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Adsorption from acetone, benzene, and carbon tetrachloride binary solutions on silica gel
Adsorption
from
Acetone, Benzene, and Carbon Binary Solutions on Silica Gel
Tetrachloride
GUY THOXAS Laboratoire
de clzimie
analytique
plzysique,
Ecole Polytech~ipue
Palaiseau
91120,
France
AND
CLAUDE D@a~~temsnt
de chiwie,
Received
Untiersiti
October
H. EON
de Sherbroohe,
26, 1976;
accepted
Qudbec, February
The behavior of silica gel toward acetone, benzene, and carbon studied in terms of surface composition and activity coefhcients. The for the experimental data. For each system the interfacial tension y three constants J, K, L, according to y = yzo + J In [l + K(1 stands for the interfacial tension between pure solute i and silica; X, The precision on the fit is always better than 1%.
Studies of adsorption at the liquid-solid interface can be undertaken for many purposes. This work originated from the need to investigate the action of well-defined systems in liquid chromatography, especially under nonisochratic conditions. Hence the present system serves as the basis for a subsequent study on the dynamics of liquid chromatography columns. For now, the thermodynamic facet only will be considered. Therefore, except for the system, this article bears some resemblance to papers by Suri and Ramakrishna (l), Armistead et al. (Z), Davis et al. (3, 4), Tyler et al. (S), Eltekov et al. (6), LMatayo and Wightman (7). The theoretical side of adsorption on solid substratum has been developed in several forms (8, 21). Although many of these treatments are quasi-equivalent the series by Everett et al. (14, 18) provides a remarkable conductor-wire because it successively introduces perfect, regular of equal size, athermal of different sizes, and nonathermal of different sizes mixtures. Also evidence is
JlK
ZRl,
Canada
18, 1977 tetrachloride binary systems is monolayer model accounts well can be expressed as a function of - Xi)] + L(1 - Xc). Here ytO is the solute bulk mole fraction.
given of the limitations inherent in the monolayer model (18). The system described here is amenable to an interpretation by Schay’s classical analysis (13) ; experimental isotherms lead to (1) the relative interfacial tension, (2) the composition of the adsorbed layer, and (3) the surface activity coefficients. EXPERIMESTAL
The silica gel, from Woelm, was first studied via B.E.T. measurements using nitrogen. Assuming a surface occupancy of 16 A2 per molecule the gel specific surface area was found to be 631 rnZ per gram. The adsorbent was dehydrated prior to any experiment by heating at 110°C under vacuum. The solvents (spectrophotometricgrade) are from Merck. Acetone and carbon tetrachloride were dehydrated by filtering on a molecular sieve, 4 A. As for benzene, it was dehydrated by reaction with sodium. For each composition two flasks containing the same liquid mixture were prepared.
259 Copyright All rights
0 1977 by Academic Press, Inc. of reproduction in any form reserved.
Journal
of Colloid
and Intc~facc
Science, Vol. 62, No. 2, November 1977 ISSN 0021-9797
260
THOMAS
AND
EON
between the hydroxyl groups of the surface with the r electronic bonds of the aromatic ring. EXPERIMENTAL RELATIVE
EVALUATION OF SURFACE TENSION
THE
Supposing that the three binary systems behave as described by the thermodynamics of the interfacial monolayer, the interfacial tension y for the mixture-adsorbent interface as compared to that yi” of the pure species i-adsorbent interface can be computed.eAccording to Schay (23), ,)/ - yio = + RT l fi(xi) &, s s a<(1 - Xi>Ui FIG. 1. Adsorption isotherms vs xi: A, acetone (i)carbon tetrachloride; B, acetone (i)-benzene; C, benzene (i)-carbon tetrachloride.
A known quantity of adsorbent was added to one of the two flasks. The flasks were next hermetically closed and kept at 30 XL O.l’C with the help of a thermostated bath. After equilibration the liquid phases were analyzed by gas-liquid chromatography. The probes served for the detector calibration. This method has proven to be fast and precise (22). For each pair of flasks the term
is calculated from the mole fraction xi0 of the species i of the initial mixture minus the mole fraction xi after equilibration. Knowing the total number of moles of mixture co and the mass m of adsorbent introduced in the flask gives access to the isotherm f(xi) as f(xi) = nOAxi/m.
of
Colloid
and Interface
Science,
Vol. 62, No. 2, November
c41
ai = fiXi.
