Environ. Sci. Technol. 1983, 27, 15 12- 15 16
Prediction of Activated Carbon Adsorption Capacities for Organic Vapors Using Quantitative Structure-Activity Relationship Methods Nagamany N. Nlrmaiakhandan'~tand Richard E. Speece* CAGE Department, New Mexico State University, Las Cruces, New Mexico 88003, and Civil and Environmental Engineering Department, Vanderbllt University, Nashville, Tennessee 37235
Quantitative structure-activity relationship (QSAR)methods were used to develop models to estimate and predict activated carbon adsorption capacities for organic vapors. Literature isotherm data from two sources for 22 organic contaminants on six different carbons were merged to form a training set of 75 data points. Two different QSAR approaches were evaluated: the molecular connectivity approach and the linear solvation energy relationship approach. The QSAR model developed in this study using the molecular connectivity approach was able to fit the experimental data with r = 0.96 and standard error of 0.09. The utility of the model was demonstrated by using predicted k values to calculate adsorption capacities of 12 chemicals on two different carbons and comparing them with experimentally determined values. Introduction The 1990 Clean Air Act (CAA) Amendments in the United States have aroused serious concerns about gaseous emissionsand their control. Hundreds of chemical process industries and commercial sources are directly impacted by these new regulations. Conventional treatment and storage facilities and certain remediation operations such as air-stripping, soil-venting, and in situ sparging may also be required under these regulations to capture and control their contaminated off-gas emissions. According to the US. Environmental Protection Agency's (EPA) Toxic Release Inventory, some 150 organic chemicals account for four-fifths of the 2.43 billion pounds of toxic air emissions in the United States. Under Title I11 of the CAA, these organic vapors are to be regulated, requiring their sources to install maximum achievable control technologies (MACTs). EPA has been charged with the responsibility of issuing MACT standards for these sources. As an incentive, a key section of Title I11 allows companies to receive a 6-year extension from meeting the MACT requirements, if they voluntarily reduce emissions to 90 % below 1987levels before the EPA issues the MACT standard. Thus, industries and major sources are very much interested in evaluating and selecting appropriate technologies for the control of air emissions of organic vapors. Current MACTs for organic vapors are condensation, incineration, carbon adsorption, and absorption. Of these technologies, carbon adsorption is a more common one offering some advantages over the others: possibility of pure product recovery for reuse; high removal efficiency at low inlet concentrations; and low fuellenergy costs. A majority of the regulated hazardous air pollutants would be amenable to carbon adsorption. A key consideration in selecting and using activated carbon is the adsorption capacity, which is often obtained ~~
t
~~
New Mexico State University. Vanderbilt University.
1512
Environ. Sci. Technoi., Voi. 27, No. 8, 1993
from experimental isotherm data. Because of the trace level concentrations and the analytical limitations, isotherm data are very scarce and require elaborate instrumentation and high degree of precision. For preliminary evaluation, experimentation, process design, and pilot testing, it would be advantageous to be able to know in advance the range of adsorption capacities of activated carbon for various organic vapors. For this reason, predictive methods for estimating adsorption capacities without any experimental data inputs may be desirable. This paper presents a simple model to estimate this basic information from the molecular structure of the vapors using quantitative structure-activity relationship (QSAR) techniques. This model is based on the adsorption potential theory proposed by Dubinin and Polanyi. In the following sections, the theoretical rationale behind the model is briefly outlined, followed by the details of the QSAR modeling approach. Dubinin-Polanyi Adsorption Potential Theory According to the Dubinin-Polanyi theory (1, 2 ) , the condensed liquid volume of the adsorbate per unit mass of the adsorbent, W ,is related to the adsorption potential A by In( Wl W,) = -kA2
(1)
where, k is a parameter for each adsorbate-adsorbent system, and WOis the limiting adsorption amount for a given adsorbent. The adsorption potential A is given by A = R T ln(PdP) (2) R being the ideal gas constant, T being the absolute temperature, PObeing the saturated vapor pressure, and P being the partial pressure of the adsorbate. By selecting a standard reference chemical and comparing other chemicals to the reference chemical, the following can be derived to estimate the adsorption capacity of any organic vapor on an adsorbent (1,2): In W = In W , -k,A2/p2
(3)
where k, is the value of k for the reference compound, and p2 = k$k = (A/A,)2, A, being the value of A for the reference compound. In this context, the parameter p may be considered as an affinity coefficient. Equation 3 can now be combined with eq 2 and expanded as follows to relate the adsorption capacity to the gas-phase partial pressure by In W = In W , -(k,/p2) (RT ln(Po/P))2 (4) Thus, if the W Oand k, values of a reference compound, and POand P values of the adsorbate are known, then W can be calculated from eq 4, if the affinity coefficient, p, can be estimated for the adsorbate. Using this approach, adsorption isotherms and capacities for any organic vapor may be determined by measuring the isotherm for a single 00 13-936X/93/0927-1512$04.00/0
