The interaction energy of a monovalent ion in an a.queous medium at 25°C is determined. It is also found that the water molecules in the first hydration shell of the ion have a mean dipole moment far in excess of their permanent dipole moments. Thus, for example, the increase in the dipole moment of the attached water molecules. due to the presence of an ion is about 60% for the small four-coordinated Li+ ion and about 30% for the larger four-coordinated 1-ion. Calculations are also carried out on the assumption that the ions are six coordinated.
I. INTRODUOTIONA formula for the Gibb's free energy of hydration of an isolated ion in an aqueous solution was first obtained by Born (1920). He assumed that the ion could be replaced by an empty spherical cavity containing a point charge at its centre with the surrounding medium having the macroscopic dielectric constant of water. This model has been used by many authors, including Webb (1926), Latimer, Pitzer, and Slansky (1939), and Noyes (1962, to mention but a few. Nevertheless the continuum model has met with much criticism since, for example, according to Powell and Latimer (1951), Cobble (1953), andConnick andPowell (1953), it cannot be used to calculate the hydration energies of other than monovalent ions. Laidler (1956) does not agree with their argument. In any case it is clear that this mathematical model is fairly crude and that a refinement should take some account of the discrete nature of the water molecules. It is with this fact in mind that we shall develop a discrete model here.As a guide we can refer to the papers of Bernal and Fowler (1933), Verwey (1941, 1942, Rowlinson (1951), Buckingham (1957), Vaslow (1963), Ross (1968a, and Ross and Levine (1968). All but the last two papers omitted the polarizability ofthe water molecules, and in each case the water molecule was replaced by a point dipole (and sometimes 1\ point quadrupole as well). In fact Ross (1968a) showed that, at 25°C, a good approximation can be obtained by replacing the polarizable water dipoles of the first hydration shell in the position of minimum electrostatic energy with the water outside this shell replaced by a dielectric continuum. Now Bernal and Fowler (1933) indicated that the most likely coordination number oia monovalent ion is four, whereas Verwey (1941Verwey ( , 1942, who took into consideration the geometrical constraints in the second hydration shell, suggested that it is six or even eight. In the present paper we shall deal only with coordination number four or six, the former being the most probable. Similar calculations were