S is the specific surface area of the adsorbent. Activity coefficients were computed as functions of xi by means of the nonrandom twoliquid equation (24) and numerical factors given by Renon et al. (24). Details regarding this procedure are to be found in the Appendix. It was also convenient to fit the isotherm in TABLE Coefficients
System
I for Eq. [S] Coefficients
n
d
A
n(l) n(2) n(3)
= 3.1257 = - 0.2588 = - 2.975
d(1) d(2) d(3) d(4)
= 1 = 0.4363 = - 0.9998 = - 0.4365
B
n(l) n(2) n(3)
= = =
0.5148 0.9588 0.4712
d(1) d(2) d(3) d(4)
= = = =
C
92(l) n(2) n(3)
= 1.2869 = - 0.1898 = - 1.1096
d(1) d(2) d(3) d(4)
= 1 = 0.2154 = - 0.9802 = - 0.1956
PI
Results are reported in Fig. 1. The three isotherms are of type II according to the classification proposed by Nagy and Schay (11). As expected, acetone, which can undergo an hydrogen-bonding interaction with silica, adsorbs strongly for systems A and B. As for system C, benzene adsorbs preferentially owing to the more specific interactions Journal
where ai, the solute activity, is related to the activity coefficient fi by
PI
Axi = xi0 - xi
[3]
1977
1 1.4872 0.5864 0.09863
ADSORPTION
terms of an approximated
f(X) = Lto W(X)/?
ON
SILICA
function f(X),
4JJTi@)I j=o (1 - x2>, PI
where X = 2xi - 1, that is, in terms of T,-(X) in a Chebyshev polynomial of order j. The least-squares procedure led to an excellent fit of the experimental data since the dispersion was constantly inferior to 0.5%. The adjustable coefficients are listed in Table I. From Eq. [3], the value of y - yi” can be calculated for various ai, that is, for various xi providing fi is known. Results are expressed in terms of an equation proposed by Semenchenko and Israilov (2.5) primarily for the purpose of fitting surface tensions of binary mixtures,
yz” - yl” = 9.36 X 1O-3 cal m--2, y3O
= -
13.41 X lop3 cal m-2,
y3O- y2O= 4.08 X 10e3 cal me2. Hence, ci,j (yi” - yJo) = 0.03 X 1O-3 cal nr?. Despite this obvious consistency, it should not be concluded that the system behaves according to the monolayer model. This was pointed out by Ash et al. (17). Indeed, systems which TABLE
A B
C
- 1.791 -2.265 -0.3816
as
SURFACE
Surface composition can be obtained by assuming that the monolayer model applies; the basic equation is Ainid + A#
= S. m,
C’il
where n”is the number of moles of the pertinent species within the adsorbed layer; A is the molar surface area or molar occupancy. Equation [7] assumes that any one of the components are always oriented in the same way toward the adsorbent. This, unfortunately, is never warranted. The surface mole fractions xc result from a trivial transformation of Eq. c71 (23h @Xi Xi<
z.z -
___-
x-g
1+ (a - 1)Xi’
J
Xi
=
a + (1 - (Y)Xj’
IIs1
Eq. [6]
where (Y; the separation factor, is calculated from the isotherm S(xJ as
Coefficients
J
COMPOSITIONS AND ACTIVITY COEFFICIENTS
II
Coefficientsfor S,~stem
labeled
must be accounted for in terms of multilayer theories may as well lead to small Ci,j (yi”- yjo) terms (18).
[6]
The precision on the fit is always better than 1%. Coefficients are listed in Table II; the outcome is reported on Fig. 2. The thermodynamic consistency can be asserted by considering the y - -yi” quantities when xx = 0: if 1 = acetone, 2 = benzene, and 3 = carbon tetrachloride then
y - y? vs xi. Systems
1.
SURFACE
+ L(1 - xi).
-
2. Variation of
FIG.
in Fig.
y - yio = J Ln [l + K(l - xi)]
yIo
261
GEL
K
-0.9994 - 0.984 -0.9988
L
0.0941
XidXj
1
+
Ajj(XJ/SXi
X/Xi
1 - A if(xi)/sxj
a=---=
0.00757
.
[I91
1.5175
Once zis is known, the surface activity coeffiJournal
of Cc&id
and Intevjace
Scie~zce,
Vol. 62, No.
