Thermodynamics and Thermochemistry 1 Question 21
24. The following reaction is performed at $298 \mathrm{~K}$
$$ 2 \mathrm{NO}(g)+\mathrm{O}{2}(g) \rightleftharpoons 2 \mathrm{NO}{2}(g) $$
The standard free energy of formation of $\mathrm{NO}(g)$ is $86.6 \mathrm{~kJ} / \mathrm{mol}$ at $298 \mathrm{~K}$. What is the standard free energy of formation of $\mathrm{NO}{2}(g)$ at $298 \mathrm{~K}$ ? $\left(K{p}=1.6 \times 10^{12}\right)$ (2015 Main)
(a) $R(298) \ln \left(1.6 \times 10^{12}\right)-86600$
(b) $86600+R(298) \ln \left(1.6 \times 10^{12}\right)$
(c) $86600-\frac{\ln \left(1.6 \times 10^{12}\right)}{R(298)}$
(d) $0.5\left[2 \times 86600-R(298) \ln \left(1.6 \times 10^{12}\right)\right]$
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Solution:
- For the given reaction,
$$ 2 \mathrm{NO}(g)+\mathrm{O}{2}(g) \rightleftharpoons 2 \mathrm{NO}{2}(g) $$
Given, $\quad \Delta G_{f}^{\circ}(\mathrm{NO})=86.6 \mathrm{~kJ} / \mathrm{mol}$
$$ \begin{aligned} \Delta G_{f}^{\circ}\left(\mathrm{NO}{2}\right) & =? \ K{p} & =1.6 \times 10^{12} \end{aligned} $$
Now, we have,
$$ \begin{aligned} \Delta G_{f}^{\circ} & =2 \Delta G_{f_{\left(\mathrm{NO}{2}\right)}^{\circ}}^{\circ}-\left[2 \Delta G{f_{(\mathrm{NO})}^{\circ}}^{\circ}+\Delta G_{f_{\left(\mathrm{O}{2}\right)}}^{\circ}\right] \ & =-R T \ln K{p}=2 \Delta G_{f_{\left(\mathrm{NO}{2}\right)}}^{\circ}-[2 \times 86,600+0] \ \Delta G{f_{\left(\mathrm{NO}{2}\right)}^{\circ}}^{\circ} & =\frac{1}{2}\left[2 \times 86600-R \times 298 \ln \left(1.6 \times 10^{12}\right)\right] \ \Delta G{f_{\left(\mathrm{NO}_{2}\right)}^{\circ}}^{\circ} & =0.5\left[2 \times 86,600-R \times(298) \ln \left(1.6 \times 10^{12}\right)\right] \end{aligned} $$
