Effects of Temperature on Free Energy

Temperature affects spontaneity because it multiplies the entropy term (TΔS) in the Gibbs free energy equation. When both enthalpy and entropy changes are positive, increasing temperature makes the TΔS term larger, eventually making ΔG negative and the reaction spontaneous. Conversely, when both are negative, higher temperatures make ΔG positive, favoring nonspontaneity at elevated temperatures.

When ΔH is negative and ΔS is positive, the reaction is spontaneous at all temperatures because both factors favor spontaneity. The exothermic nature releases heat while increased disorder in the system drives the process forward. The sodium hydroxide and hydrochloric acid reaction exemplifies this scenario, where ΔG remains negative regardless of temperature.

Water freezing demonstrates a reaction with negative enthalpy and entropy changes. Below the freezing point, the exothermic process becomes spontaneous despite decreasing disorder because the TΔS term is smaller than ΔH. Above the freezing point, the positive ΔG makes freezing nonspontaneous, showing how temperature determines the direction of phase transitions.

A cold pack dissolves spontaneously because the endothermic dissolution of ammonium nitrate has positive ΔH and positive ΔS. At room temperature, the entropy increase is large enough that the TΔS term exceeds ΔH, making ΔG negative. Lowering temperature would decrease TΔS, eventually making the reaction nonspontaneous.

When ΔH is positive and ΔS is negative, ΔG is always positive at all temperatures, making the reaction nonspontaneous regardless of conditions. This endothermic process with decreased disorder combines two factors opposing spontaneity. The positive ΔH and negative TΔS term ensure ΔG never becomes negative, preventing the reaction from occurring spontaneously.

Enthalpy favors spontaneity when reactions release heat, while entropy favors spontaneity through increased disorder. When both factors have the same sign, one dominates at all temperatures. When they have opposite signs, temperature becomes the deciding factor through the TΔS term, determining whether the second law of thermodynamics direction spontaneous changes favors the reaction.

A reaction with positive ΔH and positive ΔS is spontaneous only at higher temperatures. At low temperatures, the TΔS term is too small to overcome the positive ΔH, making ΔG positive and the reaction nonspontaneous. As temperature increases, the entropy contribution grows larger, eventually making ΔG negative and driving spontaneous processes.