1. Tardigrade
  2. Question
  3. Chemistry
  4. For the reaction at 298 K, 2A + B → C, Δ H = 400 KJ mol-1 and Δ S = 0.2 KJ K-1 mol-1 At what temperature will the reaction become spontaneous considering Δ H and Δ S to be constant over the temperature range

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Q. For the reaction at $298 \,K, 2A + B \to C, \Delta H = 400 \,KJ\, mol^{-1}$ and $\Delta\, S = 0.2 \,KJ\,K^{-1}\,mol^{-1}$ At what temperature will the reaction become spontaneous considering $\Delta H$ and $\Delta S$ to be constant over the temperature range

Thermodynamics

Solution:

According to Gibbs Helmholtz equation,
$\Delta\,G =\Delta\,H -T \Delta\,S$
Temperature at equilibrium i.e., when $\Delta \,G=0$,
$T =\frac{\Delta\,H}{\Delta\,S}=\frac{400}{0.2} =\frac{4000}{2} = 1200\,K$
Thus the reaction will be spontaneous at temperature above $2000 \,K$ as above $2000\, K$ $\Delta\,G =-ve$