Environ. Scl. Technol. 1994, 28, 1403-1409
Prediction of Activated Carbon Adsorption Isotherms for Organic Vapors J. Prakash,t N. Nlrmalakhandan,'lt and R. E. Speece* Civil, Agricultural, and Geological Engineering Department, New Mexico State University, Las Cruces, New Mexico 88003, and Civil and Environmental Engineering Department, Vanderbilt University, Nashville, Tennessee 37235
An approach to predict gas-phase activated carbon adsorption isotherms for organic vapors was developed using quantitative structure-activity relationship (QSAR) techniques. The validity of this predictive approach was demonstrated using adsorption isotherm data reported in the literature for 20 different chemicals on four different carbons at various temperatures and partial pressures. The predictions agreed well with the experimental data with a coefficient of determination exceeding 0.9 for all cases. These predictions compared well against the predictions made by other available methods that require experimental inputs. This finding enables gas-phase adsorption isotherms to be developed from limited experimental data and from the molecular structural features of the adsorbates for preliminary evaluations. Introduction Control of air emissions of organic vapors is one of the primary objectives of the stringent regulations introduced under the 1990 Clean Air Act Amendments. Several chemical process industries and other sources are seriously impacted by this Act, which requires substantial reductions in air emissions over a period of a few years. The currently available air pollution control technologies have been developed for traditional air pollutants (viz., SO,, NO,, etc.) and may not be technically andlor economically suitable for organic vapors that are required to be controlled. Activated carbon adsorption is a control process that has good potential for such applications: high removal efficiency,low energy costs, reusable, and possible product recovery. A majority of the hazardous air pollutants identified under the 1990 Clean Air Act are amenable to carbon adsorption. In the selection and design of the activated carbon adsorption process, two important considerations are the adsorption capacity of the carbon and the adsorption isotherm. The adsorption capacity is the amount of adsorbate that can be adsorbed per unit mass of the adsorbent at a given gas-phase concentration under equilibrium conditions. The adsorption isotherm is a graphical representation of the adsorption capacity, relating the variation of the amount of adsorbate adsorbed per unit mass of the adsorbent to the various equilibrium gasphase concentrations. Such data have to be obtained from laboratory experiments that are elaborate and timeconsuming. A study ( I ) reported that the time required to reach equilibrium at a given gas-phase concentration could exceed 400 h to yield 1 data point on the isotherm. This study measured isotherm data for toluene, n-butanol, and methylene chloride and concluded that the cumulative errors in the experimental procedure could average 10%. The overall uncertainty in the adsorbed amounts of the three chemicals was estimated to be about 6 % , 895,and 12%,respectively (I). + New Mexico State University. Vanderbilt University.
*
0013-936X/~4/0928-1403$04.50/0
0 1994 American Chemical Society
Because of the experimental difficulties in measuring adsorption capacities and isotherms for different combinations of adsorbate-adsorbent systems, their predictions have long been the objectives of many researchers. Given the above limitations and uncertainties, it is believed that if predictive methods could yield results within & l o % , then such methods could be confidently used for preliminary evaluations and practical applications. Predicted isotherms can also be used along with the ideal adsorbed solution theory (IAST) to analyze and predict adsorption capacities and isotherms for mixtures of organic vapors (1).
