# How does the equilibrium constant change with temperature?

Jan 11, 2014

For an exothermic reaction (ΔH is negative), $K$ decreases with an increase in temperature.

For an endothermic reaction (ΔH is positive), $K$ increases with an increase temperature.

You can calculate the effect of changing temperature on the equilibrium constant by using the van't Hoff equation

(dlnK)/(dT) = (ΔH^°)/(RT^2), where $R$ is the Ideal Gas Constant.

If you integrate this equation from ${T}_{1}$ to ${T}_{2}$, you get

ln((K_2)/(K_1)) = (ΔH^°)/R (1/(T_1) – 1/(T_2))

Thus, if you know the ΔH^° and the equilibrium constant at one temperature, you can calculate the equilibrium constant at some other temperature.