0 1993 American Chemical Society
reference compound, I t follows from this result that 0is independent of the type of carbon, which allows one to develop a generalized model to predict adsorption capacities via an estimated 0. Three approaches have been presented in the literature for estimating 0. Dubinin (3) has proposed the ratio of molar volumes or the ratio of parachors to estimate 0. Reucroft et al. (I)demonstrated that the ratio of electronic polarities could be used to get better estimates of P, if different reference compounds are selected for chemicals of different polarity. In the Reucroft et al. (I) study, 15 chemicals were divided into nonpolar, weakly polar, and strongly polar groups, and for each group, a different reference compound was arbitrarily chosen to estimate 0. They also showed that when a single reference compound was chosen for the entire data set, the percent deviation between the measured 0 and predicted 0 was unacceptably high. Urano et al. (2) examined the validity of the above equations using adsorption isotherm data for 13 chemicals on seven different carbons. Unlike Reucroft et al. (I), Urano et al. (2) used a single reference chemical, benzene, for the entire data set and were able to estimate satisfactory values for 0. They concluded that “... the differences in P were negligible...” between the different carbons and the k value for the reference compound benzene, k,, was practically constant irrespective of the type of adsorbent. The main focus of their study was on WOof the different carbons. The micropore volumes of the different carbons were found to be useful in estimating the corresponding W Ovalues. This study could be of significant benefit to engineers and designers in that the results validate a simple, yet highly practical approach to predict vapor-phase adsorption capacities. This paper presents another approach to estimate k values that can be readily used in vapor-phase adsorption process design. One of the objectives of this study is to test the hypothesis that k values are dependent on the adsorbate alone and are practically independent of the adsorbent. For this purpose, adsorption data from two different literature sources on eight different carbons are analyzed. Another objective is to integrate predictive methods to establish and validate a procedure for estimating adsorption capacities of different adsorbents without any experimental inputs. Toward this objective, experimental adsorption capacities for 13 different adsorbates on two different carbons are compared against predicted values. Finally, a sensitive analysis is performed to examine the uncertainty and the utility value of the predictive method. The method is developed using the quantitative structure-activity relationship (QSAR) approach.
The QSAR Approach QSAR approaches have been very successfully used in medicinal chemistry, drug design, and toxicologicalstudies. The basic premise on which the QSAR approach is built is that an organic chemical’s physical, and biological properties/activities are closely related to its molecular structure. By quantifying the atomic, structural, and topological features of an organic molecule by “molecular descriptors”, statistical relationships can be derived relating them to the chemical’s properties/activities. Two of the more common molecular descriptors used in QSAR studies are the molecular connectivity indexes developed and regularized by Kier and Hall ( 4 , 5 ) ,and the
solvatochromic parameters proposed by Kamlet and coworkers (6). The connectivity indexes can be calculated using a rigid set of algorithms for all classes and types of organic chemicals. The solvatochromic parameters contain four basic components that can be estimated using ground rules published by Kamlet et al. (6). Both these approaches have been previously used in developingstrong QSAR models for liquid-phase adsorption by activated carbon (6,7). This is the rationale for selecting the above two approaches in this study of gas-phase adsorption. In deriving a predictive model by the QSAR technique, an experimental data set has to be used as a training set. On searching the literature, we were able to find only two sources that contained k data for a reasonable number of chemicals: Reucroft et al. (I) and Urano et al. (2). The first source contained data for 15 chemicals for one type of activated carbon. The second one contained data for 13 chemicals and seven different types of carbons. Six chemicals were common to both data sets. [The k values reported by Urano et al. (2) were in mo12/J2unitsand were converted to mo12/ca12units to match the those reported by Reucroft et al. (I). Also, the k values are numerically scaled by a factor of lo8 in the following analysis.] As indicated earlier, according to the Dubinin-Polanyi Theory, the parameter k is chemical-dependent and practically the same for different types of activated carbons. This study was done in part to verify this using a broad based experimental data set. Therefore, instead of averaging the k values for the different carbons [as was done by Urano et al. (2)1, we opted to treat each k value as a separate data point varying with the type of carbon. The effect of different carbons was quantified by WOas indicated by the Dubinin-Polanyi Theory. Thus, when the two data sets were merged, eighty four different k values or “cases” resulted for 22 different chemicals with eight different WOvalues for the eight carbons.
