J. CHEM. SOC. FARADAY TRANS., 1994, 90(18), 2691-2695 2691 Enthalpies of Transfer of Tetrabutylammonium Bromide from Water to highly Aqueous Water-Methanol, -Ethanol, -Propan4 -01and -Acetonitrile Mixtures at 298 K :Consideration of the Extended Coordination Model Solvation Parameters Patrick Hogan, Ita McStravick, James Mullally and W. Earle Waghorne* Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland Previous studies have established that the extended coordination model of solvation can satisfactorily account for the variation in the transfer enthalpies of solutes in mixed-solvent systems. However, the model parameter relating to the solute-induced disruption of the solvent structure shows a marked dependence on the nature of the mixed solvent.This result is not consistent with the underlying model of the solvation process. In the present paper we report the transfer enthalpies of tetrabutylammonium bromide, for which this depen-dence is large, into a series of highly aqueous mixed solvents. Analysis of these in terms of the extended coordination model confirms both the model's ability to account for the experimental data, and the variability of the structural disruption parameter. The possible origins of this latter result are considered in detail. We have recently reported the enthalpies of transfer, At He, of several solutes from water to aqueous organic solvent mix- tures.'-' These data were considered in terms of the extended coordination model of ~olvation.~.' These studies have revealed the existence of a transition in the solvating proper- ties of the aqueous systems at some critical composition, x;, which depends on the organic cosolvent.They also showed that the extent to which the solutes disrupt the solvent struc- ture, as measured by the model parameter (an+ BN),varied with the organic component. This second result was inter- preted as indicating that the organic components had the effect of rigidifying the water structure, with the extent of rigi- dification increasing in the order 1,4-dioxane, methanol < ethanol < 2-methylpropan-2-01 (tert-butyl alcohol, TBA), propan-1-01.~ However, it is clear that this explanation, while plausible, cannot be strictly correct and, rather, poses a theoretical problem.To understand the theoretical point we consider the model equation6 for the transfer enthalpy of a solute from some solvent, A, to mixtures of A with some second solvent, B. This contains three model parameters: p, which is an index of preferential solvation, AAH;, , the difference between the enthalpies of interaction of the solute with the two pure sol- vents A and B, and (an+ BN), which measures the extent to which the solute disrupts the solvent-solvent interactions through cavity formation and reorganisation of the solvent around the cavity. The remaining quantities in eqn. (1) are known: thus, xA, xB, LA, L, are the mole fractions and rela- tive partial molar enthalpies of the component solvents in the mixtures and AAHo* is the difference between the enthalpies of solvent-solvent interactions in the two pure solvents (calculated as the difference between the molar enthalpies of condensation).The three model parameters are recovered from the experimental A, H" values by fitting them to eqn. (1). It is implicit in this procedure, and in the derivation of eqn. (1),6 that the three model parameters are constant over the range of solvent compositions of interest. Since p and AAH(112reflect the differences in the interaction of the solute with solvents A and B they will depend on the cosolvent. In contrast, since water is the limit of the aqueous domains (i.e. those with cosolvent concentrations below x:) the values of (an+ BN) recovered could be expected to be equal, and equal to the value for pure water, in marked con- trast to the experimental results.One possible explanation for the dependence of (an+ BN) on the cosolvent is that it varies at low cosolvent concentra- tions, the values converging to that for pure water in the limit of low cosolvent