling approach is that it provides phases, which are not in contact, for a rational, physically realistic mechaexample, with atmospheric particles nism by which diverse physicochemical and water. The equations are easily and reactivity data are combined to solved with a hand calculator. The yield behavior profile statements of the fugacity approach becomes most ad- dominant medium of accumulation, vantageous when applied at Level 111, the likely concentration ratios, and the which requires the solution of a set of overall persistence. It is difficult to algebraic equations. how judgment can be made The magnitude of the Z value gives conceive on the behavior of a substance (and a direct indication of the likely con- hence, on appropriate regulations) centration since, for any two media, without processing the data in such a the concentration ratio is simply the Z model. It is encouraging to note that ratio. Solutes thus tend to migrate regulatory agencies such as EPA in the environmentally to media of high Z. U S . and the OECD group internaFor example, Z in lipid phases is high tionally are proceeding in this direcfor PCBs; Z in air is high for freons; Z tion. in water is high for phenols. A substance that changes chemically, such Acknowledgments as to methylmercury, adopts a new set The authors gratefully acknowledge the of Z values and may partition quite scientific contributions of George Baughdifferently in its “new” form. man, Sam Karickhoff, Brock Neely. Phil A useful feature of this type of McCall. and Roland Weiler to this work modeling is that it can be used to de- and the fiancial support ofthe US. Envitermine the sensitivity of the output ronmental Protection Agency and the (for example, persistence) as a func- Ontario Ministry of the Environment. Before publication, this feature article tion of the input data by perturbing read and commented on for technical these data and observing the effect. was accuracy by W. Brock Neely, EnvironNormally, only a few data or processes mental Sciences Research Laboratory, control the fate; thus, only these need Dow Chemical Co.. Midland, Mich. be known with high accuracy. The re- 48640; and L. J. Thibcdeaux, Department sult is that considerable economies of of Chemical Engineering, University of effort are possible by estimating, Arkansas, Fayetteville. Ark. 72701. rather than measuring, properties by using structure-activity-property re- Note: lationships that are, for instance, The authors will be glad to supply, on rewidely used to calculate Kow They quest, copies of the computer programs show promise of being applicable to used in this paper. other properties, such as solubility and References various reactivities. When the model is analyzed in such ( I ) Haque, R. “Dynamics, Ex ure and Hazard Assessment of Toric C%micaIs”: a fashion, and the dominant media and Ann Arbor Science: Ann Arbor, Mich.. processes are identified, the behavior 1980.
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(2) Neely, W. B. “Chemicals in the Environment”; Marcel Dekker: New York. 1980. (3) Thibcdeaux. L. J. “Chemcdynamia”; John Wiley and Sons: New York. 1979. (4) Mackay. D. Enuiron. Sri. Technol. 1979,
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