What is the name of the equation that relates the equilibrium constant of a chemical reaction to temperature?

The equation that relates a chemical reaction’s equilibrium constant to temperature is the van 't Hoff equation.

Dutch physical chemist Jacobus Henricus van 't Hoff proposed it in 1884 in his book Études de Dynamique chimique. In differential form, it connects the slope of ln K against reciprocal temperature with the reaction’s standard enthalpy change: d ln K/d(1/T) = −ΔH°/R.

The integrated form is useful for estimating an equilibrium constant at a second temperature, provided the reaction enthalpy is treated as approximately constant. For an endothermic reaction, raising temperature generally increases K; for an exothermic reaction, it generally decreases K. This is a quantitative version of the temperature aspect of Le Chatelier’s principle.

A common mix-up is the Arrhenius equation, which relates a rate constant to temperature and activation energy, not an equilibrium constant. The Clausius–Clapeyron relation instead describes how vapor pressure or phase-transition pressure varies with temperature.