composition. The data reported pre-viously'-' were measured across the entire range of solvent compositions and, with the exception of the aqueous TBA system, the density of data points at low cosolvent concentra- tions was too low to allow such a variation to be detected. The earlier studies concentrated largely on aqueous alcohol solvent systems. The complexity of these systems, at low alcohol concentrations, could account for such variations in (an+ PN). Thus there is the possibility that introduction of the alcohol at very low concentrations rigidifies the three- dimensional water structure, while at higher (but still very low) alcohol concentrations there is clear evidence for aggre- gation of the alcohol molecules.8 At still higher alcohol con- centrations there is another transition from a water-like structure to one more closely resembling that of the alcohol; this last transition has been identified with that occurring at x* and results in marked changes in the model parameters, in particular (an+ BN) which decreases significantly.' The (an+ BN) values for tetrabutylammonium bromide, TBABr, are larger than those of most of the solutes ~tudied,'.~and corresponding show large variations with changes in the cosolvent, increasing from ca.40 for aqueous methanol and 1,4-dioxan to ca. 70 for aqueous propan-1-01. It was also found that the (an+ BN) of a series of amides were significantly higher in aqueous acetonitrile mixtures than in the aqueous alcohol systems.' Thus we have measured the transfer enthalpies, At H", of TBABr from water to highly aqueous mixtures of methanol, ethanol, propan-1-01 and acetonitrile, and have analysed these in terms of eqn. (1). Experimental The purifications of all chemicals were as described pre- vi~usly.'*~.', The enthalpies of transfer of TBABr were calculated3 from the enthalpies of dilution of a concentrated aqueous TBABr solution, ADHe, and the relative partial J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Enthalpies of transfer of tetrabutylammonium bromide from water to aqueous methanol, ethanol, propan-1-01 and acetonitrile mix- tures at 298 K" methanol-water ethanol-water propan-1-01-water acetonitrile-water ~~~ A, H" XEIOH A, H" XPrOH A, H* XMeCN A, H" ~~ O.oo00 0.0200 0.0250 0.0750 0.0900' 0.1900' 0.2700'' 0.3600' 0.4m 0.57006 0.6922' 0.0 2.1 3.3 12.7 13.5 25.5 29.2 30.9 29.2 25.9 24.2 O.oo00 0.0200 0.0376' 0.04oO 0.0600 0.0668' 0.0800 0.0929' 0.1354' 0.2000 0.261 1' 0.3739' 0.5256' 0.0 4.4 10.8 13.6 18.6 19.6 27.2 26.5 36.1 44.1 38.8 36.8 34.6 O.oo00 0.0200 0.0322' 0.0600 0.0696' 0.0800 0.1000 0.1138' 0.2305' 0.4 114' 0.5447' 0.0 10.3 17.3 33.2 32.8 35.9 38.0 40.5 39.1 35.2 27.5 O.oo00 0.0200 0.0300 0.0500 0.0800 0.1000 0.1500 0.2000 0.2500 0.3000 0.4OOo 0.5000 0.6OOo 0.7000 0.0 8.2 11.6 17.1 22.2 25.4 26.4 26.5 25.5 24.9 23.8 21.5 20.6 18.3 ~ ~~ ~~~ Units are kJ mol-', precisions are +0.5 kJ mol-I or better.'Data from ref. 3. 'Data from ref. 1. molar enthalpies of water, Lw ,in the solvent mixtures as: A, H" = AD@'(mixture) -ADH"(water) -n~, (2) where n is the number of moles of water associated with one mole of TBABr in the concentrated solution (cu. 14-19 in the systems studied here). The experimental uncertainty in A, H" values determined this way depends on those of both of ADHe and L,. In the systems studied here both of these are significant. The value of A,H"(water) is cu.-25 kJ mol-' (varying slightly with the concentration of the concentrated solution) with an esti- mated precision of 1% or better, the precisions of the other ADHe values are of the same order. The L, values for the aqueous methanol,'-' ethanol' and a~etonitrile'~ systems were recovered from excess enthalpy data, and should have precisions of 10-20 J mol-', corresponding to k0.4 kJ rnol-' or less in A, He. The excess enthalpy data for the aqueous propan-1-01 system are less c~nsistent'~*'~ and, for this system, the rela- Table 2 Relative partial molar enthalpies of water and propan-1-01 and molar excess enthalpies of aqueous propan-1-01 mixtures at 298 