Environ. Sci. Technol. 1982, 16, 645-649
Monsanto, Dayton, OH, 1980, EPA-600/2-80-042b. Benton, G.; Miller, D. P.; Reimold, M.; Sisson, R., presented at the 1981InternationalConference on Residential Solid Fuels, Portland, OR, 1981. Cadle, S. H.; Groblicki, P. J., presented at the International Sympcsiumon Particulate Carbon: Atmospheric Life Cycle, Warien, MI, 1980. Swarin, S. J.; Williams, R. L., presented at the 4th International Symposium on Polynuclear Aromatic Hydrocarbons, Columbus, OH, 1979. McCrone, W. C., Ed., “The Particle Atlas”;2nd ed.; Ann Arbor Science: Ann Arbor, MI, 1980. Nagda, N. L.; Pelton, D. J.; Swift, J. L, presented at the 72nd Annual Meeting of the Air Pollution Control Association. Cincinnati., OH.. 1979. Williams, R. L.; Swarin, S. J., presented at the Society of Automotive Engineers Meeting, Detroit, MI, 1979. Wei, E. T.; Wang, Y. Y.; Rappaport, S. M.J. Air Pollut. Control Assoc. 1980, 30, 267-271. Wolff, G. T.; Countess, R. J.; Groblicki, P. J.; Ferman, M.
A,; Cadle, S. H.; Muhlbaier, J. L. Atmos. Environ. 1981, 15, 2485-2502. (13) Courtney, W. J.; Tesch, J. W.; Stevens,R. K.; Dzubay, T. G., presented at the 73rd Annual Meeting Air Pollution
Control Association, Montreal, 1980. (14) Watson, J. G., Ph.D. Thesis, Oregon Graduate Center, Beaverton, OR, 1979. (15) U.S.Environmental Protection Agency, “Compilation of (16) (17)
(18) (19)
Air Pollutant Emission Factors”, 3rd ed.; U.S. EPA AP-42, 1977. Countess, R. J.; Wolff, G. T.; Cadle, S. H. J.Air Pollut. Control Assoc. 1980, 30, 1194-1200. Stanford Research Institute “America’s Demand for Wood 1929-1975”; Tacoma, WA, 1954. Ryan, P., personal communication. Wolff, G. T., personal communication.
Received for review November 9, 1981. Revised manuscript received April 22, 1982. Accepted May 17, 1982.
Vapor Pressure Correlations for Low-Volatility Environmental Chemicals Donald Mackay,” Alice Bobra, Donald W. Chan, and Wan Ylng Shlu
Department of Chemical Engineering and Applled Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1A4
rn Four equations are proposed and tested that relate vapor pressures at ambient temperatures for low-volatility solid and liquid chemicals of environmental interest to their boiling and melting points. The equations may be used to estimate vapor pressure from boiling point, check the reasonableness of experimental data, or correlate these data. The preferred equation, which is a version of the Rankine equation, gives a mean error in vapor pressure of a factor of 1.25 for 72 selected hydrocarbons and halogenated hydrocarbons. It is suggested that versions of the equation may be developed for other classes of compounds. Introduction The tendency for an environmental contaminant or pesticide to partition into the atmosphere is determined largely by its vapor pressure. It is thus recognized that for assessing the likely environmental behavior of new and existing chemicals a knowledge of their vapor pressures is essential. The vapor pressure P (Pa) can be regarded as a measurement of the maximum achievable amount or solubility of the substance in the vapor of air phase, the corresponding concentration being obtained from the gas law as P / R T (mol/m3) where R is the gas constant (8.314 J/mol K) and T is absolute temperature (K). It is not always recognized that high molecular weight hydrophobic substances such as DDT or PCBs, which have very low vapor pressures and hence low atmospheric concentrations, may still partition appreciably into the atmosphere as they also have low aqueous solubilities. The ratio of the concentration in the atmosphere to that in the water (Le., the air-water partition coefficient) may thus be large despite the low vapor pressure. This partition coefficient can be expressed as a dimensionless Henry’s law constant H / R T where H is defined as the ratio of partial pressure P to aqueous concentration (mol/m3). Compounds of high H tend to partition predominantly into the atmosphere, and the rate at which they evaporate from water is usually controlled by the water-phase mass-transport resistance. For substances of low H , partitioning is predominantly into 0013-936X/82/0916-0645$01.25/0
