Dipole moments of glycerol, isopropyl alcohol, and isobutyl alcohol H. A. RIZK AND 1. M. ELANWAR Deprrr'fnzerit of Clzemistry, Frrcrrlty of Science, U~riversity of Crriro, Crriro, Egypt, U.A.R. Received May 29, 1967 By the application of a modified form of Onsager's equation to dilute solutions of glycerol in isopropyl alcohol and isobutyl alcohol, and conversely to dilute solutions of each of the latter two alcohols in glycerol, it is found that the apparent solution moments of these alcohols, at the condition of infinite dilution, are 2.68, 1.61, and 1.66 D respectively over the temperature range 30 to 50 OC. Canadian Journal of Chemistry, 46, 507 (1968) The dipole moment of glycerol in dioxane, as determined by Wang (I), is 2.67 and 2.66 f 0.02 D at 15 and 30 "C respectively. Using the same solvent, Darmois and Mouradoff (2) obtained the value 2.56 D for the dipole inoment of glycerol. Debye (3), Lange (4), Stranathan (5), Ghosh (6), and Donle (7) measured the dipole moment of isopropyl alcohol in benzene, the values obtained being 1.66, 1.53, 1.74, 1.78, and 1.72-1.69 f 0.04 D respectively. According to Higasi (8), the apparent solution moinent of isopropyl alcohol, as well as that of isobutyl alcohol, using benzene as a solvent, is equal to 1.70 D. His measurements (8) in carbon disulfide gave for those two alcohols the moments 1.48 and 1.41 D respectively. The dipole moments of isopropyl and isobutyl alcohol were also measured in benzene by Maryott (9), the values obtained being 1.66 and 1.70 D respectively. On the other hand, the dipole moments of isopropyl alcohol and isobutyl alcohol in the gaseous state, as measured by Kubo (10) and by Smyth (1 I), are 1.63 and 1.65 D respectively. Also, a value equal to 1.67 D was obtained by Stranathan (12) for the vapor momeilt of isobutyl alcohol. The differing results, as obtained by various authors, concerning the dipole moments of the above alcol~ols suggested a redetermination of their moments with the help of Onsager's equation (13) applicable to dilute solutions of a polar solute in a polar solvent. Thus in the case of glycerol, isopropyl alcohol and isobutyl alcohol were alternately chosen as the polar solvent, and conversely in the case of each of the latter two alcohols, glycerol was used as the solvent. Experimental tive index were carried out as described in an earlier investigation (15). Calculations with regard to the infinite dilution condition were made using eq. [A]. This equation was derived from Onsager's equation (13), as shown in the Appendix. Results and Discussion It will be seen froin Tables I and I1 that over the temperature range 30 to 50 "C the apparent solution inoment of glycerol is equal to 2.67 D when isopropyl alcohol is used as a solvent, and equal to 2.69 D when isobutyl alcohol is used. Although the former value is slightly lower than the latter, the difference is within the limits of experimental error. Thus an average value, namely 2.68 D, may be taken to represent the dipole moinent of glycerol in isopropyl or isobutyl alcohol. This value, which is evidently in good agreement with the value, 2.66 D, obtained by Wang (1) for the dipole moment of glycerol at 30 "C using dioxane and applying the usual Debye equation (17), may suggest, when coinpared with the moment, 2.8 D, calculated for glycerol froin Girard's formula (18), that in pure glycerol there is unequal distribution of the six dipoles among the potential troughs that exist when dipole rotation takes place around a bond; in other words, in pure glycerol there is incomplete randoin orientation of the dipoles relative to one another. The apparent solution moment of isopropyl alcohol in glycerol, namely 1.61 D (Table 111), is slightly lower than the solution value in benzene, 1.66 D, which was obtained by Debye (3) and Maryott (9), and is in agreement with the vapor value, 1.63 D, as determined by Kubo (10) and Smyth (11). Similarly, the solution moment of isobutyl alcohol in glycerol, 1.66 D (Table IV), is slightly lower than the solution Glycerol, isopropyl alcohol, and isobutyl alcohol were purified according to recommended procedures (14). in (8y 9)7 and in agreement Measurements of dielectric constant, density, and refrac- with the vapor value, 1.65 D (10, 1 I).
CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968 TABLE I Glycerol in isopropyl alcohol TABLE I1 Glycerol in isobutyl alcohol w2 r PC) 12 d12 c2 30 15.27 0.7944 0 40 14.00 0.7869 0 50 12.83 0.7793
RIZK AND ELANWAR: DIPOLE MOMENTS TABLE I11 Isopropyl alcohol in glycerol W2 t ("C) 12 dl2 C2 "p2 = 1.61 D. TABLE N Isobutyl alcohol in glycerol W2 t Cc> 12 d12 Cz
510 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968 TABLE V Dipolc moments (x 1018) of glycerol, isopropyl alcohol, and isobutyl alcohol -- Glycerol Isopropyl alcohol Isobutyl alcohol 30 O C 40 O C 50 '2 30 O C 40 '2 50 O C 30 'C 40 O C 50 O C 11" D d4 l PO (Debye) ~"'ra (Onsager) gl"p (Kirkwood) gu2sa (Kirkwood) p solution It will be evident from the above that there exists a good agreement between the solution moments of glycerol, isopropyl alcohol, and isobutyl alcohol, as obtained by applying Onsager's equation at the condition of infinite dilution of a polar solute in a polar solvent, and those which are obtained wit11 the aid of usual methods. This result may suggest that it is possible to use Onsager's equation (with the assumption of ideality) to get reasonable dipole moments of alcohols dissolved in alcohols. Although there is no conclusive evidence that this method could generally be recommended for the determination of dipole moments of different types of molecules, nevertheless the simple model of a spherical cavity of a I~omogeneous dielectric used by Onsager (13) is more accurate than would be expected on first consideration. From measurements of the static dielectric constants, refractive indices for the sodium D line, and densities of glycerol, isopropyl alcohol, and isobutyl alcohol at 30, 40, and 50 "C, the dipole moments of these alcohols, as calculated from the Debye (17), Onsager (13), and Kirkwood (19) equations applied to the pure liquids, are shown in Table V. It will be seen from this table that Debye's equation (17), which is inapplicable to pure polar liquids, gives in the case of glycerol a dipole molllent value which is much lower than the measured apparent solution moment, whereas it gives a moment value in the case of isopropyl alcohol, or isobutyl alcohol, which is more or less in fortuitous agreement with that obtained from solution measurements. The apparent increase in the inoment of each alcohol calculated from Onsager's equation (13), S1/2po, as compared with the measured solution moment (Table V), may be qualitatively accounted for by complex formation in each liquid. On the other hand, hindered relative molecular rotation arising from short-range intermolecular forces in each liquid would account for the higher dipole moment calculated from Kirkwood's equation (19), g1/2p, or g1/2p0, as con~pared with the measured solution moment, p being the actual dipole inoment of the molecule in the liquid and po the vapor moment. Accordi~lg to Kirkwood (19), the correlation paraineter g of hindered molecular rotation is equal to unity in Onsager's model, since in this model only the effect of electrostatic forces on hindered rotation was considered. Tlle discrepancies between the dielectric constants calculated for highly polar liquids from Onsager's equation, in which there is no contribution to the local field from the material in the interior of the cavity, and those measured were accounted for by introd~~cing this equation a factor based on the forillation of complex molecules, namely the association factor S. The meaning and the derivation of this factor are different from the Kirkwood correlation parameter g. Thus while the value of S helps in the prediction of the probable types of aggregates in pure polar liquids, the value of g measures by its departure from unity the degree of hindered relative molecular rotation. Further, the deviation of g from unity may be either positive when short-range hindering torques favor parallel orientation of the dipole lnonlents of neighboring molecules or negative when the hindering torques favor antiparallel orientation. Following Frohlich (20), Kirkwood's equation would be very useful in the presence of strong short-range forces, since it is identical with a formula which one would obtain if the dipoles are assumed to associate. Suppose that on an average,!ilp dipoles associate forming a group
