Difference rule-a new thermodynamic principle: prediction of standard thermodynamic data for inorganic solvates

We present a quite general thermodynamic "difference" rule, derived from thermochemical first principles, quantifying the difference between the standard thermodynamic properties, P, of a solid n-solvate (or n-hydrate), n-S, containing n molecules of solvate, S (water or other) and the corresponding solid parent (unsolvated) salt: [P[n-solvate] - P[parent]]/n = constant = theta(P)[S,s-s], or n-S and other solvate, n'-S: [P[-solvate] - P[n'-solvate]]/(n - n') = [P[n-S ] - P[n'-S]]/(n - n') = constant = theta(P)[S,s-s] where P may be any one of: U(POT) (the lattice potential energy), V(m) (the molecular or formula unit volume), Delta(f)H degrees , Delta(f)S degrees , Delta(f)G degrees or (the standard thermodynamic functions of formation and the absolute entropy), and n can be noninteger. The constants, theta(P)[S,s-s], for each property, P, of solvate of type S, are established by correlation of the available set of experimental data. We also show that, when solid-state data for a particular solvate is sparse, theta(P)[S,s-s] can be reliably predicted from liquid-state values, P[S,l], or even gas-state values, P[S,g]. This rule offers a powerful means for predicting unknown thermodynamic data, extending the compass of currently known thermodynamic information. Systems considered involve the following solvates: H(2)O (hydrates), D(2)O, NH(3), ND(3), (CH(3))(2)O, NaOH, CH(3)OH, C(2)H(5)OH, (CH(2)OH)(2), H(2)S, SO(2), HF, KOH, and (CH(CH(3))(2))(2)O. Detailed examples of usage are given for hydrates and for SO(2).