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…
Clausius-Clapeyron equation
Clausius 1834 / Clapeyron 1850: phase-coexistence dp/dT = ΔS/ΔV; for vapor-liquid, d(ln p)/dT = ΔH_vap/(RT²) yields temperature-pressure…
Third law of thermodynamics (Nernst)
Nernst 1906 / Planck 1911: entropy of perfect crystal at T=0 K is zero (S → 0 as T → 0). Implies absolute zero is unattainable in finite…
Maxwell relations (thermodynamic)
Maxwell 1871: from exact-differential property of state functions, four cross-derivative identities relate (∂S/∂V)_T = (∂p/∂T)_V etc. …
Fugacity & coefficient
Lewis 1908 fugacity f corrects ideal-gas chemical-potential μ = μ° + RT ln(f/p°) for non-ideality; fugacity-coefficient φ = f/p captures…
Activity coefficient (γ)
Lewis-Randall 1923: solutions deviate from Raoult/Henry ideality via activity-coefficient γ_i where activity a_i = γ_i x_i. Models: Wilson…
Chemical potential & equilibrium
Gibbs 1876: chemical-potential μ_i = (∂G/∂n_i)_{T,p,n_j} drives mass transfer; equilibrium requires equal μ_i across phases or…
Gibbs free energy (spontaneity)
Gibbs 1873-1878: G = H - TS; spontaneous if dG < 0 at constant T,P; equilibrium dG = 0; chemical-potential mu_i = (dG/dn_i)_{T,P,n_j};…
Clausius-Clapeyron equation
Clausius 1850 + Clapeyron 1834: dP/dT = Delta-S / Delta-V = Delta-H / (T Delta-V); vapor-pressure d ln P / dT = Delta-H_vap / RT^2;…
Chemical potential / fugacity (Lewis)
Lewis 1901 fugacity f: mu = mu* + RT ln(f/f*); ideal-gas f = P, real-gas f != P (compressibility); fugacity-coefficient phi(T,P) extracted…
Activity coefficient (Debye-Huckel 1923)
Debye-Huckel 1923: log gamma_+- = -A z+ z- sqrt(I) (limiting law); ion atmosphere screening; extensions Davies + Pitzer at higher I; basis…
Chemical equilibrium / Le Chatelier
Le Chatelier 1884 / Braun 1887 principle: system at equilibrium subjected to perturbation shifts to minimize change; quantified via…
Third law (Nernst heat theorem)
Nernst 1906 / Planck 1911: lim_{T -> 0} S = 0 for perfect crystal; absolute entropies tabulated S°(298 K) standard; explains low-T heat…
Hess law (1840)
G Hess 1840 enthalpy-state-function; foundation of thermochemistry + modern computational-CCSD(T)+CBS thermochemistry validation.
Nernst 3rd law (1906)
W Nernst 1906 (Nobel 1920) S→0 as T→0; modern adiabatic-demagnetization + nuclear-cooling + Bose-Einstein condensate temps.
Mass action (Guldberg-Waage 1864)
C Guldberg-P Waage 1864 K_eq=Π[products]/Π[reactants]; modern Gibbs-formal-entropy + thermodynamic-cycles + ICE-tables.
van't Hoff (1884)
J van't Hoff 1884 (Nobel 1901) d ln K/d T = ΔH°/RT²; modern enthalpy-entropy compensation + Eyring-Polanyi rate-extensions.
Clausius-Clapeyron (1834)
B Clapeyron 1834 + Clausius 1850 dp/dT=L/TΔV; modern saturation-vapor-pressure + atmospheric-water-cycle ~7%/°C amplification.
Debye T³ (1912)
P Debye 1912 (Nobel 1936) C_v ∝ T³ low-T heat-capacity; foundation of phonon-thermodynamics + specific-heat computation.