Abstract: According to the theromodynamical formula of chemical equilibrium, for the reaction:
HAv+H_2O<=>Ac~-+H_3O~+
we have: △G~0=-RT·In(Kα)
or: △g~0=-k_bT·In(K_α)
where, △g~0=g_(Ac)~0-+g_(H3O)~0+-g_(HAc)~0-g_(H2O)~0, g_j~0 is chemical potential or partial molecule Gibbs free-energy of solute j. According to the Scaled Particle Theory (SPT), the Gibbs free-energy of solute j in a solvent is consists of two parts,the first is called the cavitation free-energy (9_j~h), which is the energy needed to transfer a particle from the vacuum to the solvent, and, the second, the interation free-energy (g_j~(OR)), the dispersion energy (g_j~(DS)) and the static energy (g_j~(EL)), So:
g_i~0=g_j~h+g_j~(IN)+g_j~(OR)+g_j~(DS)+g_j~(EL)
then we have: K_a/k_a~0=exp(-Δg~0/k_bT)
where K_a is the ionization constant of HAc in the vacuum, and, is unknown. To solve the problem, we have to select another standard solvent in which, the K_a′ of HAc is well known of course, water is the best one, in it, the K_a′ of HAc is 1.754×10~(-5) at 298 K, and finally we have
K_a=K_a′exp(-Δ(Δg~0/k_bT)
where: Δ(Δg~0)=Δg~0 (in the solvent studying)-Δg~0′ (in water)
According to the theory and formula developed above, we took a series of MeOH-Water mixtures and 1,4-Dioxane-Water mixtures as example in this article, and calculated the K_a of HAc in those mixtures. By comparing the values with that from literatures we found that they are accordance well when the weight per-cent of the non-water conponents is less than 90% and not as larger than 90%. The reasons causing the results are discussed mainly at the end.