Article pubs.acs.org/est
Correlation of Chemical Evaporation Rate with Vapor Pressure Donald Mackay*,† and Ian van Wesenbeeck‡ †
Environmental and Resource Studies, Trent University, 1600 West Bank Drive, Peterborough, Ontario K9J 7B8, Canada Dow AgroSciences, 9330 Zionsville Road, Indianapolis, Indiana 46268, United States
‡
ABSTRACT: A new one-parameter correlation is developed for the evaporation rate (ER) of chemicals as a function of molar mass (M) and vapor pressure (P) that is simpler than existing correlations. It applies only to liquid surfaces that are unaffected by the underlying solid substrate as occurs in the standard ASTM evaporation rate test and to quiescent liquid pools. The relationship has a sounder theoretical basis than previous correlations because ER is correctly correlated with PM rather than P alone. The inclusion of M increases the slope of previous log ER versus log P regressions to a value close to 1.0 and yields a simpler one-parameter correlation, namely, ER (μg m−1 h−1) = 1464P (Pa) × M (g mol−1). Applications are discussed for the screening level assessment and ranking of chemicals for evaporation rate, such as pesticides, fumigants, and hydrocarbon carrier fluids used in pesticide formulations, liquid consumer products used indoors, and accidental spills of liquids. The mechanistic significance of the single parameter as a mass-transfer coefficient or velocity is discussed.
■
INTRODUCTION Evaporation plays an important role in the fate of chemicals applied for agricultural and other purposes. It is useful to have an estimate of the potential for evaporation as a function of the physical−chemical properties of the substance [notably vapor pressure (VP)] as measured under idealized laboratory conditions from a plane surface. Empirical laboratory test data can be used for screening level assessments of chemical volatility and to rank chemicals for the tendency to evaporate. Woodrow et al.1,2 showed that the evaporation rate (ER) from inert surfaces expressed as μg m−2 h−1 correlates well (r2 of 0.989) with measured vapor pressure. Using these data along with data reported by Guth et al.3 and data from the standard ASTM D 3539-87 evaporation rate test,4 van Wesenbeeck et al.5 derived several similar correlations for a total of 82 substances and showed that the linear relationship between ln(ER) and ln(VP) holds over a range of 15 orders of magnitude of pressure (from ∼10−10 to 105 Pa). ER is a particularly important factor for fumigants, in which the product may be applied as a liquid, but the desired toxic exposure occurs via the vapor phase. There are several incentives for obtaining a robust correlation of ER with vapor pressure. In general, it is desirable when selecting chemicals for specific applications that their evaporation characteristics be fully appreciated. For example, Zeinali et al.6 have recently discussed the need to assess the evaporation rate of components of hydrocarbon carrier fluids used in pesticide formulations and, thus, their potential to contribute to ozone formation potential (OFP) using additional data on the maximum incremental activity of the specific substances. There is also interest in assessing the relative evaporation rates and, hence, inhalation exposures of chemicals used indoors. Examples include personal care products, cleaning agents, and pesticides.7−9 Relative ER data are also of interest when assessing the fate and exposures of volatile substances resulting from spills, such as petroleum products.10 We emphasize that, under environmental and especially agricultural conditions, absolute evaporation rates from soil © 2014 American Chemical Society
and vegetation surfaces are strongly influenced by a variety of factors, such as soil or vegetation properties, solar radiation, humidity, and wind speed. Additional factors influence evaporation when the liquid film is very thin and sorptive interactions with the surface influence volatility. The proposed correlation is not intended to address such conditions. Here, we discuss the theoretical basis of correlations of the evaporation rate versus vapor pressure and suggest an improved and simpler approach based on a sounder theoretical treatment of the evaporation process. The proposed correlation is regarded as being particularly suitable for assessing the relative, as distinct from absolute, rates of evaporation of a variety of liquids and can contribute to selection of substances on the basis of evaporation potential.