Development of QSAR Model Simple and stepwise multiple regression analysis procedures were used to develop the QSAR model. Preliminary evaluations were done using simple regression analysis with one variable at a time. Then, stepwise multiple regression was applied to improve the quality of fit by adding additional variables. Preliminary analysis of the composite data set indicated significantly large deviations in the case of the three values for formic acid. In order to avoid unduly high bias, this compound was considered an “outlier”and was excluded from the training set and placed in a testing set. To increase the size and diversity of the testing set, additional chemicals were selected from the remaining 81 cases. We choose three chemicals exclusive to each source to be reserved as testing chemicals. Thus, the following chemicals were picked to be added onto the testing set: dioxane, 2,2,4-trimethylpentane, and acetaldehyde from the data reported by Ruecroft et al. (I); and, ethanol, methyl ethyl ketone, and trichloroethylene from Urano et al. (2). This left us with 75 cases in the training set and nine in the testing set. Additional k values for six chemicals taken from No11 et al. (8)were added to the testing set. Out of these six, two had been already included by both Ruecroft et al. (I) and Urano et al. (2) (-benzene and carbon tetrachloride); two more were included by Urano et al. (2) (toluene and trichloroethylene); only the other two @-xylene and tetrachloroethylene) were truly new chemicals. The Envlron. Sci. Technol., Vol. 27, No. 8, 1993
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testing set now contains 15 cases, five of them being new chemicals. These chemicals also represented nonpolar, weakly polar, and strongly polar classes according to Ruecroft’s ( I ) classification, thus forming a truly diverse testing set. Considering the scarcity of experimental data on one hand and the limited number of model parameters one would like to use on the other, these sizes of the training and testing sets are considered adequate to derive and validate a statistically robust QSAR model. Connectivity Approach. In the connectivity approach, the modified, first-order, valence molecular connectivity index, lxV (calculated as per ref 91, alone correlated well with the log k values, explaining over 92 % of the variance in the data: log k = 1.585 - 0.442‘~”
(5)
n = 75; r = 0.961; r2 = 0.924; std error = 0.09 As one of the objectives of this study, we then examined the hypothesis that k values are independent of the type of carbon. First, the effect of different types of carbon was introduced into the analysis by way of WO. The stepwise procedure rejected this variable, indicating that the variation in the experimental log k values was not due to the type of carbon. This finding is in good agreement with the theory. We then examined the hypothesis that the variation in log k values may be due to the two primary raw materials for the carbon: coal in the case of Ruecroft et al. (I)and coconut shell in case of Urano et al. (2).This information was introduced into the analysis via an index (1 for coal and 2 for coconut). When the three variables lxV,the index, and WOwere used in the stepwise multiple regression procedure, again the last two variables were rejected, confirming the theory and adding credence to the fact that k values are independent of the type of adsorbent and are primarily a function of the type of adsorbate. We pursued this line of inquiry further by introducing as an independent variable the micropore fractions of the various carbons that were used in these two studies. For the carbon used by Ruecroft et al. (I), the micropore fraction was 70-75%, while in the Urano et ai. (2) study, the fractions ranged from 43% to 68%. Again, the adsorbate property represented by lxVwas found to be the only significant variable causing the variation in k values. LSER Approach. In this approach, first, the whole array of solvatochromic parameters was tested using the stepwise procedure. Out of the four solvatochromic parameters, only V1ll00 was found to be statistically significant, explaining 88% of the variance in the log k values: log k = 1.854 - 2.332 V,/lOO
(6)
