Gibbs free energy change, ΔG

Chemistry A2 · Chemical energetics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic free All Chemistry A2 topics

The idea

The Gibbs free energy change, ΔG, combines the enthalpy change and the entropy change into one number that tells us whether a reaction can happen. A reaction is feasible when ΔG is negative or zero.

Temperature decides how much the entropy term matters. At high temperature, TΔS is large, so the sign of ΔS controls the result. At low temperature, ΔH controls it.

Feasible does not mean fast. A reaction with a negative ΔG may still be too slow to see if its activation energy is high.

Rules to remember

Gibbs equation: ΔG^⦵ = ΔH^⦵ − TΔS^⦵, with T in kelvin.
Convert ΔS from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ (÷ 1000) before using it with ΔH in kJ mol⁻¹.
ΔG ≤ 0: feasible. ΔG > 0: not feasible.
ΔH negative, ΔS positive: feasible at all temperatures. ΔH positive, ΔS negative: never feasible.
ΔH negative, ΔS negative: feasible only at low temperatures. ΔH positive, ΔS positive: feasible only at high temperatures.
The temperature at which feasibility changes (ΔG = 0): T = ΔH ÷ ΔS, with both in the same energy unit.

Common mistake

The most common error is mixing units: ΔH is in kJ mol⁻¹ but ΔS is in J K⁻¹ mol⁻¹. Divide ΔS by 1000 first, and use kelvin, not °C.

Worked example

For N₂(g) + 3H₂(g) → 2NH₃(g), ΔH^⦵ = −92.0 kJ mol⁻¹ and ΔS^⦵ = −198.8 J K⁻¹ mol⁻¹. Find ΔG^⦵ at 298 K and the temperature above which the reaction is not feasible.

ΔS^⦵ = −198.8 ÷ 1000 = −0.1988 kJ K⁻¹ mol⁻¹.
ΔG^⦵ = −92.0 − (298 × −0.1988) = −92.0 + 59.2 = −32.8 kJ mol⁻¹, so it is feasible at 298 K.
ΔG = 0 when T = ΔH ÷ ΔS = −92.0 ÷ −0.1988 = 463 K.
ΔH and ΔS are both negative, so the reaction stops being feasible above 463 K.

Answer: ΔG^⦵ = −32.8 kJ mol⁻¹ at 298 K; not feasible above about 463 K

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Read the full notes

Watch: 7 | Entropy 3 | Gibbs Free Energy ΔG

Keep going

← Entropy change, ΔS Electrolysis →Take a Chemistry A2 test