Studies in Solubility Parameter Theory for Mixed Solvent Systems1

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1 Studies in Solubility Parameter Theory for Mixed Solvent Systems1 AVIJIT PURKAYASTHA AND JOHN WALKLEY~ Department of Chemistry, Simon Fraser University, Burnaby 2, British Columbia Received August 9, 1971 Data are presented for the saturation solubility and partial molal volume of iodine in a mixed benzenecyclohexane solvent and for the saturation solubility ofstannic iodide in the same solvent mixture. A successful interpretation of these data in terms of solubility parameter theory is possible if we define an effective volume fraction term. This term reflects the immediate solvent environment of the solute molecule with the preferential solvation of the solute by one of the solvent molecules. Data for iodine in a mixed carbon tetrachloridebenzene solvent mixture and for iodine in a carbon tetrachloride-perfluoroheptane mixture are also interpreted in terms of the proposed theory. Les rtsultats relatifs a la solubilitc a saturation et au volume molaire partiel de l'iode dans un solvant mixte benztne-cyclohexane, ainsi que ceux relatifs la solubilite a saturation de I'iodure stannique dans le m&me melange de solvants, sont prtsentes. En fonction d'une theorie de paramttres de solubilite, une bonne interpretation de ces donnees est possible a condition de dtfinir un terme de fraction de volume reel. Ce terme refltte l'environnement immediat des molccules du solute par le solvant ainsi que la solvatation preferentielle du solute par I'une des molecules de solvant. Les rksultats relatifs a I'iode dans un melange de solvants tttrachlorure de carbone- benztne et ceux de I'iode dans un melange de solvants tetrachlorure de carbone-perfluoroheptane, sont egalement interpret& en fonction de la thtorie proposee. Canadian Journal of Chemistry, 50, 834 (1972) Introduction Many studies have been done on the correlation of the behavior of non-electrolyte solutions with the molecular parameters of the pure components and, in general, the theories developed have been of reasonable predictive value (1). Few studies have been done on systems of more than two components though the extension of present theories appears fairly simple. A particularly useful field of study is that of a dilute solute in a two component non-polar solvent mixture. Such systems, however, appear complicated by the preferential solvation of the solute molecule by one of the solvent species. To explain the dependence of the equilibrium constant for the iodine-pyridine charge transfer complex upon the solvent used, Christian was required to assume some degree of preferential solvation (2). A similar assumption is required to explain the diffusion coefficient values of iodine in various alcohol-hydrocarbon mixed solvents. Nakanishi et al. (3) proposed a mechanism that assumed the solute iodine molecule to spend more time in an environment preferentially composed of the energetically favored 'Presented at C.I.C. Conference, May To whom correspondence should be addressed. solvent molecule. An earlier study of the partial molal volume of bromine in mixed CC1,-c- C4Cl2F6 solvent by Smith and Walkley (4) showed the preferential solvation of the bromine by the CCl,. This was such that at even a very low mole-fraction composition of CCl, in the solvent mixture the partial molal volume of the dissolved solute fell from its value in the pure chloro-fluorocarbon to a value similar to that in pure CCl,. Our present study is concerned with the interpretation of the saturation solubility and partial molal volume of simple dilute solutes in two component non-polar solvents. Data are measured over the complete range of solvent composition. Recognizing the success of Hildebrand's solubility parameter theory in interpreting the saturation solubility behavior of dilute solutes in single component solvents we have chosen to extend his theory (5) to our two component solvent data. We have extended the theory by attempting to take into account the "preferential" nearest neighbor environment of the solute molecules. The theory is remarkably successful and offers an approach to the nearest neighbor environment which is necessary to the further interpretation of the diffusion and spectroscopic studies of these systems.

2 PURKAYASTHA AND WALKLEY: ON MIXED SOLVENT SYSTEMS TABLE 1. Saturation solubility of iodine in a mixed benzene-cyclohexane solvent at 25 "C Volume fraction of Saturation solubility -In x,m Experimental (eq. 2) Calculated Eq. 3, from@, Eq. 5, from Qr TABLE 2. Saturation solubility of stannic iodide in a mixed benzene-cyclohexane solvent at 25 "C Volume Saturation Calculated fraction of solubility -In X: Experimental From 9: TABLE 3. Solubility parameter values used in calculations (cal/~c)'~~ System 6 I C6H6 - I2 - C-C6HI C6H6 - I2 - C-C6H n-c,fi,-1,-cci, C6H6 - SnI, - c-c6h Experimental The solvents (C6H6 and c-c6h12) were spectroscopic grade solvents and were used without further purification. The preparation of saturated iodine and stannic iodide solutions was by the same technique as described earlier by Walkley and Vittoria (6). The iodine concentration in the saturated solution was determined spectroscopically at 520 mp and that of stannic iodide at 360 mp. Aliquots from the saturated solution were diluted in the ratio 1 :250 with cyclohexane before optical density measurements were 6, made. Saturation solubility measurements were made over the complete range of composition of the solvent mixture. All data were measured at f 0.01 "C. For those experiments involving stannic iodide, photochemical decomposition of SnI, in solution was avoided by using black-painted dissolution cells. The partial molal volume of iodine in the mixed solvent was measured using the dilatometric technique described by Hildebrand and Glew (7). The dilatometer was of 150 ml capacity and the capillary of 2 mm internal diameter. No temperature fluctuation of the liquid level in the capillary arm was observed and the scatter of individual experimental data allowed the partial molal volumes to be measured to a precision of 0.8%. Results Saturation solubility (mole fraction x:) and partial molal volume (r2 cc mol-') of iodine in the mixed C6H6-c-C6HI2 solvent over the complete range of composition are given in Tables 1 and 3. In Table 2 saturation solubility