K" O.oo00 0 -9590 0 0.0110 -4 -9040 -103 0.0150 -20 -8700 -150 0.0200 -27 -8250 -191 0.0250 -54 -7550 -241 0.0300 -64 -6740 -264 0.0350 -83 -6000 -290 0.04oO -110 -4900 -302 0.0450 -170 -3850 -336 0.0500 -215 -2890 -349 0.0550 -293 -2090 -392 0.0600 -305 -1310 -365 0.0650 -320 -750 -348 0.0700 -360 -260 -353 0.0800 -430 320 -370 0.1000 -475 750 -353 0.1200 -484 820 -328 0.1400 -490 880 -298 0.1600 -480 860 -266 0.1800 -465 850 -228 0.2000 -470 800 -216 " Units are J mol-'; precisions of Liare the larger of k 1% or f15 J mol-'.tive partial molar enthalpies of water and propanol were measured directly. The estimated precisions of the L, values in this system are again f20 J mol-'. The calorimetric measurements were made using the automated calorimeter system described el~ewhere.~ Results The A, Hevalues for TBABr for the systems studied are listed in Table 1.Analysis of the A,H" data in terms of eqn. (1) requires the relative partial molar enthalpies of the com- ponents of the mixed solvents. These were recovered from the excess enthalpies for the aqueous ehtanol,' TBA'7*'8 and a~etonitrile'~ systems. Since the agreement between the reported excess enthalpies for the aqueous propan-1-01 was significantly poorer, we undertook the direct 4500 1 I I I I 1 I I 0.00 0.05 0.10 0.15 0.20 0.25 XPrOH Fig. 1 Comparison of the relative partial molar enthalpies of water in aqueous propan-1-01 mixtures; (0)directly measured values, (-), calculated values from the relative molar enthalpies of propan-1-01 uia eqn.(4) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0 -1 00 .--I 0 -2002 j5 II -30C 0 I I I I 0.25I-4Ot I 0.00 0.05 0.10 0.15 0.20 XprO H Fig. 2 Molar excess enthalpies of water-propan-1-01 mixtures at 298 K; (-) those reported here, (a)and (0)values from ref. 15 and 16, respectively measurement of the Livalues, as the molar enthalpies of solu-tion of water and propan-1-01 in their mixtures. In this case the excess enthalpy, AHE,is calculable as : AH^ = x&, + X,L, (3) In part this approach is dictated by the available calorimeter system. However, it has one considerable advantage over the direct measurement of AHE in that the Livalues are related by the Gibbs-Duhem relationship, making it possible to check the consistency of the experimental data.Thus values of L, may be calculated from the experimental L, data as: (4) which is easily solved by representing L, as a polynomial expansion in x '. The experimental Li values for the propan-1-01 water system are listed in Table 2, along with the calculated excess enthalpies. Fig. 1 shows a comparison of the experimental values for water with those calculated from the values for propanol-1-01 uia eqn. (4). The agreement between the two sets of Livalues shown in Fig. 1 is excellent, and provides considerable support for the data listed in Table 2. Fig. 2 compares the values of AHE with those taken from the liter- ature.' 5*16 The agreement is excellent at low propan- l-ol concentrations, but the data reported here indicate a slightly deeper minimum (by about 25 J mol-') in the excess enth- alPY.Discussion As discussed previously, there are transitions in the solvating properties of these mixed aqueous solvent systems. Thus, two sets of model parameters are required to reproduce the experimental A, He data, the transition occurring relatively abruptly at some critical composition x:. The parameters reported here refer to the water-rich compositions. Table 3 Solvation parameters for tetrabutylammonium bromide in aqueous methanol, ehtanol, propan-1-01, TBA, acetonitrile and 1,4-dioxane P (an + #?N) AAH7,fkJ mol-' methanol 0.5, f 0.05 39 f 12 235 f150 ethanol 0.5 f 0.1 60f 20 230 f500 propanol-1-01 0.6, k 0.1 67 & 20 -50 +_ 200 TBA 0.6 f0.1 60 f 8 118 f160 acetonit rile 0.5 f0.1 148 f 30 2600 & 2500 1,4-Dioxana 1.0 f0.2 34 k 5 350 & 40 Data from ref.3. The parameters recovered from these analyses are listed in Table 3, and the experimental and calculated A, Hevalues are compared in Fig. 3. The precisions indicated for the model parameters