UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper II
Q5(b). ΔᵣG<0 but Δ^ G not necessarily negative
Question
At constant P and T, for a spontaneous chemical reaction, ΔᵣG must be negative but Δ^ G must not necessarily be negative. Explain.
Answer in brief
ΔᵣG=G_(products)-G_(reactants) decides whether the reaction can go (thermodynamics). Δ^ G=G_(TS)-G_(reactants) is the barrier that decides how fast it goes (kinetics): it is normally positive, since the transition state is the highest point on the path.
Key points
- ΔᵣG<0 is the criterion of spontaneity at constant T and P and depends only on the initial and final states.
- Δ^ G refers to the unstable activated complex, which lies above the reactants, so Δ^ G>0 for an ordinary reaction, and k=(k_BT)/(h)e^(-Δ^ G/RT) (Eyring). A thermodynamically spontaneous reaction (e.g., diamond turning into…
- a reaction can be spontaneous with a large positive Δ^ G, or have a small barrier yet a positive ΔᵣG (non-spontaneous, as for an unfavoured pre-equilibrium).
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
- ΔᵣG<0 is the criterion of spontaneity at constant T and P and depends only on the initial and final states.
- Δ^ G refers to the unstable activated complex, which lies above the reactants, so Δ^ G>0 for an ordinary reaction, and k=(k_BT)/(h)e^(-Δ^ G/RT) (Eyring). A thermodynamically spontaneous reaction (e.g., diamond turning into graphite, or 2H₂ + O₂ → 2H₂O at room temperature) can have a large barrier and be extremely slow.
- The two are independent: a reaction can be spontaneous with a large positive Δ^ G, or have a small barrier yet a positive ΔᵣG (non-spontaneous, as for an unfavoured pre-equilibrium).
Coversactivated complex theoryΔᵣG<0 but Δ^ G not necessarily negative
All parts of Question 5
- 5(a) Activation energy from the souring of milk5 marks
- 5(b) ΔᵣG<0 but Δ^ G not necessarily negative5 marks