MOLECULAR ASSOCIATION OF HYDROGEN-BONDING SOLUTES
Conclusions (1) The conductance data were fitted by the semiempirical Wishaw-Stokes equation using d = 3.5 8. A reasonable fit was found in the concentrated region. The significance of such fitting is not fully explained except that the decrease of the conductance with increasing concentration is largely accounted for by the increase of the solution viscosity which has been empirically introduced into the Wishaw-Stokcs equation. (2) The A070 product at infinite dilution for (n-CsHll)4NSCiY in DMSO is not equal to the ( A V ) ~product of molten (n-C5H11)4SSCN at 55". The A070 product is found to be 0.765 em2 ??/ohm cquiv while the (Ar), product is 0.3596 em2 P/ohm equiv. This result seems to be in disagreenlent with the KEK hypothesis that the molten salt is completely dissociatcd into its ions, which was based on the observed
3591
result novo= (AT), for (CdH&Npic in some nonaqueous solvent^.^^^ (3) The thermal collision mechanism for ion-ionpair equilibrium as proposed by KEK4910is adequate in explaining the rising portion of the AT product with increasing concentration which was observed in the intermediate concentration region. (4) In the dilute concentration rcgion, (n-C.5Hll)dNSCN is slightly associatcd with an association constant K A = 16.2 l./mol. The "corrected" Stokes radius for (n-C5H11)4N+ion is fi.21 8 indicating that, by comparison to molecular volumc data, the ion is unsolvated.
Acknowledgment. This work was supported by the IJ. S. Army Mobility Equipment Research and Developmcnt Center, Fort Belvoir, Va., under Contract NO.DA-44-009-APIC-l661(T).
Molecular Association of Hydrogen-Bonding Solutes. Phenol in Carbon Tetrachloride by Earl M. Woolley, John G. Travers, Brian P. Emo, and Loren G. Hepler* Department of Chemistry, University of Lethbridge, Lethbridge, Alberta, Canada
(Received August 14, 1970)
Publication costs borne completely by T h e Journal of Physical Chemistry
The intermolecular association of phenol in eel, solution at 25" has been investigated by means of distribution and calorimetric measurements. For the distribution of monomeric phenol between the aqueous and organic phases we obtain Kd = (P)o/(P), = 0.447. It is shown that the principal association reaction of phenol in CC14 saturated with water is trimerization, for which K3 = (Ps)/(P)~= 14.9. Calorimetrically determined heats of dilution of phenol in anhydrous CC14 also show that trimerization is the principal association reaction at concentration up to -2 J4. These results lead to K3 = (PS)/(P)S= 5.6 and to AH3' = -8.54 kcal/mol of PSin anhydrous CCh. Equilibrium constants cited above are expressed in terms of molarities. Heats of solution of phenol in CC14 have also been measured and combined with data from the literature in evaluating AH" = 3.17 kcal/mol and thence AGO and AS" for transfer of monomeric phenol from water to cc14. Calculation of A H o values from equilibrium constants at several temperatures is also discussed in relation to choices of standard states.
