Effects of Temperature on Free Energy

For a reaction to be spontaneous at constant temperature and pressure, the change in Gibbs free energy, ΔG, must be less than zero.

The sign of ΔG depends on the signs and the relative values of enthalpy, entropy, and temperature.

Enthalpy favors spontaneity when the reaction releases heat to the surroundings, while entropy favors spontaneity when there is more disorder in the system.

If ΔH is negative and ΔS is positive, as in the reaction between sodium hydroxide and hydrochloric acid, ΔG is negative at all temperatures. Thus, exothermic reactions—where the entropy of the system increases—are always spontaneous.

If both ΔH and ΔS are negative, ΔG depends on the temperature. Consider the freezing of water into ice, an exothermic reaction where the entropy of the system decreases.

At temperatures below the freezing point of water, the water will freeze spontaneously, releasing heat and becoming more ordered. Thus, reactions with negative enthalpy and entropy changes are spontaneous only at low temperatures.

ΔG is also dependent on temperature if both ΔH and ΔS are positive.

A common example is a chemical cold pack, where solid ammonium nitrate dissolves in water, that absorbs heat from the surroundings. This endothermic reaction proceeds spontaneously at room temperature due to the increase in disorder of the system. Thus, reactions with positive enthalpy and entropy changes are spontaneous only at higher temperatures.

If the temperature were lowered such that the TΔS becomes smaller than ΔH, ΔG would be positive, and the reaction would become nonspontaneous.

When ΔH is positive and ΔS is negative, ΔG is always positive, and the reaction is nonspontaneous at all temperatures.