Question
For the reaction $$CO\left( g \right) + \frac{1}{2}{O_2}\left( g \right) \to C{O_2}\left( g \right),\Delta H,$$ and $$\Delta S$$ are $$ - 283\,kJ$$ and $$ - 87\,J{K^1},$$ respectively. It was intended to carry out this reaction at 1000, 1500, 3000 and 3500 $$K.$$ At which of these temperatures would this reaction be thermodynamically spontaneous?
A.
1500 and 3500 $$K$$
B.
3000 and 3500 $$K$$
C.
1000, 1500 and 3000 $$K$$
D.
1500, 3000 and 3500 $$K$$
Answer :
1000, 1500 and 3000 $$K$$
Solution :
$$\because \,\,\Delta G = \Delta H - T \times \Delta S$$
For a spontaneous reaction, $$\Delta G$$ should be negative
$$\Delta H = - 238\,kJ,\,\Delta S = - 87\,J{K^{ - 1}}$$
Hence, reaction will be spontaneous when $$\Delta H > T \times \Delta S.$$ Therefore, at 1000, 1500 and 3000 $$K$$ the reaction would be spontaneous.