The process of gas-phase adsorption is influenced both by the properties of the adsorbate and those of the adsorbents. Even though the adsorption mechanisms of vapors on carbons are still far from clear (2),the PolanyiReducskevich correlations have been accepted as an adequate theory to form the basis of methods to predict adsorption capacities and isotherms (3-6). A few approaches have been proposed in the literature to predict them from a knowledge of certain physical properties of the adsorbate-adsorbent system. To predict the adsorbaterelated parameters, the molar volume, the molecular parachor, and the electronic polarization of the adsorbates have been proposed. In this paper, we present a simple and direct method to estimate adsorption isotherms using quantitative structure-activity relationship (QSAR) techniques to estimate the adsorbate-related properties. This approach is also based on the well-accepted Polanyi-Reduskevich correlations, but does not require any experimental inputs or a prior knowledge of any experimental values. The proposed approach is validated using literature data for 20 different adsorbates on four different adsorbents at different temperatures and partial pressures. The predictions made by this approach are compared against predictions made by the above three approaches reported in the literature that require experimental inputs or estimated data. Theoretical Background The Polanyi-Reduskevich equation developed from the potential theory has been shown to be applicable to the adsorption of organic vapors on microporous adsorbents (3, 4). According to this equation, the adsorbed liquid volume of the adsorbate per unit mass of the adsorbent, W , is related to the adsorption potential, A , given by In( WI W,) = -kA2
(1)
and A = RT In (PJP) (2) where W, is the maximum adsorption space, k is the parameter for each system of adsorbate and adsorbent, R is the universal gas constant, Tis the absolute temperature, Po is the saturated vapor pressure a t temperature T,and P is the partial pressure of the adsorbate. The above equations have been demonstrated to be valid for PIP, < Environ. Sci. Technol., Vol. 28, No. 8, 1994 1409
0.2 (5);relative humidity 6 0 % (5);and pressures as low as Torr with no evidence of decreasing accuracy with decreasing pressure (7). The molar volume of the adsorbed phase may be assumed equal to the molar volume of the bulk liquid when the adsorption temperature is less than the boiling point of the adsorbate (8, 9). The following development is based on the above limitations, which are believed to be satisfied by most environmental engineering applications, at least as a first approximation. On combining eqs 1 and 2, the adsorption capacity can be related to the gas-phase partial pressure as follows (3, 4):
In W = In W, - k{RT In (PJP))’
(3)
Thus, if W,, k , and Po are known, then Was a function of P can be calculated to generate the adsorption isotherm for any adsorbate-adsorbent system at any desired temperature. Studies reported in the literature indicate that W,is practically a constant, depending only on the adsorbent (4, 5). Thus, eq 3 can be very useful in identifying process variables that are dependent only on the adsorbate (viz., k and Po),those that are dependent upon the adsorbent only (viz., W,), and those on the system (P and 7‘). Several researchers have followed the above analysis and proposed methods to predict the two key variables k and W,. These are summarized in the next section. Prediction Methods
To use eq 3 in predicting adsorption capacities for “new” chemicals, first the adsorption capacity for a standard reference chemical is experimentally determined. Then, by comparing other chemicals to the reference chemical, the following equation can be used:
where k, is the value of k for the reference compound and p2 = k,/k = (A/A,)2,with A, being the value of A for the reference compound. The parameter p has been referred to as an affinity coefficient. Thus, if the W, and k , values of a reference compound and Po and P values of the adsorbate are known, then W can be calculated from eq 4, if the affinity coefficient can be estimated for the adsorbate. Three approaches have been presented in the literature for estimating p. Dubinin (9) has proposed the ratio of molar volumes or the ratio of parachors to estimate 0. Reucroft et al. (3) demonstrated that the ratio of electronic polarities could be used to get better estimates of /3 if different reference compounds are selected for chemicals of different polarity. In the Reucroft et al. (3) study, 15chemicals were grouped into nonpolar, weakly polar, and strongly polar groups, and for each group, a different reference compound was arbitrarily chosen to estimate 8. They also showed that when a single reference compound was chosen for the entire data set, the percent of deviation between the measured p and predicted p was unacceptably high. Urano et al. ( 4 ) measured adsorption capacities for 13 chemicals on seven different carbons to analyze the relationships between the various parameters of eq 4. They concluded that W , was approximately constant for a given adsorbate and could be estimated from the micropore volume for that carbon. Crittenden et al. (5)too confirmed the finding that W, values are dependent only on the 1404