RIZIC AND ELANWAR: DIPOLE MOMENTS 511 of dipoles with moment p. Here p is the molecular dipole moment in the liquid and p the total inoinent of the content of a Lorentz cavity (19) centered on a molecule of fixed orientation in the absence of an external field, p x p being equal to gp2. The number of such groups per unit volume is equal to 1 /(p/p) of the original volume, n, i.e. equal to nplp, which on multiplying by the square of the inoment of each group gives npp = ngp2. Thus, applying Onsager's formula to these groups leads, as was pointed out by Frohlich (20), to Kirkwood's equation. From a knowledge of the vapor phase dipole moments of isopropyl alcohol and isobutyl alcohol, which are 1.63 and 1.65 D respectively (10, 1 l), an estimate was made of S and g for these two alcol~ols, the nlolecules of which are of the type R-OH. The results obtained are shown in Table VI. TABLE VI Estimates of S and g for isopropyl alcohol and isobutyl alcohol case than in the latter. This in turn results in stronger dipole-dipole interactions between a central dipole and surrounding dipoles, thus giving rise to more coordination through hydrogen bonds in liquid isobutyl alcohol than in liquid isopropyl alcohol. It may be noted here that the coordination which exists in these alcohols, as has been concluded from X-ray scattering data, is chainwise (19). On the other hand, when the association factor S of isobutyl alcohol, 3.65, at 30 "C is compared with that of 12-butyl alcohol, 3.16, at 25 "C, which was determined by Huyskens and Cracco (21), it can be deduced that the former alcohol is more associated than the latter. That the relative molecular rotation is more strongly hindered in liquid isobutyl alcohol than in liquid n-butyl alcohol is revealed by comparing the correlation parameter value, 3.69, which we obtained for the former alcohol at 30 "C with the value, 3.21, which was observed for the latter alcohol at 20 "C by Oster and Kirkwood (22) and by Oster (23). Isopropyl alcohol Isobutyl alcohol Appendix 1 ("C> S R S g Onsager's equation (13) in a modified form, 30 3.12 3.19 3.65 3.69 without taking association into consideration, 40 3.03 3.12 3.61 3.69 may be written in Bottcher's expression (16) as 50 2.95 3.02 3.61 3.65 r z [I] 12-1 = ~ TCN, It will be seen that for each alcohol the i 1kx association factor S, or the correlation parameter g, decreases with increasing temperature, this being presumably due to decrease in association or in the degree of hindered relative molecular 3 12(,; - 1) rotation arising from short-range intermolecular ai - (2612 f Em,) 1 forces. Also, it can be seen that for each alcohol the value of the correlation parameter g, which where N, is the number of molecules of type i departs significantly froin unity, is slightly per cc of the solution, E,~ square of refractive higher than the value of the association factor S. index of component i, pi dipole moment of type i And that the association factor S, as well as the in the vapor state, and a, radius of the hypocorrelation parameter g, is smaller in the case of thetical spherical molecule containing the point isopropyl alcohol than in the case of isobutyl dipole, p,, the subscript 12 being for the solution. alcohol. Therefore, it can be inferred that there Ni is related to C,, which is the number of gramis more association, or more hindrance to relative molecules of component i per liter of solution, molecular rotation, in liquid isobutyl alcohol by the equation than in liquid isopropyl alcohol. This may be ascribed in part to the location of the hydroxyl group. Being more remote from the branch in the chain of the molecule in the case of isobutyl alcohol than in the case of isopropyl alcohol, the hydroxyl group is less screened in the former where N, is Avogadro's number. Assuming that the hypothetical volume of N, spherical molecules in a gram-molecule of
