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The application of BET-type equations to adsorption from mixed vapors of miscible liquids
The Application of BET-Type Equations to Adsorption from Mixed Vapors of Miscible Liquids Recently, the BET theory was extended to the adsorption of mixed vapors by Gu (1), who gave the BETtype mixed adsorption equations which only contained the parameters of BET equations for single vapors. On the other hand, in principle, the assumption that each multilayer single-molecule column can consist only of molecules of the same kind means that the equations should be only applicable for mixed vapors of immiscible liquids (1). Nevertheless, the equations are so simple and attractive that it is valuable to test whether or not they may be applied to adsorption of mixed vapors of miscible liquids. In this note, we report the application of the BET-type mixed equations to the adsorption of mixed vapors of miscible organic liquids. The vapor mixtures were cyclohexane-ethanol, benzene-ethanol, and benzene-cyclohexane; the adsorbent was Cab-O-Sil (a flame-hydrolyzed silica); and the temperature was 30°C. Reference (2) included all the necessary data (including BET parameters for single vapor adsorption) for testing except the vapor pressure of liquids. For the latter, we take 79, 119, and 121 Torr for ethanol, benzene, and cyclohexane, respectively (3). The BET surface area of Cab-O-Sil was 223 mZ/g (4). The calculated results are summarized in Table I. For comparison, the experimental data (2) are also included. The equilibrium relative pressure of each component is shown in the first two columns. The quantity of each component adsorbed (2) is shown in the third and sixth columns, respectively. The calculated adsorption of each component from BET-type mixed equations (n = oo type) is shown in the fourth and seventh columns, respectively. For comparison, Table I also includes the calculated adsorption of each component from a single BET two-parameter equation (the fifth and eighth columns) as if it were present alone at the same partial pressure. According to the theory (1), if the equations can represent the experimental results, the plot of nA/n B against XA(1 -- XB)2/XB( 1 - XA) z should give a straight line through the origin, whose slope is CAnAm/CBnBm, where nA and n B are respective adsorbed quantities of vapors A and B; nA and n~ are the respective quantities of A and B adsorbed when the entire adsorbent surface is covered with a complete monomolecular layer of A and B; XA and XB are the respective relative pressures; and CA and CB are respective constants related to the energies of adsorption and liquefaction of vapors A and B and may be calculated from single vapor adsorption data through the BET equation. Alternatively, the plot of log
(nA/n B) against log [XA(1 - XB)2/XB(I -- XA) 2] also should give a straight line, whose slope is 1 and intercept is log [CAnA/CBnBm]. Figure 1 shows that for ethanolbenzene the BET-type mixed adsorption theory can fit the experimental results quite nicely, but for benzenecyclohexane the systematic deviation is apparent. It should be noted that three data in ethanol-cyclohexane and one datum in ethanol-benzene were not shown in Fig. 1, these being where the adsorption of cyclohexane and benzene was zero. Similarly, Table I shows that for ethanol-benzene the adsorption calculated from BET-type mixed equations agrees with the experimental data quite nicely; for ethanol-cyelohexane the agreement is only semiquantitative. The BET-type mixed equations also indicate that each vapor in the mixture should be adsorbed to a smaller extent than if it were present alone at the same partial pressure. Table I shows that is true for ethanolcyclohexane and ethanol-benzene, but not for benzenecyelohexane. For the latter system, the adsorption of benzene or cyclohexane from mixed vapors may be even more than if it were present alone at the same partial pressure. This result illustrates that under certain conditions the different kind of molecules on the surface may enhance the adsorption of each other. Now the question is when and why the BET-type mixed equations may or may not be used to represent the experimental results. According to the simple calculations based on the BET model made by Brunauer et al. (5), if the parameter C in BET equation is 100, the number of adsorbed layers calculated from BET equation at P/Po = 0.9 is 10. At P/Po = 0.4, the statistical number of adsorbed layers is 1.64. The results illustrate that the lower the P/Po, the less the relative adsorption (compare with the adsorption in the first layer) in the second and higher layers. Moreover, when there are 90 adsorbed molecules in the first layer and 50 empty spaces, the surface coverage is about twothirds. With C = 100, BET equation indicates that such surface coverage is reached at about X = 0.02. According to the derivation of BET equation, it turns out that the number of molecules in the second and third layers is 0.02 and (0.02) 2 times the number of molecules in the first layer, respectively; in other words, the number of molecules in the second and third layers should be 1.8 and 0.036, respectively. If a value of 10 for C is assumed, the BET equation indicates that the same surface coverage is reached at about X = 0.12. This means
599 0021-9797/82/080599-03502.00/0 Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
NOTES
600
TABLE I Mixed Vapor Adsorption n c (mole/m 2) × l0 s
n E (mole/m 2) × 106 XE
Xc
Expt.