Environ. Sci. Technol., Vol. 28, No. 8, 1994
adsorbent. In contrast to the conclusion of Reucroft et al. (31, Urano et al. (4) concluded that when benzene is used as the reference compound for 13 chemicals with different polarities, satisfactory predictions of p could be made, They further concluded that the value of k, for benzene could be treated as a constant and the differences in are negligible for the different carbons. No11 et al. (6) developed adsorption isotherm data for 10 organic vapors ranging from nonpolar to strongly polar and compared them against isotherms predicted by the three approaches. One of their objectives was to evaluate whether the predictions were influenced by the choice of the reference chemical. When they grouped their data into similar systems (nonpolar adsorbatelnonpolar reference vapor or polar adsorbate/polar reference vapor) and nonsimilar systems (nonpolar adsorbate/polar reference vapor or polar adsorbate/nonpolar reference vapor), they found that for optimum prediction the reference vapor should have similar polarity to the vapor whose isotherm is beingpredicted. Their study further demonstrated that, once an appropriate reference adsorbate had been chosen the three methods were equally accurate in their predictions. On the basis of availability of data and ease of use, they recommended the molar volume method to predict isotherms at different temperatures. The available predictive methods have been shown to be adequate for predicting adsorption isotherms. However, for reliable predictions, the molar volume of the adsorbate and its electronic polarization should be known in advance to estimate p and to choose the appropriate reference adsorbate. Molar volume data are readily available while the electronic polarization needs to be experimentally measured or estimated. In the absence of reported data, molar volume may be determined from the adsorbates molecular weight and liquid density. Electronic polarization may be estimated from a knowledge of the refractive index of the liquid adsorbate at the sodium D wavelength, molecular weight, and the liquid density. The latter may have to be estimated if measured data at the adsorption temperature are not available. The selection of the reference chemical still remains an arbitrary choice. Thus, the best available method using molar volume has certain limitations for rapid estimation of adsorption capacities. In the QSAR-based approach being proposed, the k values (instead of k, or p) for the different adsorbates are predicted directly from a knowledge of the molecular structure of the adsorbates as proposed elsewhere by Nirmalakhandan and Speece (IO). The advantage of this approach over the others is that no experimental inputs are required for estimating k for various chemicals. Further, this approach does not require an appropriate reference chemical to be chosen. The QSAR approach proposed by Nirmalakhandan and Speece (10) uses a single variable model to estimate the value of k. Using the modified, first-order, valence molecular connectivity index, lxV(calculated as per ref 11 and outlined in Chart l),the following QSAR model was developed (10)by linear regression of experimental k values reported in the literature vs lxVvalues for 75 data points: log k = 1.585 - 0.442’~’
(5)
n = 75; r = 0.961; r2 = 0.924;std error = 0.09 This model explained over 92% of the variance in the adsorption capacity data covering 22 nonpolar, weakly
the QSAR approach into eq 3. It is hypothesized that adsorption isotherms at different temperatures for different carbons can be generated without any experimental inputs directly from k,without selecting a specificreference chemical to match the polarity of the adsorbate. The validity of the approach will be demonstrated by comparing the predictions with the three methods reported in the literature.
Chart 1 Algorithm for calculation of molecular connectivity index, 'x,":
ixv =
Tn% 1
where, n is the number of subgraphs containing single bonds and, v l and v2 are the valence values at the terminal points of each bond. For carbon atoms, v's are equal to the number of bonds at each atom; for other atoms used in this paper, v's are as follows: 0 CI OH Atom 6.0 0.69 5.0 Valence value, v Sample calculation for ethyl acetate, CH3COOCHZCH3:
Materials and Methods
Step 1 : Draw hydrogen-suppressed molecular skeleton and label each node-
II0 Step 2: For each node, assign valence nodal values Node ID1 2 3 4 5 Atom c c o c c Valence value, v 1 4 6 2 1
6
o 6
Step 3: Identify subgraphs containing 1 bond eachSubgraphID 1 2 3 4 5 Terminal node IDS 1,2 2,3 3,4 4,5 2,6 Step 4: For each subgraph, calculate nW where, v l and v2 are the terminal valence valuesSubgraph ID 1 2 3 4 5 nvl,v2 4 24 12 2 24 Step 5: Calculate the contribution from each subgraph to
'xV which is
5:n% 1
SubgraphID n-0.5 "1.V2
giving
=
1
2
3
4
5
.50
20
.29
.71
.20
5: n$z
= 1.90 for ethyl acetate.
