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(24) J. P. McCullough and J. F. Messerly, U.S. Bur. Mines, Bull, No. 596 (1961). (25) T. 8. Douglas, G. T. Furukawa, R. E. McCoskey, and A. F. Ball, J. Res. Nat. Bur. Stand, 53, 139 (1954). (26) D. R. Douslin and H. M. Huffman, J. Amer. Chem. Soc., 68, 173 (1946). (27) D. W. Scott, G. B. Guthrie, J. F. Messerly, and S. S. Todd, J. Fhys. Chem., 66, 911 (1982). (28) 0. Redlich and A. T. Klster, Ind. Eng. Chem., 40,345 (1948). (29) C. C. Tsao and J. M. Smith, Chem. Eng. Progr. Symp. Ser., 7, 107 (1953). (30) A. R. Mathieson and J. C. J. Thynne, J. Chem. Soc., 3706 (1956).
Schenz and Milton Manes
(31) T. L. Hill, “An Introduction to Statistical Thermodynamics,” AddisonWesley, Reading, Mass., 1960, Chapter 20. (32) K. Banerjee and L. Salem, Mol. Phys.. 11, 405 (1966). (33) A. I. M. Rae and R. Mason, Proc. Roy. SOC.,Ser. A, 304,467 (1968). (34) Rowlinson and Sutton’ use a parameter A12 = d12/T. A12 is inversely proportional to T, and d12 is a true constant having the dimension of temperature. (35) H. E. Eduljee, D. M. Newitt, and K. E. Weale, J. Chem. SOC.,3086 (1951). (36) K. Shinoda and J. H. Hildebrand, J. Phys. Chem.,65, 183 (1961). (37) A. Abe and P. J. Flory, J. Amer. Chem. Soc., 87, 1838 (1965).
Application of the Polanyi Adsorption Potential Theory to Adsorption from Solution on Activated Carbon. VI. Adsorption of Some Binary Organic Liquid Mixtures’ Timothy W. Schenz and Milton Manes* Chemistry Department, Kent State University, Kent, Ohio 44242 (Received September 5, 1974) Publication costs assisted by Calgon Corporatlon
Adsorption isotherms on a previously studied activated carbon have been determined for the following dilute binary solutions of miscible (a) and of partially miscible (b) components: (a) benzene and/or toluene in methanol, n-hexane ((3, n-heptane (C7), n-octane (Cg), n-decane (C~O),and 2,2,4-trimethylpentane (TMP); and Clo in Cg and TMP; and (b) C7, Cg, Cg, (210, and TMP in methanol. Except for Cg, vapor-phase isotherms on the same carbon were determined for all components. Except for some upward deviation (higher capacity) for methanol at low capacities (presumably due to chemisorption), the vapor-phase isotherms of methanol, benzene, and toluene were in good agreement with expectations from the Polanyi theory. The paraffins all showed significant downward deviations in the low capacity range that increased with increasing molecular size. The adsorption of benzene and of toluene in the paraffins, over the experimental mole fraction range of the order of was well accounted for by incorporating the experito mental vapor-phase data into the Hansen-Fackler modification of the Polanyi theory. The adsorption of benzene and of toluene in methanol could be accounted for by application of an empirical scale factor to the adsorption potential of methanol in the theoretically derived adsorption isotherm (without the presumed chemisorptive effects). The adsorption of the paraffins in methanol could be accounted for in terms of an earlier Polanyi-based treatment of partially miscible systems, and the adsorption of Clo in C g and in TMP could be accounted for by the Hansen-Fackler treatment; however, it was here necessary to use the theoretically ’derived isotherms for the paraffin solutes, i.e., without regard for the observed vapor-phase deviations that accounted for their behavior as solvents.
