Question

The values of $\Delta H$ and $\Delta S$ of a certain reaction are $-400kJ{mol}^{-1}$ and $-20kJ{mol}^{-1}{K}^{-1}$ respectively. The temperature below which the reaction is spontaneous is:

• A. $100K$
• B. ${20}^{o}C$
• C. $20K$
• D. ${120}^{o}C$

Answer 1

The correct option is C $20K$

Given, $\Delta H=-400kJ{mol}^{-1}$
$\Delta S=-20kJ{mol}^{-1}{K}^{-1}$

Gibbs Helmholtz equation is given by:
$\Delta G=\Delta H-T\Delta S$

For a reaction to be spontaneous, $\Delta G$ must be less than $0$, i.e., negative.

$\therefore 0\ge \Delta H-T\Delta S$

$T\Delta S\ge \Delta H$

The temperature below which the reaction is spontaneous is:

$T=\frac{\Delta H}{\Delta S}=\frac{-400}{-20}=20K$

Hence, option $C$ is correct.