512 CANADIAN JOURNAL OF CHEMISTRY. VOL. 46, 1968 component i is equal to the molar volume, V,, we have [31 4ax 1 ai3ni = 3 1 x ViCi. Substituting for Ni in eq. [l] from eqs. [2] and [3], and putting Therefore and one gets [6] 12-1 = x (A icipi2 + BiCi) a I Assuming an ideal solution of two components, and designating the polar solute by the subscript 2 and the polar solvent by the subscript 1, the volume additivity is given by where A' and B' are the derivatives of A and B with respect to C2, that is A2, - (em2 + 4~12t,2 -?el?) dela A?-- ~12(2~1r + 1) (2~1? f c,?) dc2' B~' = --& BI dt12 -, ancl 12(2 1? + 1) dc? Substitution of C1 = 1 00 x for the Substituting for A,', A2', Bll, alld B2' from molar concentration of pure solvent and eq. [l],] ineq. [ 1 0 1, ~ ~ d ~ ~ ~ ~ i ~ ~ V2 = M2/(1000 x d2) for the molar volume (in liters) of pure solute gives [l2] F = 1 - C2p2-A? --~--7~ (E-2 + 4~1?~,? - 3elr) ~12(2~12 + 1) (- + E,?) [81 c, = Cl0(l - C2V2). Equation [8] expresses the solvent concentration in gram-molecules per liter of solution, C1, in terms of that of the solute, C2, provided that the solution is ideal. For a binary mixture, eq. [6] can be written as [g] 12-1 = (A1p12 + B1)Cl + (A2~2~ + B2)C2. Substituting in eq. [9] for C1 from eq. [8] and taking the derivative of c12 with respect to C2, we obtain we finally obtain 2 d l2 [A] p2 = F---. cl C2 - C1fl ----A-p-- ~lr(2~12 A 2 Em 1 + ~ ~ ' 1 ) Taking the slope, de12/dc2, in the limit as C2 approaches zero, the terms Al, A2, B1, and B2 can be calculated using the dielectric constant of the solvent, 1, instead of that of the solution, e12. Similarly, in deriving the numerical value of the factor F for the condition of infinite
RIZK AND ELANWAR: DIPOLE MOMENTS 513 dilution, the second and fourth terms of F involving C2p22 and C2 respectively disappear, C1 becomes equal to Clo, and then 12 becomes equal to el. 1. Y. L. WANG. Z. Physik. Chem. Leipzig, B45, 323 (1940). 2. M. E. DARMOIS and L. MOURADOFP. Bull. SOC. Chim. France, 16,446 D (1949). 3. P. DEBYE. Hand. Radiol. (Marx), Akademische Nerlagsgesellschaft m.b.h., Leipzig. 6,597 (1925). 4. L. LANCE. Z. Physik, 33,169 (1925). 5. J. D. STRANATHAN. Phys. Rev. 31, 156,653 (1928). 6. P. N. GHOSH. Nature, 123,413 (1929). 7. H. L. DONLE. Z. Physik. Chem. Leipzig, B14, 362 (1931). 8. K. HIGASI. Bull. Inst. Phys. Chem. Res. Tokyo, 15, 9. A. A. MARYOTT. J. Am. Chem. Soc. 63,3079 (1941). 10. M. Kuno. Sci. Papers Inst. Phys. Chem. Res. Tokyo, 26,242 I 11. C. P. SMYTH. J. Am. Chem. Soc. 63,57 (1941). 12. J. D. STRANATHAN. J. Chem. Phys. 5,828 (1937). 13. L. ONSAGER. J. Am. Chem. Soc. 58,1486 (1936). 14. A. WEISSBERGER and E. PROSKAUER. Organic solvents, physical constants and methods of purification. Clarendon Press, Oxford. 1935. pp. 125, 127,133. 15. A. R. TOURKY, H. A. RIZK, and Y. M. GIRGIS. J. Phys. Chem. 64,565 (1960). 16. C. J. F. BOTTCHER. Rec. Trav. Chim. 62,119 (1943). 17. P. DEBYE. Physik. Z. 13,97 (1912); Polar molecules. Chemical Catalog, New York. 1929. Chap. KU. 18. P. GIRARD. Trans. Faraday Soc. 30,763 (1934). 19. J. G. KIRKWOOD. J. Chem. Phys. 7, 911 (1939); Ann. N.Y. Acad. Sci. 40, 315 (1940); Trans. Faraday Soc. A, 42,7 (1946). 20. H. FROHLICH. Trans. Faraday Soc. A, 42, 3 (1946). 21. P. HUYSKENS and F. CRACCO. Bull. Soc. Chim. Belges, 69,422 (1960). 22. G. OSTER and J. G. KIRKWOOD. J. Chem. Phys. 11, 175 (1943). 23. G. OSTER. J. Am. Chem. Soc. 68,2036 (1946).