Gibbs free energy change, ΔG

Whether a reaction is thermodynamically feasible (spontaneous) is decided by the Gibbs free energy change:

$\Delta G = \Delta H - T\Delta S$

• If ΔG ≤ 0 (negative), the reaction is feasible.
• If ΔG > 0 (positive), it is not feasible in that direction.

The equation balances two drives: the enthalpy term (ΔH, favoured when exothermic) and the entropy term ($-T\Delta S$, favoured when ΔS is positive). At higher temperature the $-T\Delta S$ term becomes more important.

Units matter. ΔH is in kJ mol⁻¹ but ΔS is in J K⁻¹ mol⁻¹ — convert ΔS to kJ (÷1000) before combining, and use T in kelvin.

When ΔH and ΔS have the same sign, ΔG changes sign as temperature changes — so there is a threshold temperature at which the reaction just becomes (or stops being) feasible. At that point ΔG = 0:

$\Delta G = 0 \Rightarrow T = \frac{\Delta H}{\Delta S}$

Worked (CaCO₃ → CaO + CO₂). ΔH = +178 kJ mol⁻¹, ΔS = +161 J K⁻¹ mol⁻¹ (= +0.161 kJ K⁻¹ mol⁻¹): $T = \frac{178}{0.161} = 1106\,\text{K} \;(\approx 833\,^{\circ}\text{C})$

Both ΔH and ΔS are positive, so the reaction is feasible above ~1106 K — which is why limestone must be heated strongly to decompose it. At 298 K, ΔG = 178 − 298(0.161) = +130 kJ mol⁻¹ (not feasible).

You can read off the temperature behaviour straight from the signs of ΔH and ΔS:

ΔH	ΔS	Feasibility
−	+	ΔG always negative → feasible at all temperatures
+	−	ΔG always positive → never feasible
−	−	feasible at low temperature (small TΔS)
+	+	feasible at high temperature (large TΔS)

The borderline cases (−/− and +/+) are exactly the ones where the threshold temperature $T = \Delta H/\Delta S$ applies.

A practical caution. ΔG ≤ 0 only tells you a reaction is possible. It says nothing about the rate — a reaction can be feasible but immobile because of a high activation energy (e.g. the conversion of diamond to graphite).