Introduction Earlier work in this series2i3has dealt with the application of the Polanyi adsorption potential theory4 to account for the adsorption onto activated carbon of partially and completely miscible organic liquids from water solution. The present study progresses to the adsorption of partially and completely miscible binary organic liquid mixtures. Although there is considerable earlier work on such mixtures, most of which has been reviewed by Kipling,5 this work is largely concerned with adsorption isotherms (or “composite isotherms”) over the entire composition range, and does not deal with highly dilute solutions. By contrast, the present study has emphasized the dilute to trace concentration range, which is of particular interest to the final purification of compounds by adsorption, as distinguished from bulk separatiop. Moreover, we expected the low concentration range to be particularly amenable to theoretical treatThe Journd of Physical Chemistry, Vol. 79, No. 6 , 1975
ment by the earlier-used modifications of the Polanyi theory. The miscible systems comprised benzene and/or toluene in methanol, n-hexane (CG), n-heptane (c7),n-octane ( c g ) , n-decane (C~O),and 2,2,4-trimethylpentane (TMP). The partially miscible systems comprised Cy, Cg, Cg, C10, and TMP in methanol. (Cg was not used as a solvent for budgetary reasons.) Except for Cg, vapor-phase adsorption isotherms were determined for all of the solution components. Following the procedures of the earlier work on water solutions, we constructed theoretical liquid-phase adsorption isotherms from the corresponding vapor-phase isotherms of the individual components. However, whereas estimated vapor-phase isotherms had previously sufficed in the calculations, some of the present liquid-phase isotherms showed strong deviations from expectations; these deviations appeared to be ascribable to deviations from theory of the sol-
Adsorption of Binary Organic Liquid Mixtures vent vapor-phase isotherms, which led to the extensive vapor-phgase determinations. Methanol was chosen as a relatively weakly competing solvent for both the paraffins and the aromatic solutes, on the basis of its relatively low refractive index. Benzene and toluene were similarly expected to be adsorbed from the paraffins, which could therefore be observed both as solvents and as solutes. The characterization of a particular isotherm as normal or anomalous was considerably facilitated by the use of a carbon sample on which there was a considerable background of adsorption data.
605
each adsorbate in the adsorption potential abscissa. Dubinin8 suggested that this scale factor should be proportional to the adsorbate molar volume, at least approximately, so that a plot of the adsorbate volume against e/T7 (now called a “correlation curve”) should be the same for all adsorbates. It turns out that whereas a single correlation curve describes the adsorption of a series of similar compounds (e.g., the lower homologous paraffins)? significant differences do exist, and they turn out to be crucial for liquidphase adsorption. For the adsorption of a solid from solution (and, by extension, for the adsorption also of a partially miscible liquid), Polanyi gives the equations
Theoretical (2) cS1 RT In C,/C = E, - E ~ ( V , / V J The underlying theory, which is here briefly summarized, is more fully explained in the cited r e f e r e n c e ~ . ~ - ~ , ~or ~~ %L=f9-fi (3) The Polanyi theory4 assumes a heterogeneous “adsorpvs v, Vl tion space” within which a molecule from the bulk phase where e, and c are the saturation and equilibrium concenloses an amount of potential energy (the “adsorption potrations, t, and €1 the adsorption potentials (at comparable tential,” t), that for a given molecule is independent of volumes) of the solute and solvent, and Vs and VI the corretemperature (because it arises from temperature-indepensponding molar volumes. (We shall omit the superscript dent London forces), and increases with closer proximity to bars wherever the subscript clearly indicates that we are the solid surface; t is highest in fissures or within fine dealing with a molar volume rather than an adsorbate volpores. In vapor-phase adsorption the vapors are concenume.) trated in the adsorption space, relative to the bulk phase, Since t/P is the abscissa of a correlation curve, eq 3 to an extent that depends on the local value of e. Wherever implies that the abscissa in the correlation curve for the ade suffices to concentrate the vapor to saturation concentrasorption of the liquid solute may be estimated as the differtion, the vapor liquefies; this liquefaction accounts for ence between the abscissas of the corresponding curves for practically all of the physical adsorption on the solid. the solute and solvent. Since both of the latter are in turn In the adsorption from solution of a solid or of a partially derivable from the corresponding vapor-phase isotherms, miscible liquid, one similarly gets condensation of either eq 3 links liquid- to gas-phase adsorption for partially misthe