1
polar, and strongly polar chemicalson six different carbons. It was also found that k values were practically independent of theadsorbent and were dependent only on the adsorbate. When the predictive ability of the model was evaluated on a testing set of 12 different chemicals and two different carbons, the experimental and predicted k values agreed well with r2 exceeding 0.96. A sensitivity analysis showed that the uncertainty in the predicted adsorption capacities due to that in the k values estimated from eq 5 was typically within f10% (10). Additional data are presented in this paper to illustrate the predictive ability of this equation for a wider range of chemicals. The above results are now extended to develop adsorption isotherms by incorporating the k values calculated by
The QSAR model reported in ref 10 for predicting k values is first validated using adsorption data reported by Dubinin (9). This data set (Table 1) contained experimentally measured adsorption capacities for one type of carbon (of Wo = 0.336 mL/g) at three different relative pressures (of P/Po= 1 x 10-4,1 x 10-3, and 1 X and two different temperatures (of 0 and 20 "C). The proposed approach to predict adsorption isotherms using k values from the QSAR model is validated using isotherm data from three different literature sources (6, 1, 12): Reference 6 contained data for eight chemicals on one type of activated carbon at one temperature and for two of the chemicals at three different temperatures on the same activated carbon. The carbon used in this source was carbon A, 20 X 30 BAC (Union Carbide), made from oil pitch of surface area = 800-1100 m2/g; bulk density = 25-35 lb/ft3; Wo= 0.45 mL/g. Reference 1contained data for three chemicals on one kind of activated carbon at one temperature. The carbon used in this source was carbon B, 6 X 16 Pittsburgh BPL (Calgon Corp.), made from coal of surface area = 10501150 m2/g; bulk density = 25-30 lb/ft3; Wo = 0.30-0.49 mL/g. Reference 1 2 contained data for three chemicals on one kind of carbon at one temperature. The carbon used in this source was carbon C, 4 X 6 Columbia JXC (Union Carbide), surface area = 1201-1186 m2/g; Wo= 0.41 mL/ g.
Thus, in all, isotherm data of 13 different organic solvents are used in this study to validate the proposed approach to predict isotherms. Physical properties and adsorption data of the selected solvents that are used in the isotherm calculations are included in Tables 2 and 3.
Table 1. Properties of Chemicals for Use with Adsorption Data Reported by Ref 9
P/Po= 1 x 10-4
calcd ID no.
k
chemical
2.00 2.00 2 cyclohexane 3.00 3.00 3 toluene 2.41 4 propane 1.41 5 n-butane 1.91 6 n-pentane 2.41 2.41 7 n-hexane 2.91 8 n-heptane 3.41 9 chloroform 1.96 1.96 10 carbon tetrachloride 2.26 11 ethyl chloride 1.50 1.50 MCI, molecular connectivity index, 1
benzene
MCIa
lo9
temp [ ( m ~ l / J ) ~ l t"C1 X
2.87 2.87 1.03 1.03 1.89 5.23 3.14 1.89 1.89 1.14 0.68 2.98 2.98 2.20 4.77 4.77
20 0 20 0 20 20 20 20 0
20 20 20 0 20 20 0
PIP,, = 1 x 10-3
P/Po= 1 x 10-2
exp W tmg/gl
calcd W [mg/gl
exP W [mg/gl
calcd W [mg/gl
eXP W [mg/gl
74.98 93.73 77.40 88.34 140.04 9.26 33.71 70.71 91.63 102.55 132.26 87.16 101.49 110.74
69.60 84.92 155.24 127.55 112.42 11.78 39.28 81.16 94.95 124.91 162.90 111.13 138.79 176.62
35.48
38.50
136.69 160.12 134.61 153.96 193.48 42.77 75.56 122.66 139.97 152.54 177.35 182.68 212.53 256.85 66.45 85.15
130.98 147.05 195.10 155.54 170.52 37.31 78.55 123.10 136.33 160.46 189.37 214.69 245.84 286.96 73.65 95.95
223.39 228.86 215.38 227.16 256.13 101.42 136.00 180.38 189.75 204.24 228.45 334.32 372.53 415.26 156.76 180.63
W
calcd [mg/gl
205.77 217.66 229.70 179.23 229.61 85.01 128.86 165.77 176.52 191.90 210.88 343.64 369.84 405.86 156.14 184.23
Environ. Sci. Technol., Vol. 28, No. 8 , 1984
1405
Table 2. Properties of Chemicals for Use with Adsorption Data Reported by Refs 1 and 6 constants in eq 6 ID no.