■
THEORY In this derivation, we use SI units of kilograms, meters, and seconds and molar mass as kg/mol. The pressure is expressed in Pascals with fundamental units of kg m−1 s−2. If a pure liquid of molar mass M (kg mol−1) and vapor pressure P (Pa) (corresponding to the ambient temperature) is present on a solid, non-absorbing surface, it can be assumed that the air immediately in contact with the liquid surface achieves a partial pressure of P (Pa). Applying the ideal gas law, this corresponds to a concentration of P(RT)−1 (mol m−3) or PM(RT)−1 (kg m−3) (also referred to as the saturated vapor concentration at temperature T), where R is the gas constant (8.314 Pa m3 mol−1 K−1) and T is the absolute temperature. The evaporation rate can be estimated as the product of the saturated vapor concentration and a mass-transfer coefficient or velocity k (m s−1), which is essentially the velocity at which the saturated air layer is conveyed from the surface. This velocity can Received: Revised: Accepted: Published: 10259
June 15, 2014 August 5, 2014 August 8, 2014 August 8, 2014 dx.doi.org/10.1021/es5029074 | Environ. Sci. Technol. 2014, 48, 10259−10263
Environmental Science & Technology
Article
Table 1. Properties of the Chemicals at 25 °C, Reported Evaporation Rates and Rate Coefficients Calculated Using Units Employed in Equation 5 chemical name
VP (Pa)
MW (g/mol)
ER (kg m−2 s−1)
Emass/(P × MW)
acetone benzene isobutyl acetate n-butyl acetate (99%) sec-butyl acetate (90%) isobutyl alcohol n-butanol isobutyl isobutyrate cyclohexanol cyclohexanone diethylene glycol monobutyl ether diethylene glycol monoethyl ether diethylene glycol monomethyl ether diacetone alcohol diethyl ketone diisobutyl ketone ethyl acetate ethanol (100%) ethyl amyl ketone ethylbenzene ethylene glycol monobutyl ether ethylene glycol monoethyl ether ethyl lactate n-hexane isophorone mesityl oxide methanol methyl ethyl ketone methyl isobutyl ketone methyl isopropyl ketone methyl n-propyl ketone nitroethane nitromethane 1-nitropropane n-octane n-propyl acetate isopropyl alcohol n-propyl alcohol tetrahydrofuran toluene p-xylene dodecane n-octanol tridiphane trifluralin pendimethalin 2,4-D diazinon toxaphene dieldrin pp′-DDT mean
3.08 × 10 1.27 × 104 2.41 × 103 1.54 × 103 2.95 × 103 1.53 × 103 9.46 × 102 6.27 × 102 9.20 × 101 5.39 × 102 2.80 × 100 2.00 × 101 3.75 × 101 1.65 × 102 4.71 × 103 2.23 × 102 1.26 × 104 7.86 × 103 2.60 × 102 1.28 × 103 7.29 × 101 7.66 × 102 5.00 × 102 2.02 × 104 5.73 × 101 1.46 × 103 1.70 × 104 1.21 × 104 2.69 × 103 6.74 × 103 4.72 × 103 2.80 × 103 4.77 × 103 1.37 × 103 1.85 × 103 4.49 × 103 5.69 × 103 2.83 × 103 2.17 × 104 3.80 × 103 1.17 × 103 1.23 × 101 1.73 × 101 2.93 × 10−2 1.47 × 10−2 4.00 × 10−3 2.67 × 10−3 1.49 × 10−3 5.33 × 10−4 6.59 × 10−4 4.40 × 10−5
58.08 78.11 116.16 116.16 116.16 74.12 74.12 144.22 100.16 98.15 204.27 134.18 120.15 116.16 86.13 142.24 88.11 46.07 128.22 106.17 104.11 132.16 118.13 86.18 138.21 98.15 32.04 72.11 100.16 86.13 86.13 75.07 61.04 89.09 114.23 102.13 60.1 60.1 72.11 92.14 106.17 170.34 130.23 320.43 335.29 281.31 221.04 304.35 413.82 380.91 354.49
