Environ. Sci. Technol. 2002, 36, 4395-4402
Using Extrathermodynamic Relationships To Model the Temperature Dependence of Henry’s Law Constants of 209 PCB Congeners HOLLY A. BAMFORD,† DIANNE L. POSTER,‡ R O B E R T E . H U I E , ‡ A N D J O E L E . B A K E R * ,† Chesapeake Biological Laboratory, University of Maryland, Center for Environmental Science, P.O. Box 38, Solomons, Maryland 20688, and Analytical Chemistry Division, Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8392
Our previous measurements of the temperature dependencies of Henry’s law constants of 26 polychlorinated biphenyls (PCBs) showed a well-defined linear relationship between the enthalpy and the entropy of phase change. Within a homologue group, the Henry’s law constants converged to a common value at a specific isoequilibrium temperature. We use this relationship to model the temperature dependencies of the Henry’s law constants of the remaining PCB congeners. By using experimentally measured Henry’s law constants at 11 °C for 61 PCB congeners described in this paper combined with the isoequilibrium temperatures from our previous measurements of Henry’s law constants of 26 PCB congeners, we have derived an empirical relationship between the enthalpies and the entropies of phase change for these additional PCB congeners. A systematic variation in the enthalpies and entropies of phase change was found to be partially dependent on the chlorine number and substitution patterns on the biphenyl rings, allowing further estimation of the temperature dependence of Henry’s law constants for the remaining 122 PCB congeners. The enthalpies of phase change for all 209 PCB congeners ranged between 10 and 169 kJ mol-1, where the enthalpies of phase change decreased as the number of ortho chlorine substitutions on the biphenyl rings increased within homologue groups. These data are used to predict the temperature dependence of Henry’s law constants for all 209 PCB congeners.
Introduction In many industrial, toxicological, and environmental processes, the Henry’s law constant (KH) and its dependency on temperature play an important role in modeling the diffusive exchange of semivolatile chemicals between gaseous and aqueous phases (1, 2). From an environmental standpoint, KH is a fundamental parameter used to accurately model the * Corresponding author phone: (410)326-7205; fax: (410)326-7341; e-mail:
[email protected]. † University of Maryland. ‡ National Institute of Standards and Technology. 10.1021/es020599y CCC: $22.00 Published on Web 09/19/2002
2002 American Chemical Society
fate and transport of semivolatile chemicals between surface waters and the atmosphere (3-8). Organic contaminants, such as polychlorinated biphenyls (PCBs), are transported through the environment by exchange between the atmosphere and surface waters, and accurate estimates of KH and how it changes with environmental conditions such as temperature are essential to model contaminant exchange processes between air and water. Very few experimental measurements of KH and its temperature dependence for PCBs are available (9, 10). Previous studies modeling diffusive exchange of PCBs between the atmosphere and surface waters estimated KH using an empirical relationship derived by Brunner et al. (11) corrected to ambient temperature using an average enthalpy of phase change (∆HH) for all PCBs (3, 5, 7, 12, 13). In a previous study, we experimentally measured KH and modeled the temperature dependencies of 26 PCB congeners (10). The enthalpy of phase change (∆HH) varied from 14.5 kJ mol-1 for 2,2′,4,6,6′-pentachlorobiphenyl (IUPAC no. 104) to 167 kJ mol-1 for 2,2′,3,3′,4,4′,5,6-octachlorobiphenyl (IUPAC no. 195), indicating a wide range in the temperature dependence among different PCB congeners. Furthermore, the ∆HH measured in our previous study varied systematically with the number of ortho chlorine substitutions on the biphenyl rings. Within a homologue group, ∆HH decreased as the number of ortho chlorine substitutions increased. These observations demonstrate the importance of knowing the temperature dependence of KH for individual PCBs to accurately assess the variability of KH among all 209 PCB congeners. Rather than experimentally measure the temperature dependence of the remaining 183 PCB congeners, it is more feasible to investigate existing relationships and correlations among our measurement data (10) to develop prediction tools to estimate the temperature dependencies of KH values for the remaining PCB congeners. The temperature dependence of KH is derived from the Gibbs equations:
∆GH ) -RT ln KH′
(1)
∆GH ) ∆HH - T∆SH
(2)
and
where ∆GH is the standard Gibbs free energy change (J mol-1) between gas and aqueous phases, T is temperature (K), R is the ideal gas constant (J mol-1 K-1), and KH′ is the dimensionless Henry’s law constant (KH′ ) KH/RT). Equating these two expressions for ∆G and solving for ln KH′ yields the GibbsHelmholtz equation:
ln KH′ ) -∆HH/RT + ∆SH/R
(3)
By directly measuring KH′ at different temperatures and plotting ln KH′ versus 1/T, ∆HH and ∆SH are determined from the slope and intercept, respectively. If ln KH′ versus 1/T plots are produced for a series of compounds and the resulting ∆HH are plotted against ∆SH, there is often a linear relationship between ∆HH and ∆SH. This extrathermodynamic phenomenon is known as the enthalpy-entropy compensation effect (14). That is, for a homologous series the ∆H and ∆S pairs are related in such a manner that changes in one are compensated for by changes in the other. The net result is that the free energy changes are small as compared to the changes in either ∆H or T∆S. This effect was first discussed in detail by Leffler and Grunwald (14), and since then the VOL. 36, NO. 20, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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compensation effect has been observed in a wide range of chemical equilibria and rate processes (15-21). This relationship between entropy and enthalpy is usually linear; thus, for the enthalpy of phase change:
