Question

For a chemical reaction $A+B\rightleftharpoons C+D({\Delta }_r{H}^o=80kJmo{l}^1)$ the entropy change ${\Delta }_r{S}^o$ depends on the temperature $T$ (in $K$) as ${\Delta }_r{S}^o=2T\left(J{K}^{-1}mo{l}^{-1}\right)$. Minimum temperature at which it will become spontaneous is ________ $K$ .

Answer 1

$\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$
To make the process spontaneous,
$\Delta G^{\circ }<0$
$\Delta H^{\circ }-T\Delta S^{\circ }<0$
$T>\frac{\Delta H^{\circ }}{\Delta S^{\circ }}$

$T>\frac{80000}{2T}$

$2T^2>80000$
$T^2>40000$
$T$ > 200
The minimum temperature to make it spontaneous is $200K.$