Environ. Sci. Technol. 1999, 33, 3390-3393
Empirical Prediction of Heats of Vaporization and Heats of Adsorption of Organic Compounds
The temperature dependence of the saturated vapor pressure, piL*, of a (subcooled, superheated) liquid organic compound i is given by the Clausius-Clapeyron equation
ln piL* ) -
∆vapHi 1 + consti R T
(1)
KAI-UWE GOSS* AND R E N EÄ P . S C H W A R Z E N B A C H Swiss Federal Institute for Environmental Science and Technology (EAWAG), and Swiss Federal Institute of Technology (ETH), CH-8600 Du ¨ bendorf, Switzerland
where T is the absolute temperature in Kelvin, R is the gas constant, and ∆vapHi is the enthalpy of vaporization. Over a narrow temperature range (i.e., ambient temperatures) ∆vapHi is almost constant. The adsorption from the gas phase to a solid or liquid surface is commonly described by an adsorption constant Ki,ads:
Partitioning between the gas phase and ambient condensed phases is an important process in determining the transport and fate of organic chemicals in the atmosphere as well as in other environmental compartments exhibiting a vadose zone (e.g., soils). In general, partition processes including the gas phase are strongly temperature dependent and the respective enthalpies of transfer need to be known. Unfortunately, such data are often not available. In this paper, we evaluate the possibilities of estimating both the enthalpies of vaporization from the pure liquid and the enthalpies of gas/surface adsorption of organic compounds from either their (subcooled) liquid vapor pressure or their equilibrium adsorption constant at a particular temperature. Such an approach becomes possible when linear relationships between the enthalpy and entropy, and hence between the enthalpy and the logarithm of the partition constant, exist. Using literature data reported for almost 200 compounds covering a wide range of compound classes we have derived an empirical relationship that can be used to estimate the enthalpy of vaporization, ∆vapHi, of a given compound i from its saturated liquid vapor pressure, piL*, at 25 °C: ∆vapHi (kJ/mol) ) -3.82((0.03) ln piL* (Pa, 25 °C) + 70.0((0.2); n ) 195; r 2 ) 0.99. An analogous equation is given for the estimation of the enthalpy of adsorption of organic vapors to mineral surfaces. The application of this equation to other surfaces including liquid and solid organic phases as well as the liquid water surface is discussed. The equations presented are useful practical tools for approximating the temperature dependence of liquid vapor pressure and of vapor/ surface adsorption constants of organic chemicals in the ambient temperature range.
Ki,ads(m) ≡
Introduction Among the various partition processes that govern the transport and fate of organic compounds in the environment, those involving the gas phase exhibit the strongest temperature dependence. In this paper, we evaluate the possibility to predict the temperature dependence of two important equilibrium processes, i.e., vapor/pure liquid compound partitioning (vapor pressure) and the adsorption from the gas phase to solid or liquid surfaces from the corresponding experimental equilibrium constants determined at a single temperature (e.g., 20 or 25 °C). * Corresponding author phone: +41-1-823 5468; fax: +41-1-823 5471; e-mail:
[email protected]. 3390
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amnt of adsorbate i per surf area of adsorbent (mol m-2) amnt of adsorbate i per vol of gas phase (mol m-3) The effect of temperature on Ki,ads is described by the analogous van’t Hoff eq 2
ln Ki,ads ) -
∆adsHi + RTa 1 + consti′ R T
(2)
where ∆adsHi is the enthalpy of adsorption and Ta is an average temperature in the considered temperature range. The additional term RTa in eq 2 results from the conversion of volumetric gas-phase concentration (used in Ki,ads) to partial pressure units as defined in eq 1 (1). From eqs 1 and 2, it directly follows that if ∆vapHi or ∆adsHi are known, piL*(T2) or Ki,ads (T2) at a temperature T2 can be calculated from the corresponding values at T1 (within the temperature constraints of constant ∆H):
ln piL*(T2) ) ln piL*(T1) + ln Ki,ads(T2) ) ln Ki,ads(T1) +
(
∆vapHi 1 1 R T1 T2
(
)
∆adsHi + RTa 1 1 R T1 T2
(3)
)
(4)
Hence, the temperature dependence of piL* or Ki,ads can be described if the appropriate enthalpy is known. If these enthalpies are not available from experimental data, reliable estimation methods are of great interest. In the following, we inspect the possibilities to use empirically derived linear relationships between the logarithm of the partition constant of a compound i, ln piL* or ln Ki,ads, at a given temperature and its ∆vapHi or ∆adsHi value, respectively. To date a number of linear relationships between the logarithm of partition constants and the corresponding ∆Hi values have been reported (2-6). Since ln Ki of a given partition process is related to the free energy change