solid or liquid solute in the adsorption space; here, cible liquids. however, the driving force for adsorption, esl, is equal to the Manes and Rofer7 have suggested that in the absence bf (vapor-phase) adsorption potential of the solute, reduced experimental adsorption data for the components, the ratio by that of an equal volume of the displaced solvent. of eLIVLto EJV, (where the subscript i refers to a compoIn the adsorption of miscible mixtures, according to the nent and r to some reference substance) may be estimated Hansen-Fackler6 modification of the Polanyi theory, the from the refractive indices of the liquids by the equations driving force for adsorption is the same. Here, however, there is no phase separation in the adsorption space; instead, the adsorbate concentration varies continuously throughout the adsorption space and the resulting change where p is defined as (n2 - 1)/(n2 + 2) and n is the refracin the solution concentration is calculated by integration tive index. The factor that relates the correlation curve for over the entire adsorption space. the adsorption to the hydrocarbon correlation curve (which In vapor-phase adsorption the adsorbate volume comManes and Hofer used as their reference) then becomes prises that volume in which the adsorption potential either equals or exceeds the value required for condensation, (5) which Polanyi gives as RT In p,/p where p , is the saturation pressure of the liquid and p the equilibrium pressure. A plot of the adsorbate volume against the equilibrium value of e, as calculated from eq 1, is called a “characteristic curve.” It depends for a given adsorbate on the nature and structure of the adsorbent, but is temperature independent. It is readily calculated from an adsorption isotherm at any convenient temperature; the reverse calculation of an adsorption isotherm from the characteristic curve makes it possible to calculate adsorption isotherms over a wide temperature range from one experimental isotherm. Since the ratio of the tidsorption potentials of any two adsorbates in any equivalent location should be constant over the entire adsorption space, the Polanyi theory predicts that all characteristic curves for a given adsorbent should be the same, except for a constant scale factor for E
2
Wohleber and Manes2 used these equations to estimate the adsorption of a number of partially miscible organic solutes from water solution. Although the adsorption of water was anomalously weak, most of the data could be successfully correlated by the use of a constant empirical value of y for water, together with the hydrocarbon correlation curve for the carbon and the calculated values for the y factors of the adsorbates. For adsorption from miscible liquids, Hansen and Fackler6 derived the equations10
and
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In eq 6 2x4, ZIB, 2 2 4 , XZB refer to the mole fraction of each component in bulk and in the adsorbate, in any volume element dc$, and the various values of e refer to the same element of volume. Equation 6 is used to determine the composition of the adsorbate in each element of the adsorption space. Equation 7 is used to determine the experimentally determined adsorption. In this equation V4 and V Brefer to the average volume per mole of the bulk and adsorbate mixtures; m is the mass of the adsorbent. V is the solution volume and Ac the reduction in concentration of component 1in solution. For miscible systems, as for partially miscible systems, one may either determine t for each component as a function of the adsorbate volume from its vapor-phase isotherm or, alternately, one may estimate it by use of eq 5. The treatment by Wohleber and Manes2 of partially miscible liquid systems neglects any solubility of solvent in the solute adsorbate. We have derived equations to include this effect; the derivation applies the Hansen-Fackler6 treatment to account for variations in the composition of the adsorbate within the adsorption space. The derived equations were applied to our data on partially miscible systems, but did not improve the correlation, presumably because of the relatively low solubility limits. The derivation, which may be useful for some systems, is given in the Appendix.ll Vapor pressures were calculated from the Antoine equation constants given by National Bureau of Standards12 and by Hala, et al.13 Solubility data for the hydrocarbonmethanol systems were obtained from the compilations by Stephen and Stephen14and by Kiser, et a1.15 Experimental Section All of the experiments described in this article and the earlier ones in this series were carried out with carbon samples from a single batch; this enables comparison of the reported results with the results of earlier experiments. The carbon, of 1140 m2/g surface area (BET), was used as received except for oven drying at 110' for 24 hr. The batch was Pittsburgh Activated Carbon grade CAL. The paraffins (c6, C7, CS, Cg, Clo, and TMP), and benzene, toluene, and methanol were all reagent grade chemicals (Matheson Coleman and