chemical
1 2 3 4 5 6 7 8 9 10 11
benzene carbon tetrachloride p-xylene tetrachloroethylene 1-butanol ethyl acetate pyridine acetone toluene trichloroethylene methylene chloride
mol wt
U
b
C
d
PC [bar]
78.1 153.8 106.2 165.8 74.1 88.1 79.1 58.1 92.1 131.4 84.9
-6.98 -7.07 -7.63 -7.31 -8.01 -7.69 -7.08 -7.46 -7.29 -7.38 -7.44
1.33 1.71 1.51 1.83 0.54 2.71 1.22 1.20 1.38 1.95 2.18
-2.63 -2.90 -3.20 -3.48 -9.34 -5.35 -2.77 -2.44 -2.83 -3.03 -4.07
-3.33 -2.49 -2.79 -1.00 6.69 -2.34 -2.87 -3.36 -2.79 -5.35 3.51
45.6 35.1 47.6 44.2 38.3 56.3 47.0 41.0 50.5 63.0
[Kl
MCIa
calcd X 109 [(mol/J)2]
562.2 556.4 616.2 620.2 563.1 587.0 620.0 508.1 591.8 572.0 510.0
2.00 2.26 2.82 2.51 2.02 1.90 1.85 1.20 2.41 2.07 1.60
2.87 2.20 1.24 1.71 2.81 3.18 3.34 6.47 1.89 2.67 4.31
TC
k
MCI, molecular connectivity index. Table 3. Properties of Chemicals for Use with Adsorption Data Reported by Ref 12
chemical n-heptane
density [mgimLI
sat. press. [kPal
684.0
5.3
MCIa
calcd k x IO9 [(mol/JPI
vapor concn [PPml
3.41
0.68
56 99 212
1-butanol
806.8
0.9
2.02
2.80
methylisobutyl ketone
800.0
2.1
2.63
1.51
a
368 497 643 53 110 199 353 610 891 82 156 295 362 423 650 814
adsorption capacity exP calcd [mg/gl [mg/gl 214 223 233 241 244 247 225 252 269 288 300 303 263 275 287 290 292 300 303
228.9 236.2 245.3 251.3 254.4 256.9 209.9 236.7 257.5 276.1 292.0 301.7 246.9 262.7 277.3 281.7 285.0 293.5 297.6
MCI, molecular connectivity index.
The first-order, valence molecular connectivity index lxV(calculated as per ref 11and outlined in Chart 1)was substituted in eq 5 to estimate the k values for the adsorbates. The molecular connectivity index values and the resulting k values are also included in Tables 1-3 for all the data sets. The vapor pressures of the various adsorbents at the different temperatures were estimated using the following equation (13),using the parameters listed in Table 2:
500
-e ?
I
400
+
ID#l
x
ID#2
0
ID#3
+ ID#4 0 ID#5
o ID#6 A
ID#7
4
ID#0
V
lD#9 ID#lO
where P, is the vapor pressure (bar); P, is the critical pressure (bar); a , b, c , and d are the constants [-I; T, is the critical temperature (in Kelvin); Tis the temperature (in Kelvin); and x = 1. - T/T,. The various physical constants and coefficients used in eq 6 were obtained from ref 13. The experimental isotherm data in the literature reported the concentrations in ppm and the adsorption capacity in g/g of carbon. To use these in the Polanyi-Reduskevich equation, the concentrations were converted to partial pressures (kPa) and adsorption capacity to condensed liquid volume per unit mass of carbon, W (mL/g), using the appropriate liquid densities (obtained from ref 14). 1406
Envlron. Sci. Technol., Vol. 28, No. 8 , 1994
o ID#ll
Predicted adsorption capacity [mgigr]
Flgure 1. Observedvs predicted adsorption capacities for 11chemicals at three relative pressures and two temperatures. For I D numbers and other details refer to Table 1. (Experimental data from ref 9.)