3 836 CANADIAN JOURNAL OF CHEMISTRY. VOL data for SnI, in mixed C6H6- c-c6hl2 solvent are presented. Discussion The solubility parameter theory equation expressing the saturation solubility of a solute (x,) in terms of its ideal solubility (a;) and the 6-parameters of the solvent and the solute (6, and 6,) has been well tested (5). With the usual notation this equation is Generally, for any chosen solute (of known 6, value) the equation is tested by comparing the experimental 6, value (for a range of solvents) to the thermodynamic value ((molar energy of vaporization/molar v~lume)'~~). For a wide range of solute-solvent systems this self-consistency has been shown to exist (8). For systems in which a solute is dissolved in a binary solvent mixture (of components I and 3), it has been suggested (5) that eq. 1 could be rewritten as where [31 6, + Q3h3 and cd, the volume fraction of the solvent mixture, i.e. cdl + cd, + 1, cd, + 0. In Tables 1 and 2 we make a comparison of G,(experimental) and the 6, value given by eq. 3. It is seen that the comparison is bad. The experimental data allow 6,, dl, and 6, to be calculated to an accuracy of 0.1% for a given value of 6,. To better emphasize the role of 6, we derive from eq. 1 and 2 the relationship where x: is the saturation solubility of solute (2) in the pure solvent component (3). We use eq. 4 for those systems for which cd, + 0, i.r. 0, + cd, = 1. In the derivation of eq. 4 the dependence upon the solvent composition, a,, arises solely through the definition of 6, by eq. 3. The linear relationship expected between cd, and the experimental quantity (In a; - In x?)''~ does l FIG. I. Iodine in benzene-cyclohexane solvent, [In (a;/ XY)]~/~ plotted as a function of benzene volume fraction (0) and as a function of benzene "effective volume fraction" (0). Data at 25.0 "C. FIG. 2. Stannic iodide in mixed benzene-cyclohexane solvent; [In (ai/~?)]'/~ plotted as a function of benzene volume fraction (0) and as a function of the benzene erective volume fraction (0). Data at 25 "C. not, however, depend upon the assumption of actual ai values. From the linear relationship expected of eq. 4 the intercept at cd, = 0 and the ratio of slope/intercept may be compared to experimental values. In Figs. 1 and 2 we plot (In a; - In x,m)'i2 US. (Dl using our data for the systems I, - C6H6 - c-c6h12 and SnI, - C6H6 -

4 PURKAYASTHA AND WALKLEY : ON MIXED SOLVENT SYSTEMS 837 of solution of the solute identical to that found from solubility parameter theory. Following this approach for those systems in which the solubility of the solute in the binary solvent mixture is small the nearest neighbor environment may be defined as FIG. 3. Iodine in a mixed benzene carbon tetrachloride solvent; [In ( u~/x~)]"~ plotted as a function of benzene volume fraction (0) and as a function of the benzene effective volume fraction (0). All data at 25 "C. c-c6h12 and in Fig. 3 using the data of Wood et al. (9) for the I,-C6H6-CCl, system. It is seen that for all three systems the expected linearity is not observed. From the graphical dependence discussed above and from the direct comparison of 6, values it would appear that the definition of 6, by eq. 3 is not acceptable. Following the suggestion that the immediate solvent environment is not reflected by the bulk solvent composition but requires the assumption of the preferential "solvation" by one of the solvent components we have attempted to define an "effective volume reflecting this solvation, and so define Christian (2) suggested that the relative number of each of the two solvent molecules in the solute nearest neighbor environment could be regarded as a Boltzmann weighting term involving the heat of solution of the solute in each of the pure solvents. If we use this approach to calculate an "effective volume fraction" term then the comparison of experimental and theoretical 6, values is no better than that found assuming the immediate solute environment to be represented by bulk solvent mixture composition. The solvent environment of a solute molecule can be discussed in a simplistic way using the arguments of the quasi-lattice theory (5). For very dilute solutions Hildebrand has shown that this model leads to an expression for the heat In eq. 6 the effective volume fraction terms are related to the bulk volume fraction terms by the inverse of the heats of mixing of the solute in each of the pure solvents. Using eq. 6 to define 0: and using eq. 5 to define 6, it is easily shown that eq. 4 can be reformulated to require a linear relationship to exist between (In a: - In xy)'l2 In Figs. 1-3 such a linearity is seen to exist for each of the systems considered. The intercept values = 0 and the expected values of (In a; - ln x:)'i2 are 1.663, 1.655; 1.840, 1.835; 1.785, 1.80; respectively for the three systems considered. Furthermore the ratio of slope/intercept for each of the three systems is found self-consistent with those 6 values used in evaluating the 0: terms and satisfying the saturation solubility of the solute in each of the pure solvents (Table 3). Benzene was chosen as one of the solvent components for the iodine solute study as it was anticipated that the well known charge transfer (10) interaction between them should make benzene the energetically preferred nearest neighbor. It is seen that the preferential solvation still exists when stannic iodide is made the solute and for this system no specific solutesolvent interaction occurs. As a final test of our (In a: - In x,m)'12 US. (Dl (or 0:) relation we plot in Fig. 4 the theoretical lines for the system iodine- CCl, - n-c,f16 (4). Only two data points exist for this system and we compare them to the theoretical lines calculated from the known solubility of iodine in the pure perfluorocarbon and the accepted 6 values (5). The wide difference in the solute parameter (14.1) and that of one of the solvent pairs (6.0) puts a considerable strain upon the proposed theory. As may be seen, however, the data points lie on that line drawn using the effective volume fraction (a:) term. As a further test of the acceptability of the proposed "effective volume fraction" term we examine the partial molal volume data for

5 838 CANADIAN JOURNAL OF CHEMISTRY. VOL. 50, 1972 TABLE 4. The partial molal volume of iodine in a mixed benzene-cyclohexane solvent at 25 "C Volume Partial molal volume (cc mol-i) fraction of Vz (expt.) v2 (calc.) vz (talc.)* FIG. 4. Iodine in mixed carbon tetrachloride- perfluoroheptane solvent. Data points plotted against simple volume fraction of carbon tetrachloride in mixed solvent (0) and against "effective volume fraction" of carbon tetrachloride (0). Solid line represents the theoretical [In ( u~/x~)]"~ relationship. Data at 25.0 "C. iodine in the mixed benzene-cyclohexane solvent. In terms of the mixed solvent 6, parameter we may reformulate the usual equation relating the partial molal volume of the solute (V,M) to the isothermal compressibility of the solvent DM and the solubility parameters of solute and solvent as where V! is the reference volume of the solute (5). We can assume a value of unity for nm (the ratio of the internal pressure to the cohesive energy density (5)) and define DM in terms of the isothermal compressibility of the pure solvents without any loss in the predictive value of eq. 7 as, DM + a3b3. Since eq. 7 cannot be rearranged allowing V,M to be directly analyzed in a manner emphasizing the dependence on a, or we compare in Table 4 the experimental V,M values with those calculated from eq. 7 using either the bulk volume fraction or effective volume fraction definition of 6,. It is obvious that an acceptable comparison with experiment is found only with the use of the effective volume fraction terms. We have made experimental studies for systems for which in eq. 2 the approximation that a,-+ 1 cannot be made, e.g. the naphthalene- 'Calculated using 6, CCl,- c-c,h12 system as reported by Heric and Yeh (1 1). For these systems the "effective volume fraction" approach is again found necessary for the interpretation of the data. These systems often involve a maximum in the saturation solubility value (i.e. those for which 6, < 6, < 6,) but as the formulation of the saturation solubility equation is more complex they will be dealt with in another paper. It is clear that within its limitations solubility parameter theory may be extended so that the solubility thermodynamic properties of dilute solutes in two component solvent mixtures can be predicted. We wish to thank the National Research Council of Canada for their support of this project. 1. R. L. SCOTT and D. V. FENBY. Ann. Rev. Phys. Chem. 20, 11 (1969). 2. S. CHRISTIAN. J. Am. Chem. Soc. 91, 6514 (1969). 3. K. NAKANISHI, T. OZASA, and K. ASHITANI. J. Phys. Chem. 75,963 (1971). 4. E. B. SMITH, J. Walkley, and J. H. HILDEBRAND. J. Phys. Chem. 63,703 (1959). 5. J. H. HILDEBRAND and R. L. Scorr. The solubility of non-electrolytes. 3rd Ed. Dover Publications Inc., New York. (1964). 6. M. VITTORIA and J. WALKLEY. Trans. Faraday Soc. 65, 57,62 (1969). 7. J. H. HILDEBRAND and D. N. CLEW. J. Phys. Chem. 60,616 (1956). 8. E. B. SMITH and J. WALKLEY. Trans. Faraday Soc. 56, 220 (1960). 9. S. E. WOOD, B. D. FINE, and L. M. ISAACSON. J. Phys. Chem. 61, 1605 (1957). 10. R. S. MULLIKEN. J. Am. Chem. Soc. 70, 600 (1950); J. Phys. Chem. 56, 801 (1952). 11. E. L. HERIC and K. N. YEH. J. Chem. Eng. Data, 15, 13 (1970).

' polar liquids, leading to an entropy of mixing I term from liquid state, of value -Rln Xi; and

' polar liquids, leading to an entropy of mixing I term from liquid state, of value -Rln Xi; and Solubility of some iodides in non-polar solvents S. K. SURI AND V. RAMAKRISHNA' Department of Chemistry, Indian Institute of Technology, New Delhi-29, India Received February 20, 1969 The solubilities