5.04 × 102 3.62 × 102 1.36 × 102 8.94 × 101 1.62 × 102 4.50 × 101 3.19 × 101 4.30 × 101 7.05 × 100 2.89 × 101 2.55 × 10−1 8.41 × 10−1 1.09 × 100 8.20 × 100 1.93 × 102 1.60 × 101 4.00 × 102 1.19 × 102 2.24 × 101 6.82 × 101 3.03 × 100 2.38 × 101 1.80 × 101 5.87 × 102 2.17 × 100 7.23 × 101 1.37 × 102 3.40 × 102 1.35 × 102 2.37 × 102 1.91 × 102 1.21 × 102 1.57 × 102 7.62 × 101 1.17 × 102 1.92 × 102 7.56 × 101 6.00 × 101 4.68 × 102 1.82 × 102 7.00 × 101 2.75 × 10−1 3.75 × 10−1 1.98 × 10−3 4.41 × 10−4 2.89 × 10−4 1.86 × 10−4 2.52 × 10−4 5.53 × 10−5 4.78 × 10−5 1.27 × 10−5
1015 1315 1744 1795 1709 1426 1635 1712 2755 1967 1602 1128 872 1537 1710 1815 1298 1181 2424 1812 1438 845 1096 1215 988 1820 905 1401 1799 1472 1690 2078 1936 2247 1993 1504 796 1271 1078 1873 2024 474 599 759 322 924 1135 2004 902 685 2935 1463.9
4
also be regarded, as in Fick’s law, as a ratio of the diffusivity in the air layer D (m2 s−1) and the diffusion path length Y (m); i.e., k is DY−1. The evaporation rate E can then be expressed on either a molar or mass basis as Emolar = Pk(RT )−1
(mol m−2 s−1)
or Emass = PMk(RT )−1
(kg m−2 s−1)
(2)
There is a clear near-linear dependence of E upon P as exploited in the successful correlations described earlier. An issue then arises about the selection of the units of E. If E is expressed as a
(1) 10260
dx.doi.org/10.1021/es5029074 | Environ. Sci. Technol. 2014, 48, 10259−10263
Environmental Science & Technology
Article
mass flux (Emass), such as kg m−2 s−1, or a similar quantity, then the correlation should be with the chemical property PM and not P. However, if E is expressed in units of mol m−2 s−1 (Emolar), then the correlation should be with P alone. Whether correlating Emolar [Pk(RT)−1] with P or correlating Emass [PMk(RT)−1] with PM, care must be taken to use consistent SI units. The Woodrow et al.1,2 and van Wesenbeeck et al.5 correlations are in principle of Emass versus P and not PM. The slopes of the correlations of log E versus log P are consistently less than 1.0, ranging from 0.85 to 0.93 in both studies. This may be due in part to the absence of M in the correlation. Substances of low vapor pressure tend to have higher molar masses; thus, correlating the evaporation rate in mol m−2 s−1 instead of kg m−2 s−1 has the effect of lowering the evaporation rate more for less volatile chemicals, thus increasing the slope. To test this assertion, we modify the correlation to express E as mol m−2 s−1 (i.e., Emolar) and determine if the resulting slope of the plot is closer to 1.0. If the slope is close to 1.0, there may be no need to use log quantities and a simple correlation of Emolar versus P can be suggested, in which the single parameter is the slope and there is no intercept. The slope can be determined in two ways. The simpler way is to determine the average value of the ratio Emolar/P or equivalently Emass/PM. Alternatively, a least-squares regression can be used. Both methods should give similar results. Any systematic dependence of the slope or ratio can be revealed by a plot of the ratio Emolar/P versus P. When the van Wesenbeeck et al.5 correlations were developed, three data sets were used and regressed separately. The regression coefficients were similar, and the parameters differences were statistically insignificant. Accordingly, the standard procedure of dividing the data into a training and validation set was not needed. In essence, the correlation involves obtaining one fitted parameter that has a sounder theoretical basis.