Results and Discussion
Adsorption Capacities. Data reported by Dubinin (9) for 11 chemicals are first used to demonstrate the
predictive ability of eq 5. The chemicals,their appropriate molecular connectivity indexes, their k values calculated
Table 4. Comparison between Predicted and Calculated Capacities at Different Temperatures (Data from Ref 9) amount adsorbed, W predicted0 adsorption temp [Kl
partial pressure
obsd [mg/gl
298
0.021 0.042 0.209 0.421 0.076 0.085 0.209 0.421 0.021 0.085 0.421 2.051
401.5 455.5 563.6 605.9 360.4 424.9 506.3 552.9 201.9 310.0 461.4 591.2
(a) Trichloroethylene 360.6 416.4 540.9 589.6 338.4 395.3 471.3 527.8 201.1 303.8 440.9 571.2
0.035 0.071 0.172 0.360 0.017 0.071 0.360 1.733 0.017 0.071 0.360 1.733
346.5 367.5 386.7 399.3 270.7 320.0 364.9 394.0 193.4 258.8 325.4 386.2
(b) Toluene 316.7 341.6 369.7 388.9 247.8 305.8 353.7 401.8 195.3 255.5 324.0 377.1
313
333
298
313
333
a
by MV [mdd
by MCI [mg/gl
predictive error by MCI by MV
[%I
[%I
378.6 432.4 550.1 595.4 396.4 405.1 476.2 528.7 205.9 305.5 435.2 556.3 av
10.2 8.6 4.0 2.7 6.1 7.0 6.9 4.5 0.4 2.0 4.4 3.4 5.0
5.7 5.1 2.4 1.7 10.0 4.7 5.9 4.4 2.0 1.5 5.7 5.9 4.6
304.9 326.9 351.6 368.3 239.1 291.0 342.2 375.3 186.5 241.3 301.7 348.4 av
8.6 7.0 4.4 2.6 8.5 4.4 3.1 2.0 1.0 1.3 0.4 2.4 3.8
12.0 11.0 9.1 7.8 11.7 9.1 6.2 4.7 3.6 6.8 7.3 9.8 8.2
MV, molar volume; MCI, molecular connectivity index. 1000 ,
+
ID#l
x ID#2
Line of perlect prediction
800
600
Q
ID#3
+
ID#4
0 ID#5
400
0
ID#6
A
ID#7
e ID#8
v ID#9
200
ID#10 0 ID#ll
0 0
200
400
600
800
11
Predicted adsorption capacity [rng/gr]
Flgure 2. Observed vs predicted adsorption Capacities for 1 1 chemicals at various partial pressure. ID numbers refer to Table 2. (Experimental data from refs 1 and 6.)
from eq 5, the experimentally measured adsorption capacities, W, as reported in the original source, and those predicted in this study are listed in Table 1. The predicted values for these 11 chemicals agreed well with the experimental values as shown in Figure 1 with an overall r2 = 0.916 for the range of experimental conditions for 35 sets of data points. Adsorption Isotherms. The adsorption capacities for the 11 chemicals listed in Table 2 were predicted at various pressures to develop the isotherms. The predicted capacities are compared against the observed capacities at various gas-phase partial pressures (totaling to 68 sets of data points in all) as shown in Figure 2. The overall agreement between the two is highly significant at 95% with a coefficient of determination of 0.982. Typical
predicted isotherms for three chemicals from this list are compared with the experimental data points as shown in Figure 3. Isotherms developed for the three chemicals listed in Table 3 also compare well with the experimental data from ref 12 as shown in Figure 4. The benefit of predicted isotherms is illustrated in these plots-the chemicals have different adsorption characteristics yet can be readily evaluated by calculations without resorting to detailed and costly laboratory experiments. The deviation from perfect predictions stems mainly from the slight inadequacy of the QSAR model in predicting k. Nevertheless, this degree of prediction is comparable to the experimental uncertainty in the isotherm testing procedures. Isotherms for Different Carbons. Two data sources (refs 1and 6) contained isotherm data for two chemicals (viz., 1-butanoland toluene) on two different carbons (viz. carbon A and carbon B). We used the QSAR approach to predict the isotherms for these cases for comparison with the reported experimental data. These comparisons are shown in Figure 5. In developing these isotherms, the different carbons were represented by appropriate W,, values reported in the original sources. These values had been calculated using regression of the experimental data and may, therefore, be error-prone. Even though the quality of the predictions is not high for all the cases, the results support the validity of the integrated approach in predicting isotherms without experimental inputs. Isotherms at Different Temperatures. Adsorption isotherm values for trichloroethylene and toluene at three temperatures and at four different partial pressures have been reported by No11 et al. (9). This data set is used to demonstrate the ability of the proposed approach in predicting isotherms at different temperatures. The capacities predicted by the molar volume approach and Environ. Sci. Technol., Vol. 28, No. 8, 1994 1407
