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The Journal of Physical Chemistry, Vol. 83, No. 3, 1979
Communications to the Editor
A Prototype Hydrophobic Interaction. The Dimerization of Benzene in Water
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Downloaded by FLORIDA ATLANTIC UNIV on September 15, 2015 | http://pubs.acs.org Publication Date: February 1, 1979 | doi: 10.1021/j100466a026
Publication costs assisted by the National Science Foundation
Sir: Several types of evidence have been adduced to show that hydrocarbon groups and chains on aqueous solute molecules tend to cluster together; the term hydrophobic interaction is now widely used to denote the association of such entities.' Although the origin of hydrophobic effects has been much debated, there are almost no primary thermodynamic or structural data relating to specific aggregates of dissolved hydrocarbon molecules. In developing theories to explain the role of hydrophobic effects in conformational changes in biopolymers and in the association of other complex aqueous solute species, it would be valuable to have accurate physical information pertaining to hydrocarbon aggregates of known stoichiometry and structure. Ben-Naim et ala2have examined solubility data for alkane and aromatic hydrocarbon solutes in water and, by using larger hydrocarbon molecules as analogues of dimers of the smaller hydrocarbons, they have predicted energies and free energies of dimerization. In particular, by using diphenyl as a model for the benzene dimer, Ben-Naim et al. have estimated that the free energy of dimerization of benzene is -1136 cal/mol and that the enthalpy of dimerization is +3200 cal/mol at 20 "C. However, an early study by Saylor et al.3 a report from this l a b ~ r a t o r yand ,~ a recent investigation by Green and Frank5 suggest that benzene obeys Henry's law reasonably well up to saturation. Therefore, as Green and Frank note, the degree of association implied by Ben-Naim's thermodynamic model calculations (24% a t saturation at 20 OC) appears to be much too large. Considering the importance of the prototype interaction 2B = B2 (where B and Bz denote the monomer and the dimer of benzene, respectively, in dilute aqueous solution) we thought it would be worthwhile redetermining vapor pressure-composition data for solutions of benzene in water. For this experiment we have used a new calculator-computer-controlled vapor pressure apparatus, employing an automatically operated liquid chromatography valve to introduce accurately reproducible quantities of liquid benzene (22.15 f 0.02 pL) into a chamber containing initially only liquid water and water vapor. The total pressure is read initially (to f0.003 torr) and at equilibrium after each addition of benzene to the chamber, which has a total volume of 709 mL. The volume of liquid water (accurately known) was approximately 145 mL in the experiments described here. Data obtained from the vapor pressure experiments are readily converted into sets of values of the fugacity of benzene, f B , a t known values of the mole fraction of benzene in the liquid phase, xB. The observed pressure increase owes almost entirely to the partial pressure of benzene; by using the known virial coefficient of benzene vapors,6 it is possible to correct the observed pressure increments to obtain values of the fugacity of benzene. From the known volumes of the liquid and vapor phases and the total number of moles of benzene added, the compositions of both phases can be calculated with great accuracy. Figure 1 is a plot of the Henry's law constant of benzene ) X B for the two sets of data at 35 "C. The (KH = f ~ / x B vs. high quality of the results is indicated both by the reproducibility of data in replicate experiments and by the goodness of fit of all of the fugacity-mole fraction data to empirical equations (vide infra). Although previous vapor 0022-3654/79/2083-0426$0 1.OO/O
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MOLE FRACTIONBENZENE 104
Figure 1. Dependence of the Henry's law constant for benzene (KH) on the mole fraction of benzene in water at 35 O C .
