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{n-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: UPOT (the lattice potential energy), V-m (the molecular or formula unit volume), Delta(1)Hdegrees, Delta(f)Sdegrees, Delta(f)Gdegrees or S-298(degrees) (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, PIS,11, 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: H2O (hydrates), D2O, NH3, ND3, (CH3)(2)O, NaOH, CH3OH, C2H5OH, (CH2OH)(2), H2S, SO2, HF, KOH, and (CH(CH3)(2))(2)O. Detailed examples of usage are given for hydrates and for SO2.