the water, and the evaporation rate tends to be controlled by the resistance in the air phase, where the concentration is lower. It is noteworthy that many of the data pubKshed in the literature for vapor pressures are erroneous, especially for very low vapor pressure substances (Spencer et al. (I)). Little difficulty is encountered experimentally in measuring vapor pressures exceeding 1 kPa, since an isoteniscope can be used. For lower vapor pressures, the preferred approach is to flow a stream of gas through a vessel containing the volatile solid or liquid solute coated on packing, such that the gas stream is saturated. The exit gas is then analyzed for solute concentration. Such methods have been described by Spencer et al. (I), Sinke (Z),and Macknick and Prausnitz (3),and although straightforward, they require meticulous exflerimentaltechnique. For some substances of environmental interest the only vapor pressure information that may be available is the boiling point, and it is useful to devise methods of using these data to estimate vapor pressures approximately at lower temperatures. In this paper we thus examine the physicalchemical factors that influence vapor pressure, suggest correlationsfor fitting vapor pressure data, for determining vapor pressure from boiling point in the absence of experimental vapor-pressure data, and for checking the reasonableness of experimental vapor pressure data. Our focus here is thus on low vapor pressure solids or liquids well below their boiling point. For more volatile compounds, direct vapor pressure measurement is easy and there is little merit in prediction. Thermodynamic Basis A comprehensive discussion of the theory underlying liquid vapor pressure is provided by Reid et al. ( 4 ) , and only the salient points are reviewed here. Typical vapor pressure characteristics of a substance are illustrated in Figure la. The range of environmental temperatures may lie anywhere on this diagram for a given substance, relative to the phase transition points. The solid and liquid vapor pressure lines are highly nonlinear, and no method is currently available for calculating from theory the mag-
0 1982 American Chemical Soclety
Environ. Sci. Technoi., Vol. 16, No. 10, 1982 645
a
P
ATM
SOLID
I
In this work we use only the Trouton and Kistiakowsky Rules. Temperature Dependence of AH'. The enthalpy of vaporization is zero at the critical point Tc but rises rapidly at temperatures approaching the normal boiling point (which is often approximately 0.66TB),and then it rises more slowly at lower temperatures. The most successful correlating equation is that of Watson (8)
CRITICAL POINT
LIQUID
/
In
UBCOOLED TRIPLE OR
AHl/AH2 = [(I - TI/TC)/O - Tz/Tc)IO.38 BOILING POINT
T
'/T
Figure 1. Illustrative plots of (a) vapor pressure ( P ) vs. absolute temperature ( 7 ) and (b) In vapor pressure vs. reciprocal absolute temperature ( 1/ T).
nitude of vapor pressure or its dependence on temperature. The second law of thermodynamics provides a constraint on the vapor pressure-temperature curve in the form of the differential Clapeyron and Clapeyron-Clausius equations, below, which give the slope of the curves as a function of the enthalpy of vaporization AH" and the volume change on vaporization AV. Here we ignore compressibility effects since the pressure is low and the gas law can be applied by ignoring the relatively small liquid molar volume. The resulting equation in rearranged form suggests that d(ln P)/d(l/T) should be fairly constant if AH" is fairly constant. Figure l b shows this plot, which is close to linear over small temperature ranges. dP/dT = W / T A V = A€PP/RP (1) d(ln P)/d(l/T) = -AH"/R (2) Integration of the equation with the assumption of constant AH" leads to eq 3 and 4, which are successfully used to correlate vapor pressure data over narrow temperature ranges. In (P1/P2)= ( W / R ) ( l / T 2 - l/Tl) In P = A - B / T
(3)
