A certain reaction is spontaneous at temperatures below 400. K but is not spontaneous at temperatures above 400. K. If $\Delta H^\circ$ for the reaction is $-20$. $\pu{ kJ mol^{-1}}$ and it is assumed that $\Delta H^\circ$ and $\Delta S^\circ$ do not change appreciably with temperature, then the value of $\Delta S^\circ$ for the reaction is

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$$\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ$$

Rearranging the equation and solving for $\Delta S^\circ$

$$\Delta S^\circ = \frac{\Delta G^\circ - \Delta H^\circ}{-T}$$

We can set $\Delta G^\circ$ to be zero when the reaction is in equilibrium. Make sure to convert units to Joules.

$$\Delta S^\circ = \frac{0-(-20{,}000)}{-400}$$ $$\Delta S^\circ = \frac{-20{,}000}{-400}$$ $$\Delta S^\circ = -50$$