For a chemical reaction $A+B \rightleftharpoons C+D\left(\Delta_{r} \mathrm{H}^{\ominus}=80 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ the entropy change $\Delta_{r} \mathrm{~S}^{\ominus}$ depends on the temperature $\mathrm{T}$ (in $\mathrm{K}$ ) as $\Delta_{r} S^{\ominus}=2 T\left(J \mathrm{~K}^{-1}\right.$ mol $\left.^{-1}\right)$ Minimum temperature at which it will become spontaneous is ________________$\mathrm{K}$.
(200)
$\Delta \mathrm{G}^{\circ}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}$
To make the process spontaneous
$\Delta G^{\circ}<0$
$\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}<0$
$T>\frac{\Delta H^{\circ}}{\Delta S^{\circ}}$
$T>\frac{80000}{2 T}$
$2 T^{2}>80000$
$T^{2}>40000$
$T>200$
The minimum temperature to make it spontaneous is $200 \mathrm{~K}$.
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