Introduction Many recent investigations have clearly shown that various compounds containing -OH groups (acetic acid, ethanol, and phenol are examples) are associated by way of intermolecular hydrogen bonding when dissolved in "inert" solvents. For some hydrogenbonding solutes the associated species are sufficiently stable that it has been possible to identify the species (usually as dimers) and to determine their thermodynamic properties in reasonably satisfactory
fashion. The situation is considerably different for phenol and some other solutes for which there are disagreements as to the most important species in solution snd few reliable thermodynamic data. Although several admirable exceptions can be cited, it is our opinion that many investigations have been based on uncritical acceptance of the idea that all of some measured effect can be attributed to equilibrium between monomers and dimers. Pimentel and McClellan, Davis,2 and Whetsel and T h e Journal o j Phyaical Chemistry, Vol. 76, No. $3,1971
WOOLLEY, TRAVERS, ERNO,AND HEPLER
3592
Ladys have cited a considerable number of investigations of association of phenol in CCld solution. There is little agreement as to which associated species (dimers, trimers, etc.) are most important and virtually no agreement on numerical values for equilibrium constants. Results of several spectroscopic investigations4-6 have been interpreted in terms of monomer-dimer equilibrium. A number of other investigations present convincing evidence that trimers or other species larger than dimers are present in significant quantities when phenol is dissolved in CCld, as reviewed briefly below. Saunders and Hyne’ have carefully tested the results of their nmr investigations in terms of monomer-dimer, monomer-trimer, and monomer-tetramer equilibria, They found that they could account quantitatively for their results in terms of the monomer-trimer equilibrium but could not do so with either the monomerdimer or the monomer-tetramer equilibrium. Extensive measurements by Johnson, Christian, and AffsprungBof the distribution of phenol between water and CCh and the solubility of water in solutions of phenol in CC14 have been interpreted in terms of several associated species containing more than one molecule of phenol, with the suggestion that trimeric phenol is a major species in CC14 solutions that contain some water. Pimentel and R4cClellan1 havc cited an unpublished ir investigation by Rea, who also concluded that trimers are the most important associated species of phenol in CC1,. Equilibrium constants (expressed in molarities) have been obtained at several temperatures and used for evaluation of AH” and AS” for the trimerization reaction. Most recently, Whetsel and Ladya have reviewed several earlier investigations, with particular emphasis on results that have been interpreted in terms of one equilibrium constant for dimerization and another equilibrium constant for successive additions of monomeric phenol to form trimers, tetramers, etc. They have also concluded that their own extensive ir data should be similarly interpreted in terms of two equilibrium constants, They have used their equilibrium constants (expressed in molarities) for calculation of AH” and ASo values. Before turning to our own experimental work and our interpretation in relation to earlier investigations, we consider the general problem of calculating AHo and ASo from K values at several temperatures. A number of recent investigations, particularly of the thermodynamics of ionization of acids, have demonAtrated that uncertainties associated with AH” values derived from K values at several temperatures are commonly undere~timated.~~~O There is also a matter of fundamental thermodynamics to be considered in connection with calculation of heats of reaction by T h e Journal of Physical Chemistry, Vol. 76, N o . 28, 1.971
way of the van’t Hoff equation d In K/dT
=
AH”/RTz
(1)
Direct application of (1) to K values based on different standard states or expressed in terms of different concentration units can lead to different AH O values, all referring t o the enthalpy of reaction with all solute species at infinite dilution. This is incorrect, since the value of AH” at infinite dilution for a particular reaction is independent of how people choose t o express concentrations. The essential thermodynamic requirement for direct application of the van’t Hoff equation (eq 1) is that the standard states chosen must be independent of temperature, which is a formal way of saying that equilibrium constants to be used in this fashion must be expressed in terms of mole fractions or molalities (or other temperature-independent units) rather than in terms of molarities (or other temperature-dependent units). This is not to suggest that it is thermodynamically incorrect or even undesirable t o choose a standard state based on molarity. In practice, such a choice often offers real convenience in terms of experimental procedures or calculations n ith experimental data. Further, there are sound arguments that comparisons of equilibrium constants, A G O , and AS” values for a particular reaction in several solvents are best made in terms of molarities or some other concentration unit based on equal volumes of solution. One way t o use the van’t Hoff equation correctly is to convert all equilibrium constants expressed in terms of molarities to new constants expressed in terms of mole fractions or molalities. These calculations require only knodedge of the density of solvent over the temperature range of interest. It is often more convenient to apply the van’t Hoff equation (eq 1) directly to equilibrium constants based on molarities and separately allow for the thermal expansion of the solvent. We consider this calculation for a general association reaction represented by
nP
=
P,
(2)
(1) G. C. Pimentel and A , L. McClellan, “The Hydrogen Bond,” W. H. Freeman, San Francisco, Calif., 1960. (2) M. N. Davis, Nut. Bur. Stand. ( U . S.), Monogr., No. 105 (1968). (3) K . B. Whetsel and J. H. Lady, “Spectrometry of Fuels,” Plenum Press, New York, N. Y., 1970, pp 259-279. (4) D. L. Powell and R. West, Spectrochim. Acta, 2 0 , 983 (1964); M. M. Maguire and R . West, ibid., 17, 369 (1961). (5) M. Ito, Mol. Spectrosc., 4, 125 (1960). (6) S. Singh and C. N . R. Rao, Can. J . Chem., 44, 2611 (1966). (7) M . Saunders and J. B. Hyne, J . Chem. Phys., 2 9 , 1319 (1958). (8) J. R. Johnson, S. D . Christian, and H. E. Affsprung, J . Chem. Soc., 1 (1965).