n = 75; r = 0.942; r2 = 0.888; std error = 0.12 Then, the effect of different types of carbon was introduced into the analysis by way of Wo as was done earlier. Again, WOwas rejected in favor of V1/100. On introducing the index as a variable as was done before, the previous hypothesis was confirmed again by the inclusion of only VIllOO. The overall quality of eq 6 is not significantly different from that of the connectivity model as indicated by the statistical parameters. The two equations are comparable in form and are mechanistically very similar as both lxV and V1/100 are closely related to one another in their information content. It has been reported that is a 1514 Envlron. Scl. Technol., Vol. 27, No. 8 , 1993
topological molecular descriptor rich in size and volumerelated properties and is highly correlated with the molar volume. For the data set used in this study, the intercorrelation between lxVand V1ll00was found to be 0.965. Due to the ease and consistency of the method of calculation of the molecular connectivity index and the slightly better quality of fit, we recommended the connectivity index and eq 5 to predict k values. Table I lists the 75 compounds, their experimental and fitted log k values, and the error and the distribution of the standard errors. The maximum raw error range is f0.2 log units. Figure 1 illustrates the quality of fit given by eq 5. These results are in good agreement with previous theoretical studies. For example, Ruecroft et al. (I) concluded that electronic polarization can be used to get good estimates of k while Kier and Hall (4,5) have shown strong correlation between electronic polarization and the first-order connectivity index ( r = 0.99). Electronic polarization has been previously estimated from molar refractivity, which in turn is again very highly correlated with first-order connectivity index ( r > 0.99) for many different classes of chemicals ( 4 , 5 ) . For practical applications, it may be easier to use calculated values of the connectivity index rather than to determine the electronic polarization or the molar refraction which requires measured values for refractive index and the density. The QSAR analyses presented above support the hypothesis that k values are indeed independent of the adsorbent and are adsorbate dependent, again agreeing with the theoretical indications. This conclusion has significant utility value in that the primary variables describing the adsorption process can be cleanly dissected into those depending on the adsorbent alone (WO and k,) and those depending on the adsorbate alone (k). Thus, the QSAR-based predictive model such as eq 5 can be confidently used to quantify the adsorbate-related aspect of the process. Validation of QSAR Model We next tested eq 5 in predicting the log k values for the chemicalsreserved in the testing set. The experimental and predicted log k values for these 15cases are compared in Table 11. In the case of formic acid, the predicted k value is higher than the experimental value, with the error at 7 SE. At this time, we are unable to explain or reconcile this deviation. In the case of dioxane and 2,2,4-trimethylpentane, the predicted errors are high compared to the overall error of fitting. For the remaining cases, the deviations fall within *3 SE of the QSAR model or within a factor of 2. In evaluating these predictions, it has to be noted that the “experimental k values” themselves are obtained by linear regression analysis of the isotherm data and are error-prone. For example, in the case of 2,2,4-trimethylpentane, the original r for the linear isotherm data was reported as 0.770, which is considerably lower than the corresponding values for the rest of the chemicals which generally exceeded 0.98. Similarly, in the case of dioxane, r was somewhat lower at 0.912. The respective errors of 0.31 and 0.42 for these two chemicals are rather high compared to the rest of the predictions, suggesting a possible experimental error and/or inadequacy of the isotherm model as well as a deficiency of this predictive model.
=le
I. ComDarison between Exgerimental and Fitted log k Values
SE
SE
no.
chemical
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
carbontetrachloride carbontetrachloride carbontetrachloride carbontetrachloride carbontetrachloride carbontetrachloride benzene benzene benzene benzene benzene benzene benzene benzene hexane chloroform chloroform chloroform chloroform chloroform chloroform ethylacetate ethylacetate ethylacetate ethylacetate ethylacetate methanol methanol methanol methanol methanol methanol methanol methanol fluorobenzene tetrachloroethane acetone acetone acetone acetone
2.26 2.26 2.26 2.26 2.26 2.26 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.91 1.96 1.96 1.96 1.96 1.96 1.96 1.90 1.90 1.90 1.90 1.90 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 2.10 2.85 1.20 1.20 1.20 1.20