∆HH ) R + β∆SH
(4)
in which R and β are constants. In the above equation, the constant β has the dimension of temperature and is often called the isokinetic or isoequilibrium temperature. This temperature may represent an intersection point for the plots of, in this case, ln KH vs 1/T; that is, a point at which all the values of KH are equal. This is not however a necessary result of this relationship (22). This point we examine further for the 26 PCB congeners later in the paper. The compensation effect and isoequilibrium temperature are extrathermodynamic relationships that are empirical correlations of thermodynamic properties that are not part of the formal structure of thermodynamics but may be used to investigate the role of molecular interactions and structural parameters in various chemical processes. This relationship has been widely implemented in the field of chromatography for the analysis, interpretation, and prediction of retention data and in the fields of organic and biophysical chemistry to characterize the role of molecular structural parameters in equilibrium and rate processes (23-26). In the present paper, we explore an implementation of this relationship to the prediction of KH for PCB congeners and their variation with temperature. The first objective of the present study is to present the compensation effect observed for 26 PCB congeners in our previous investigation in a systematic fashion and to develop a method to predict the temperature dependence of the remaining congeners. The second objective is to extend the database by making experimental determinations of KH for 61 additional PCBs at one temperature and to combine these data with the isoequilibrium temperatures for the various homologue groups to obtain the temperature dependence of KH for these PCB congeners. The third objective is to utilize systematic variations in ∆HH and ∆SH for the combined 87 PCB congeners to estimate the values and temperature dependence of KH for the remaining 122 PCB congeners.
Experimental Section A gas-stripping apparatus was used to measure the KH values at 11 °C for 61 additional PCB congeners. The 61 congeners ranged from mono- to octachlorobiphenyls and included congeners with zero to four ortho-substituted chlorines. The apparatus used here, the experimental setup, sampling methods, and KH calculations have been described elsewhere (10, 27-29). The PCB congeners used in this study were a mixture of individual PCB congeners (AccuStandand, Inc., New Haven, CT) and the National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) 2274, a solution of 11 PCB congeners in 2,2,4-trimethylpentane at certified concentrations ranging from 2.00 to 2.02 µg mL-1. A solution of 61 baseline-resolved PCB congeners was developed at concentrations ranging between 0.6 and 1.0 µg mL-1. An aliquot (≈1 mL) of this solution was spiked into the reactor, resulting in initial dissolved PCB concentrations in the reactor ranging from 60 to 100 ng L-1. Initial PCB concentrations were less than 10% of their aqueous solubilities. The volume of solution added to the reactor was 0.01% of the total volume of water in the reactor. After the PCB solution was added to the reactor, the system was purged with air for 2-3 days to allow the analytes to become wellmixed and equilibrate with the apparatus prior to sampling. For each experiment, simultaneous air and water samples were collected every 6 h for 2 days. 4396
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Sample Analysis and Quality Control. PCB congeners were analyzed using a Hewlett-Packard 5890 gas chromatograph (GC) with a 5% phenyl-methyl-polysiloxane capillary column (J&W Scientific, Folsom, CA) and an electron capture detector (GC-ECD). All analyte peaks were baseline-resolved. Internal standards (Ultra Scientific, North Kingstown, RI) consisting of 2,3,6-trichlorobiphenyl (IUPAC no. 30) and 2,2′3,4,4′,5,6,6′-octachlorobiphenyl (IUPAC no. 204) were added to each sample prior to GC analysis to calculate relative response factors for each congener by comparing a known mass of a congener in the calibration standard to the known mass of each internal standard. Two PCB congeners (2,3,5,6-tetrachlorobiphenyl, IUPAC no. 65, and 2,3,4,4′,5,6-hexachlorobiphenyl, IUPAC no. 166) were added as surrogates to each sample prior to extraction to monitor analytical recovery. The average surrogate recoveries for the dissolved samples were 72 ( 12% (average ( SD, n ) 10) for IUPAC no. 65 and 81 ( 19% (n ) 10) for IUPAC no. 166. Surrogate recoveries for gas-phase samples were 90 ( 8% (n ) 10) for IUPAC no. 65 and 95 ( 12% (n ) 10) for IUPAC no. 166. All PCB congeners in the samples were surrogate-corrected by the recovery of the nearest eluting surrogate. Two independent KH experiments were conducted at 11 °C for the 61 PCB congeners. For each independent experiment, several KH values (n ) 5) were calculated from air and water pairs collected over the duration of the experiment. These replications provide a measure of the precision of the experimental method. For most compounds, the relative standard deviations associated with the mean KH value (n ) 5) observed for each PCB congener were less than 10% within each of the two independent experiments. More importantly, the percent coefficient of variation between the mean KH measured in the first experiment and that measured in the second experiment was less than 15% for most compounds. The KH values from the two experiments were pooled together, and the mean and standard deviation were calculated for each of the 61 PCB congeners measured at 11 °C.