ln Ki ) -
∆Gi + consti RT
(5)
and since
∆Gi ) ∆Hi - T∆Si
(6)
such relationships imply also a linear relationship between ∆Hi and ∆Si (i.e., ∆Hi ) a∆Si + c). Intuitively, the existence of a relationship between ∆H and ∆S for a partition process is plausible since a change in the strength of the interactions between molecules, i.e., in ∆H, should also involve a change 10.1021/es980812j CCC: $18.00
1999 American Chemical Society Published on Web 08/24/1999
FIGURE 1. Plot of the enthalpy of vaporization against the logarithm of the saturated liquid vapor pressures at 25 °C for compounds that cover a wide range of different chemical classes. The regression line (eq 7) does not include the outliers which are indicated by their names. in their translational, vibrational, and rotational degrees of freedom, i.e., in ∆Si. It also seems plausible, however, that H-bond interactions which require a particular orientation of the interacting molecules imply a relatively stronger decrease in the entropy of the molecules than van der Vaals interactions which are rather insensitive to the orientation of the interacting molecules. Hence, the quantitative relationship between enthalpy and entropy would not be the same for compounds which are dominated by different types of interactions. So far, linear relationships among ∆Hi, ∆Si, and ∆Gi of partitioning processes have been demonstrated for rather small data sets. They were found to work well for compounds from a given compound class or for partitioning in phases where only van der Vaals interactions take place (2-6). These restrictions may be the reason why such relationships have not yet attained any practical importance in the estimation of enthalpies of partitioning.
Results and Discussion Heats of Vaporization. Experimental data for enthalpies of vaporization and saturated (subcooled) liquid vapor pressures for about 200 compounds, at 25 °C, have been collected from refs 7 and 8. This data set which is given as Supporting Information represents a wide range of different chemical classes: alkanes, alkenes, PAHs, chlorinated C1,C2-compounds, halogenated benzenes, alkylbenzenes, ethers, ketones, amines, phenols, nitriles, sulfides, anilines, pyridines, aldehydes, carboxylic acid esters, and carboxylic acids. Figure 1 shows that the vast majority of this diverse group of compounds fits nicely to a linear regression line between ln piL* and ∆vapHi. The increase in spread from correlation at lower vapor pressures is likely due to higher experimental errors in ln piL* and ∆vapHi. The regression equation (( standard deviation) for all compounds except those indicated by their names in Figure 1 is
∆vapHi (kJ/mol) ) -3.82((0.03) ln piL* (Pa, 25 °C) + 70.0((0.2); n ) 195; r 2)0.99 (7) Equation 7 fits the ∆vapHi values with a relative standard deviation of 4%. An error of 4% in ∆vapHi ) 40 kJ/mol leads to an error of 3.5% in the predicted vapor pressure if extrapolation is done from 25 to 10 °C (a relevant temperature range for environmental applications). For ∆vapHi ) 90 kJ/ mol the same calculation leads to an error of 8% in the extrapolated vapor pressure. These errors are small and easily
acceptable for practical applications. Moreover, a very wide range of ∆vapHi values (20-150 kJ/mol), vapor pressures (15 orders of magnitude), and different compound classes (including H-bonding compounds) appear to obey eq 7. In general, we found that branched compounds (e.g. isoalkanes) and compounds that form strong H-bonds in their pure phase exhibit a larger deviation from the regression line than other compounds. The outliers to eq 7 (see Figure 1) like alcanols and carboxylic acids are the same compounds that show strong deviations from Trouton’s rule which assumes a constant entropy of vaporization for a wide range of compounds at their boiling temperature (9). Acetic acid, for example, is known to form dimers in the gas phase which explains its special behavior. For diisodecyl phthalate the literature value may be erroneous since other alkyl phthalates fit nicely to the regression line. Finally, for vapor pressure data measured at temperatures different from 20 °C (but within the ambient temperature range) one can easily derive the respective equation by combining eq 7 with eq 3 (where T1 is 25 °C and T2 is the target temperature) and assuming a constant ∆vapHi. For vapor pressure data at 20 °C this yields
