The values of $\Delta H$ and $\Delta S$ for the given reaction are $170 ext{ kJ}$ and $170 ext{ J K}^{-1}$

Question

The values of $\Delta H$ and $\Delta S$ for the given reaction are $170 	ext{ kJ}$ and $170 	ext{ J K}^{-1}$, respectively.
$C(	ext{graphite}) + CO_2(g) ightarrow 2CO(g)$
This reaction will be spontaneous at:

Accepted Answer

For a reaction to be spontaneous, the change in Gibbs free energy ($\Delta G$) must be negative ($\Delta G < 0$). According to the Gibbs equation, $\Delta G = \Delta H - T\Delta S$. For $\Delta G < 0$, $\Delta H - T\Delta S < 0$, which implies $T > \frac{\Delta H}{\Delta S}$. Given: $\Delta H = 170 ext{ kJ} = 170000 ext{ J}$ $\Delta S = 170 ext{ J K}^{-1}$ Substituting the values: $T > \frac{170000 ext{ J}}{170 ext{ J K}^{-1}}$ $T > 1000 ext{ K}$ Among the given options, only $1110 ext{ K}$ is greater than $1000 ext{ K}$. Therefore, the reaction will be spontaneous at $1110 ext{ K}$ .

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