BET (mixed)
B E T (single)
Expt.
BET (mixed)
B E T (single)
0.94 0.39 0.36 0.09 0.28 0 0 0
0.84 0.50 0.31 0.21 0.20 0.08 0.03 0.01
1.41 1.02 1.06 0.87 0.86 0.59 0.32 0.16
Ethanol-Cyclohexane 0.046 0.052 0.117 0.135 0.132 0.199 0.253 0.272
0.244 0A65 0.171 0.137 0.133 0.086 0,042 0,021
0.77 1.02 1.76 2.14 2.61 2.78 4.65 4.98
1.80 2.25 3.38 3.79 3.77 4.53 5.13 5.34
2.78 2.95 3.96 4.13 4.08 4.72 5.22 5.39
n E (mole/m 2) × 106 Xe
XB
Expt.
BET (mixed)
n B (mole/m 2) × 106 BET (single)
Expt.
BET (mixed)
BET (single)
2.34 1.87 1.02 1.13 0.74 0.28 0 0.07 0.12 0.05
2.60 1.52 0.98 0.88 0.58 0.45 0.26 0.15 0.10 0.03
3.08 2.25 2.09 1.79 1.78 1.46 1.36 1.06 0.72 0.39
Ethanol-Benzene 0.027 0.042 0.074 0.066 0.124 0.112 0.184 0.221 0.190 0.331
0.310 0.192 0.170 0.133 0A32 0.096 0.087 0.061 0.036 0.018
0.85 1.40 2.34 2.04 2.84 3.19 3.91 4.10 4.38 5.42
0.68 1.43 2.31 2.29 3.24 3.27 4.18 4.67 4.48 5.90
2.14 2.68 3.36 3.23 4.02 3.88 4.59 4.92 4.65 5.96
n B (mole/m 2) × 106 XB
Xc
Expt.
BET (mixed)
n c (mole/m 2) × 106 BET (single)
Expt.
BET (mixed)
BET (single)
1.84 1.49 1.21 0.94 0.85 0.69 0.50 0.31 0.28
1.14 0.86 0.68 0.52 0.43 0.28 0.14 0.08 0.06
1.33 1.17 0.95 0.75 0.75 0.51 0.27 0.27 0.29
Benzene-Cyclohexane 0.040 0.074 0.071 0.071 0.110 0.108 0.105 0.231 0.321
0.228 0.196 0.152 0.114 0.115 0.073 0.035 0.036 0.039
0.80 1.15 1.32 1.40 1.87 1.68 2.23 2.97 3.33
0.39 0.75 0.80 0.88 1.25 1.34 1.43 2.42 3.06
that the number of molecules in the second and third layers should be 11 and 1.3, respectively. These simple calculations illustrate that the higher the C, the less the relative adsorption (compare with the adsorption in the first layer) in the second and higher layers. Therefore, the assumption which involved the properties of the second and higher layers is only secondary for the adsorpJournal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
0.77 1.23 1.19 1.19 1.59 1.57 1.55 2.53 3.16
tion amount, if C is high enough and P/Pois low enough. As the values of C for ethanol, benzene, and cyclohexane are 35.8, 9.50, and 4.61, respectively (2), we can thus predict that the BET-type mixed equations should best fit the ethanol-benzene data and fit the benzene-cyclohexane worst, and, indeed, this is the case. In conclusion, though in principle the BET-type
NOTES
601
Moreover, if the modified BET model (5) which employs a third parameter K is accepted, we can easily obtain modified BET-type mixed equations which may be used to represent the experimental results even over a wider pressure range.
,o~
ACKNOWLEDGMENT I thank Ms. Catherine Mary Kotwica for her kind assistance. o'~
•
FIG. 1. The adsorption from mixed vapors on Cab-OSil, according to the BET-type mixed adsorption equation. Straight lines were calculated from theory; points were experimental results. Straight line 1. O, A - ethanol, B--cyclohexane; 2. ID; A--ethanol, B--benzene; 3. O; A--benzene, B--cyclohexane.
mixed equations should be particularly applicable to the mixed vapors of immiscible liquids, actually they are also useful in adsorption from mixed vapors of miscible liquids if the BET parameter C is high enough and the relative pressure is low enough. In addition, there is no difficulty in extending the BET-type mixed equations for adsorption from a mixture of more than two vapors.