∆vapHi (kJ/mol) ) -3.72 ln piL* (Pa, 20 °C) + 68.2
(8)
It must be noted that a number of group-contribution methods have been described for the estimation of ∆vapHi (10-12). These methods yield a similar or even better accuracy as eq 7 and have the advantage of predicting the temperature dependence of ∆vapHi. However, they require the knowledge of the critical temperature of the considered compound. In many cases for organic pollutants, only the subcooled liquid vapor pressure at 25 °C is known (from interpolation of gas chromatographic retention data (13)), while other data related to the vaporization process are unavailable. Besides the prediction of ∆vapHi, the existence of a linear relationship between ln piL* and ∆vapHi is helpful for a better general understanding and interpretation of gas phase partitioning data in many instances. Heats of Adsorption. In case of the adsorption equilibrium of organic vapors to surfaces the question was whether a single relationship between ln Ki,ads and ∆adsHi would exist not only for different organic compounds but also for different surfaces. Note, that here only adsorption data measured for “zero coverage conditions” were used so that heats of adsorption and adsorption constants are independent of the surface coverage. Adsorption on Mineral Surfaces. The surfaces of minerals are probably the most relevant surfaces for vapor adsorption in the environment. The ln Ki,ads versus ∆adsHi relationship for mineral surfaces was evaluated with experimental data determined for quartz, kaolinite, hematite, corundum, and lime at relative humidities between 30 and 70% (14-16). In all cases the reported adsorption constants had to be extrapolated to 20 °C using the measured ∆adsHi. For the plot in Figure 2 the adsorbates were divided into three classes: apolar compounds (no H-bonds, e.g., saturated hydrocarbons), weakly polar compounds (weak H-bonds, e.g., aromatic compounds), and strongly polar compounds (strong H-bonds, e.g., ketones, ethers, and alcohols). It appears that all compound classes correlate to the same ln Ki,ads - ∆adsHi relationship and that there was no significant difference between the relationships for different minerals at different relative humiditities. The overall regression equation for all data is (( standard deviation) (Figure 3)
∆adsHi (kJ/mol) ) -4.57((0.17) ln Ki,ads(m3/m2, 20 °C) - 92.2((2.1); n ) 78; r 2 ) 0.91 (9) This fit, while not as good as the one in eq 7 for the enthalpy VOL. 33, NO. 19, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Plot of the enthalpy of adsorption against the logarithm of the corresponding adsorption constants at 20 °C on five different mineral surfaces at various humidities. The regression line corresponds to eq 9 (b - compounds without H-bonds, 0 compounds with weak H-bonds, + - compounds with strong H-bonds.)
FIGURE 3. Plot of the enthalpy of vaporization against the enthalpy of adsorption for different compounds on mineral surfaces (same ∆adsHi data as in Figure 2). of vaporization, has a relative standard error of 6% in the fitted ∆adsHi and is sufficiently accurate for most practical applications. For example, an extrapolation of Ki,ads from 20 to 10 °C for a compound with a 6% error in ∆adsHi ) 50 kJ/mol leads to an error of 3% in the extrapolated Ki,ads. With the help of eq 4, eq 9 can be converted to other temperatures within the temperature range where ∆adsHi is nearly constant like it was done for ∆vapHi (see eq 8). To date, heats of vaporization have been used to estimate heats of sorption of the corresponding compounds. This method has the disadvantage of not considering the properties of the sorbing phase which affect the sorbate-sorbent interactions and hence ∆adsHi. Figure 3 shows a plot of ∆adsHi versus ∆vapHi data for the same compounds and surfaces used in Figure 2. As expected, there is a poor correlation between both parameters. Obviously, the adsorption coefficient, ln Ki,ads, which implicitly includes information about adsorbate-adsorbent interactions, is a much better predictive parameter for ∆adsHi. The data in Figure 2 have shown that a single regression line could fit data for different mineral surfaces. This may in part be due to the adsorbed water that covers all these mineral surfaces at relative humidities above 30% and that tends to 3392
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FIGURE 4. Plot of the enthalpies of adsorption against the logarithm of the corresponding adsorption constants at 20 °C on various organic surfaces in comparison with the regression line for the mineral surfaces (eq 9).