2. November
1917
262
THOMAS TABLE
Surface Functions Tetrachloride
.d
0.001
0.002 0.005 0.01 0.05 0.1 0.2 0.3 0.4
In
0.443 0.510 0.576 0.624 0.790 0.876 0.946 0.975 0.99
EON
III
TABLE
Composition and Activity Coefficients of x1 for the System Acetone (1)-Carbon (2)
21
AND
fl”
as
Surface
-0.167 -0.409 -0.853 -1.222 - 1.866 - 1.914 - 1.704 -1.351 -0.862
Tetrachloride x1
XP
0.01
0.151 0.173 0.237 0.334 0.496 0.806 0.950 0.977
0.02 0.05 0.1 0.2 0.5 0.8 0.9
Ln fir = Ln fi + Ln (xJxi”) Note that Everett (14) gives an alternative procedure for the determination of /i”. In any case, the physical meaning of fi” is unclear for surface activity coefficients are function of both surface and bulk concentrations. Obviously fi” reflects deviations from ideal behavior, but usually no correlation whatever can be established with its bulk counterpart, even for the simplest systems (23). When such a correlation does ‘occur we believe it is incidental. The molar surface occupancies A were estimated via B.E.T. measurements, again by assuming a monolayer-type adsorption. If S TABLE
xi 0.001
0.005 0.01 0.02 0.05 0.1 0.2 0.4 0.8 Journal
of Co&d
IV as Func(2)
XP
In fi”
In fz”
0.076 0.268 0.392 0.518 0.671 0.784 0.864 0.900 0.96
- 1.05 -0.85 -0.70 -0.534 -0.347 -0.258 -0.172 -0.077 -0.012
-0.066 -0.217 -0.560 -0.842 -1.218 - 1.940 -2.835
and Intevface
In
fl”
-0.92 -0.50 -0.106 0.055 0.109 0.071 0.029 0.016
In fP
-0.24 -0.335 -0.448 -0.510 -0.526 -0.383 -0.158 -0.151
A = S/m.
- -GO). Cl01
Surface Composition and Activity Coefficients tions of x1 for the System Acetone (l)-Benzene
as
is the silica specific surface area and m the number of moles adsorbed (per gram) at completion of the monolayer then
cient fi” becomes accessible (23) : + (A;/RT)(r
Composition and Activity Coefficients xr for the System Benzene (I)-Carbon (2)
Functions of
In fz”
- 1.123 -0.864 -0.536 -0.319 0 0.043 0.016 -0.029 -0.06
V
Science, Vol. 62, No. 2, November
Pertinent values for A are: acetone = 200 m2 per mmole, benzene = 307 m2 per mmole, and carbon tetrachloride = 255 m2 per mmole. Results for various bulk mole fractions are reported in Tables III-V. The bulk concentration range is purposely restricted to that which corresponds to xi u 5 0.9.5-0.99. The reason for this is obvious if we recall that Ji” is a function of xi and xi”. Suppose a strong relative adsorption, i.e.; the system acetone-carbon tetrachloride, then xi” reaches a value close to unity for relatively small values of xi, in this case about 0.4, compared to unity. However, fi” keeps varying within the interval 0.4 < xi < 1 since both xi and y vary (key Eq. [lo]). Therefore one cannot practically consider the function fir versus xi” when xi0 is very close to unity. In the absence of any reliable statistical theories for specific adsorption one can hardly comment profitably on the values of f? except to say that the functions fi” vs xi” bear no resembIance to their bulk counterparts. Clearly the adjacent monolayer cannot be considered as a bidimensional solution. It is notable that the divergencies from ideality in the surface solution are comparable for acetone in systems A and B and benzene in system C although the specific adsorption of acetone on hydroxyl1977
ADSORPTION
ON
ated silica gel is much stronger than that of benzene. Still, even though the adsorbed monolayer model does not provide a rigorous description of the actual process, it remains a useful and reasonable model for the systems and concentration ranges investigated here.
SILICA
REFERENCES
The three binary systems studied here are shown to behave in a thermodynamically mutually consistent fashion. Their individual behavior may be reasonably accounted for by means of the monolayer model. Besides, adoption of equations for the isotherms and activity coefficients greatly facilitate the determination of the interfacial tensions.
2. 3.
3.
6. 7. 8.
