Question

For a chemical reaction $A+B\rightleftharpoons C+D$ $({\Delta }_r{H}^0=80kJmo{l}^{-1})$ the entropy change ${\Delta }_r{S}^0$ depends on the temperature $T$ (in K) as ${\Delta }_r{S}^0=2T\left(J{K}^{-1}mo{l}^{-1}\right)$.
Minimum temperature at which it will become spontaneous is _____K (Integer)

Answer 1

$A+B\rightleftharpoons C+D$

For the reaction to be spontaneous,
${\Delta }_{r}G<0$

${\Delta }_r{G}^0<0$

$\Rightarrow {\Delta }_r{H}^0-T\times 2T<0$

$\Rightarrow 80\times 1000-T\times 2T<0$

$\Rightarrow T^2>40000$

$T>200$