Question

For a reaction $M_{2}O\left(s\right)\to 2M\left(s\right)+\frac{1}{2}{O}_2\left(g\right);\Delta H=30kJmo{l}^{-1}and\Delta S=0.07kJ{K}^{-1}mo{l}^{-1}at1atm.$ Calculate minimum temperature (in $K$) at which the reaction would become spontaneous.

Answer 1

Given, for the change, $\Delta H=30\times {10}^{3}Jmo{l}^{-1},\Delta S=70J{K}^{-1}mo{l}^{-1}$
For a spontaneous reaction,
$\Delta G<0$
For minimum temperature, taking the limiting condition
$\Delta G=0$
Since, $\Delta G=\Delta H-T\Delta S$

or $\Delta H=T\Delta S$
or $T=\frac{\Delta H}{\Delta S}\Rightarrow T=\frac{30\times {10}^3}{70}\Rightarrow T=428.57K$
Above this temperature, the reaction would be spontaneous.