We may again apply Le Chatelier's principle to this situation. Heating a system at equilibrium should result in a shift in the direction of the endothermic reaction. (View this as the system taking in the supplied heat to minimise the temperature increase, and using it to drive the endothermic reaction.) Conversely, lowering the temperature will shift the equilibrium in the direction of the exothermic reaction.

Thus for endothermic reactions, increasing the temperature favours products, whereas for exothermic reactions increasing temperature favours the reactants at equilibrium.

The variation of the equilibrium constant with temperature may be quite simply derived: By manipulation of the fundamental relation ΔG_rº = -RT ln K , we obtain:

which, upon differentiation with respect to T, gives:

We may now manipulate this equation using the Gibbs-Helmholtz equation, which tells us that

Which is one form of the van't Hoff equation. For exothermic reactions, ΔH < 0 , which makes (d ln K / dT) negative. This implies that for such reactions, as the temperature increases the equilibrium constant becomes smaller (meaning reactants are favoured in the equilibrium mixture). This is in line with the prediction of Le Chatelier's principle. The reverse is true for endothermic reactions (ΔH > 0) . The above equation may be converted, by a change of variable, into:

This is the most commonly used form of the van't Hoff equation. It shows that a plot of ln K against 1/T gives a straight line of slope ΔH_rº / R

We may integrate this expression to allow us to find the value of the equilibrium constant at one temperature from a knowledge of its value at some other temperature:

If we assume that the standard enthalpy of reaction is independent of temperature over the range being considered, we may treat it as a constant, allowing us to write: