New differential Bottcher-Onsager method used to determine polarizability and apparent radius of tungstosilicate (SiO4(WO3)124-)

Abstract

A differential form for the Bottcher--Onsager law is derived. Based on this form, a new method is presented for determining the polarizability and apparent radius of the molecules of a solute from measurements of the temperature variation of the density and specific refractive increment of its solutions. The method is particularly applicable to solutes which are only slightly soluble in a given solvent. The density and specific refractive increment of aqueous solutions of tungstosilicic acid have been measured at four temperatures: nominally, 20, 25, 35, and 45/sup 0/C. The densities are found to be linear functions of concentration in the range 0 to 0.03 M. From the density measurements, the apparent molar volume of H/sub 4/SiO/sub 4/(WO/sub 3/)/sub 12/ at each temperature is determined. The specific refractive increment is determined for radiation at 589 m..mu... Using our differential method, we find ..cap alpha../sub 2/ = 50 +- 5 A/sup 3/ and a/sub 2/ = 3.2 +- 0.2 A, where ..cap alpha../sub 2/ and a/sub 2/ are the polarizability and effective radius, respectively, of SiO/sub 4/(WO/sub 3/)/sub 12//sup 4 -/.