9. APPENDIX
Bulk activity coefficients were generated from N.R.T.L. equation (24, 26) which, in spite of its half theoretical basis, accounts well for all types of Ln ji(xJ functions. The equation involves three adjustable parameters C12, Czl, and OL,some of which are listed with their temperature coefficient in (24). The function Ln fi(xJ is
10. 11. 12. 13. 14. 1.5. 16. 17.
G,j + ‘ij -___(xi + xiGiJ” > ’
7ij = CiJRT
and
Gij = exp[-
(~ij)].
The set of pairs of Q-‘sand G’s which are relevant to this study were obtained from Cij, Cji, and OLfrom (24); they are given below. System
A B C
712
121
-0.4097 - 0.4665 -0.5356
1.5557 0.7403 0.7529
G12
G21
1.0854 1.0978 1.1131
0.7326 0.8624 0.8602
ACKNOWLEDGMENT Thanks
18. 19. 20.
where
are due to G. Guiochon
for his support. Jourml
S. K., AND RAMAKRISHNA, V., T$*ans. Faraday Sot. 65, 1690 (1969). AR&~ISTEAD, C. G., TYLER, A. J., AND HOCKEY, J. A., Trans. Faraday Sot. 67, 493 (1971). Dtlvrs, K. 1M. C., DEUCHAR, J. A., ASD IBBITSON, D. A., Trans. Faraday Sm. 69, 1117 (1973). DAVIS, K. 31. C., DEUCHAR, J. A., AND IBBITSON, D. A., Trans. Famday Sot. 70, 417 (1974). TYLER, A. J., TAYLOR, J. A. G., PETHICA, B. A., AND HOCKEY, J. A., Tram. Faraday Sot. 67, 483 (1971). ELTEKOV, Yu. A., KHOPIXA, V. V., AP;D KISELEV, A. V., Trans. Faraday Sot. 68, 889 (1972). MATAYO, D. R., AND WIGHTMAN, J. P., J. Colloid Interface Sci. 44, 162 (1973). ONO, S., Am KONDO, S., in “Handbuch der Physik” (S. Fltigge, Ed.), Vol. 10, p. 134. Springer, Berlin, 1960. KISELEV, A. V., AND PAVLOVA, L. F., Bull. Aced. Sci. U. S. S. R. Chem. Ser., 12, 15 (1965). KISELEV, A. V., AND KHOPINA, V. V., Trans. Faraday Sot. 65, 1936 (1969). NXY, L. G., AND SCHAY, G., Act. Chim. Acad. Sci. Nungary 39, 365 (1963). NAGY, L. G., SCH.~Y, G., AND SZEKRENYESY, T., Periodica Polytecknica 6, 91 (1962). SCHAY, G., J. Colloid Integace Sci. 42, 478 (1973). EVERETT, D. H., Trans. Falpaday Sot. 60, 1803 (1964). EVERETT, D. H., Trans. Faraday Sot. 61, 2478 (1965). ASH, S. G., EVERETT, D. H., AND FINDENEQQ, G. H., Trans. Faraday Soc. 64, 2639 (1968). ASH, S. G., Bowx, R., AND EVERETT, D. H., Trans. Faraday Sot. 71, 123 (1975). BROWN, C. E., EVERETT, D. H., ,~ND MORGAN, C. J., J. Clzem. Sot., Faraday Trans. 71, 883 (1975). LANE, J. E., Amt. J. Chem 20, 827 (1967). ALTENBERGER, A. R., AND STECKI, J., Ckem. Phys. Lett. 43, 119 (1939).
1. SURI,
4.
CONCLUSION
263
GEL
21. LARIONOV, 0. G., AND ,MYERS, A. L., Chew Eng. Sci. 26, 1025 (1971). 22. DAVYDOV, V., AND KISELEV, A. V., Dokl. Akad. iliauk. SSSR 192, 1299 (1970). 23. SCHAY, G., k “Surface and Colloid Science” (E. Matijevic, Ed.), Chap. 3. Wiley-Interscience, New York, 1969. 24. RENON, H., ASSELINEAU, L., COHEN, G., AND RAW BAULT, C. in “Calcul sur ordinateur des Cquilibres liquide-vapeur et liquide-liquide” (Technip, Ed.), 1971. 25. SEYENCHENKO, V. K., AXD ISRAILOV, I. U., Russ. J. Phys. Chem. 48, 1801 (1974). 26. RENON, H., AND PRAUSNITZ, J. M., AIChE J. 14, 135 (1968). of Colloid
awd Inlerface
Science,
Vol. 62, No. 2, November
1977
from
Acetone, Benzene, and Carbon Binary Solutions on Silica Gel
Tetrachloride
GUY THOXAS Laboratoire
de clzimie
analytique
plzysique,
Ecole Polytech~ipue
Palaiseau
91120,
France
AND
CLAUDE D@a~~temsnt
de chiwie,
Received
Untiersiti
October
H. EON
de Sherbroohe,
26, 1976;
accepted
Qudbec, February
The behavior of silica gel toward acetone, benzene, and carbon studied in terms of surface composition and activity coefhcients. The for the experimental data. For each system the interfacial tension y three constants J, K, L, according to y = yzo + J In [l + K(1 stands for the interfacial tension between pure solute i and silica; X, The precision on the fit is always better than 1%.
