Gibbs free energy change, ΔG

· Gibbs free energy change, ΔG⦵, predicts whether a reaction/process is thermodynamically feasible under stated conditions.
· Main equation: ΔG⦵ = ΔH⦵ − TΔS⦵.
· ΔH⦵ = standard enthalpy change, usually in kJ mol⁻¹.
· T = temperature in K only.
· ΔS⦵ = standard entropy change, usually given in J K⁻¹ mol⁻¹; convert to kJ K⁻¹ mol⁻¹ before using with ΔH⦵.
· Standard conditions use ⦵; in this syllabus, standard conditions are 298 K and 101 kPa.

This diagram summarises the Gibbs equation and identifies each variable. It is useful for remembering that temperature must be in K and that entropy units must match enthalpy units. Source

Using ΔG⦵ to judge feasibility

· If ΔG⦵ < 0, the reaction/process is feasible.
· If ΔG⦵ > 0, the reaction/process is not feasible under those conditions.
· If ΔG⦵ = 0, the system is at the feasibility boundary/equilibrium point for the calculation.
· Feasible does not mean fast: ΔG⦵ only predicts thermodynamic possibility, not rate.
· A feasible reaction may still be very slow if the activation energy is high.

Calculation method

· Step 1: Write ΔG⦵ = ΔH⦵ − TΔS⦵.
· Step 2: Convert ΔS⦵ from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ by dividing by 1000.
· Step 3: Use T in K; if given °C, convert using K = °C + 273.
· Step 4: Substitute carefully, including positive/negative signs for ΔH⦵ and ΔS⦵.
· Step 5: Give ΔG⦵ in kJ mol⁻¹ and state whether the reaction is feasible.

Temperature and feasibility

· Temperature affects feasibility because of the −TΔS⦵ term.
· If ΔH⦵ < 0 and ΔS⦵ > 0, then ΔG⦵ is always negative → feasible at all temperatures.
· If ΔH⦵ > 0 and ΔS⦵ < 0, then ΔG⦵ is always positive → never feasible.
· If ΔH⦵ < 0 and ΔS⦵ < 0, the reaction is feasible at low temperature.
· If ΔH⦵ > 0 and ΔS⦵ > 0, the reaction is feasible at high temperature.
· At the temperature where feasibility changes, ΔG⦵ = 0, so T = ΔH⦵ / ΔS⦵ after units are made consistent.

This table shows how the signs of ΔH and ΔS control whether temperature makes a reaction more or less feasible. It is especially useful for predicting feasibility without doing a full calculation. Source

Exam traps

· Do not use °C in the Gibbs equation; always use K.
· Do not mix J and kJ; convert ΔS⦵ before multiplying by T if ΔH⦵ is in kJ mol⁻¹.
· Keep the minus sign in −TΔS⦵; sign errors often reverse the feasibility conclusion.
· Do not say “spontaneous = fast”; feasibility is about thermodynamics, not kinetics.
· Always quote the final unit for ΔG⦵, normally kJ mol⁻¹.