Last updated: 2026-06-16

The van ’t Hoff equation describes how a reaction's equilibrium constant shifts with temperature, and in doing so it provides a way to measure the reaction's enthalpy without a calorimeter. Given the equilibrium constant at two temperatures, this calculator returns the standard enthalpy of reaction $\Delta H^\circ$. It is a staple of physical chemistry, where the temperature dependence of equilibrium is used to extract thermodynamic data.

Two-point form

The differential van ’t Hoff relation, $\dfrac{d\ln K}{dT} = \dfrac{\Delta H^\circ}{RT^2}$, integrates between two temperatures — assuming $\Delta H^\circ$ is roughly constant over the range — to:

$\ln\!\frac{K_2}{K_1} = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

Solving for the enthalpy:

$\Delta H^\circ = -\frac{R\,\ln(K_2/K_1)}{\,1/T_2 - 1/T_1\,}$

where $R = 8.314\ \mathrm{J/(mol\cdot K)}$ and the temperatures are in kelvin. Dividing the result by 1000 reports it in kJ/mol.

Worked example

Suppose $K$ rises from $K_1 = 0.0010$ at $298.15\ \mathrm{K}$ to $K_2 = 0.050$ at $318.15\ \mathrm{K}$:

The positive sign marks an endothermic reaction, consistent with the equilibrium constant growing as the temperature rises.

Why the constant moves with temperature

Treating heat as a reactant or product, Le Chatelier's principle predicts that warming an endothermic reaction shifts it toward products and raises $K$, while warming an exothermic reaction lowers $K$. The van ’t Hoff equation makes this quantitative: a plot of $\ln K$ against $T^{-1}$ is a straight line whose slope is $-\Delta H^\circ/R$. This mirrors the Arrhenius plot for rate constants — see the Arrhenius Equation Calculator. For the closely related vapour-pressure version, use the Clausius-Clapeyron Equation Calculator, and to connect enthalpy to free energy and entropy, the Gibbs Free Energy Calculator.