The Thermodynamic Difference Rule (TDR) for non-aqueous solvates. Part 1. Review of methodology, investigation and prediction of thermodynamic data for sulfur dioxide solvates, MpXq.nSO2, routes to expand the database and forecast of future science and technology

Highlights: • Estimation Methods for obtaining new SO₂ solvate thermochemical data. • Validation methods for existing data • Thermodynamic Difference Rules (TDR) • Future Directions for Research. • Simple Relationships found for Thermochemical Data. -- Abstract: This paper investigates methods of estimation of new as well as already known data for the standard enthalpy of formation, ${\Delta }_f{H}^o$ the standard free energy of formation, ${\Delta }_f{G}^o$ and the standard (absolute) entropy, $S_{298}^o$ for SO₂ solvates, M_pX_q.nSO₂ at 298 K and validation of the latter solvates' existing data. A new approach enabling extension of the existing database is presented which involves the use of additional thermodynamic data for hydrates M_pX_q·nH₂O or, ammoniate salts M_pX_q·nNH₃ if and when available. This supplements the normal TDR approach which uses thermodynamic data for the parent compounds, M_pX_q. In principle use of these procedures will extend to other solvates too. The whole of the thermochemical data for these and for other solvate materials can be thought of as a vast matrix of self-consistent cross-linked linear equations of the type displayed below. Several TDR equations are involved which take the analytical form: [Δ_fG^o(M_pX_q.nSO₂,s) − Δ_fG^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Gf(SO₂, s − s) n = −299.9n (N = 2, R² = 1.00) [Δ_fH^o(M_pX_q.nSO₂,s) − Δ_fH^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Hf(SO₂, s − s)) n = −338.3n (N = 9, R² = 0.999) [$S_{298}^o$ (M_pX_q.nSO₂,s) − $S_{298}^o$ (M_pX_q,s)]/J K⁻¹ mol⁻¹ = ϴ_So(SO₂, s − s)) n = 106.9n (N = 2, R² = 0.999) [Δ_fG^o(M_pX_q·nH₂O,s) − Δ_fG^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Gf(H₂O, s − s)) n = −242.4n (N = 93, R² = 0.998) [Δ_fH^o(M_pX_q·nH₂O,s) − Δ_fH^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Hf(H₂O, s − s)) n = −298.6n (N = 342, R² = 0.999) [$S_{298}^o$ (M_pX_q·nH₂O,s) − $S_{298}^o$ (M_pX_q,s)]/J K⁻¹ mol⁻¹ = ϴ _So(H₂O, s − s) n = 40.9n (N = 83, R² = 0.978) [Δ_fG^o(M_pX_q.n NH₃,s) − Δ_fG^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Gf(NH₃, s − s) n = −21.0n (N = 4, R² = 0.922) [Δ_fH^o(M_pX_q·nNH₃,s) − Δ_fH^o(M_pX_q,s)]/kJ mol⁻¹ = ϴ_Hf(NH₃, s − s)) n = −104.2n (N = 277, R² = 0.930) [$S_{298}^o$ (M_pX_q·nNH₃,s) − $S_{298}^o$ (M_pX_q,s)]/J K⁻¹ mol⁻¹ = ϴ _So(NH₃, s − s)) n = 64.1n (N = 9, R² = 0.989) [Δ_fG^o(M_pX_q.nSO₂, s)]/kJ mol⁻¹ = [Δ_fG^o(M_pX_q.nH₂O, s)] − 57.5 n [Δ_fH^o(M_pX_q.nSO₂, s)]/kJ mol⁻¹ = [Δ_fH^o(M_pX_q.nH₂O, s)] − 39.7 n [$S_{298}^o$ (M_pX_q.nSO₂, s)]/J K⁻¹ mol⁻¹ = [$S_{298}^o$ (M_pX_q.nH₂O, s)] + 66.0 n [Δ_fG^o(M_pX_q.nSO₂, s)]/kJ mol⁻¹ = [Δ_fG^o(M_pX_q.nNH₃, s)] − 278.9 n [Δ_fH^o(M_pX_q.nSO₂, s)]/kJ mol⁻¹ = [Δ_fH^o(M_pX_q.nNH₃, s)] − 234.1 n [$S_{298}^o$ (M_pX_q.nSO₂, s)]/J K⁻¹ mol⁻¹ = [$S_{298}^o$ (M_pX_q.nNH₃, s)] + 42.8 n