Enthalpy, Entropy, and Energy

Although the exact calculation of temperature changes upon an equilibrium is somewhat more involved than we can treat here, we can make several approximate relationships that are very useful. Remember that the equlibrium constant is related to the standard free energy change of the reaction:

ΔGº = – RTlnK_eq

And recall that the free energy change upon reaction is related to both enthalpy and entropy changes:

ΔGº = ΔHº – TΔSº

Although the free energy change is strongly dependent on temperature, usually the enthalpy and entropy changes upon reaction are not temperature dependent (or at least not very much so). This implies that free energy is a linear function of temperature. Combining the above two equations:

– RTlnK_eq = ΔHº – TΔSº

Remember that the enthalpy and entropy changes are regarded as constants with respect to temperature, so the equilibrium constant is exponentially dependent on temperature. Rearranging the above equation gives:

K_eq = e ^{^{– ΔHº}/_RT} • e ^{^ΔSº/_R}