Chemical thermodynamics — IUPAC Division I treatment of the full thermodynamic framework (Gibbs and Helmholtz free energies, chemical potential, phase rule) beyond the bookkeeping scope of thermochemistry. Foundations: first law dU = δq −…
chemical-thermodynamics
Gibbs free energy G = H − TS (spontaneity at fixed T, P)
Foundational framework of chemical thermodynamics: the Gibbs free energy G = H − TS is the equilibrium / spontaneity criterion at fixed (T,…
Van't Hoff equation: ln(K₂/K₁) = −ΔH/R · (1/T₂ − 1/T₁)
Van't Hoff equation (1884, Études de Dynamique Chimique): the temperature dependence of the equilibrium constant follows the reaction…
Gibbs-Helmholtz: d(G/T)/dT = −H/T²
Gibbs-Helmholtz equation: the temperature derivative of G/T at fixed pressure equals −H/T², the dual of the van't Hoff relation one step…
ΔG(T) = -T/10 - 100 in ΔH<0, ΔS>0 quadrant: always spontaneous (T*<0)
Sympy-exact symbolic witness of the Gibbs-free-energy spontaneity criterion evaluated in the (ΔH<0, ΔS>0) quadrant. Setup: pick ΔH = −100…
Van't Hoff toy: ΔH=-R, T₁=1, T₂=1/2 ⇒ ln(K₂/K₁) = 1, K₂/K₁ = e
Sympy-exact symbolic witness of the one-natural-log-unit shift of an exothermic equilibrium under a temperature halving. Setup…
d(G/T)/dT simplifies to -H/T²; residual 0 (operator-level identity)
Sympy-exact symbolic witness of the Gibbs-Helmholtz identity at the operator level. Setup: write G(T) = H − T S treating (H, S) as…