Bronsted Acids and Bases in Solution

As already emphasized in Section 3.3.1, the ionization equilibrium of an acid, Eq. (4-5), or of a base, Eq. (4-6), is affected by a solvent change, not only because of the 

Application of this equation to acid/base reaction (4-5) leads to a net change in Gibbs energy per mol as shown in Eq. (4-8), if only pure electrostatic interactions are considered [8]. 

the Gibbs energy difference AAG for the ionization of a mol of HA in solvent 1 and solvent 2 with relative permittivities er(i) and r(2), respectively, provided that the radii of the reactants are the same in both solvents, is given by Eq. (4-9). 

Because the Gibbs energy of reaction, AG, is related to the equilibrium constant Aa, according to Eq. (4-3), Eq. (4-9) can be converted into Eq. (4-10). 

(4-10) can be used only for solvents of equal acid and base strength, because only the effect of the solvent relative permittivity on the degree of ionization is considered. Under these conditions, Eq. (4-10) predicts that the logarithm of the ionization constant of HA should be inversely proportional to the relative permittivity of the solvent in which HA is dissolved. However, one has to take into account the fact that the relative permittivities near solute ions can differ considerably because of the effect of dielectric saturation, which hinders the precise calculation of electrostatic interactions. Because of these restrictions, Eq. (4-10) can be expected to yield only semiquantitative results. Nevertheless, it allows us to predict qualitatively how the charge type of an acid affects the ionization constant in solvents of different relative permittivities. 

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