REFERENCES 1. Gu, T., J. Colloid Interface Sci. 82, 584 (1981). 2. Perfetti, G. A., and Wightman, J. P., J. Colloid Interface ScL 49, 313 (1974). 3. International Critical Tables. 4. Matayo, D. R., and Wightman, J. P,, J. Colloid Interface Sci. 44, 162 (1973). 5. Brunauer, S., Skalny, J., and Boder, E. E., J. Colloid Interface Sci. 30, 546 (1969). TIREN .Gu ~ Department o f Chemistry Kent State University Kent, Ohio 44242 Received November 16, 1981; accepted January 7, 1982 I On leave from the Department of Chemistry, Peking University, Peking, China. Present address: Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pa. 19104.
Journalof Colloidand InterfaceScience, Vol. 88, No. 2, August 1982
(nA/n B) against log [XA(1 - XB)2/XB(I -- XA) 2] also should give a straight line, whose slope is 1 and intercept is log [CAnA/CBnBm]. Figure 1 shows that for ethanolbenzene the BET-type mixed adsorption theory can fit the experimental results quite nicely, but for benzenecyclohexane the systematic deviation is apparent. It should be noted that three data in ethanol-cyclohexane and one datum in ethanol-benzene were not shown in Fig. 1, these being where the adsorption of cyclohexane and benzene was zero. Similarly, Table I shows that for ethanol-benzene the adsorption calculated from BET-type mixed equations agrees with the experimental data quite nicely; for ethanol-cyelohexane the agreement is only semiquantitative. The BET-type mixed equations also indicate that each vapor in the mixture should be adsorbed to a smaller extent than if it were present alone at the same partial pressure. Table I shows that is true for ethanolcyclohexane and ethanol-benzene, but not for benzenecyelohexane. For the latter system, the adsorption of benzene or cyclohexane from mixed vapors may be even more than if it were present alone at the same partial pressure. This result illustrates that under certain conditions the different kind of molecules on the surface may enhance the adsorption of each other. Now the question is when and why the BET-type mixed equations may or may not be used to represent the experimental results. According to the simple calculations based on the BET model made by Brunauer et al. (5), if the parameter C in BET equation is 100, the number of adsorbed layers calculated from BET equation at P/Po = 0.9 is 10. At P/Po = 0.4, the statistical number of adsorbed layers is 1.64. The results illustrate that the lower the P/Po, the less the relative adsorption (compare with the adsorption in the first layer) in the second and higher layers. Moreover, when there are 90 adsorbed molecules in the first layer and 50 empty spaces, the surface coverage is about twothirds. With C = 100, BET equation indicates that such surface coverage is reached at about X = 0.02. According to the derivation of BET equation, it turns out that the number of molecules in the second and third layers is 0.02 and (0.02) 2 times the number of molecules in the first layer, respectively; in other words, the number of molecules in the second and third layers should be 1.8 and 0.036, respectively. If a value of 10 for C is assumed, the BET equation indicates that the same surface coverage is reached at about X = 0.12. This means
599 0021-9797/82/080599-03502.00/0 Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
NOTES
600
TABLE I Mixed Vapor Adsorption n c (mole/m 2) × l0 s
n E (mole/m 2) × 106 XE
Xc
Expt.
BET (mixed)
B E T (single)
Expt.
BET (mixed)
B E T (single)
0.94 0.39 0.36 0.09 0.28 0 0 0
0.84 0.50 0.31 0.21 0.20 0.08 0.03 0.01
1.41 1.02 1.06 0.87 0.86 0.59 0.32 0.16
Ethanol-Cyclohexane 0.046 0.052 0.117 0.135 0.132 0.199 0.253 0.272
0.244 0A65 0.171 0.137 0.133 0.086 0,042 0,021
0.77 1.02 1.76 2.14 2.61 2.78 4.65 4.98
1.80 2.25 3.38 3.79 3.77 4.53 5.13 5.34
2.78 2.95 3.96 4.13 4.08 4.72 5.22 5.39
n E (mole/m 2) × 106 Xe
XB
Expt.
