Temperature at which a reaction becomes feasible

Worked example

For the thermal decomposition CaCO₃(s) → CaO(s) + CO₂(g), ΔH = 179.1 kJ mol⁻¹ and ΔS = 163 J K⁻¹ mol⁻¹. Calculate the minimum temperature at which the reaction is feasible.

1. 1. Gibbs energy from ΔH and ΔS: solve for T where ΔG = 0

   $T = \dfrac{\Delta H - \Delta G}{\Delta S}$

   = 1099 K

Answer: T = 1100 K

Method

A reaction is feasible when ΔG ≤ 0. Setting ΔG = ΔH − TΔS = 0 gives T = ΔH/ΔS. Convert ΔH to J mol⁻¹ first (or ΔS to kJ K⁻¹ mol⁻¹); dividing 178 by 161 directly gives a meaningless 1.1 K.

Formulas used

• Gibbs energy from ΔH and ΔS

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

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