Difference RuleA New Thermodynamic Principle:  Prediction of Standard Thermodynamic Data for Inorganic Solvates

• Published in: Journal of the American Chemical Society Vol. 126; no. 48; pp. 15809 - 15817
• Main Authors: Jenkins, H. Donald Brooke, Glasser, Leslie
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 08.12.2004
• Subjects: Chemical thermodynamics; Chemistry; Exact sciences and technology; General and physical chemistry; General. Theory; Alkali metal Compounds; Gibbs free energy; Thermodynamic model; Enthalpy; Lattice model; Heat of crystallization; Theoretical study; Entropy; Thermodynamic properties; Heat of formation
• ISSN: 0002-7863; 1520-5126
• DOI: 10.1021/ja040137f

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 = θ 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 = θ 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), Δf H°, Δf S°, Δf G° or (the standard thermodynamic functions of formation and the absolute entropy), and n can be noninteger. The constants, θ 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, θ 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:  H2O (hydrates), D2O, NH3, ND3, (CH3)2O, NaOH, CH3OH, C2H5OH, (CH2OH)2, H2S, SO2, HF, KOH, and (CH(CH3)2)2O. Detailed examples of usage are given for hydrates and for SO2.