23.4 Gibbs free energy change, ΔG

The standard Gibbs equation is ΔG° = ΔH° − TΔS°, where temperature is in kelvin and ΔH° and TΔS° use the same energy units.

Enthalpy favours exothermic change, while the entropy term becomes more influential as temperature increases. The equation combines these competing contributions for a specified standard state.

An endothermic reaction can still have negative ΔG° at high T if its positive ΔS° makes TΔS° larger than ΔH°.

Do not insert Celsius or combine kJ enthalpy with J entropy without conversion.

Substitute ΔH° and TΔS° into ΔG° = ΔH° − TΔS°. Convert entropy from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ when enthalpy is in kJ mol⁻¹.

Write the units beside each term and keep the sign of ΔS. Round only after the final calculation, then state what the sign means.

If ΔH° = 40 kJ mol⁻¹, ΔS° = 100 J K⁻¹ mol⁻¹ and T = 298 K, TΔS° = 29.8 kJ mol⁻¹ and ΔG° = +10.2 kJ mol⁻¹.

A negative entropy value makes −TΔS positive; do not drop that double sign.

If ΔG° < 0, the forward process is thermodynamically feasible under the specified standard conditions; if ΔG° > 0, the reverse direction is favoured. ΔG° = 0 indicates equilibrium.

Feasible does not mean fast, safe or complete. Kinetics, activation energy, heat transfer and actual concentrations can determine what is observed.

A combustion reaction may have a strongly negative ΔG° but still need ignition because its activation energy is high.

Do not equate negative ΔG° with an instantaneous reaction or 100% yield.

Because ΔG° = ΔH° − TΔS°, raising T makes a positive ΔS° more favourable and a negative ΔS° less favourable. The crossover occurs when ΔG° changes sign.

For ΔH°>0 and ΔS°>0, high temperature can make a process feasible; for ΔH°<0 and ΔS°<0, low temperature is favoured. The other sign combinations are usually temperature-independent in the simple model.

If ΔH°=+50 kJ mol⁻¹ and ΔS°=+150 J K⁻¹ mol⁻¹, feasibility begins above T≈333 K because ΔH°/ΔS° sets the threshold.

Do not say “higher temperature always makes reactions spontaneous”; inspect both signs.