The principal region of predictive interest for environmental chemicals is the low-pressure region well below the boiling point in which the two problems are estimation of the absolute value of AH and estimation of its temperature dependence, the In P vs. 1/T plot being invariably curved, as shown in Figure lb. The assumption that A€P is constant implies that this line is straight and results in an overestimation of vapor pressure at low temperatures. AZP tends to increase at low temperatures, thus the vapor pressure decreases more rapidly as shown. It is thus necessary to devise methods to predict AH" and its temperature dependence. Prediction of HVB.Trouton's rule states that the entropy of vaporization at the normal boiling point (subscript B) IpB/TBis 20.67 cal/mol K or 86.4 J/mol K. Kistiakowsky (5) improved on this by relating the entropy of vaporization to boiling point, i.e. AH"B/TB = 36.6 + R In T B (6) Greater accuracy can be obtained by correlating classes of compounds separately, for example, by Fishtine (6, 7). 646
in which the subscripts 1 and 2 refer to different temperatures, one of which may be the boiling point. Since most high molecular weight compounds have critical temperatures in the 700-900 K range, environmental conditions fall in the region where TITc is 0.30-0.45. The temperature range of interest here is thus from TITc of 0.30 to 0.66. The usual approach for developing vapor pressure correlations at higher temperatures is to substitute the Watson equation and the Haggenmacher compressibility equation into the Clapeyron-Clausius equation and integrate. Direct analytical integration is unfortunately impossible, and the alternative is to devise an empirical correlation based on numerical integration or to integrate a series expansion. Notable in this regard are the equations developed by Miller (9) and Thek and Stiel (IO). The Watson equation requires a knowledge of the critical temperature Tc, and for substances of low volatility reliable estimates may not be available. Methods are available to estimate Tc by additive structural contributions, for example, that of Lyderson, but in principle it seems unwise to rely on a TCestimate if it can be avoided. Vapor Pressure Equations 1. Trouton Constant AHV(TCH). If Trouton's rule is adopted and AH" is assumed to be constant and equal to AH"B, the Clapeyron-Clausius equation can be integrated directly to give In (Pl/PJ = - ( u ~ / R ) ( l / T i- 1/TJ
where B = AH"/R
(4) The fit of the equation can be considerably improved by introducing a third parameter in the form of the Antoine equation, which is widely used to correlate experimental vapor pressure data. Values of C are typically -20 to -50 K, and rules have been suggested to correlate C. In P = A - B/(T + C) (5)
Envlron. Scl. Technol., Vol. 18, No. 10, 1982
(7)
(8)
If Tz is the boiling point TB, P2becomes 1atm, replacing m B / R by 86.4TB/8.314or 10.6TB,and substituting yields In (P1/P2)= -10.6TB(1/T1 - l/T2) or In Pl = -10.6(TB/T1 - 1)
(eq TCH)
(9)
2. Kistiakowsky Constant AH' (KCH). In this case O B / R is replaced by TB(36.6 -!- R In T B ) giving In (P1/P2)= -T~(4.40+ In TB)(l/Tl - 1/Tz)
or In P1= -(4.40
+ In TB)(TB/Tl - 1)
(10)
These equations are variants of eq 4, in which, for example, ifi the TCH equation, A is 10.6 and B is 10.6T~. The TCH equation can be used to estimate vapor pressure from boiling point (although overestimation is likely), or it can be used to fit boiling point and experimental vapor pressure data in a one-parameter equation, i.e., fitting a constant instead of 10.6. If the constant deviates greatly from 10.6, i.e., by 1076, it is likely that one measurement is in error or the molecule has exceptional properties. 3. Trouton Linear AH (TLH). Adopting Trouton's rule and allowing AH to vary linearly with temperature in the range below the boiling point introduce another parameter, which must improve the data fit. A suitable AH equation with one constant K is
AH = AHB(1 + K ( l - T/TB))
(11)