■
versus ln P for the compounds used in this study resulted in a slope of 0.93 and intercept = 12.3 (figure not shown), very similar to the regression parameters obtained for the data set with 82 compounds reported by van Wesenbeeck et al.5 This is expected because the 51 compounds studied here are a subset of the 82 compounds. A plot of the regression of ln Emolar versus ln P is given in Figure 1. Changing from mass to molar unit rates
Figure 1. Plot of ln(Emolar) versus ln(P).
increases the slope to 1.02 (r2 = 0.99). This is much closer to 1.0 than the regression of ln Emass versus ln P in the studies by Woodrow et al.1,2 and van Wesenbeeck et al.,5 where the slope was consistently between 0.87 and 0.93. This suggests that the concept of expressing E on a molar basis does indeed compensate for the effects of lower volatility of high-molecular-weight compounds and increases the linearity of the relationship. The regression of ln Emass versus ln(PM) results in an identical slope (1.02) and a negligible intercept and is not shown. As noted above, the fact that the slope of the line is very close to 1.0 obviates the need for performing the logarithmic transformation on E and P. As a result, Emass can be plotted against PM (Figure 2)
METHODS
The data set used in this study contains 51 of the 82 compounds from the data sets analyzed by van Wesenbeeck et al.5 for which molar mass (M) information could be easily obtained. The other 31 compounds were commercial products of uncertain molecular structure and identity, being subject to commercial confidentiality. The data at 25 °C for evaporation rate E (μg m−2 h−1) and vapor pressures reported in that study were used directly and expanded to include molar mass (M), and E was recalculated on a molar basis (Emolar) using eq 1 with units of mol m−2 s−1 and plotted against P. Alternatively and equivalently, as shown in the previous section, the mass evaporation rate (Emass) with units of kg m−2 s−1 using eq 2 could be plotted against PM (Pa kg mol−1) or PM(RT)−1 (kg m−3), with the latter quantity being the vapor density of the substance in the air phase. Both approaches were tested. It is noteworthy that, in the ASTM D3539 test,4 the evaporation rate of the liquid is measured from a filter paper disk 9 cm in diameter using a liquid volume of 0.7 cm3; thus, the liquid film has a thickness of approximately 0.1 mm, which is sufficient that any sorptive influences from the substrate are negligible. Under agrochemical conditions of high soil surface area and low application rates, such as kg/ha, the films are much thinner and sorption can be a controlling factor.
Figure 2. Plot of Emolar versus P.
or Emolar could be plotted against P to obtain the relationship between the two. If a slope of 1.0 is forced, the ratio of Emass to PM or the ratio of Emolar to P can be regarded as constant and a simple one-parameter correlation results. This one parameter is most readily estimated as either the mean ratio Emass/(PM) or the identical ratio Emolar/P. The average value of this ratio is 4.07 × 10−7, and the standard deviation is 1.55 × 10−7; thus, there is 95% confidence that the
■
RESULTS Table 1 contains the chemical parameters at 25 °C for the 51 compounds used in this study. A linear regression of ln Emass 10261
dx.doi.org/10.1021/es5029074 | Environ. Sci. Technol. 2014, 48, 10259−10263
Environmental Science & Technology
Article
value of the ratio lies between 3.6 × 10−7 and 4.5 × 10−7. There is a trend for the 9 compounds with vapor pressures above 5000 Pa to exhibit a lower slope. To explore if there is a systematic dependence upon P, the ratio is plotted against P for the 51 chemicals in Figure 3, confirming this trend, but the overall effect
proposed here can be used as a “reality check” that estimated values or values obtained from field studies are of the correct order of magnitude. In their models of pesticide evaporation, Davie-Martin et.al.11 expressed the flux correctly, using PM rather than P only. The effect of the temperature is readily assessed by adjusting the vapor pressure using the Clapeyron−Clausius equation. An advantage of the linear relationship is that doubling P doubles ER, whereas this does not apply if the log−log slope is less than 1.0. It is often convenient to express evaporation rates as halftimes or rate constants; however, evaporation from a pure liquid surface is a zero-order process, and half-times can only be estimated if the quantity of the evaporating substance is known. For a defined quantity of liquid, the time for complete evaporation is (quantity of liquid, g m−2)/(evaporation rate, g m−2 h−1). Comparing eqs 1 and 5 to the fitted parameter of 4.07 × 10−7 shows that this parameter is a mass-transfer velocity or coefficient k (m s−1) divided by RT; thus, k is 4.07 × 10−7RT. At 20 °C, k is then 9.91 × 10−4 m s−1 or 3.57 m h−1, which is in fair agreement with measured mass-transfer coefficients in the air phase at low wind speed conditions (