log k distribution no. ref exp fitted error *3SE a b b b b b a b b b b b b b a a b b b b b a b b b b a b b b b b b b a a a b b b
0.66 0.63 0.60 0.64 0.65 0.59 0.74 0.71 0.68 0.62 0.71 0.72 0.66 0.66 0.50 0.78 0.77 0.79 0.79 0.86 0.76 0.80 0.67 0.72 0.71 0.68 1.59 1.52 1.52 1.42 1.52 1.58 1.50 1.48 0.67 0.42 0.94 0.88 0.89 0.89
0.58 0.58 0.58 0.58 0.58 0.58 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.30 0.72 0.72 0.72 0.72 0.72 0.72 0.74 0.74 0.74 0.74 0.74 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.39 0.66 0.32 1.05 1.05 1.05 1.05
0.08 0.05 0.02 0.05 0.06 0.01 0.04 0.01 -0.02 -0.08 0.01 0.02 -0.04 -0.04 0.20 0.06 0.05 0.07 0.07 0.14 0.04 0.05 -0.07 -0.03 -0.03 -0.07 0.20 0.14 0.13 0.03 0.14 0.20 0.11 0.09 0.01 0.10 -0.12 -0.18 -0.16 -0.16
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41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
chemical
x
acetone acetone nitromethane acetonitrile propionaldehyde toluene toluene toluene toluene toluene toluene toluene o-xylene o-xylene o-xylene o-xylene o-xylene nitrobenzene nitrobenzene nitrobenzene ethanol ethanol ethanol ethanol ethanol ethanol methylethyl ketone methyl ethyl ketone methylethyl ketone methyl ethyl ketone trichloroethylene trichloroethylene trichloroethylene trichloroethylene trichloroethylene minimum maximum mean median
1.20 1.20 0.58 0.72 1.35 2.41 2.41 2.41 2.41 2.41 2.41 2.41 2.82 2.82 2.82 2.82 2.82 2.41 2.41 2.41 1.02 1.02 1.02 1.02 1.02 1.02 1.76 1.76 1.76 1.76 2.07 2.07 2.01 2.07 2.07
log k distribution ref exp fitted error A3SE b b a a a b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
0.91 0.82 1.38 1.23 0.96 0.50 0.51 0.42 0.51 0.53 0.47 0.43 0.40 0.40 0.39 0.43 0.39 0.56 0.57 0.58 1.10 1.03 1.14 1.16 1.07 1.06 0.71 0.71 0.73 0.73 0.57 0.56 0.58 0.64 0.58 0.39 1.59 0.80 0.71
1.05 1.05 1.33 1.27 0.99 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.34 0.34 0.34 0.34 0.34 0.52 0.52 0.52 1.13 1.13 1.13 1.13 1.13 1.13 0.81 0.81 0.81 0.81 0.67 0.67 0.67 0.67 0.67 0.30 1.39 0.80 0.72
-0.14 -0.23 0.05 -0.03 -0.03 -0.02 -0.01 -0.10 -0.01 0.01 -0.05 -0.09 0.06 0.06 0.05 0.09 0.05 0.04 0.05 0.07 -0.03 -0.11 0.00 0.03 -0.06 -0.07 -0.10 -0.10 -0.07 -0.08 -0.10 -0.11 -0.09 -0.03 -0.08 -0.23 0.20 0.00 0.01
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n = 75; r = 0.961 ; P 2 = 0.924; std error
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Table 11. Predicted V B Experimental log k Values for Test Chemicals
0.09
0)
-0
-3
1.5
no.
E
chemical
ref
LL
1.o
0.5
0.0 0.0
1.o
0.5
1.5
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Experimental log k Flgure 1. Comparison between observed and fitted log k values for training set.
Application of QSAR Model Using the equations mentioned earlier, a procedure can now be established for predicting isotherms and adsorption capacities of various organic vapors using experimental data obtained by testing a single reference compound. This test will yield WOand k, values. Using the QSAR model developed in this study, k can be estimated for the chemical of interest, and the affinity coefficient from p = v'(k$k). Then, from eq 2, the adsorption potential, A , can be calculated using the appropriate vapor pressure of the
1 2 3 4 5 6 7 8 9
dioxane 2,2,44rimethylpentm acetaldehyde ethanol methyl ethyl ketone trichloroethylene formic acid formic acid formic acid benzene toluene p-xylene carbon tetrachloride trichloroethylene tetrachloroethylene
1,v
log k pred exp
error
2.15 3.42 0.81 1.02 1.76 2.07 0.49 0.49 0.49 2.00 2.41 2.82 2.26 2.07 2.64
0.63 0.94 0.31 0.07 0.49 0.42 a 1.23 1.01 -0.21 a 1.13 1.13 0.00 b 0.81 0.64 -0.17 b 0.67 0.64 -0.03 b 1.37 0.73 -0.63 b 1.37 0.78 -0.58 b 1.37 0.67 -0.70 10 c 0.70 0.54 -0.16 11 c 0.52 0.23 -0.29 12 c 0.34 0.06 -0.28 13 c 0.58 0.56 -0.02 14 c 0.67 0.55 -0.12 15 c 0.42 0.24 -0.18 Reucroft et al. (I). Urano et al. (2). No11 et al. (8). a
a
*
adsorbate and any desired temperature and the partial pressure. Finally, eq 4 will yield W , the adsorption capacity, as the volume of the adsorbate per unit mass of the adsorbent. Multiplying W by the density of the adsorbate then yields the engineering design parameter, Q, the adsorption capacity in mass of adsorbate per mass of adsorbent. From this, the minimum volume of carbon Environ. Scl. Technol., Vol. 27, No. 8, 1993
I616
0.5
0.4 0.3
-T
W
-
Y
2
:
:
:
Y
0.2 0.1
0.8 0.7 0.6
0.5 0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.3
Experimentally Measured Capacity [gr/gr] Figure 2. Comparison between experimentaland predicted adsorption capacities of two different carbons.