Studies of adsorption at the liquid-solid interface can be undertaken for many purposes. This work originated from the need to investigate the action of well-defined systems in liquid chromatography, especially under nonisochratic conditions. Hence the present system serves as the basis for a subsequent study on the dynamics of liquid chromatography columns. For now, the thermodynamic facet only will be considered. Therefore, except for the system, this article bears some resemblance to papers by Suri and Ramakrishna (l), Armistead et al. (Z), Davis et al. (3, 4), Tyler et al. (S), Eltekov et al. (6), LMatayo and Wightman (7). The theoretical side of adsorption on solid substratum has been developed in several forms (8, 21). Although many of these treatments are quasi-equivalent the series by Everett et al. (14, 18) provides a remarkable conductor-wire because it successively introduces perfect, regular of equal size, athermal of different sizes, and nonathermal of different sizes mixtures. Also evidence is
JlK
ZRl,
Canada
18, 1977 tetrachloride binary systems is monolayer model accounts well can be expressed as a function of - Xi)] + L(1 - Xc). Here ytO is the solute bulk mole fraction.
given of the limitations inherent in the monolayer model (18). The system described here is amenable to an interpretation by Schay’s classical analysis (13) ; experimental isotherms lead to (1) the relative interfacial tension, (2) the composition of the adsorbed layer, and (3) the surface activity coefficients. EXPERIMESTAL
The silica gel, from Woelm, was first studied via B.E.T. measurements using nitrogen. Assuming a surface occupancy of 16 A2 per molecule the gel specific surface area was found to be 631 rnZ per gram. The adsorbent was dehydrated prior to any experiment by heating at 110°C under vacuum. The solvents (spectrophotometricgrade) are from Merck. Acetone and carbon tetrachloride were dehydrated by filtering on a molecular sieve, 4 A. As for benzene, it was dehydrated by reaction with sodium. For each composition two flasks containing the same liquid mixture were prepared.
259 Copyright All rights
0 1977 by Academic Press, Inc. of reproduction in any form reserved.
Journal
of Colloid
and Intc~facc
Science, Vol. 62, No. 2, November 1977 ISSN 0021-9797
260
THOMAS
AND
EON
between the hydroxyl groups of the surface with the r electronic bonds of the aromatic ring. EXPERIMENTAL RELATIVE
EVALUATION OF SURFACE TENSION
THE
Supposing that the three binary systems behave as described by the thermodynamics of the interfacial monolayer, the interfacial tension y for the mixture-adsorbent interface as compared to that yi” of the pure species i-adsorbent interface can be computed.eAccording to Schay (23), ,)/ - yio = + RT l fi(xi) &, s s a<(1 - Xi>Ui FIG. 1. Adsorption isotherms vs xi: A, acetone (i)carbon tetrachloride; B, acetone (i)-benzene; C, benzene (i)-carbon tetrachloride.
A known quantity of adsorbent was added to one of the two flasks. The flasks were next hermetically closed and kept at 30 XL O.l’C with the help of a thermostated bath. After equilibration the liquid phases were analyzed by gas-liquid chromatography. The probes served for the detector calibration. This method has proven to be fast and precise (22). For each pair of flasks the term
is calculated from the mole fraction xi0 of the species i of the initial mixture minus the mole fraction xi after equilibration. Knowing the total number of moles of mixture co and the mass m of adsorbent introduced in the flask gives access to the isotherm f(xi) as f(xi) = nOAxi/m.
of
Colloid
and Interface
Science,
Vol. 62, No. 2, November
c41
ai = fiXi.