Table 5. Comparison between Four Methods of Estimating W (Data from Ref 9) vapor concn [PPml
obsd W [mg/gl
MV [mgigl
W estimated by” MP EP [mgigl [mgigl
carbon tetrachloride
191 386 1,909 3,842
371.0 434.6 563.9 608.4
388.5 445.0 573.0 584.7
379.6 436.8 567.3 619.8
350.8 410.1 548.5 605.2
p-xylene
150 600 1,500 6,000
351.9 378.8 396.2 411.5
346.9 381.4 398.0 412.0
347.1 381.5 398.0 412.0
346.3 381.1 347.8 412.0
tetrachloroethylene
181 733 1,810 7,275
643.2 714.9 741.5 776.3
562.8 659.8 711.1 764.0
573.3 666.0 714.8 764.8
566.6 662.0 712.4 764.3
1-butanol
201 806 4,034 8,064
308.2 344.0 369.4 372.9
295.2 352.9 394.1 400.1
294.0 352.3 394.0 400.1
306.4 358.4 394.8 400.2
pyridine
229 917 4,587 22,936
316.9 393.9 450.3 480.4
267.6 359.8 447.2 482.2
303.3 383.3 455.1 483.0
345.0 409.0 463.4 483.8
acetone
251 1,004 5,024 25,120
82.2 143.0 229.1 313.6
82.9 141.0 234.2 324.6
82.2 143.3 233.5 324.2
25.0 135.1 226.6 320.7
adsorbate
MCI [mg/gl
MV
392.3 442.3 552.7 596.2 av 334.3 361.2 374.1 384.9 av 565.1 639.4 677.5 716.3 av 283.6 329.1 359.9 363.8 av 275.8 348.1 413.1 440.8 av 47.7 96.6 181.2 276.5 av overall av
4.7 2.4 1.6 3.9 3.2 1.4 0.7 0.5 0.1
[%I
error in estimated W by MP EP MCI
[%I
[%I
[%I
2.3 0.5 0.6 1.9 1.3 1.4 0.7 0.5 0.1
5.4 5.6 2.7 0.5 3.6 1.6 0.6 12.2 0.1 3.6 11.9 7.4 3.9 1.5 6.2 0.6 4.2 6.9 7.3
5.7 1.8 2.0 2.0
0.7
0.7
12.5 7.7 4.1 1.6 6.5 4.2 2.6 6.7 7.3 5.2 15.6 8.7 0.7 0.4 6.3 0.9 1.4 2.2 3.5 2.0 4.0
10.9 6.8 3.6 1.5 5.7
4.6 2.4 6.7 7.3 5.2 4.3 2.7 1.1 0.5
4.7
8.9 3.8 2.9 0.7
2.1
4.1
0.0 0.2 1.9 3.4 1.4 2.7
69.6 5.5 1.1 2.3 19.6 7.0
2.9
5.0 4.6 5.6 6.5 5.4
12.1
10.6 8.6 7.7 9.8
8.0 4.3 2.6 2.4 4.3 13.0 11.6 8.3 8.2 10.3 42.0 32.4 20.9 11.8 26.8 9.9
MV, molar volume; MP, molecular parachor; EP, electronic polarization; MCI, molecular connectivity index.
the proposed QSAR approach and the percent of errors from the two approaches are compared in Table 4. In the proposed approach, the average error in the predictions can be seen to be 6.4%for the two chemicals for the range of conditions tested, with the maximum error being less than 12 7%. These predictions compare very favorably against those of the molar volume approach where the overall average error is 4.4 % . Comparison between Reported and Proposed Methods. The data reported by No11 et al. (9) were used to predict W for six chemicals using the proposed approach. These predictions were compared with Wvalues calculated by them using the three methods: molar volume,molecular parachor, and electronic polarization. Their calculations used different reference compounds to match each chemical‘spolarity to ensure the best results: benzene was chosen as the reference compound for carbon tetrachloride, p-xylene, and tetrachloroethylene; ethyl acetate was chosen for 1-butanol,pyridine, and acetone. These comparisons are presented in Table 5. The overall average percent of error in W was 4.0,2.7, and 7.0, respectively, for the three methods reported in the literature and 9.8 for the method proposed in this study. This larger error is propagated from the vapor pressure estimated from eq 6, it calculated from the QSAR model, eq 5, and the interpolated density values used to convert the literature data for comparison purposes. In the molar volume approach, if experimental data are not available for molar volume, then density data would be required to complete the predictions. Density data for liquid chemicals are not readily available at different temperatures and may have to be in turn estimated. This can result in additional errors in W by the molar volume approach. In the case of toluene, for example, a 10% error 1408
Environ. Scl. Technol., Vol. 28, No. 8,
1994
.
a) Benzene
#
0.40.30.2-
0.1
1
0.00
I
I
I
I
1.oo
I
0.50
1.50
2.00
2.50
Partial pressure [ kPa] 0.5
b) Carbon tetrachloride
0.00
0.12
0.24
0.36
0 I8
Partial pressure [ kPa] 0.08 . c) Methylene chloride
0.06-
0.000
0.005
0.010
0.015
Partial pressure [ kPa] Figure 3. Experimental data points vs predicted isotherm curves for
(a) benzene, (b) carbon tetrachloride, and (c) methylene chloride.