pressure314and partition5 studies of the benzene-water system have not been accurate enough to show that KH does change with total concentration of benzene, the present results make it clear that KH decreases monotonically as XB increases. The equation f B = 3.527 X 105xB- 3.07 X 107xB2(where f B is expressed in torr) fits all of the data for the two runs to an average error in fugacity of less than 0.03 torr. In the limit as XB approaches zero, the Henry's law constant approaches the infinite dilution value KHm= 3.527 X lo5 torr. KH decreases to a value of 3.433 X lo5 torr at XB = 0.0003 and, assuming continued linear behavior to saturation, KH should reach a value of 3.392 X l o 5 torr at saturation (where XB = 0.000428). Thus the overall decrease in KH, and hence in activity coefficient of benzene, is about 3.9% from infinite dilution to saturation. The simplest way to interpret the observed departures from the limiting Henry's law is to attribute the total negative deviation to formation of associated benzene species. According to this model, the monomer of benzene has a mole fraction given by X B , = fB/KHm, ~ ~ and ~ ~ the ~ total mole fraction of benzene in the various aggregates ~ , At ~this ~point, ~ mass ~ action ~ ~ is equal to XB - x equations can be tested statistically to determine if the associated benzene mole fraction can be attributed entirely to dimers, or whether the inclusion of higher order polymers is necessary. In fact, the data in Figure 1 are quite adequately represented (to a root mean square deviation in fugacity of 0.03 torr) by ascribing all of the deviation from the limiting Henry's law to formation of the benzene dimer, Bz, with a formation constant K2 = x ~ ~ / ( x = ~46.9, f~ 1.2. ~ ~ Inclusion ~ ~ ~ of ~ additional ) ~ equilibrium constants for formation of trimers and larger polymers only slightly improves the goodness of fit, without significantly modifying the inferred value of Kz. The dimerization constant may be converted to a constant consistent with unit molarity solute standard states by multiplying the K z value based on the mole fraction standard states by the molar volume of pure water. This yields K2 = 0.85 f 0.02 L/moI, a value comparable to association constants which have been reported for several weakly associating pyrimidines and purines in aqueous solution^.^ Using the unit molarity ideal dilute solution states, we calculate AGO = 99 f 10 cal for the dimerization of benzene, which may be compared with the value estimated by Ben-Naim et al. (-1136 ca1).2B11 0 1979 American Chemical Society
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Downloaded by FLORIDA ATLANTIC UNIV on September 15, 2015 | http://pubs.acs.org Publication Date: February 1, 1979 | doi: 10.1021/j100466a026
Communicationis to the Editor
The Journal of Physical Chemistry, Vol. 83, No. 3, 7979 427
An alternative interpretation may be given to the deviations from Henry's law observed for the very dilute solutions of benzene in water. Following McMillan and Mayer,') one may show that the coefficient of the quadratic B P X B (and ~ hence term in the fugacity expression fB = ~ X + the dimerization constant) is directly proportional to the virial coefficient for pairwise interaction of solute molecules. The virial coefficient can be expressed in terms of cluster integrals involving the intermolecular potential energy functi.on for pairs of molecules. Thus, the dimerization constant may in principle be predicted provided that sufficiently accurate information about the attractive and repulsive forces between dissolved benzene molecules is available, This calculational method is entirely analogous to that used to relate equilibrium constants for the formation of molecular aggregates in the vapor phase to virial coefficients and ultimately to intermolecular potential energy function^.^^^ Although attempts have been made to predict properties of dissolved hydrocarbon aggregates from assumed potential energy functions, the lack of accurate th.ermodynamic data for dilute aqueous solutions of the hydrocarbons has in our opinion hampered the development of theories of hydrophobic interaction. Currently we are obtaining vapor pressure data for the water-benzene system at a number of temperatures in the range 20-45 O C . Our preliminary results clearly show that AHo for the di.merization of benzene is a relatively large positive quantity, as might have been anticipated for an aggregation stabilized in large part by hydrophobic interactions. The final derived values of AGO, AH", and ASo for the association of benzene in water should be of considerable interest in relation to our understanding of hydrophobic effects. We are also investigating the dependence of the limiting Henry's law constant, KH", on temperature in order to infer thermodynamic constants for the transfe.r reaction benzene (ideal gas) = benzene (ideal dilute solution in water)
that "diphenyl is not to be considered a good model for the actual benzene dimer".
Our initial results indicate that AHo for this solution process is about -6.9 kcal/mol a t 35 " C and that, ACpo is on the order of 70 cal/deg, in fair agreement with results inferred from earlier calorimetric and solubility studies.1°
Acknowledgnzent. This study was supported by Grant No. CHE77-03668 from the National Science Foundation. We thank Professor H. S. Frank for sending us a manuscript copy of ref 5 in advance of publication.