S is the specific surface area of the adsorbent. Activity coefficients were computed as functions of xi by means of the nonrandom twoliquid equation (24) and numerical factors given by Renon et al. (24). Details regarding this procedure are to be found in the Appendix. It was also convenient to fit the isotherm in TABLE Coefficients
System
I for Eq. [S] Coefficients
n
d
A
n(l) n(2) n(3)
= 3.1257 = - 0.2588 = - 2.975
d(1) d(2) d(3) d(4)
= 1 = 0.4363 = - 0.9998 = - 0.4365
B
n(l) n(2) n(3)
= = =
0.5148 0.9588 0.4712
d(1) d(2) d(3) d(4)
= = = =
C
92(l) n(2) n(3)
= 1.2869 = - 0.1898 = - 1.1096
d(1) d(2) d(3) d(4)
= 1 = 0.2154 = - 0.9802 = - 0.1956
PI
Results are reported in Fig. 1. The three isotherms are of type II according to the classification proposed by Nagy and Schay (11). As expected, acetone, which can undergo an hydrogen-bonding interaction with silica, adsorbs strongly for systems A and B. As for system C, benzene adsorbs preferentially owing to the more specific interactions Journal
where ai, the solute activity, is related to the activity coefficient fi by
PI
Axi = xi0 - xi
[3]
1977
1 1.4872 0.5864 0.09863
ADSORPTION
terms of an approximated
f(X) = Lto W(X)/?
ON
SILICA
function f(X),
4JJTi@)I j=o (1 - x2>, PI
where X = 2xi - 1, that is, in terms of T,-(X) in a Chebyshev polynomial of order j. The least-squares procedure led to an excellent fit of the experimental data since the dispersion was constantly inferior to 0.5%. The adjustable coefficients are listed in Table I. From Eq. [3], the value of y - yi” can be calculated for various ai, that is, for various xi providing fi is known. Results are expressed in terms of an equation proposed by Semenchenko and Israilov (2.5) primarily for the purpose of fitting surface tensions of binary mixtures,
yz” - yl” = 9.36 X 1O-3 cal m--2, y3O
= -
13.41 X lop3 cal m-2,
y3O- y2O= 4.08 X 10e3 cal me2. Hence, ci,j (yi” - yJo) = 0.03 X 1O-3 cal nr?. Despite this obvious consistency, it should not be concluded that the system behaves according to the monolayer model. This was pointed out by Ash et al. (17). Indeed, systems which TABLE
A B
C
- 1.791 -2.265 -0.3816
as
SURFACE
Surface composition can be obtained by assuming that the monolayer model applies; the basic equation is Ainid + A#
= S. m,
C’il
where n”is the number of moles of the pertinent species within the adsorbed layer; A is the molar surface area or molar occupancy. Equation [7] assumes that any one of the components are always oriented in the same way toward the adsorbent. This, unfortunately, is never warranted. The surface mole fractions xc result from a trivial transformation of Eq. c71 (23h @Xi Xi<
z.z -
___-
x-g
1+ (a - 1)Xi’
J
Xi
=
a + (1 - (Y)Xj’
IIs1
Eq. [6]
where (Y; the separation factor, is calculated from the isotherm S(xJ as
Coefficients
J
COMPOSITIONS AND ACTIVITY COEFFICIENTS
II
Coefficientsfor S,~stem
labeled
must be accounted for in terms of multilayer theories may as well lead to small Ci,j (yi”- yjo) terms (18).
[6]
The precision on the fit is always better than 1%. Coefficients are listed in Table II; the outcome is reported on Fig. 2. The thermodynamic consistency can be asserted by considering the y - -yi” quantities when xx = 0: if 1 = acetone, 2 = benzene, and 3 = carbon tetrachloride then
y - y? vs xi. Systems
1.
SURFACE
+ L(1 - xi).
-
2. Variation of
FIG.
in Fig.
y - yio = J Ln [l + K(l - xi)]
yIo
261
GEL
K
-0.9994 - 0.984 -0.9988
L
0.0941
XidXj
1
+
Ajj(XJ/SXi
X/Xi
1 - A if(xi)/sxj
a=---=
0.00757
.
[I91
1.5175
Once zis is known, the surface activity coeffiJournal
of Cc&id
and Intevjace
Scie~zce,
Vol. 62, No.