which has the correct property that AH is AHB when T is TB. The Watson equation can be used to estimate the likely magnitude of K. A compound of Tc = 800 K will have a TB of 528 K, environmental temperature TI being 290 K. Substitution in the Watson equation gives a A H l / A H B ratio of 1.27, thus K should have a value of approximately 0.6. Substituting into the Clapeyron-Clausius equation yields In Pl/P2 =
L2 Ti
AHB(1 + K(1- T/TB)) dT/RT2
= -AHB(1
+ K)(l/T1 - 1/T2)/R
-
In (TI/T2)/RTB (12) and substituting 10.6TBfor In
(Pl/P2) =
-10.6TB(1
or In P1 = -10.6{(1
gives
+ K)(l/Tl - 1/T2) - 10.6K In (T1/T2)
+ K)(TB/T1-
1)- K ln(TB/Tl))
(eq TLH) (13)
The vapor pressure calculated by eq TLH will always be lower than that of eq TCH for a positive value of K. 4. Kistiakowsky Linear AH (KLH). From the previous derivation, the quantity 10.6 in the TLH equation can be replaced by 4.40 + In TB to yield the KLH equation. The TLH equation is a form of the Rankine or Kirchoff equation: In P = A - B / T + C In T (14) If data are available for the boiling point and vapor pressures at lower temperatures, the TLH of KLH equations can be used to correlate the data by regarding 10.6 and K as adjustable parameters. The advantage of the TLH or TKH equations is that they can be used to predict vapor pressures from boiling point by using a reasonable value for K or they can be used to check the reasonableness of data by determining K. Solid Vapor Pressures. If the compound is solid, its vapor pressure PS will be lower than that of the subcooled liquid PL by the factor of the fugacity ratio Ps/PL. This has been previously shown to be expressible by In (Ps/PL)= -6.8(TM/T - 1) (15) where TM is the melting point (Yalkowsky (II), Mackay et al. (12),and Mackay and Shiu (13)). The constant 6.8 is an average empirical value and may be substantially in error for certain compounds. For solids, this (negative) group is added to the liquid vapor pressure equation as follows, as illustrated for the TCH equation: In (Ps/PB)= In (Ps/PL)- In (PL/PB) = - ~ . ~ ( T M -/ T1)- IO.~(TB/T- 1) (16) For other equations the appropriate second term is substituted. In summary, four equations have been stated, all of which enable liquid vapor pressures to be predicted at low (environmental) temperatures from the boiling point. The first pair (TCH and KCH) contain one parameter (e.g., 10.61, the second pair (TLH and KLH) two parameters (e.g., 10.6 and K ) . The parameter K is not freely adjust-
able, and it is expected that it will have similar values, at least for a class of structurally similar compounds.
Data Analysis Vapor pressure, boiling point, and melting point data were gathered in Table I for 72 compounds of environmental interest, all of which boil above 100 "C, the principal sources being various compilations of toxic substance properties (ref 14-18). The compounds selected were hydrophobic (low aqueous solubility) organic compounds such as hydrocarbons and halogenated hydrocarbons. Compounds containing polar groups were excluded for two reasons. These more soluble compounds tend to partition negligibly into the atmosphere (i.e., H is low) thus a knowledge of P is less useful. They also tend to have higher and more variable AH values. The vapor pressure data were then compared to the TCH and KCH equation predictions as shown. Comparison was also made with the TLH and KLH equations, and a "best" value of K was found to be 0.7626 for the TLH equation and 0.803 for the KLH equation. The procedure by which these K values are obtained should avoid giving excessive weight to higher vapor pressures, and thus direct least-squares fitting is undesirable. This problem was solved by regression of the logarithm of the vapor pressures, and thus the quantity minimized was effectively the ratio between experimental and correlated values rather than the difference. Inspection of the data showed that the TCH and KCH equations tend to predict high vapor pressures by a mean factor of 2.64 and 2.66, respectively. The mean absolute values of the logarithm of the ratio of the calculated and literature values for these two equations were 0.342 and 