FIGURE 5. Plot of the enthalpy of adsorption against the logarithm of the corresponding adsorption constants at 20 °C on a water surface in comparison with the data for mineral surfaces from Figure 2 (O - apolar compounds on water surface, b - polar compounds on water surface, + - data for the mineral surfaces). level out the influence of the different pure mineral surfaces on the adsorption interactions (16). To check how universal this relationship is we also collected literature data for the adsorption on the following organic surfaces: different carbon fibers (0%RH) (17), cellulose (>92% RH) (18), wood fibers (0% RH) (4), soot (70% RH) (19), glycerol (20), and mono-, di-, and triethyleneglycol (21, 22). For the liquid organic phases, adsorption and absorption of organic compounds occur simultaneously, and for phases thicker than about 1 µm absorption becomes the dominant process (20-22). The data used here, however, represent the adsorption process only. Although Figure 4 shows that the differences in the data sets for different organic surfaces are significant, all data still fall in the vicinity of the regression line for the mineral surfaces (eq 9). Hence, we calculated an overall regression with all these data for mineral and organic surfaces:
∆adsHi (kJ/mol) ) -4.17((0.11) ln Ki,ads (m3/m2, 20 °C) - 88.1((1.3); n ) 182; r 2 ) 0.89 (10) This regression fits the ∆adsHi values with a standard error
of 9%. While this is not as good as a specific regression for a particular surface (due to the wide range of surfaces used for its derivation), eq 11 can provide rough estimates of ∆adsHi values for a wide range of surfaces for which no experimental enthalpies of adsorption are known. Adsorption on a Water Surface. In certain cases, e.g., the enrichment of compounds in fog droplets, adsorption on the water surface is important for the environmental fate of organic compounds (23-25). Adsorption constants and their corresponding enthalpies of adsorption for this process (taken from refs 26 and 27) are plotted in Figure 5 together with the mineral surface data from Figure 2. It appears that the water surface exhibits a behavior different from the other surfaces. The apolar and polar compounds cannot be fitted by a single line. Furthermore there is a larger deviation from the mineral surfaces regression line for the apolar compounds than for any of the other surfaces tested in this paper. The following regression line was found for the apolar compounds adsorbing on a water surface:
∆adsHi (kJ/mol) ) -5.26((0.11) ln Ki,ads (m3/m2, 20 °C) - 112((1.6); n ) 17; r 2 ) 0.99 (11) The distinct difference in the results for the water surface and the mineral surfaces is somewhat unexpected since mineral surfaces at high humidities are covered by an adsorbed water layer and were found to resemble a bulk water surface with respect to the adsorption constants of organic compounds (16). It is not clear yet why water and hydrated mineral surfaces exhibit significantly different ln Ki,ads - ∆adsHi relationshipssespecially for the apolar compoundsswhile the regressions for the mineral surfaces and very different organic surfaces are quite similar. In conclusion we find that the empirical regressions presented here which relate the logarithm of vapor pressure or adsorption constants to their corresponding enthalpies of partitioning are very useful practical tools for the temperature extrapolation of gas phase partition coefficients. The standard deviations associated with these estimations are rather small and acceptable for most practical applications. As a result there are probably few cases where the effort to measure a more accurate experimental value of ∆Hi would be justified. The proportionality between the logarithm of gas phase equilibrium constants and their corresponding enthalpies of partitioning which has been demonstrated here for two different partitioning processes also works for the partitioning between air and a hexadecane phase (data not shown) and may prove helpful for other environmental partitioning equilibria as well.
Supporting Information Available Experimental data for enthalpies of vaporization and saturated liquid vapor pressure for about 200 compounds. This
information is available free of charge via the Internet at http://pubs.acs.org.
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Received for review August 7, 1998. Revised manuscript received May 17, 1999. Accepted June 14, 1999. ES980812J
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