Bell) with a minimum purity of 99.5% as determined by gas chromatography; they were used as received. Where analysis was made by uv spectrophotometry (benzene and toluene) the-adsorbate reagents were Spectroquality grade. As in earlier articles, the weighed carbon samples were shaken with measured volumes of solutions of measured concentrations in 125-ml screw-capped erlenmeyer flasks for 16 hr in a water bath thermostated at 25'. Following equilibration the carbon was allowed to settle in the bath and samples of the supernatant liquid were either filtered through sintered glass or else centrifuged. Paraffinic adsorbates were analyzed by glc in a Victoreen Series 4000 gas chromatograph equipped with a dual flame ionization detector and electrometer interfaced to a Digital Equipment Corp. (DEC) Lab 8/E computer. The computer integrated the peak areas to a reproducibility of 0.2%. The column packing was Porapak Q (porous polymer beads of polystyrene-divinylbenzene), except for the analysis of Clo (from either CS or from TMP), where the column packing was Durapak (Carbowax bonded to a silicone base). Both packings were obtained from Waters Associates. Spectrophotometric measurements were carried out in a Cary 14 spectrophotometer in the ultraviolet range. The Journal of Physical Chemistry, Vol. 79, No. 6, 1975
Timothy W . Schenz and Mllton Manes
Vapor-phase adsorption isotherms were determined on a McBain balance with quartz springs and buckets. Elevated temperatures were maintained around the sample by placing the sample tube in a dewar flask internally wound with heater tape. Temperatures were controlled by a variable voltage supply and measured by a thermocouple external to the sample tube. Results and Discussion Vapor Phase. Table 111gives the experimental data for the vapor-phase adsorption of methanol, benzene, toluene, c6, c7, Cs, Clo, and TMP. In addition to the loading as a function of temperature and pressure, Table 1 gives the same data calculated in terms of the volume adsorbed and TIP log pslp (e/4.6m, following the notation of earlier articles. Figure 1shows the data for benzene and toluene; Figures 2 and 3 show similar data for methanol and for (26, Cs, and Clo. In all cases the curves are calculated from the hydrocarbon (paraffin) correlation curve7 for the carbon and the refractive index of the liquid phase. Figure 1 illustrates that benzene and toluene are in good agreement with theory. Figure 2 shows good agreement of methanol adsorption with theory at the higher loadings, with positive deviations (high loading for a given adsorption potential or high adsorption potential for a given loading) at the lower loadings. Figure 3 shows good agreement at high capacities for the paraffins, with negative deviations that increase with reduced loading and with increasing molecular size of the adsorbate. Similar plots for C7 and for TMP (not shown to save space) show C7 to be intermediate between Cg and Cs, and TMP to be somewhat more deviant than Clo. The positive deviations for methanol at low loadings are consistent with earlier observations16 that methanol tends to chemisorb on carbon, presumably by interaction with surface oxygenated groups. The downward deviations for the paraffins, since they are most pronounced at low loadings and for larger molecules, would appear to be consistent with some sort of molecular sieving. However, the presumed molecular sieving would have to be due to fine pores of limited depth rather than of limited cross section, since the limiting cross sections of the normal paraffins should be about the same. We shall see, however, that these considerations do not appear to apply when the same paraffins are solutes. Consider now the validity of the generalized hydrocarbon (paraffin) correlation curves as reported, for example, by Grant, Manes, and Smithg and by Grant and Manes.17 Whereas these curves were based on the adsorption of paraffins from methane to hexane, the authors noted that for experimental reasons the low capacity range was based only on the adsorption of methane and ethane, and therefore that there was no direct experimental verification of the validity of the paraffin correlation line for the higher paraffins a t the low capacities. Having circumvented the earlier experimental limitations, we now find that the generalized correlation line does not in fact account for all of the vapor-phase adsorption of the higher paraffins. Nevertheless, we shall soon see that it is useful for predicting the adsorptive behavior of the higher paraffins as solvents. Partially Miscible Liquids. Table 211 gives the experimental data for the adsorption of C7, c8, Cg, Clo, and TMP from methanol solution. Figure 4,which is typical of the results, shows the adsorption data for TMP from methanol,
Adsorption of Binary Organic Liquid Mixtures
607
I
I
I
10
10
30
IO
10
Flgure 1. Vapor-phase adsorptlon of b_enrene_(O)and toluene (O), plotted as volume adsorbed vs. €14.6V (= T/V log hip). The solid line was calculated from paraffin correlation line and refractive Indices.
