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Q.
The values of $ΔH$ and $ΔS$ of a certain reaction are $- 400\, kJ\, mol^{-1}$ and $-20\, kJ\, mol^{-1}K^{-1}$ respectively. The temperature below which the reaction is spontaneous is
Given,
$\Delta H =-400\, kJ \,mol ^{-1} $
$\Delta S =-20\, kJ \,mol ^{-1} K ^{-1}$
Gibbs Helmholtz equation is
$\Delta G=\Delta H-T \Delta S$
For a reaction to be spontaneous, $\Delta G$ must be less than 0 , i.e., negative.
$\therefore 0 \geq \Delta H-T \Delta S$
$T \Delta S \leq \Delta H $
$T \leq \frac{\Delta H}{\Delta S} \leq \frac{-400}{-20} \leq 20\, K$