Some thermodynamic properties of ions in aqueous solution.

Abstract

Some methods of obtaining the partial molal entropies of ions are reviewed, and the equations proposed for monatomic ions are discussed. The entropies of oxy-anions in aqueous solution are shown to obey the following relationship. Soabs=40.2+32 R1n m-27.2z20.25 nr˙ In this equation, Soabs is the partial molal entropy relative to a value of -5.5 e.u. for the proton, m is the molecular weight, z the number of charges on the ion, n the number of charge-bearing ligands, and r is equal to r12 + 1.40, where r12 is the interatomic distance between the central atom and the surrounding oxygens, and 1.40 is the van der Waals radius of oxygen. The significance of the empirical equation is discussed. The density data for aqueous solutions of electrolytes have been analyzed, and the partial molal volumes at infinite dilution have been calculated. The values are shown to be additive, and a set of volumes for individual ions has been prepared, based arbitrarily on a value of zero for the hydrogen ion. It is shown that for a given value of the charge, the volumes vary linearly with the cube of the ionic crystal radii, and that for a given radius, they vary with the first power of the charge. In the case of monatomic cations the equation obeyed is V+=16+4.9r3-20 z+ while for monatomic anions it is V-=4+4.9r3-20 z-. If the volume of the hydrogen ion is taken as -6.0 ml. instead of zero, the same equation is obey for both monatomic cations and anions, namely V&d1;' +/-=16+4.9r3-26 z+/- . In the case of oxy-anions, the volumes relative to a value of -50 ml. for the proton are represented by the equation V&d1;' -=58.8+0.890.25nr 3-26z- , where r, as with entropies, is given by r 12 + 1.40. These empirical equations are explained in terms of a simple model for ions in solution and the significance of the effective radius used for oxy-anions is discussed. The importance of these equations is discussed with reference to their application to reactions involving ions in aqueous solution.