0.356, corresponding to factors of 2.20 and 2.27. It is thus concluded that, as expected, these equations overpredict the vapor pressures by a factor of 2-3 because of the assumed constancy of AH. The TLH and KLH equations give mean errors in the absolute logarithm term of 0.0960 and 0.0957, respectively corresponding to factors of 1.247 and 1.246. These equations are thus superior to the TCH and KCH equations and are recommended for use in calculating vapor pressures from boiling point. It is surprising that the KLH equation is not significantly more accurate than the TLH equation, but this may be due to masking by the errors in the data. In principle the KLH equation is judged to be the best of the four. It is believed that the TLH and KLH equations should yield predicted vapor pressures with an average error of only a factor of 1.25, but errors of over a factor of 2.0 are expected with a frequency of 10% for compounds similar in characteristics to those used to develop the correlation. Since the equation is most likely to be used for solid compounds of high boiling point for which no vapor pressure data are available, it is likely that the errors will generally be larger, but it is impossible to estimate their likely magnitude. Figure 2 illustrates the KLH correlation in two forms. The A set of curves are calculated solid and liquid vapor pressures of a substance of boiling point 500 K. The effect of melting point is apparent. Also shown is the linear TCH equation, which overestimates vapor pressure due to the assumption of constant enthalpy of vaporization. The B curves give the calculated vapor pressure at 25 "C of substances with the indicated boiling point. Again the effect of melting point is apparent, the solid vapor pressures being displaced downward by the fugacity ratio by an equal factor or interval on the logarithmic scale. Table I1 illustrates the caution that must be exercised in using the correlation by applying it to other compounds. Envlron. Scl. Technol., Vol. 16, No. 10, 1982 647
Table I. Vapor Pressure Data at 25 "C for 72 Compounds and Correlated Valuesa chemical
a
648
melting point, K
octane 216.40 3-methylheptane 152.50 2,3,4-trimethylpentane 163.80 nonane 222.00 2,2,54rimethylhexane 167.20 4-methyloctane 159.80 decane 243.30 undecane 247.41 dodecane 263.40 hexadecane 291.17 1-octene 171.30 me thy Icy clohexane 146.40 e thylcyclopentane 134.56 ethylcy clohexane 161.68 cis-l,2-dimethylcyclohexane 222.90 trans-1,4-dimethylcyclohexane 236.00 1,1,3-trimethylcyclopentane 258.80 propylcy clopentane 155.70 toluene 178.00 ethylbenzene 178.00 p-xylene 286.20 m -xylene 225.10 o-xylene 247.80 1,2,44rimethylbenzene 229.20 1,2,3-trimethylbenzene 247.60 1,3,5-trimethylbenzene 228.30 cumene 176.40 propylbenzene 171.40 1-ethyl-2-methylbenzene 192.20 1-ethyl-4-methylbenzene 210.60 n-butylbenzene 185.00 isobutylbenzene 221.50 sec-butylbenzene 197.50 tert-butylbenzene 215.20 1,2,4,54etramethylbenzene 193.80 1-isopropyl-4-methylbenzene 205.10 n-pentylbenzene 198.00 naphthalene (S) 353.20 1.methylnaphthalene 251.00 a-methylnaphthalene* (S) 307.60 1-ethylnaphthalene* 259.20 2-ethylnaphthalene* (295.9 K ) 256.60 biphenyl (S) 344.00 acenaphthene* (S) 369.20 fluorene* (S) 389.00 1,1,2-trichloroethane 236.50 l,l,1,24etrachloroethane 202.80 ltl,2,2-tetrach1oroethane 237.00 1,1,2,2,2-pentachloroethane 244.00 tetrachloroethene 254.00 trichloropropane 258.30 lt2-dibromomethane 238.30 264.70 bromoform 227.40 chlorobenzene o-dichlorobenzene 256.00 248.30 m-dichlorobenzene p-dichlorobenzene* (S) 326.10 1,2,3-trichlorobenzene* (S) 326.00 1,2,4-trichlorobenzene 289.95 1,3,5-trichlorobenzene* (S) 336.00 1,2,3,4-tetrachlorobenzene*(S) 320.50 1,2,3,5-tetrachlorobenzene*(S) 327.50 1,2,4,5-tetrachlorobenzene*(S) 413.00 234.00 a-chlorotoluene a ,a,a-trifluorotoluene 243.89 242.18 bromobenzene m-dibromobenzene* (308 K) 266.00 360.33 p-dibromobenzene (S) 205.50 2-bromoe thylbenzene* 241.79 iodobenzene 341.00 1,4-bromochlorobenzene (S) 258.30 trichlorohydrin (S) refers to solids. Asterisked values are extrapolated.
