If for a certain reaction ${∆}_{r}H$ is 30 kJ ${\mathrm{mol}}^{-1}$ at 450 K, the value of ${∆}_{\mathrm{r}}\mathrm{S}$(in ${\mathrm{JK}}^{-1} {\mathrm{mol}}^{-1}$) for which the same reaction will be spontaneous at the same temperature is

For spontaneous reaction, ${∆}_{\mathrm{r}}\mathrm{G}$ must be less than zero.

$\begin{array}{l}\text{ So, }{\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}={\mathrm{\Delta }}_{\mathrm{r}}\mathrm{H}-{\mathrm{T\Delta }}_{\mathrm{r}}\mathrm{S}<0\\ \text{ or, }{\mathrm{\Delta }}_{\mathrm{r}}\mathrm{S}>\frac{{\mathrm{\Delta }}_{\mathrm{r}}\mathrm{H}}{\mathrm{T}}\\ >\frac{30,000}{450}=66.67\mathrm{J}\end{array}$

$\therefore$For reaction to be spontaneous, the value of ${∆}_{\mathrm{r}}\mathrm{S}$ must be greater than 66.67 J