Van't Hoff Equation Calculator

How it works

ln(K₂/K₁) = −(ΔH°/R)·(1/T₂ − 1/T₁); ln K = −ΔH°/(RT) + ΔS°/R (a plot of ln K vs 1/T has slope −ΔH°/R)

Integrating d(ln K)/dT = ΔH°/RT² gives the van’t Hoff equation, which quantifies Le Chatelier: exothermic reactions have smaller K at higher temperature, endothermic ones larger. Measuring K at several temperatures and plotting ln K against 1/T yields ΔH° from the slope and ΔS° from the intercept — the standard way to get reaction thermodynamics from equilibrium data, from ammonia synthesis to protein unfolding and drug binding. It assumes ΔH° is roughly constant over the range.

Worked example

Ammonia synthesis, K = 6 × 10⁵ at 298 K, ΔH° = −92.2 kJ: at 500 K, ln(K₂/K₁) = 11,090 × (1/500 − 1/298) = −15.0, so K₂ ≈ 0.18 — a 3-million-fold drop.

Frequently asked questions