Apparent transport numbers from Seebeck coefficients for ion-exchange membranes

Abstract

We present a new procedure to find apparent transport numbers for ion-exchange membranes from the Seebeck coefficient as function of the electrolyte partial molar entropy. The method is relevant for several membrane processes, e.g. reverse and normal electrodialysis. Here, we report data for single-electrolyte solutions, as well as aqueous solutions of both MgCl${}_2$ and NaCl with molalities varying from 0.001 to 0.3 mol/kg, and for molality ratios $ϵ=m_{{\mathrm{MgCl}}_2}/m_{\mathrm{NaCl}}=0.02$ and 0.03. Apparent transport numbers of the Fumasep FKS-75 $\mu$m membranes in contact with single-electrolyte solutions were $0.99\pm 0.06$, $1.02\pm 0.03$, $0.35\pm 0.04$ and $0.43\pm 0.04$ for chlorides of Na${}^{+}$, K${}^{+}$, Mg${}^{2+}$ and Ca^2＋, respectively. The membrane apparent transport numbers of Mg${}^{2+}$ and Na${}^{+}$ in the two salt mixture were estimated by a weighting method, involving an empirically defined hydration coefficient. The results showed a significant selectivity towards Mg${}^{2+}$. The presence of Mg${}^{2+}$ in an aqueous solution of NaCl (sea water) may therefore significantly lower the efficiency of the Fumasep FKS-membrane for, say, reverse electrodialysis.