Derivation of el'Yanov and Hamann's empirical formula and another new formula for pressure dependence of ionization constants

Abstract

El'yanov and Hamann's empirical formula for the pressure dependence of the ionization constant, RTln(K_p/K_0)=-ΔV^^-_o^0P/(1+bP) has been derived theoretically from the Born model for ionic salvation by taking account of the pressure dependence of the dielectric constant of water. Although b does not depend on temperature and is equal to 9.20×10^-5bar^-1 according to El'yanov and Hamann, the present derivation shows that b depends on temperature, being 8.98, 9.46 and 11.67×10^-5bar^-1 at 15.25 and 45℃, respectively. Another new formula for the pressure dependence of the ionization constant has been also obtained, which becomes equal to Owen-Brinkley's formula under some condition. All the formulas proposed by several authors until now have been compared, and their similarities and differences are discussed.