Thermodynamics and Thermochemistry 1 Question 67
70. Show that the reaction, $\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}{2}(g) \longrightarrow \mathrm{CO}{2}(g)$ at $300 \mathrm{~K}$, is spontaneous and exothermic, when the standard entropy change is $-0.094 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. The standard Gibbs’ free energies of formation for $\mathrm{CO}_{2}$ and $\mathrm{CO}$ are -394.4 and $-137.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively.
(2000, 3M)
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Solution:
- $\Delta_{r} G^{\circ}=\Delta_{f} G^{\circ}$ (products) $-\Delta_{f} G^{\circ}$ (reactants)
$$ =-394.4-(-137.2)=-257.2 \mathrm{~kJ}<0 $$
The above negative value of $\Delta G$ indicates that the process is spontaneous.
Also, $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$
$$ \begin{aligned} \Rightarrow \quad \Delta H^{\circ} & =\Delta G^{\circ}+T \Delta S^{\circ} \ & =-257.2+300(-0.094) \ & =-285.4 \mathrm{~kJ}<0 \end{aligned} $$