(9) E. J. King, “Acid-Base Equilibria,” Pergamon Press, Oxford, 1965. (10) J. W. Larson and L. G. Hepler in “Solute-Solvent Interactions,” J. F. Coetzee and C. D. Ritchie, Ed., Marcel Dekker, New York, N. Y., 1969.
MOLECULAR ASSOCIATION OF HYDROGEN-BONDING SOLUTES with equilibrium constants K M and K, where subscripts NI and m indicate that standard states are based on molarities and molalities, respectively. These equilibrium constants are related to each other and the density p of the solvent by
K,
= pn-'K~
(3)
We take logarithms of both sides of (3) and combine with the van't Hoff equation (eq 1) to obtain AH" = RT2(d In KM/dT)
+ RT2(n - l)(d In p/dT)
(4)
Since coefficients of thermal expansion of liquids are commonly tabulated as Q!
= (l/V)(dV/dT) = d l n V/dT
+ RT2(1 - n)a
which carbon dioxide was carefully excluded. Titration curves were obtained with a Beckman Research Model 1019 pH meter coupled with a Beckman 39004 pH 0-14 glass electrode and a calomel reference electrode. The pH-measuring system was standardized with pH 10.00 and pH 12.45 buffers. In calculating the equivalence point for each aliquot titrated, we made use of material balance, the electroneutrality relation, and equilibrium constants for ionization of water (pK, = 14.00) and phenol (pK, = 9.96) with activities expressed on the molar ~cale.~~'O Activity coefficients for aqueous phenol were taken to be unity and for the ions were calculated fromQ
(7) (5)
it is convenient to use (5) in the form AH" = RT2(d In KM/dT)
3593
(6)
Applications of equations similar to (4) and (6) to ionization of aqueous acidsg and deuterium oxidell have been described previously. With cc14 as solvent for a reaction of typo (2) with n = 3 at 298°K and a = 1.23 X low3from Rowlinson,12 RT2(1 - n)a = -430 cal/mol, which is not ordinarily negligible in comparison to RT2(dIn KM/dT). Although several earlier workers (for example, Maguire and West4) have converted K M values expressed in terms of molarities to K , or KX values expressed in terms of molalities or mole fractions and then correctly applied the van't Hoff equation (eq 1) to evaluation of AH", random inspection of papers cited by Pimentel and "lClellanl shows that a majority have calculated AH" values from RTZ(d In KM/dT) without using the required terms involving either density or coefficient of thermal expansion of the solvent as done in our eq 4 and 6. I n an effort to obtain further evidence for or against the variously proposed associated species of phenol in CCl,, we have made both distribution and calorimetric measurements with results and subsequent calculations that are described in this paper.