2. November
1917
262
THOMAS TABLE
Surface Functions Tetrachloride
.d
0.001
0.002 0.005 0.01 0.05 0.1 0.2 0.3 0.4
In
0.443 0.510 0.576 0.624 0.790 0.876 0.946 0.975 0.99
EON
III
TABLE
Composition and Activity Coefficients of x1 for the System Acetone (1)-Carbon (2)
21
AND
fl”
as
Surface
-0.167 -0.409 -0.853 -1.222 - 1.866 - 1.914 - 1.704 -1.351 -0.862
Tetrachloride x1
XP
0.01
0.151 0.173 0.237 0.334 0.496 0.806 0.950 0.977
0.02 0.05 0.1 0.2 0.5 0.8 0.9
Ln fir = Ln fi + Ln (xJxi”) Note that Everett (14) gives an alternative procedure for the determination of /i”. In any case, the physical meaning of fi” is unclear for surface activity coefficients are function of both surface and bulk concentrations. Obviously fi” reflects deviations from ideal behavior, but usually no correlation whatever can be established with its bulk counterpart, even for the simplest systems (23). When such a correlation does ‘occur we believe it is incidental. The molar surface occupancies A were estimated via B.E.T. measurements, again by assuming a monolayer-type adsorption. If S TABLE
xi 0.001
0.005 0.01 0.02 0.05 0.1 0.2 0.4 0.8 Journal
of Co&d
IV as Func(2)
XP
In fi”
In fz”
0.076 0.268 0.392 0.518 0.671 0.784 0.864 0.900 0.96
- 1.05 -0.85 -0.70 -0.534 -0.347 -0.258 -0.172 -0.077 -0.012
-0.066 -0.217 -0.560 -0.842 -1.218 - 1.940 -2.835
and Intevface
In
fl”
-0.92 -0.50 -0.106 0.055 0.109 0.071 0.029 0.016
In fP
-0.24 -0.335 -0.448 -0.510 -0.526 -0.383 -0.158 -0.151
A = S/m.
- -GO). Cl01
Surface Composition and Activity Coefficients tions of x1 for the System Acetone (l)-Benzene
as
is the silica specific surface area and m the number of moles adsorbed (per gram) at completion of the monolayer then
cient fi” becomes accessible (23) : + (A;/RT)(r
Composition and Activity Coefficients xr for the System Benzene (I)-Carbon (2)
Functions of
In fz”
- 1.123 -0.864 -0.536 -0.319 0 0.043 0.016 -0.029 -0.06
V
Science, Vol. 62, No. 2, November
Pertinent values for A are: acetone = 200 m2 per mmole, benzene = 307 m2 per mmole, and carbon tetrachloride = 255 m2 per mmole. Results for various bulk mole fractions are reported in Tables III-V. The bulk concentration range is purposely restricted to that which corresponds to xi u 5 0.9.5-0.99. The reason for this is obvious if we recall that Ji” is a function of xi and xi”. Suppose a strong relative adsorption, i.e.; the system acetone-carbon tetrachloride, then xi” reaches a value close to unity for relatively small values of xi, in this case about 0.4, compared to unity. However, fi” keeps varying within the interval 0.4 < xi < 1 since both xi and y vary (key Eq. [lo]). Therefore one cannot practically consider the function fir versus xi” when xi0 is very close to unity. In the absence of any reliable statistical theories for specific adsorption one can hardly comment profitably on the values of f? except to say that the functions fi” vs xi” bear no resembIance to their bulk counterparts. Clearly the adjacent monolayer cannot be considered as a bidimensional solution. It is notable that the divergencies from ideality in the surface solution are comparable for acetone in systems A and B and benzene in system C although the specific adsorption of acetone on hydroxyl1977
ADSORPTION
ON
ated silica gel is much stronger than that of benzene. Still, even though the adsorbed monolayer model does not provide a rigorous description of the actual process, it remains a useful and reasonable model for the systems and concentration ranges investigated here.
SILICA
REFERENCES
The three binary systems studied here are shown to behave in a thermodynamically mutually consistent fashion. Their individual behavior may be reasonably accounted for by means of the monolayer model. Besides, adoption of equations for the isotherms and activity coefficients greatly facilitate the determination of the interfacial tensions.
2. 3.
3.
6. 7. 8.
9. APPENDIX
Bulk activity coefficients were generated from N.R.T.L. equation (24, 26) which, in spite of its half theoretical basis, accounts well for all types of Ln ji(xJ functions. The equation involves three adjustable parameters C12, Czl, and OL,some of which are listed with their temperature coefficient in (24). The function Ln fi(xJ is
10. 11. 12. 13. 14. 1.5. 16. 17.