BET (mixed)
n B (mole/m 2) × 106 BET (single)
Expt.
BET (mixed)
BET (single)
2.34 1.87 1.02 1.13 0.74 0.28 0 0.07 0.12 0.05
2.60 1.52 0.98 0.88 0.58 0.45 0.26 0.15 0.10 0.03
3.08 2.25 2.09 1.79 1.78 1.46 1.36 1.06 0.72 0.39
Ethanol-Benzene 0.027 0.042 0.074 0.066 0.124 0.112 0.184 0.221 0.190 0.331
0.310 0.192 0.170 0.133 0A32 0.096 0.087 0.061 0.036 0.018
0.85 1.40 2.34 2.04 2.84 3.19 3.91 4.10 4.38 5.42
0.68 1.43 2.31 2.29 3.24 3.27 4.18 4.67 4.48 5.90
2.14 2.68 3.36 3.23 4.02 3.88 4.59 4.92 4.65 5.96
n B (mole/m 2) × 106 XB
Xc
Expt.
BET (mixed)
n c (mole/m 2) × 106 BET (single)
Expt.
BET (mixed)
BET (single)
1.84 1.49 1.21 0.94 0.85 0.69 0.50 0.31 0.28
1.14 0.86 0.68 0.52 0.43 0.28 0.14 0.08 0.06
1.33 1.17 0.95 0.75 0.75 0.51 0.27 0.27 0.29
Benzene-Cyclohexane 0.040 0.074 0.071 0.071 0.110 0.108 0.105 0.231 0.321
0.228 0.196 0.152 0.114 0.115 0.073 0.035 0.036 0.039
0.80 1.15 1.32 1.40 1.87 1.68 2.23 2.97 3.33
0.39 0.75 0.80 0.88 1.25 1.34 1.43 2.42 3.06
that the number of molecules in the second and third layers should be 11 and 1.3, respectively. These simple calculations illustrate that the higher the C, the less the relative adsorption (compare with the adsorption in the first layer) in the second and higher layers. Therefore, the assumption which involved the properties of the second and higher layers is only secondary for the adsorpJournal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
0.77 1.23 1.19 1.19 1.59 1.57 1.55 2.53 3.16
tion amount, if C is high enough and P/Pois low enough. As the values of C for ethanol, benzene, and cyclohexane are 35.8, 9.50, and 4.61, respectively (2), we can thus predict that the BET-type mixed equations should best fit the ethanol-benzene data and fit the benzene-cyclohexane worst, and, indeed, this is the case. In conclusion, though in principle the BET-type
NOTES
601
Moreover, if the modified BET model (5) which employs a third parameter K is accepted, we can easily obtain modified BET-type mixed equations which may be used to represent the experimental results even over a wider pressure range.
,o~
ACKNOWLEDGMENT I thank Ms. Catherine Mary Kotwica for her kind assistance. o'~
•
FIG. 1. The adsorption from mixed vapors on Cab-OSil, according to the BET-type mixed adsorption equation. Straight lines were calculated from theory; points were experimental results. Straight line 1. O, A - ethanol, B--cyclohexane; 2. ID; A--ethanol, B--benzene; 3. O; A--benzene, B--cyclohexane.
mixed equations should be particularly applicable to the mixed vapors of immiscible liquids, actually they are also useful in adsorption from mixed vapors of miscible liquids if the BET parameter C is high enough and the relative pressure is low enough. In addition, there is no difficulty in extending the BET-type mixed equations for adsorption from a mixture of more than two vapors.
REFERENCES 1. Gu, T., J. Colloid Interface Sci. 82, 584 (1981). 2. Perfetti, G. A., and Wightman, J. P., J. Colloid Interface ScL 49, 313 (1974). 3. International Critical Tables. 4. Matayo, D. R., and Wightman, J. P,, J. Colloid Interface Sci. 44, 162 (1973). 5. Brunauer, S., Skalny, J., and Boder, E. E., J. Colloid Interface Sci. 30, 546 (1969). TIREN .Gu ~ Department o f Chemistry Kent State University Kent, Ohio 44242 Received November 16, 1981; accepted January 7, 1982 I On leave from the Department of Chemistry, Peking University, Peking, China. Present address: Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pa. 19104.
Journalof Colloidand InterfaceScience, Vol. 88, No. 2, August 1982