Results Compensation Effect and Isoequilibrium Temperatures. A plot of the ∆HH and ∆SH pairs for the 26 PCB congeners derived from eq 3 fit a linear regression line, suggesting an enthalpy-entropy compensation effect (Figure 1). It should be noted that in some cases an apparent compensation effect is simply a result of correlated experimental error in the measured values (22, 30, 31). Plotting ∆HH and ∆SH with error bars is a simple, clear, and correct method to verify the existence of a compensation effect from experimental data (22). Figure 1 includes the 95% confidence intervals around the ∆HH and ∆SH pairs for the 26 PCB congeners, which indicate that the error in the data pairs are much smaller than their total variation and is evidence that the relationship is not due to random error but that a true compensation effect exists for the congeners. The linear relationship between ∆HH and ∆SH indicates the possibility of a common intersection point at some temperature, TC. From the least-squares fit to the data, this temperature is TC ) 298 K. Linear enthalpyentropy plots with TC near 298 K are not uncommon for solvation in polar solvents and are probably due to the formation of solvated complexes (14). When all the 26 GibbsHelmholtz lines of ln KH versus reciprocal temperature were plotted together however, it was clear that this temperature represented only an area of convergence. An examination of individual plots grouped by homologue suggested that grouping congeners by number of chlorine atoms yielded better intersection points (Figure 2). From the plots in Figure 2, we obtained different intersection points, where TC varies with the number of chlorine atoms. The intersection points
FIGURE 1. Plot of ∆SH vs ∆HH for the 26 PCB congeners with 95% confidence regions. Each data point was obtained by the slope and intercept of the Gibbs-Helmholtz plots. The inset shows Gibbs-Helmholtz plot of the original temperature dependence data for 2,2′,3,5′tetrachlorobiphenyl (PCB 44) as an example (10). for penta-, hexa-, and heptachlorobiphenyl compounds are well-defined (Figure 2) because of an increase in the range of ∆HH values for these congeners (Figure 3). The tetrachlorobiphenyl compounds exhibited a less well-defined intersection point, as did the mono-, di-, and trichlorobiphenyl compounds, which were grouped together because of their more limited experimental data set. This variation in the intersection points may be due to the inherent molecular interactions that are responsible for the extrathermodynamic relationship. For example, the shift in the isoequilibrium point for each homologue group may be caused by a change in the dominant hydrogen bond interactions, effecting the overall quantitative relationship between ∆HH and ∆SH (16). The shifts may also be a function of solvent-solute interactions and hydrophobic interactions, which may be driven by the number of chlorines on the biphenyl rings (15). To establish the validity of these groupings and the existence of common points of intersection, we utilized a statistical relationship estimation based on maximum likelihood to determine the isoequilibrium points and their errors (32, 33). Using the original data, linear regressions of the experimental Gibbs-Helmholtz plots for congeners in each homologue group were performed, and the residual sum of squares was calculated for trial values of the compensation point until the maximum likelihood estimator of the intersect was found. The TC ranged between 306 and 387 K for the different homologue groups. The results of this method were evaluated by comparing the TC estimated from two other independent statistical methods (i.e., least-squares fitting and bootstrap analysis) (34). The points of intersections for each homologue group estimated from the three statistical
methodologies were in good agreement, with