30
40
6/4.6v
el449
Flgure 3. Vapor-phase adsorption of nhexane (0),n-octane ( O ) , and ndecane (A),plotted as in Figure 1. Calculated :orrelation n-octane (- -), and ndecane (- -). curves are nhexane (--),
-
~14.69
Figure 2. Vapor-phase adsorption of methanol, plotted as in Figure 1.
plotted as volume adsorbed us. T / P log xsIx, as compared with the predicted line based on the earlier work of Wohleber and Manes.2 The predicted value of the abscissa at the lowest adsorption point overestimates the equilibrium solute concentration by about two orders of magnitude. However, the experimental data follow a curve that appears to differ from the predicted curve only by an abscissa scale factor, in analogy with the results of Wohleber and Manes on water solutions. Moreover, because the calculated y values for methanol and the paraffins are rather close together (0.87 and 1.00), one would expect the adsorption data to be quite sensitive to any deviations from theory.
2
4
b
8
IO
ul44v
Flgure 4. Adsorption of TMP from methanol, plotted as volume ad. 6T/V log x,Ix): calculated curve (-); experisorbed vs. ~ ~ ~ 1V4(= mental curve (- - - - - -1.
Empirical factors were determined for all of the adsorption data as follows: C, 0.70; Cs, 0.74; TMP, 0.76; Cg, 0.79; and C ~ O0.78, , for a mean of 0.75. Thus the empirical scale factors are lower than the calculated factors by approximately 15%. With the application of the empirical scale factor, the results fall quite nicely into coincidence, over a wide range of concentrations. The use of an empirical y factor for methanol, together with the theoretical isotherms for the components as calcuThe Journalof Physical Chemistry, Vol. 79, No. 6,1975
Timothy W. Schenz and Milton Manes
608
lated from the paraffin correlation curve for the carbon, leads to considerably better correlation of the observations than does the use of the experimental vapor-phase isotherms. The ignoring, in effect, of the observed upward deviations of the methanol vapor-phase isotherm may be justified if these deviations are due to chemisorptive interactions with oxygenated groups on the carbon, since the chemisorptive binding sites probably differ from those of high energy physical adsorption. However, it is more difficult to justify an empirical factor for methanol as a solvent when that empirical factor differs significantly from the vapor-phase isotherm. Moreover, it is similarly difficult to justify ignoring the observed negative deviations of the vapor-phase isotherms of the paraffin solutes, which deviations are not at all reflected in the experimental observations on liquid mixtures. If:one ascribes the vapor-phase deviations to structural or steric or molecular sieving effects, it is difficult to explain, on the basis of the Polanyi model, why these effects do not influence the adsorption of the same component when it is a solute. Finally, the validity of the observed deviations in the gas-phase isotherm is supported by the liquid-phase isotherms in which the paraffins are solvents. These we now consider, Miscible Liquids. Table 311 gives the adsorption data for benzene in methanol, Ce,C,, Cg,Clot and TMP; toluene in methanol, Ce, and Cg; and Clo in CS and TMP. The data were reduced to volume adsorbed as a function of bulk mole fraction, using the method of Hansen and FacklereB As input to this treatment we could use, for both solvent and solute, either the correlation curves derived from the paraffin correlation curve and the refractive index, or the experimental vapor-phase isotherm. For benzene and toluene in methanol the input data for the method were the correlation curve for the solute (for which the experimental and thy calculated curves coincided) and the theoretical correlation