Experimental Section Analytical reagent grade phenol, reagent grade chlorobenzene, and spectroanalyzed carbon tetrachloride were used. Considerable care was taken to make and keep all calorimetric solutions free of water. All distribution and calorimetric measurements were made a t 25.0 f 0.1". Distribution measurements were made on solutions containing known total amounts of water, CC14, and phenol. After equilibrium was attained by samples in closed flasks placed in a constant-temperature bath, portions of the aqueous layers were analyzed by titration with standard NaOH solutions. These titrations were carried out in a nitrogen atmosphere from
All solutions at the equivalence point had ionic strengths I less then 0.1 M . Results of all of our distribution measurements are reported and interpreted in terms of molarities. Calorimetric titration measurements of heats of dilution of phenol and chlorobenzene in anhydrous ccl4 solutions were made with the LKB 8700 precision titration calorimetry system and a Metrohm Herisau Dosimat automatic buret to deliver the titrant solution. Heats of solution of solid phenol in C c 4 were made with the I X B 5700 system and the LKB 100-ml reaction calorimetry vessel, with glass ampoules to contain the phenol. All results of our calori0.1" and are metric measurements refer to 25.0 reported in terms of the calorie that is defined equal to 4.184 J. All solution compositions are described in terms of molarities.
*
Results and Calculations The composition and analytical data from our distribution measurements lead to the molarity of phenol (monomeric) in the aqueous phase and the total molarity of phenol in the organic phase, hereafter represented by (P), and C,, respectively. The distribution constant Kd that refers to the equilibrium P(aq) = P(in CCL)
(8)
is written as Kd
=
(p)/(p)a
(9)
in which (P) represents the molarity of monomeric phenol in CCL. On the basis of the tentative assumption that association of phenol in CCl, can be described in terms of a single equilibrium as in eq 2, we also have Kn
=
(Pn)/(P)"
(10)
where (P,) and (P) represent molarities of associated Pn molecules and monomeric phenol in CC1, solution. (11) R. N. Goldberg and L. G. Hepler, J. Phys. Chem., 72, 4654 (1968). (12) J. S. Rowlinson, "Liquids and Liquid Mixtures," Butterworths, London, 1959.
The Journal of Physical Chemistry, Vol. 76, N o . 83,1971
3594
WOOLLEY, TRAVERS, ERNO, AND HEPLER
0.06
0.02
0.10
I PI," Figure 1. Results of measurements of distribution of phenol between water and carbon tetrachloride, displayed as suggested by eq 14. Every point is the average of two or more duplicate determinations.
The total concentration C, of phenol in the organic phase is given by the sum Co = (P)
+ n(Pd
(11)
Combination of eq 9-11 leads to
co/(P),
=
Kd
+ nKnKd"(P):-'
(12)
If we know or can guess the value of n, a graph of Co/(P), against (P),"-l should yield a straight line with the intercept Kd and slope (nK,Kd"). One way to obtain a value for n is to obtain first a value of Kd by extrapolation of Co/(P)a to (P), = 0. Then from (12) me obtain log { [co/(p)a] - Kd] log (nK&d")
+ (n - 1) log (p),
(13)
Although use of this equation magnifies experimental uncertainties in C, and (P)a and depends markedly on the value of Kd used in evaluating the left-side term, a graph of log { [C,/(P),] - Kd) against log (P), leads to slope r y 2 and thence t o n = 3. We therefore write eq 12 specifically in terms of n = 3 for the monomertrimer equilibrium in the organic phme as
co/(p)a
=
Kd
+ 3K3Kda(P)a2
(14)
We have used the results of our distribution measurements to construct a graph of C,/(P), against (P)a2as shown in Figure 1. The intercept of the straight line leads to Kd = 0.447 and the slope leads to
K,
=
14.9.
