ERNESTGRUNWALD AND DODD-WING FONG
650
refined than previous work in this area, are not sufficiently accurate to employ the formalism of section I1 in full quantitative detail. However, they allow a number of qualitative conclusions to be drawn about the B-HFB system. The nonadditivity of R shows the presence of specific I3-HFB interactions which it seems reasonable to interpret in terms of formation of a complex. This complex has very little polar character, with a permanent dipole moment probably not in excess of 0.1 D, the remainder of A being associated with atomic polarizability effects whose magnitude seems reasonable on the basis of our rough theoretical estimates. Previous estimates of the permanent dipole moment of the complex appear to be too large. Finally, the implications of these results for the nature of the bonding in the R-HFB complex should be noted. In the case of undoubted charge-transfer complexes, e.g., 1 2 with benzene, the degree of mixing of the chargetransfer state into the ground state is usually estimated to be on the order of 5-10%, leading to dipole moments
of the complex on the order of 1 D or greater. The bonding energy of the complex and the dipole moment are both roughly proportional t o this degree of mixing,3 and a dipole moment of that magnitude is usually implied by energies in the kilocalorie range arising from charge transfer. The enthalpy of formation of the B-HFB complex is in this range and it seems difficuIt to see how a charge transfer mechanism could account for such a large effect without a greatly larger dipole moment than can be inferred from our work. We conclude that although some charge transfer may occur in the R-HFB mixtures, the formation of a complex is attributable in the main t o entirely different effects.
Acknowledgment. We thank Professor R. L. Scott and Dr. D. V. Fenby for many helpful discussions on this work, and Mr. R. H. Wang for performing some preliminary refractive index measurements. Professor C. I?, Smyth kindly provided us with the results of his microwave measurements.
Acidity and Association of Aluminum Ion in Dilute Aqueous Acid1
by Ernest Grunwald and Dodd-Wing Fong Department of Chemistry, Brandeis Universizy, Waltham, Massachusetts
0215.4
(Received September 11, 1 9 6 8 )
The acid dissociation of A1(OH2)s3+in water at 30' was examined by measuring the change of pH as HCI is added in very small increments to 0.007-0.06 vol. F AlC13. The data show clearly that dimerization of (H2O)sA10H2+is significant. Equilibrium constants (referred to infiiiite dilution) were determined as follows: for acid dissociation of Al(OH&3+,K~O=2.44X le5 114 at 30': for association constant (H20)5 A10H2+to a dimer, K0=60 i1f-l at 30°, A H o = -11 kcal, A8'M -28 gibbs.
I n water, aluminum ion exists largely in the form of the hexahydrate, Al(OH2)63+,2Jwhich is a weak a ~ i d . ~ However, -~ the pH of pure aqueous solutions of aluminum salts is consistent with a model of simple acid dissociation (eq 1) only a t low aluminum concentration (