curve for methanol (with an abscissa scale factor of 0.75 as was used for the partially miscible systems with methanol solvent). It turned out that the adsorption in methanol was well accounted for by this procedure; again it was better to ignore the positive deviations in the vapor-phase methanol isotherm. For the paraffin solvent systems, however, the data are best correlated by using the theoretical correlation curve for the solute (as in the previous section, where methanol was the solvent), and the experimental correlation curves for the solvents. Figures 5-7 are plots of the adsorbate volume against the log of the solute mole fraction, as calculated by the Hansen-Fackler method. Figure 5 shows, for example, the adsorption of benzene from TMP, and Figure 6 the adsorption of toluene from hexane, In these figures the dotted line is calculated on the assumption of theoretical correlation curves for both solvent and solute, and the solid line is calculated by incorporating the experimental gas-phase isotherm for the solvent. The deviations of the solvent vaporphase isotherms, which had previously shown no experimental consequences, have here made themselves manifest. Up to this point a comparison of the adsorption of benzene from the paraffins and of the paraffins from methanol would suggest that downward deviations of the vaporphase isotherms are reflected in the behavior of the solvent, but not of the solute. The possibility arises, however, that failure of the deviations in the solute vapor isotherms to be reflected in the corresponding liquid-phase isotherm may be peculiar to methanol solutions. We now consider the adsorption of Clo from TMP and from CS. Figure 7 The Journal of Physical Chemistry, Vol. 79, No. 6, 1975
0.01 -1
-a
-1
1%
-4
XZB
Flgurr 5. Adsorptlon of benzene from TMP plotted as volume adsorbed vs. log of solute (bulk) mole fractlon: (-) calculated from experimental vapor phase Isotherm of solvent: (- -) calculated from refractlve indlces.
-
:
0 01
-1
- 1 log
X2B
-3
-4
Adsorptlon of toluene from nhexane. Plot and legend similar to Figure 5. Figure 8.
shows the plot of the adsorption of C ~ from O CS as compared with the theoretical curve calculated both from the experimental gas-phase isotherms of both components (dotted line) and from the experimental isotherm of the solvent and the theoretical isotherm of the solute. Again, the combination of the experimental solvent and theoreti-
Adsorption of Binary Organic Liquid Mixtures
609
\ \ \
-I
-3
-2
-4
-5
at lower capacities and with increasing molecular size of the paraffin. These deviations may be tentatively ascribed to structural or steric effects such as inability to be accommodated by shallow pores, rather than to molecular sieving in the usual sense of inability to enter fine pores of indefinite depth. (2) For dilute solutions of benzene, toluene, and the paraffins in methanol solution, the liquid-phase adsorption isotherms are what one would predict from the theoretically derived isotherms (rather than the experimental ones), with the exception of a small empirical correction factor for the adsorption isotherm of methanol. (3) For solutions of benzene in the paraffins, and for solutions of decane in octane and in TMP, the adsorption isotherms are what one would expect from using a Polanyibased (Hansen-Fackler) treatment, using the experimental adsorption isotherms of the solvent and (where they differ from the experimental) the theoretical isotherms of the solutes. (4) We have not found a satisfactory model to account for the observations that the downward deviations of adsorption isotherms, presumably due to structural effects, do not affect the adsorptive behavior of a component when it is g solute.
log X 2 B
Figure 7.