The most thorough comparable investigation is that carried out by Johnson, Christian, and AffspThe Journal of Physical Chemistry, Vol. '76,N o . bs, 19'71
rung.* Interpretation of their results in terms of the monomer-trimer equilibrium leads to Kd = 0.467 and Ks = 12.7, in satisfactory agreement with our values for these quantities. Although the results of our distribution measurements and similar results from Johnson, Christian, and Affsprungs have been shown to be consistent with monomer-trimer equilibrium, it is also important to consider these results in relation to the possibility that other associated species may be present. The calculations reported by Johnson, Christian, and Affsprung* rule out dimers as principal species in these solutions. Another way to reach the same conclusion is by consideration of their display of their results on a graph of (our symbols) C o / ( P ) a against (P)a. According to eq 12 with n = 2 for monomer-dimer equilibrium, this graph should be a straight line with slope equal to (2K2Kd2)a Both their results and ours lead to distinctly curved lines on this kind of graph. The slopes of the lines at small (P)a are certainly very small and may be approaching zero as (P)&approaches zero, which shows that dimeric phenol is not a principal species in these CCL solutions. Calculations reported by Johnson, Christian, and Aff sprung* indicate that equilibria involving the combinations monomer-tetramer, monomer-trimer-tetramer, monomer-trimer-pentamer, and monomer-trimer-hexamer are all compatible with their distribution results. They selected the monomer-trimer-hexamer combination as being the most plausible. Our results support their preference for the monomer-trimer interpretation rather than the monomer-tetramer interpretation, since a graph of our C,/(P), against (P)3leads to a line with steadily decreasing slope at small concentrations that becomes approximately straight at high (P,). Similar graphs based on n > 4 also lead t o curved lines rather than the straight lines required by eq 12. Although our results do not definitely rule out simultaneous presence of several P, species with n 5 3 as proposed by Johnson, Christian, and Affsprung,S we can say that our results are adequately interpreted in terms of monomer-trimer equilibrium alone so that there is no need for US to postulate other species. It is difficult to estimate accurately the uncertainties to be associated with Kd and & values either from our work or from that of Johnson, Christian, and Aff sprungs for several reasons, First, experimental errors are relatively most important for the most dilute solutions. On the other hand, it is for the most dilute solutions that the implicit but sometimes unstated assumption that activity coefficients are unity is most satisfactory. Further, it is for dilute solutions that we can most confidently interpret experimental results in terms of a single equilibrium rather than in terms of consecutive equilibria and the accompanying increase in number of adjustable parameters. Fi-
3595
MOLECULAR ASSOCIATION OF HYDROOEN-BONDING SOLUTES nally, for the most concentrated solutions the relatively high concentration of water in the organic phase can have a very large effect on hydrogen-bonding reactions in ways that cannot be understood solely on the basis of distribution data. In spite of these difficulties, UT can say that qualitative conclusions concerning the importance of trimers and numerical values of Kd and Ks reported here and calculated from results of Johnson, Christian, and Aff sprung8 are in good agreement. Although we may now regard it as well established that tximerization is the principal association reaction of dilute phenol in CCI, that is saturated with water, we do not necessarily know from the distribution results that we can properly rule out dimers as important species in anhydrous CCle solvent. We now set about interpretation of our heat of dilution results, which are reported and used in the form of 4 L values. The relative apparent molar enthalpy represented by + L is equal to the negative of the enthalpy of dilution of 1 mol of phenol from a solution of specified molarity to infinite dilution. In our interpretation, we assume that all differences between actual q5L values and +L = 0 for ideal solutions are due to association reactions. In order to test the validity of this assumption, Ive have measured heats of dilution