0.45
1
I
"'"
/
1-Butanol
Carbon A
0.20 0.15
I
I
I
I
I
I
,
I
,
I
'
I
~
I
~
I
'
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.06 0.09 0.10 Partial pressure [kPa] 0.45 0.40
b) n-Butanol
:
0 , 0.00001
1,,,1,,1
I
0.0001
1 , 1 1 1 1 1 (
0.001
I
11.1111,
0.01
a
I 1 1 1 U 1 1 ,
I 1 1 1 1
0.1
Partial pressure (kPa]
0,251
0.5 .
I
nyn
0.20
0 . 1 5 1 , I 0.00 0.01
I
I
I
I
0.03
0.02
0.04
::::]
I
I
I
'
'
Carbon A
0.05 0.06 0.07 Partial pressure [kPa]
0.45 ,
I
c) Methyl isobutyl ketone
w
I
0.30
I
0.254
0.204 0.151, 0.00 0.01
I
,
0.02 0.03
I
l
I
I
.
I
0
I
0.00001
0.07 0.08 0.09 Partial pressure [kPa]
0.04 0.05 0.06
Flgure 4. Experimental data points vs predicted isotherm curves for
(a) *heptane, (b) 1-butanol, and (c) methyl isobutyl ketone.
in density would result in 8% error in the final W values. As can be seen from eq 4, errors in density (via P) as well as errors in It, will propagate into the final W values. In the proposed approach, however, k values are predicted directly for use in eq 1,whereby, some of the above errors can be avoided. Since the molecular connectivity indexes are error-free and are calculated from the molecular structures using rigid algorithms, the error arises from the inadequacy of the QSAR model described by eq 5. The quality of this QSAR model may be enhanced by testing additional chemicals of diverse molecular structures.
Literature Cited (1) Rasmuson, A. C. Adsorption equilibria on activated carbon
of mixtures of solvent vapors. An evaluation of the ideal adsorbed solution theory; Royal Institute of Technology: Stockholm, Sweden, May 1984. (2) Tsunoda, R. J. Colloid Interface Sci. 1989,130 ( 1 ) ) 60-68. (3) Reucroft, P. J.; Simpson, W. H.; Jonas, L. A. J.Phys. Chem. 1971, 75, 3526-3531. (4) Urano, K.; Omori, S.;Yamamoto, E. Environ. Sci. Technol. 1982,16, 10-14. (5) Crittenden, J. C.; Cortright, R. D.; Rick, B.;Tang, S.;Perram, D. J. Am. Water Works Assoc. 1988, 90 (9,73-84.
0.0001
0.001
0.01
0.1
1
Partial pressure [kPa] Figure 5. Experimentaldata points vs predicted isotherms for carbons A and B for (a) 1-butanol and (b) toluene.
(6) Noll, K. E.; Gounaris, V.; Hou, W.-S. Adsorption Technology; Lewis Publishers, Inc.: Chelsea, MI, 1992. (7) Grant, R. J.; Manes, M. Znd. Eng. Chem. Fundam. 1964,3 (31, 221-224. ( 8 ) Agrawal, R. K.; Schwarz, J. A. Carbon 1988, 6, 873-887. (9) Dubinin, M. M. Chemistry and Physics of Carbon;Walker, P. L., Jr., Ed.; Marcel Dekker: New York, 1966; Vol. 2, p 51. (10) Nirmalakhandan, N.; Speece, R. E. Environ. Sci. Technol. 1993,27, 1512-1516. (11) Nirmalakhandan, N. Ph.D. Dissertation, Drexel University, Philadelphia, PA, 1988. (12) Golovoy, A.; Braslaw, J. J. Air Pollut. Control Assoc. 1981, 31 (8), 861-865. (13) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids; McGraw-Hill Book Co.: New York, 1986. (14) Beaton, C. F.; Hewit, G. F. Physical Property Data for the Design Engineer; Hemisphere Publishing Corp.: Bristol, PA, 1989.
Received for review September 2, 1993. Revised manuscript received March 8, 1994. Accepted April 25, 1994.' 0
Abstract published in Advance ACS Abstracts, June 1, 1994.
Environ. Scl. Technol., Vol. 28, No. 8 , 1994 1409