warrant some comment. As discussed above, the experimental errors in the A, He are significant, reflecting those in both the ADHOand the L, values. In addition, there are significant uncertainties in the calculated At He values, reflecting the precisions of the Lidata. These factors dictate significant uncertainties in the reported model parameters.However, since the central point of the present paper was to investigate the observed variations in the (an+ PN) values, the uncertainties quoted for the model parameters are very much upper limits, so as to ensure that these differences are not artefacts. The curves shown in Fig. 3 were calculated using the best-fit parameters listed in Table 3. The parameters for the aqueous methanol, ethanol and TBA systems are the same as those reported previ~usly,~ but those for the aqueous propan- l-ol system differ somewhat from the earlier values. The difference in the latter case results principally from the greater precision in the shape of the A, He against solvent composition profile provided by the I I 1 0.0 0.2 0:4 ( 6 Xorg Fig.3 Comp$rison of the calculated and experimental enthalpies of transfer, A, H , of tetrabutylammonium bromide from water to aqueous methanol (0,---), ethanol (a,-), propan-1-01 (A, ---), TBA (A,-) and acetonitrile (+,-) additional At He data; there is also, however, some contribu- tion from the revised Livalues used. It can be seen from Fig. 3 that the agreement between the experimental At H" values and those calculated using eqn. (1) and the parameters from Table 3 is excellent in all cases and, significantly, in each case, this agreement extends from pure water to x; (with clear deviations at higher concentrations of the organic component). The agreement between the calcu- lated and experimental values at low concentrations of the organic cosolvent indicates that any contributions to the transfer enthalpies from structural changes or solvent aggre- gation are accounted for by the variations in the L, values (which will reflect these changes).Operationally this confirms that the parameters listed in Table 3 will reproduce the experimental At He data over the water-rich composition domains of each of these solvent systems. That is, eqn. (1) can be used to predict the A,H" data for these, and by implica- tion, those for the other systems studied previously with con- siderable precision. The theoretical problem, however, remains. The (an+QN) values in the aqueous alcohol systems are broadly in agree- ment, within the rather wide limits listed in Table 3 (and these precisions are very much upper limits); however, the value recovered for the aqueous acetonitrile system is clearly larger, by far more than the sum of the estimated precisions.Clearly not all of these values can be that for pure water. This result is entirely consistent with those of our previous studies. Thus the (an+QN)values for a series of amides in mixtures of methanol with dimethyl s~lfoxide'~ or acetonitrile" differs markedly from each other and from those obtained for the same solutes in the organic-rich aqueous acetonitrile5 and aqueous methanol4 systems. In effect then, the (an+QN)values recovered from the analyses of transfer enthalpies using eqn. (1) depend on both of the components of the mixed solvent. That is, they appear to be properties of solvation by the mixed solvent rather than by the individual components of the mixture.This is not truly consistent with the derivation of eqn. (l),which incorporates the approximations that the values of a and /? are the same for each of the componepts of the mixed solvent and that both of these and n (= nA +nB) and N (= N, +NB)are con- stant over the range of solvent compositions where eqn. (1) applies. This problem cannot easily be resolved. One possible approach is to make the approximation that a and Q are con- stant, but different for the component solvents; i.e. aA # aB and PA # QB.This leads to a tractable equation with four model parameters: p, AAH;,, (an+QN)A and (an+#IN)B; however, analysis of