Mass transport of phosphoric acid in water: A H1 and P31 pulsed gradient spin-echo nuclear magnetic resonance study

Abstract

Aqueous solutions of phosphoric acid (H3PO4) of varying concentrations have ionic conductivities as high as 0.25 Scm−1 at ambient temperatures which cannot be accounted for on the basis of regular hydrodynamic movement of mobile ions. We report careful measurements of self-diffusion coefficients (D) of mobile species for the 85 wt% (14.6 M) phosphoric acid solution over a range of temperature from 293 to 353 K, using H1 (I=1/2) and P31 (I=1/2) pulsed gradient Hahn spin-echo (PGSE) techniques. The experimental D values are interpreted together with previously published viscosity (η) and conductivity (σ) data. The data show that protons diffuse faster than the phosphorus carrying species. The diffusion data for both nuclear species are found to be linear on an Arrhenius plot with activation energies of 25 and 36 kJ mol−1 for H1 and P31 species, respectively. Analysis on the basis of the Nernst–Einstein relation yields a proton transference number of t≈0.99 and a proton charge carrier number density of n≈1.6×1028 m−3. A plot of the product Dη as a function of temperature suggests that the proton and phosphorus species undergo significantly different mass transport mechanisms. In particular the P31 data show a nonlinear increase in Dη with temperature, while the H1 data exhibit a decrease in Dη with increasing temperature which is not expected for hydrodynamically simple fluids. The latter behavior is attributed to the water mediated transfer of protons between the phosphate groups. Room temperature P31 diffusion coefficients of condensed phosphates are also reported, and as expected the diffusion coefficient is dependent on the size of the moving species.