Environ. Scl. Technol., Vol. 16, No. 10, 1982
boiling point, K
exptl, atm
KLH, atm
398.66 388.00 386.50 423.80 397.10 415.40 447.10 468.90 489.30 560.00 394.30 373.90 376.40 402.90 402.70 392.40 377.90 376.00 383.60 409.20 411.00 412.00 417.40 442.35 449.10 437.70 437.70 432.20 438.20 435.00 456.00 445.80 446.00 442.00 469.80 450.10 478.40 491.00 517.64 514.10 531.70 530.90 528.90 550.50 568.00 386.80 403.50 419.20 435.00 394.00 429.90 440.30 422.50 405.00 453.50 446.00 447.00 491.00 486.50 481.00 527.00 519.00 516.00 452.30 375.06 429.00 491.00 492.00 491.00 461.30 469.00 429.85
0.186 X lo-' 0.257 X lo-' 0.355 X lo-' 0.564 X 0.218 X lo-' 0.891 x 0.173 X 0.515 X 0.155 X 0.905 X lo-' 0.229 X lo-' 0.610 X lo-' 0.526 X lo-' 0.169 X lo-' 0.190 x lo-' 0.298 X lo-' 0.523 X 10" 0.162 X lo-' 0.370 X lo-' 0.130 X lo-' 0.115 X lo-' 0.109 x lo-' 0.860 X lo-' 0.267 X lo-' 0.199 x 10-2 0.318 X lo-' 0.605 X lo-' 0:451 X lo-' 0.326 X lo-' 0.388 X lo-' 0.135 X lo-' 0.271 X lo-' 0.238 X lo-' 0.282 X lo-' 0.650 X 0.200 x lo-' 0.431 X lo-) 0.108 X lo-' 0.921 X 0.715 X 0.248 X 0.336 X lob4 0.130 X 0.588 X lo-' 0.874 X 0.399 X lo-' 0.183 X lo-' 0.856 X lo-' 0.592 X lo-' 0.245 X lo-' 0.408 X lo-' 0.267 X lo-' 0.710 X lo-' 0.156 X lo-' 0.193 X l o w 1 0.303 X lo-' 0.888 x 10'' 0.276 X 0.598 X 0.760 X 0.514 X 0.967 X 0.711 X 0.171 X lo-' 0.491 X lo-' 0.545 X 10'' 0.563 X lo-' 0.212 x 10-3 0.322 X 0.130 X 0.340 X 0.408 X lo-'
0.203 X lo-' 0.319 X lo-' 0.339 X lo-' 0.675 X lo-' 0.217 X lo-' 0.979 X lo-' 0.235 X 0.851 X 0.321 X 0.942 X 0.244 X 10-1 0.573 X lo-' 0.517 X lo-' 0.169 X lo-' 0.170 X lo-' 0.265 X l o - ' 0.486 X lo-' 0.525 X lo-' 0.383 X lo-' 0.128 X lo-' 0.119 x 10-1 0.114 X lo-' 0.896 X lo-' 0.292 X 0.214 X lo-' 0.361 X lo-' 0.361 X lo-' 0.463 X lo-' 0.353 X lo-' 0.408 X l0-l 0.156 X lo-' 0.249 X lo-' 0.247 X lo-' 0.297 X lo-' 0.815 X lo-' 0.205 X lo-' 0.542 X 0.840 X 0.802 X 0.768 X 0.398 X 0.414 X 0.160 X 10+ 0.302 X 0.782 X 0.335 X lo-' 0.164 X lo-' 0.828 X lo-' 0.408 X lo-' 0.247 X lo-' 0.514 X 0.321 X lo-' 0.715 X lo-' 0.154 X lo-' 0.175 X lo-' 0.247 X lo-' 0.124 X lo-' 0.156 X loT3 0.368 X lo-' 0.201 x 10-3 0.301 X 0.383 X 0.631 X 0.185 X lo-' 0.546 X lo-' 0.535 X lo-' 0.296 X 0.680 X lo-' 0.296 X 0.122 x 10-1 0.317 X 0.515 X lo-'
TEMP E RAT UR E lo5
IO4
103
IO2
a w
a
a
10
g Y
K
a
E
l
B
s
10”
used to (i) predict environmental vapor pressures from boiling points, (ii) check the reasonableness of experimental vapor pressure and boiling point data, or (iii) correlate vapor pressure and boiling point data in a single equation. The equations apply to solid and liquid substances, an extra term being required for solids. The equations are subject to the qualification that they apply only to hydrocarbons and halogenated hydrocarbons that boil above 100 “C. The preferred equation is the KLH version, which can be stated as In P = -(4.4 In TB) X { 1 . 8 0 3 ( T ~ /-T1) - 0.803 In (TB/T)]- ~ . ~ ( T M 1) /T-
+
where P is the vapor pressure (atm) at environmental temperature T (K) and TB and TM are the boiling and melting point temperatures (K). The third term including the melting point is ignored for liquids, i.e., when the melting point is lower than the environmental temperature. I t is suggested that versions of this equation be developed for other classes of compounds of environmental interests, notably organophosphorus, -nitrogen, -sulfur, and -oxygen compounds.
10-
Literature Cited 1
0.004
0.003
1
I
10.:
0 002
RECIPROCAL ABSOLUTE TEMPERATURE, K-’
Flgure 2. Plot of vapor pressure vs. reciprocal absolute temperature for (A) the TCH and KLH equatlons applied to a substance of bolllng polnt 500 K and (B) the vapor pressure at 298 K (25 “C) of substances with the indicated bolling point.