the transfer enthalpies in this way leads to no significant improvement in the fits to the data.More- over, the values recovered for (an+/?N)Aand (an+BN)Bare essentially equal and also equal to those recovered using eqn. (1). A second approach is to assume that n (=nA +nB) and N (NA+NB)are not constant but vary to reflect the differences in the volumes of the cosolvent molecules. This simply involves recasting eqn. (1) in terms of the volume fractions, rather than the mole fractions, of the component solvents and leads to an equation entirely analogous to eqn. (1). For the systems studied here this leads to only marginal changes in the (an+QN)values recovered, leaving the variations essen- tially unchanged, and again gives no improvement in the fits to the experimental data.In effect then, the problem appears not to lie in the form of eqn. (1). This points to the possibility that the parameters used to account for the contributions from changes in solvent-solvent interactions are unsatisfactory. The form of eqn. (1) dictates that the values for (an+PN) are recovered from the term involving the Livalues, since J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 those involving AAH:, and AAHo* having the same mathe- matical form. Thus we must question the direct use of the Li values when applying eqn. (1). The use of a common value of (an+PN) effectively assumes that all of the solvent-solvent interactions are equally perturbed by the introduction of the solute or, that all such interactions are equal.Clearly this would be the case for solvent systems such as mixtures of rare gases, where the solvent-solvent interactions would be symmetrical. However, in the systems considered here it need not be. In effect, the Li values contain contributions from each of the various solvent-solvent interactions. In the case of an aqueous alcohol system for example, these include, at the very least, the water-water, water-alcohol and alcohol-alcohol hydro- gen bonds and also the interactions of the water or alcohol molecules with the alkyl residue of the alcohol; each of these will differ in strength. In a situation wherein the tetra-alkylammonium ions are caged within the hydrogen-bonded network of the solvent system, leaving the alkyl residues of the cosolvent molecules relatively unaffected, changes in the strengths of the solvent-solvent hydrogen bonding would contribute significantly to At H*, but those involving the alkyl residues would not.In effect then, the common (an+QN) would apply only to those contributions of Li,which result from the hydrogen-bonding interactions. Thus, inclusion of contributions from the alkyl group interactions (which are reflected in the raw Livalues) would lead to (an+QN)values which varied with the contribution from the alkyl group interactions; that is, in the order: methanol < ethanol <propan-1-01, TBA, as observed. Of course, one could reverse the argument, taking the primary solute-solvent interactions to be with the solvent alkyl residues, but this leads to a similar conclusion.If this explanation of the variations in (an+BN) is correct then it has implications for the other model parameters recovered from eqn. (1). Most clearly, the values of AAH;, would not accurately reflect the differences in the direct solute-solvent interactions in the pure solvents, since their calculation involves the use of (an+PN); although this would be offset by the use of the enthalpies of condensation, which, like the Livalues, contain contributions from all solvent-solvent interactions. The values of p may be some- what compromised, but it is not possible, a priori, to assess the extent of this. One should not overstate the negative aspects of these points. Clearly caution is indicated in the use of their absol- ute values ;however, comparisons of parameters, particularly for similar solutes in a mixed-solvent system, are likely to remain valid.Moreover, the marked breaks in solvating properties of aqueous systems (at xt) are observed for far too wide a range of