required and the reactor size to treat a given volume flow rate of contaminated gas can be easily determined. Urano et al. (2)have presented a very useful procedure in which predictive methods are integrated to estimate all the above parameters, except p. They proposed wellestablished approaches to predict vapor pressure and density of the adsorbate. Based on their own studies, they developed and validated an approach to predict WOfrom the pore size distribution of the adsorbent. The equations proposed by Urano et al. (2) for the various parameters are summarized here for easy reference: predicting vapor pressure of adsorbate, PO:log PO= a - b/(c+ t ) ;predicting density of adsorbate, dt: dt = do- at;predicting the limiting adsorption amount, WO:WO= 0.055 + V3.2where a, b, and c are the parameters of Antoine equation; do is the density at a reference temperature; a is the density temperature correction factor; t is the temperature in "C; and v3.2 is the volume of pores less than 3.2 nm in diameter. To demonstrate the validity of their approach, Urano et al. (2)measured Q values for the 13 chemicals on two different carbons and compared them with predicted Q values calculated using estimated vapor pressure, density, and Wovalues, and experimental fl values. We followed the same approach and used their data along with predicted fl values to estimate Q values without any experimental inputs. The results of Urano et al. predictions and ours are compared against the experimentally measured Q values in Figure 2. The quality of Urano et al. (2) predictions is better than that of our study with r2 averaging 0.99, while the r2 in our predictions were 0.96 and 0.97 for the two carbons. Considering that our results are based purely on predicted model parameters, the agreement with the experimental Q values can be considered very satisfactory. Sensitivity Analysis Having established a predictive model for k and demonstrated its applicability in estimating adsorption capacities, a sensitivity analysis was performed to evaluate the above procedures. As indicated in Table I, the maximum raw error on the predicted log k values was f0.20. This error can be expected to propagate into the adsorption capacities estimated from these log k values. To determine the extent of the propagated error, simulations were done with log k values ranging f0.20 log units, and the corresponding capacities were calculated for the 11 chemicals on the two carbons [B and E as per Urano et al. (2)l. The results of these simulations are presented in Figure 3, from which it can be seen that the propagated error on the final result is less than f 1 0 5% for all chemicals 1516 Envlron. Sci. Technol., Vol. 27, No. 8, 1993
0
I
I
I
I
I
I
I
I
Reucroft, P. J.; Simpson, W. H Jonas, L. A. J.Phys. Chem. 1971,75,3526-3531. Urano, K.; Omori, S.; Yamamoto, E. Environ. Sci. Technol. 1982,16, 10-14. Dubinin, M. M. Chemistry and Physics of Carbon; Walker, P. L., Jr., Ed.; Marcel Dekker: New York, 1966; Vol. 2, p 51. Kier,L. B.; Hal1,L. H. Molecular Connectivity i n Chemistry and Drug Design; Academic Press: New York, 1976. Kier, L. B.; Hall, L. H. Molecular Connectivity in Structure Activity Analysis; Academic Press: New York, 1986. Kamlet, M. J.; Doherty, M. R.; Abraham, M. H.; Taft, R. W. Carbon 1986, 23, 549-554. Nirmalakhandan, N.; Speece, R. E. Environ. Sci. Technol. 1990, 24, 575-580. Noll, K. E.; Gounaris, V.; Kou, W.-S. Adsorption Technology; Lewis Publishers, Inc.: Chelsea, MI, 1992. Nirmalakhandan, N. Ph.D. Thesis, Drexel University, Philadelphia, 1988.
Received for review June 26, 1992. Revised manuscript received March 2,1993. Accepted March 23,1993.
