Variation of Reaction Enthalpy with Temperature (Kirchhoff's Law)

Consider a chemical reaction where reactants A and B combine to form products C and D.

As the temperature increases, the enthalpy of both the reactants and the products rises. However, the reaction's overall enthalpy changes only if the enthalpy increases of the reactants and products differ.

Enthalpy is differentiated to get its slope with temperature. At constant pressure, this slope equals the difference in heat capacities of both the reactants and products, expressing the thermal dependence of reaction enthalpies at constant pressure. This equation is known as Kirchhoff’s equation.

A similar relation at constant volume uses the temperature dependence of internal energy. Internal energy then connects to enthalpy by adding the pressure–volume term, allowing reaction enthalpy to be evaluated under constant-volume conditions.

For small temperature ranges, these equations can be directly integrated, assuming constant heat capacities.

For large temperature ranges, where heat capacities vary with temperature, substitute these values into the Kirchhoff equation.

Additionally, integrating it between two given temperatures yields the integrated form of Kirchhoff’s equation.