of chlorobenzene in CC14. Chlorobenzene \yas chosen as a test compound because its molecules have about the same dipole moment and are about the same size and shape as the phenol molecule. The small values we found for chlorobenzene in CCl, can be expressed by q6L = AM in which A = -14 cal l./mo12. Thus we see that it is in fact reasonable to attribute nearly all of the much larger heats of dilution of phenol (h - 1800 cal/mol for 1 M phenol) t o AH " values for association reactions rather than to long-range solute-solute interactions. We have also made density measurements on solutions of chlorobenzene in CCl, and have found that the partial molar volumes of chlorobenzene in dilute solutions are nearly identical with the molar volume of liquid chlorobenzene, as required for an ideal solution. On the basis of the calorimetric and volumetric data for Chlorobenzene, it is also reasonable to take all (molar) activity coefficients equal to unity for dilute solutions of phenol in
to monomers, we can express the heat of dilution to infinite dilution in terms of
4~ = (a/n)AH,"
(15)
in which h! and AH," represent the fraction of monomers that is associated and the molar enthalpy of reaction 2. We thus have (P) = M ( l - a) and (P,) = alM/n, which we substitute in the defining eq 10 to obtain
K,
= (a/n)M"-'(l
- a),
(16)
We have tested eq 15 and 16 with our 4L results by using a small digital computer t o find the value of Kn that leads to the most consistent value of AH," over the whole range of concentrations. Standard deviations in AH," and AH4' values calculated in this way are considerably larger than for AH*" values based on n = 3 in eq 15 and 16, corresponding to monomer-trimer equilibrium. Even more convincing evidence that trimers are more important species than either dimers or tetramers in these solutions is the large concentration dependence of the difference between calculated and average AHz" and AH4" values. In summary, we can say that all of our 4L results can be accounted for quantitatively in terms of monomer-trimer equilibrium by way of eq 15 and 16, while similar treatments in terms of either dimers or tetramers are unsatisfactory. This analysis of all of our 4L values and also separate analysis of groups of values obtained in single calorimetric runs leads to AH3" = -8.55 l.;cal/ mol of P3formed and to K s = 4.8. We have also developed another approach t o interpretation of +L results in terms of the general association reaction represented by eq 2. Consider the dilution of a solution containing 1 mol of phenol from its initial concentration ill to infinite dilution, for which we write
AH,"(P,)
(17)
(Pn) = Ke(P)"
(18)
M+L =
We also have from eq 10. Next we substitute (18) into (17) and rearrange to obtain
cc14. Our results for phenol are listed in Table 1 . 1 8 These results are based on several separate dilution runs with the calorimetric titration apparatus, in which the starting solutions were independently prepared, having concentrations M = 1.0970 mol/l. and M = 2.0808moI/l. We begin interpretation of the (pL results in terms of the single general association reaction represented by eq 2. Since at any finite concentration there will be both monomeric and associated species present while at infinite dilution all associated species will be dissociated
Further substitutions of (18) and (19) into the material balance equation
M
=
(P)
+ n(P,)
(20)
yield
M
=
(M4L/AH,"Kn)lin 4- nM4JAHn"
(21)
(13) Table I will appear immediately following this paper in the microfilm edition of this volume of the journal. Single copies may be obtained from the Reprint Department, ACS I'ublications, 1155 Sixteenth St., N.W., Washington, D. C. 20036, by referring to author, title of article, volume, and page number. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche.
T h e Journal of Physical Chemistry, Vol. 76, No. 93,1971
3596
WOOLLEY, TRAVERS, ERNO, AND HEPLER
200
fore desirable to calculate K and AH" values from A ~ values L as follows. We rewrite eq 15 as
I50
(23) for a reference solution of concentration M' with corresponding a' and subtract from eq 15 to obtain qbL' =
44
@L
100
501
IO
20
30
Figure 2. Results of heat of dilution measurements displayed as suggested by eq 22 with n = 3. Only half of the values given in Table I have been used in constructing this graph, hut all of the results were used in obtaining values of Ka and AHao reported in this paper.
Finally, we arrange (21) to obtain a linear equation suitable for graphical testing and subsequent evaluation of both K, and AH," from the slope and intercept
(AH,"/n) .(l/n) (AH ," ) ( n- ')In (l/Kn) l"n(+L/Mn-l)l'n (22) A graph of -4L against ( 4 L / M 2 ) 1 / acorresponding , to n = 3, is shown in Figure 2. From the slope and intercept we obbain K3 = 4.9 and AH," = -8.57 kcal/mol of Pa. A similar graph of -h against (4L/M)1'2, corresponding to n = 2, exhibits a mark+L
=
edly curved line that has both intercept and limiting slope very close to zero. A graph of - h against (4L/M3)1/4 shows a line with marked curvature at low concentrations that becomes approximately straight for M > 0.3 mol/l. We therefore conclude again that dimers and tetramers of phenol are of little importance compared to trimers in our anhydrous CC14solutions. Our Ks and AH3" values obtained by way of eq 15 and 16 and eq 22 differ slightly from each other because these different treatments weight the different experimental results differently. Our tabulated 4L values are based upon measured heats of dilution from one finite concentration to another finite concentration combined with our extrapolated heat of dilution to zero concentration. Differences in our 4Evalues are therefore properly regarded as purely experimental quantities, while absolute +L values are subject to adjustment following any different extrapolation to infinite dilution. It was thereThe Journal of Physical Chemistry, Vol. 76, N o . $3, 1071
(a'/n)AH,"
- 4 ) ~ '= A ~ = L
(a -
a')AH,"/n
(24)
We have tested eq 24 and 16 and an equation like (16) written in terms of M' and a' by using a digital computer to obtain the values of K, and AH,' that best account for the A$L values. For these calculations we have chosen our two titrant solutions (M' = 1.0970 and 2.0808 mol/l.) as reference solutions and then obtained K3 = 6.2 and 6.3 with AH," = -8.53 and -8.52 kcaI/mol. We were unable to fit our experimental results with n # 3. By four sliglitly different treatments of our heats of dilution we have now obtained K3 = 4.8, 4.9, 6.2, and 6.3 with 4H3" = -8.55, -8.57, -8.53, and -8.52 kcal/mol. We adopt K3 = 5.6 and AH," = =8.54 kcal/mol as "best" values for further calculations. From this K3 we obtain 4G3" = -1.02 kcal/ mol and combine with AH3' to obtain AS3' = -25.2 cal/deg mol. Our Ks = 14.9 from distribution data is not directly comparable to our "best" K 3 = 5.6 above, bccause the former applies to CC14 solutions that are saturated with water. Johnson, Christian, and Affsprung8 have combined their distribution and water solubility results to obtain information about the hydration of phenol in wet CCL solutions and thence have calculated K 3 = 4.1 for association of nonhydrated monomeric phenol to form nonhydrated trimeric phenol in CC14. This KB value is in good agreement with our K3 from heats of dilution. The nmr results of Saunders and Hyne7 have led them to K3 = 4.78 at 21") also in good agreement with our work. Interpolation of the K 3 values attributed' to Rea leads to Ka E 11 at 25". To the extent that a single equilibrium such as (2) is a realistic representation of the association of phenol in ccI4 solutions up to A4 2 2 mol/l. we believe that our results and those of earlier i n v e ~ t i g a t o r s * ~ pro~J vide convincing support for monomers and trimers as the principal species. However, it is necessary to recognize that it may be possible to fit experimental data with equations derived from unrcalistic models. We therefore consider our heats of dilution in relation to stepwise association of monomeric phenol to form dimers and trimers. To do so we write eq 15 in terms of both dimers and trimers as
M$L
=
(P2)AH2"
+ (P3)AH3"
(25)
and combine with a material balance equation similar to (20) and expressions for Kz and Ks of the form of eq 10. Since we have already shown that our heats of dilution can be interpreted satisfactorily in terms of
