Theoretical Expression for Solubility Product

Abstract

WHEN an ionizable compound BA is dispersed in water to form a saturated solution, equilibrium is attained with the rate at which the ions detach themselves from unit area of the surface of the solid particles (crystals) and go into solution, and is equal to the rate at which the ions recombine to form the molecules which are deposited on the same area of the surface. The rate of recombination of the oppositely charged ions B^˙ and A′ to form BA, being deposited on unit area of the solid surface, is given by the expression : k₁$n_{B^{\dot{}}}$n_A′.exp(− E₁/RT), where $n_{B^{\dot{}}}$ and n_A′ are the numbers of cations B^˙ and anions A′ per unit volume of the solution; k₁ is a constant and E₁ is the energy per gm.-mole which the ions should possess to escape from the ionic atmosphere and from the solvation layers around the ions. This energy term was neglected in the earlier communication¹ and it should be correctly expressed as: where the first term represents the Coulomb attraction and the second² the energy of interaction between an ion of charge zɛ and c equidistant molecules of water at a distance R₂ from its centre ; A = ½α(zɛ)² ; B = zɛµ. N₀ is the Avogadro number ; z₊ and z₋ denote the valencies of the positive and negative ions ; ɛ is the electronic charge, α the polarizability and µ the dipole moment of the water molecules; R₁ is the radius of the ionic atmosphere, and D is the dielectric constant of the medium.