Adsorption
similar to Figure 6.
of
ndecane from natane. Plot and legend
cal solute correlation curves accounts for the data. The plot for Clo from TMP (not shown) is quite similar. Final Comments. Although the presumed structural effects on the vapor-phase isotherms have not here shown any effects on the liquid-phase adsorption of solutes, molecular sieving of solutes is well known in, for example, the removal of color bodies from sucrose. Moreover, Chiou and Manesls found steric effects to profoundly affect the adsorption of octahedral acetylacetonate complexes. We would therefore expect such effects to appear with larger or more hindered solutes than we have here observed. Finally, the correlation methods that have been used here may well be applicable to a t least a somewhat greater variety of binary mixtures than we have here been able to observe. Whereas the principal difficulty to further application would appear to be the necessity of determining the low-capacity adsorption isotherm of each new solvent, this apparent difficulty could be readily circumvented by determining the adsorption of a reference solute, such as benzene, in a new solvent. Any deviations due to the solvent should be the same for a wide variety of solutes and should be readily incorporated into the calculations by the methods described here. Conclusions (1)For benzene and toluene, the vapor-phase adsorption isotherms on activated carbon are in keeping with predictions from the Polanyi approach. For methanol, positive deviations appear, particularly a t low capacities; these may be ascribed to adsorptive interaction with surface groups on the carbon. The paraffin hydrocarbons from hexane and above fit the theory at high capacities, but deviate downward a t low capacities, the downward deviation increasing
Acknowledgments. We thank the Goodyear Tire and Rubber Company for support of T.W.S. in the form of a Goodyear Fellowship. Supplementary Material Available. Tables 1-3 and an Appendix will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D.C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-75-604. References and Notes (1) This article is based on the Ph.D. dissertation of T. W. Schenz, Kent State University, Dec 1973. (2) D. A. Wohleber and M. Manes, J. Phys. Cbern., 75,61 (1971). (3).D. A. Wohleber and M. Manes, J. Phys. Cbern., 77,809 (1973). (4)M. Polanyi, Verh. Deut. Phys. Ges., 16, 1012 (1914);18, 55 (1916);2. Elekfrochern.,26, 370 (1920). (5)J. J. Kipling, "Adsorption from Solution of Non-Electrolytes," Academic Press, New York, N.Y., 1965. (6) R. S. Hansen and W. V. Fackler, J. Phys. Cbem., 57,634(1953). (7) M. Manes and L. J. E. Hofer, J. Phys. Chern., 73, 584 (1969). (8)M. M. Dubinin and D. F. Timofeyev, C. R. Acad. Sci. URSS,54 (8),701 (1946). (9)R. J. Grant, M. Manes, and S. B. Smith, A/Cb€J., 8, 403 (1962). (IO)The notation has been slightly changed for convenience. Attention is directed to typographical errors in eq 4 of ref 3, which is properly rendered in eq 7. (11) See paragraph at end of text regarding supplementary material. (12)National Bureau of Standards, "Selected Values of Properties of Hydrocarbons," Circular No. C461,Washington, D.C., 1947. (13)2. Hala, I. Wichterle, J. Polak, and T. Boublik, "Vapor-Liquid Equilibrium Data at Normal Pressures," Pergamon Press, Oxford, 1968. (14)H. Stephen and T. Stephen, Ed., "Solubilities of Inorganic and Organic Compounds," Vol. 1, Part 2, MacMillan, New York, N.Y.. 1963. (15)R. W. Kiser, G. D. Johnson, and M. D. Shetlar, J. Chem. Eng. Data., 6, 338 (1961). (16)Reference 5,p 173. (17)R. J. Grant and M. Manes, Ind. Eng. Chern., Fundam., 3, 221 (1964). (18)C.C. T. Chiou and M. Manes, J. Phys. Cbem., 77,809 (1973).
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