Table 11. Application of the KLH Equations to Selected Oxygen, Nitrogen, and Sulfur Compounds Illustrating Its Poor Predictive Accuracy (Ref 18 and 19) KLH vapor pressures, atm exptl calcd compound phenol 314 455 20 2.6 x 10-4 7.1 x 10-4 o-cresol 304 464 25 3.2 x 10-4 9.4 x 10-4 p-cresol 308 475 25 1.5 x 10-4 5.1 x 10-4 1-pentanol 194 411 20 3.7 X lo-’ 8.8 X lo-’ 1-octanol 256 468 54 1.3 x 10-3 5.7 x 10-3 nitrobenzene 279 484 20 2.0 x 10-4 2.8 x 10-4 diphenyl sulfide 233 569 96 3.7 x 10-3 1.2 x 10-3 benzo[ blthiophene 304 493 20 2.6 x 10-4 1.4 x 10-4 dibenzothiophene 373 605 20 2.6 X 8.2 X 10-8 quinoline 257 511 25 1.2 x 1 0 - 5 1.1 x 10-4
The potential for misuse is obvious, it being necessary to develop different correlations for oxygen-, nitrogen-, phosphorus-, and sulfur-containing substances. An implication of this work is that in gathering property data for new chemicals, a measurement of boiling point is always justified even when the boiling point greatly exceeds any conceivable environmental temperatures. When no vapor pressure data are available, a “default” value can be estimated from the boiling point by using the KLH equation.
Conclusions Four equations have been proposed, all of which can be considered as versions of existing equations and can be
(1) Spencer, W. F.; Shoup, T. D.; Cliath, M. M.; Farmer, W. J.; Haque, R. J. Agric. Food Chem. 1979, 27, 273. (2) Sinke, G. C. J. Chem. Thermodyn. 1974,6, 311. (3) Macknick, A. B.; Prausnitz, J. M. J . Chem. Eng. Data 1979, 24, 175. (4) Reid, R. D.; Prausnitz, J. M.; Sherwood, T. K. “The Properties of Gases and Liquids”;McGraw Hill: New York, 1977. (5) Kistiakowsky, W. Z. Phys. Chem. 1923, 107, 65. (6) Fishtine, S. H. Ind. Eng. Chem. 1963,55(4), 20; (5),49; (6), 47. (7) Fishtine, S. H. Hydrocarbon Process. 1966, 45, 173. (8) Watson, K. H. Ind. Eng. Chem. 1943, 35, 398. (9) Miller, D. G. J. Phys. Chem. 1964, 68, 1399. (10) Thek, R. E.; Stiel, L. I. AIChE J. 1966, 12, 599. (11) Yalkowsky, S. H. Ind. Eng. Chem. Fundam. 1979,18,108. (12) Mackay, D.; Bobra, A.; Shiu, W. Y.; Yalkowsky, S. H. Chemosphere 1980, 9, 701. (13) Mackay, D.; Shiu, W. Y. J. Chem. Eng. Data 1977,22,399. (14) Zwolinski, B. J.; Whilhoit, R. C. “Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds”; API-44, TRC Publication No. 101: Texas A&M University, College Station, TX, 1971. (15) Boublik, T.; Fried, V.; Hala, E. “The Vapor Pressure of Pure Substances”; Elsevier: Amsterdam, 1973. (16) Mackay, D.; Shiu, W. Y.; Bobra, A. M.; Billington, J. W.; Chau, E.; Yuen, A.; Ng, C.; Szeto, F. Report submitted to U.S.EPA, November, 1980. (17) Mackay, D.; Shiu, W. Y. J . Phys. Chem. Ref. Data 1981, 10, 1175. (18) Smith, J. H.; Mabey, W. F.; Bohonos, N.; Hot, B. R.; Lee, S. S.; Chou, T. W.; Bomberger, D. D.; Mill, T. “Environmental Pathways of Selected Chemicals in Fresh Water Systems”; Part 11, Laboratory Studies, EPA-600/ 7-78-074. (19) Verschuern, K. “Handbook of Environmental Data on Organic Chemicals”;Van Nostrand Reinhold: New York, 1977.
Received for review September 2, 1981. Revised manuscript received May 10,1982. Accepted June 2,1982. We aregrateful to the U.S. EPA and the Canadian Department of the Environment for financial support.
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