The Free Energies of Hydration of Gaseous Ions

Abstract

Values of hydration energies of individual ions have usually been obtained by division of sums of energies of hydration of pairs of ions, and those calculated by different authors are usually mutually inconsistent. " Experimental " figures, whenever these are quoted, have always been obtained by assuming the truth of theoretical equations whose accuracy has not been independently checked. The distinction between free energy of ion/water-molecule interaction and the real free energy of hydration of a gaseous ion is pointed out, and the importance of Klein and Lange's measurement of the Volta-potential Hg/Hg+ (soln.), which makes possible the direct calculation of real free energies of hydration of individual ions, thus providing a check on theoretical values, is emphasized. Utilizing this value, the equation - ΔFh° = - ΔFf° + ΔFi° + ΔFs°- 103.92 z kcal. (where ΔFs° is the free energy of formation of the gaseous monatomic element, ΔFi° is the free energy of ionization, ΔFf°is the free energy of formation of the aqueous ion, and ΔFh° is the real free energy of hydration of the ion, of valency z, at 298.2° K.) is derived from fundamental considerations. By means of this equation, the real free energies of hydration of 49 ions are calculated, using the most reliable data. It is proposed that these be provisionally accepted as standard values. Several subsidiary values for important ions are calculated indirectly. The difference between ΔFh° and the free energy of ion/water-molecule interaction is discussed in relation to the surface structure of water : a value of -0.30 v. is derived for the X-potential at the surface of pure water, and it is concluded that at the water/gas interface the positive poles of the surface layer are oriented towards the gas phase. The applicability of a modified Born equation in the calculation of free energies of hydration is discussed, and a modified equation is proposed which yields values of ΔFh° for gaseous ions with noble gas structure in excellent agreement with those calculated independently by the method described above.