Comparison of osmotic pressures from EMF measurements,obtained according to cell-model considerations and exact Gibbs-Duhem integrations

Osmotic pressures of aqueous solutions of poly(diethylaminoethyl methacrylate) hydrochloride, in equilibrium with a precipitate of the un-ionized polybase, at various concentrations of polymer and NaCl in solution and at different values of pH are derived from emf measurements and the “cell” theory for polyelectrolytes. Single-ion activities are evaluated according to two procedures. The first is based on measurements with ion-specific electrodes versus a calomel electrode. The second makes use of a salt bridge, but assumes that the co-ions have activity coefficients equal to the mean activity coefficient of the salt in a polyelectrolyte-free solution of the same concentration. The results show that the calculated values of the osmotic pressures are consistent with those obtained by the exact integration of the Gibbs-Duhem relationship, when the first procedure is employed. If, however, the single-ion activities are evaluated by the second procedure, the osmotic pressures obtained are consistently lower by about 10%. These differences arise because the two methods yield different values of the activity coefficients of the single ions.