MOLECULAR ASSOCIATIONOF HYDROGEN-BONDING SOLUTES only monomers and trimers, we are not surprised to find that we obtain agreement between calculated and experimental heats only when K2 is corisiderably smaller than K3. Computer calculations show that we can calculate $L values in good agreement with experimental values when we combine any very small Kz with K3 S 5 and AH3" E 8.5 kcal/mol. Since a small Kz corresponds to small concentrations of dimer, most of these calculations are insensitive to the value of AHzO. Although we have no unambiguous a prioyi way to choose any particular small Ka on the basis of our computer calculations with eq 2 5 we may make some progrcss by imposing the additional requirements that AHz" be a few kilocalories per mole exothermic and that ASZ" be negative as characteristic of association reactions. On this basis, me can select K 2 of the order of or and AHzO -2 kcal/mol. Corresponding AH3' values differ very little from the "best" value given earlier, while corresponding K3 values are slightly smaller than the "best" 5.6 given earlier. We now consider an explanation for the relative importance of dimers and trimers in CCl, solution. The approximate AHz" value above leads to a reasonable hydrogen-bond strength for the dimer. Since AH3" is considerably more than twice AHz", we suspect that the principal trimeric species may be cyclic with three hydrogen bonds per molecule. Recent quantum mechanical calculation^^^ are consistent with this suggestion and the possibility that the total hydrogen-bond energy in the cyclic trimer is greater than 3 times the hydrogen-bond energy in the dimer. Thus the relative magnitudes of AHz" and AH3" and the corresponding equilibrium constants KZ and K 3 can be understood in terms of a cyclic trimer. Our heats of dilution of phenol in cc14and some other solvents are discussed elsewhere15 in relation to the recent ir investigations of Whetsel and Lady3 and the stepwise association model they have used. We have measured heats of solution of solid phenol in CCl, and combined the results with our $L values to obtain AH" = 6.27 =k 0.04 kcal/mol for this heat of solution at infinite dilution where all dissolved phenol is monomeric. The only comparable value we know of is a recently reportedl6 AH = 6.27 =k 0.07 kcal/mol "at high dilution." We combine our AH" = 6.27 kcal/mol above with AH" = 3.10 kcal/mol for the heat of solution of solid phenol in water from earlier calorimetric measurement^'^ to obtain AHo = 3.17 kcal/mol for the transfer reaction previously represented by eq 8. Values of Kd obtained in this work and earlier by Johnson, Christian, and Affsprungs are not directly useful for our present calculation, since these quantities
3597
refer to transfer of phenol from aqueous solution of CCld that is saturated with water and in which some of the monorncric phenol may be associated with water. As mentioned earlier, Johnson, Christian, and Affsprungs have taken hydration of phenol in wet CCL into account to obtain a value of Kt in good agreement with K3 values obtained by us and by Saunders and I-Iyne' from investigations of anhydrous solutions. It is therefore reasonable to accept their Kt = 0.46 for the transfer reaction corrected for hydration of phenol in CCL. This K t then leads to AGO = 0.46 kcal/mol for the transfer reaction. We combine AGO and AH" values to obtain AS" = 9.1 cal/deg mol for the transfer represented by eq 8, with an ideal 1 M solution as the standard state. The increase in entropy accompanying transfer of 1 mol of phenol from 1 1. of water to 11. of Cc14may be expressed as
AS"
=
9.1 cal/deg mol = AS, iASssi
(26)
in which AS, and As,,, refer to entropy effects associated with available or free volumes for solute molecules and to solute-solvent interactions, respectively. We can express AS, in terms of the free volumes associated with 1 1. each of water and organic solvent as AS, = R In (Vf,/Vf,) and substitute in (26) to obtain AS,,,
=
9.1
4- R In (Vf,/Vfo)
(27)
Since water is well known to have an unusually open structure, we anticipate that Vfw for 1 1. of water is greater than Vf, for 1 1. of cC14 so that R In (Vf,/Vf,) is positive and ASssi
> 9.1 cal/deg
mol
(28)
Our conclusion from this positive ASssi is that solutesolvent interactions (hydration) in water lead to a loss of entropy considerably greater than do solutesolvent interactions in CCL. This conclusion is consistent with our AH" = +3.17 kcal/mol for the transfer of phenol from water to CC14, which also indicates stronger attraction of phenol for water than for CCl,.
Acknowledgment. We are grateful to the National Research Council of Canada and the University of Lethbridge Research Committee for support of this research, to Dr. Gary Bertrand for helpful comments, and to Dr. Peter Reilly for help with computer calculations. (14) L. Del Bene and J. A. Pople, Chem. Phys. Lett., 4, 426 (1969);
J. Chem. Phys., 52, 4858 (1970). (15) E. M. Woolley and L. G. Hepler, in preparation. (16) E. M. Arnett, L. Joris, E. Mitchell, T. S. S. R. Murty, T.M . Gorrie, and P. v. R. Sohleyer, J . Amer. Chem. SOC.,92, 2365 (1970). (17) L. P. Fernandez and L. G. Hepler, ibid., 81, 1783 (1959).
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