G,j + ‘ij -___(xi + xiGiJ” > ’
7ij = CiJRT
and
Gij = exp[-
(~ij)].
The set of pairs of Q-‘sand G’s which are relevant to this study were obtained from Cij, Cji, and OLfrom (24); they are given below. System
A B C
712
121
-0.4097 - 0.4665 -0.5356
1.5557 0.7403 0.7529
G12
G21
1.0854 1.0978 1.1131
0.7326 0.8624 0.8602
ACKNOWLEDGMENT Thanks
18. 19. 20.
where
are due to G. Guiochon
for his support. Jourml
S. K., AND RAMAKRISHNA, V., T$*ans. Faraday Sot. 65, 1690 (1969). AR&~ISTEAD, C. G., TYLER, A. J., AND HOCKEY, J. A., Trans. Faraday Sot. 67, 493 (1971). Dtlvrs, K. 1M. C., DEUCHAR, J. A., ASD IBBITSON, D. A., Trans. Faraday Sm. 69, 1117 (1973). DAVIS, K. 31. C., DEUCHAR, J. A., AND IBBITSON, D. A., Trans. Famday Sot. 70, 417 (1974). TYLER, A. J., TAYLOR, J. A. G., PETHICA, B. A., AND HOCKEY, J. A., Tram. Faraday Sot. 67, 483 (1971). ELTEKOV, Yu. A., KHOPIXA, V. V., AP;D KISELEV, A. V., Trans. Faraday Sot. 68, 889 (1972). MATAYO, D. R., AND WIGHTMAN, J. P., J. Colloid Interface Sci. 44, 162 (1973). ONO, S., Am KONDO, S., in “Handbuch der Physik” (S. Fltigge, Ed.), Vol. 10, p. 134. Springer, Berlin, 1960. KISELEV, A. V., AND PAVLOVA, L. F., Bull. Aced. Sci. U. S. S. R. Chem. Ser., 12, 15 (1965). KISELEV, A. V., AND KHOPINA, V. V., Trans. Faraday Sot. 65, 1936 (1969). NXY, L. G., AND SCHAY, G., Act. Chim. Acad. Sci. Nungary 39, 365 (1963). NAGY, L. G., SCH.~Y, G., AND SZEKRENYESY, T., Periodica Polytecknica 6, 91 (1962). SCHAY, G., J. Colloid Integace Sci. 42, 478 (1973). EVERETT, D. H., Trans. Falpaday Sot. 60, 1803 (1964). EVERETT, D. H., Trans. Faraday Sot. 61, 2478 (1965). ASH, S. G., EVERETT, D. H., AND FINDENEQQ, G. H., Trans. Faraday Soc. 64, 2639 (1968). ASH, S. G., Bowx, R., AND EVERETT, D. H., Trans. Faraday Sot. 71, 123 (1975). BROWN, C. E., EVERETT, D. H., ,~ND MORGAN, C. J., J. Clzem. Sot., Faraday Trans. 71, 883 (1975). LANE, J. E., Amt. J. Chem 20, 827 (1967). ALTENBERGER, A. R., AND STECKI, J., Ckem. Phys. Lett. 43, 119 (1939).
1. SURI,
4.
CONCLUSION
263
GEL
21. LARIONOV, 0. G., AND ,MYERS, A. L., Chew Eng. Sci. 26, 1025 (1971). 22. DAVYDOV, V., AND KISELEV, A. V., Dokl. Akad. iliauk. SSSR 192, 1299 (1970). 23. SCHAY, G., k “Surface and Colloid Science” (E. Matijevic, Ed.), Chap. 3. Wiley-Interscience, New York, 1969. 24. RENON, H., ASSELINEAU, L., COHEN, G., AND RAW BAULT, C. in “Calcul sur ordinateur des Cquilibres liquide-vapeur et liquide-liquide” (Technip, Ed.), 1971. 25. SEYENCHENKO, V. K., AXD ISRAILOV, I. U., Russ. J. Phys. Chem. 48, 1801 (1974). 26. RENON, H., AND PRAUSNITZ, J. M., AIChE J. 14, 135 (1968). of Colloid
awd Inlerface
Science,
Vol. 62, No. 2, November
1977