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The values of $\Delta H$ and $\Delta S$ for the reaction, $C(graphite) + CO_2(g) \rightarrow 2CO(g)$ are 170 kJ and 170 J $K^{-1}$ respectively. This reaction will be spontaneous at
A
510 K
B
710 K
C
910 K
D
1110 K
Detailed Solution
A reaction is spontaneous when $\Delta G = \Delta H - T\Delta S < 0$
With $\Delta H$ and $\Delta S$ both positive, this needs $T\Delta S > \Delta H$, i.e., $T > \frac{\Delta H}{\Delta S}$
$\frac{\Delta H}{\Delta S} = \frac{170\times10^3\ J}{170\ J\,K^{-1}} = 1000$ K
So the reaction is spontaneous only above 1000 K.
Among the given temperatures, only 1110 K is above 1000 K.
With $\Delta H$ and $\Delta S$ both positive, this needs $T\Delta S > \Delta H$, i.e., $T > \frac{\Delta H}{\Delta S}$
$\frac{\Delta H}{\Delta S} = \frac{170\times10^3\ J}{170\ J\,K^{-1}} = 1000$ K
So the reaction is spontaneous only above 1000 K.
Among the given temperatures, only 1110 K is above 1000 K.