solutesolvent systems to be artefacts. In this context it is worth noting that, in some cases at least, there is strong evidence that the values of p and AAH;, are physically reasonable. Thus, in the acetonitrile-methanol solvent system the values of the model parameters for the silver halides can be determined independently of the A,H" data in the mixed solvents, and these predict accurately the variation in these with solvent composition.2 1*22 Moreover, the values of AAHy2 recovered for the silver halides in this system, and for a series of alkali-metal halides in aqueous methanol systems,6 are substantially equal to their transfer Gibbs energies between the pure solvents.Again, this result is predicted theoretically, in this case by application of Ben Naim's compensation prin~iple.,~ These results indicate either that the values of (an+BN), for these systems at least, are reasonable or, possibly, that the error induced by the use of the raw Livalues is compensated by the use of the enthalpies of condensation in calculating J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2695 AAHo* as indicated above. The ultimate resolution of this 4 G. Carthy, D. Feakins, C. O’Duinn and W.E. Waghorne, J. situation will require dissection of the Li and AAHo* values into their various contributions and a corresponding adjust- ment of eqn. (1). Conclusions 5 6 7 Chem. SOC.,Faraday Trans., 1991,87,2447. D. Feakins, P. Hogan, C. O’Duinn and W. E. Waghorne, J. Chem. SOC.,Faraday Trans., 1992,88,423. D. Feakins, E. de Valera and W. E. Waghorne, J. Chem. SOC., Faraday Trans. I, 1983,79, 1061. D. Feakins, E. de Valera and W. E. Waghorne, J. Chem. SOC., Faraday Trans. I, 1985,81,2703. Operationally it has been confirmed that the extended coor- dination model, via eqn. (l), will satisfactorily reproduce the transfer enthalpies of solutes in these complex aqueous mixed solvents and, by implication, those of other solute-mixed solvent systems.However, the exact physical significance of the model parameters recovered from the transfer enthalpies remains an open question and these must be treated with some caution. In particular the values of the model structural disruption parameter (an+ PN) for some of the systems con- sidered here are probably too large, with the value of 35-40 obtained from the aqueous methanol and 1,4-dioxan systems being a likely upper limit for tetrabutylammonium bromide 8 9 10 11 12 13 14 15 16 F. Franks and J. Desnoyers, Water Sci. Rev., 1985, 1, 170. M. K. Dutta-Choudry and H. B. Mathur, J. Chem. Eng. Data, 1974,19,2321. V. P. Belousov and M. Yu. Panov, Vestn. Leningrad Univ. Fiz. Khim., 1976, 2, 149. S. Murakami, R. Tanaka and R. Fujishiro, J. Solution Chem., 1974,3, 71.R. F. Lama and B. C. Y. Lu, J. Chem. Eng. Data, 1965,10,216. M. J. Costigan, L. J. Hodges, K. N. Marsh, R.H. Stokes and C. W. Tuxford, Aust. J. Chem., 1980,33,2103. R. H. Stokes, J. Chem. Thermodyn., 1977,19,977. V. P. Belousov, Vestn. Leningrad Univ., Fiz. Khim., 1961, 16, 144. V. P. Belousov, N. L. Makarova and M. Yu. Panov, Vestn. Leningrad Univ., Fiz. Khim., 1971, 113. in water. In turn, the values of AAHy2 must also be treated carefully. 17 18 H. Arm, Helv. Chim. Acta, 1962,45, 1803. J. Kenttamaa, E. Tommilia and M. Martti, Ann. Acad. Sci. Fenn., Ser. A, 1959,93, 1. We gratefully acknowledge support from the European Union. 19 20 D. Feakins, C. C. O’Duinn and W. E. Waghorne, J. Solution Chem., 1987,16,907. A. Costigan, D. Feakins, I. McStravick, C. O’Duinn, J. Ryan and W. E. Waghorne, J. Chem. SOC.,Faraday Trans., 1991, 87, References 21 2443. B. G. Cox and W. E. Waghorne, J. Chem. SOC.,Faraday Trans. 1 G. Carthy, D. Feakins and W. E. Waghorne, J. Chem. SOC., Faraday Trans. I, 1987,83,2585. 2 D. Feakins, J. Mullally and W. E. Waghorne, J. Solution Chem., 22 23 I, 1984,80,1267. W. E. Waghorne, Chem. SOC.Rev., 1993,22,285. A. Ben-Naim, J. Chem. Phys., 1978,82,874. 1990, 19,401. 3 D. Feakins, J. Mullally and W. E. Waghorne, J. Chem. SOC., Faraday Trans., 1991,87,87. Paper 41005495; Received 28th January, 1994