Mutual Diffusion Coefficients of Aqueous Na2SO4 at C = 0.02989 mol·dm–3 and 298.15 K by Using Rayleigh Interferometry with Free Diffusion Boundary Conditions: Experimental Test of the Effect of the C3/2 Concentration Dependence of Refractive Index at Low Concentration

Abstract

Rayleigh interferometry is one of the most precise and accurate methods for the experimental determination of the mutual diffusion coefficients of both electrolytes and non-electrolytes in liquid solutions. For binary solutions at moderate and high concentrations where the concentration dependences of both diffusion coefficient and refractive index can be assumed to be linear or almost linear and the concentration difference ∆C between a pair of solutions undergoing free diffusion is not large compared to their average concentration, and by using proper combinations of the interference fringe positions as they vary with time, under these conditions diffusion coefficients are obtained that are independent of the size of ∆C. However, this situation becomes more complicated at low concentrations for electrolyte solutions where the concentration dependences of both the diffusion coefficient and refractive index are non-linear, with C1/2 dependence for the diffusion coefficient and C3/2 dependence for the refractive index. As a test of these effects on calculated mutual diffusion of electrolyte solutions at low concentrations as measured by Rayleigh interferometry, apparent mutual diffusion coefficients Dv,a (volume-fixed reference frame) were measured for fixed average concentrations C = (0.02989 ± 0.00001) mol·dm–3 of Na2SO4(aq) at 298.15 K while varying ∆C/C from 0.66673 to 2, a threefold variation. The dependence of the diffusion coefficient on ∆C/C was found to be linear, yielding Dv = 1.0416 × 10–9 m2·s–1 for an infinitely small concentration difference between the diffusing solutions.