References and Notes (1) W. Kauzmann, Adv. Protein Chem., 14, 1 (1959); F. Franks, Water, Compr. Treat., 4, 1-94 (1973). (2) A. Ben-Naim, J. Wilf, and M. Yaacobi, J. Phys. Chem., 77, 95 (1973). (3) J. H. Saylor, J., M. Stuckey, and P. M. Gross, J . Am. Chem. Soc., 60, 373 (1938). (4) A. A. Taha, R. D.Grigsby, J. R. Johnson, S.D. Christian, and H. E. Affsprung, J. Chem. Educ., 43, 432 (1966). (5) W. J. Green, and H. S. Frank, J . Solution Chem., in press. (6)A. E. Korvezen, Red. Trav. Chim., Pay-Bas, 70, 697 (1951); 72, 483 (1953). (7) See, for example, P. 0. P. Ts'o in "Basic Principles of Nucleic Acid Chemistry", Vcl. 1, Academic Press, New York, 1974, pp 537-562. (8) W. McMillan and J. Mayer, J . Chem. Phys., 13, 176 (1945). (9) N. Davidson, "Statistical Mechanics", McGraw-Hili, New York, 1962, pp 337-341. (10) S. J. Gill, N. F. Nichols, and I. Wadso, J. Chem. Thermodyn.,8, 445 (1976), and references therein. (1 1) A reviewer has objected to our making a direct comparison between the thermodynamic constants of hydrophobic Interaction obtained by Ben-Naim for 2(benzene) = diphenyl and the present dimerization data for benzene in water. Ben-Naim uses model compounds to deduce the indiirect part of the free energy of association for a particular configuration of the "dimer", and this value should not neCeSSarih/amroximate the total free enerav of dimerization reoorted here. Irt ihe'words of another reviewer, 6 6 present results confirm
0022-3654/79/2083-0427$01 .OO/O
Department of Chemistry The University of Oklahoma Norman, Oklahoma 730 19
Edwin E. Tucker" Sherrll D. Christian
Received July 20, 1978
Identification of Catalytically Active Sites on Reduced Molybclena-Alumina Catalysts Publication costs assisted by the National Science Foundation
Sir: Kokes and Dent1 were able to identify active intermediates in the hydrogenation of olefins over ZnO using IR spectroscopy. 'This approach is not generally applicable, however, because either the steady state concentration of the intermediate is too low, or else its lifetime is too short. We report herein an alternative approach in which information concerning the nature of the active sites may be deduced from IR studies of "poison" molecules which are selectively andl very strongly adsorbed on the catalytic centers. NO has been found2 to be a selective poison for propylene metathesis over molybdenum carbonyl supported on silica or alumina (after activation a t elevated temperatures). Recently we have found it to selectively poison olefin hydrogenation, but not metathesis or isomerization, over reduced molybdena-alumina catalystsQ3IR spectra from these poison molecules for the latter system are presented in Figure 1. These spectra are characteristic of a dinitrosyl surface complex similar to those formed in homogeneous sys,tems as described by Cotton and J o h n ~ o nsimilar ;~ epectra have been reported for reduced chromia-silica catalyst^.^" Kemball and Howe2 also reported similar spectra but assumed the poisoning was due to a single NO molecule per site. With our system both bands (Figure 1)grew a t the same rate when small doses of NO were introduced. When a 51 mixture of H2:C3H6was allowed to react over an activated (at 200 "C) molybdenum carbonyl on yalumina catalyst (prepared by vacuum sublimation),7 the product distribution was similar to that obtained for our reduced (to about I. e/Mo) molybdena-alumina catalyst, but the overall rate of reaction (propylene disappearance) was over 15 times greater. Both catalysts were equally poisoned (99% reduction in rate) by about 50 bmol of NO, Le., by about 2 NO for 40 to 50 Mo. The metathesis rate was also repressed with the carbonyl catalyst, but not with the reduced molybdena-alumina. Isotopic 15N0was used to confirm that species formed on molybdena-alumina were dimeric. Table I shows the frequencies observed for 14N0,15N0,and mixtures of these molecules. With 15N0,the two bands were shifted to lower frequencies by the expected amount [U('~NO)/U(~~NNO) =: 1.0151,as observed by Kugler and Grydera5r6A 1:1mixture of 14N0 and I5MO produced the expected spectrum consisting of two sets of triplet bands. The relative intensities of each of the triplet sets was about as expected, Le., 14N0-14NO:14NO-15NO:15NO-15N0 N 1:2:1. The complex was quite stable. Half saturation with '"0 produced the two bands for 15NO-J5N0. After evacuation and adding I4NO,the two bands for 14NO-14N0 were found along with those for 15NO-15N0. No bands for 14NO-15N0 were detected even after standing for 1 h a t about 40 " C in 5 torr of 14N0. However, because these bands could not be resolved to the base line, it is not possible to say that @ 1979 American Chemical Society
