Thermodynamics and Thermochemistry - Result Question 24
####24. The following reaction is performed at $298 K$
$$ 2 NO(g)+O _2(g) \rightleftharpoons 2 NO _2(g) $$
The standard free energy of formation of $NO(g)$ is $86.6 kJ / mol$ at $298 K$. What is the standard free energy of formation of $NO _2(g)$ at $298 K$ ? $\left(K _p=1.6 \times 10^{12}\right)$ (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,
$$ 2 NO(g)+O _2(g) \rightleftharpoons 2 NO _2(g) $$
Given, $\quad \Delta G _f^{\circ}(NO)=86.6 kJ / mol$
$$ \begin{aligned} \Delta G _f^{\circ}\left(NO _2\right) & =? \ K _p & =1.6 \times 10^{12} \end{aligned} $$
Now, we have,
$$ \begin{aligned} \Delta G _f^{\circ} & =2 \Delta G _{f _{\left(NO _2\right)}^{\circ}}^{\circ}-\left[2 \Delta G _{f _{(NO)}^{\circ}}^{\circ}+\Delta G _{f _{\left(O _2\right)}}^{\circ}\right] \ & =-R T \ln K _p=2 \Delta G _{f _{\left(NO _2\right)}}^{\circ}-[2 \times 86,600+0] \ \Delta G _{f _{\left(NO _2\right)}^{\circ}}^{\circ} & =\frac{1}{2}\left[2 \times 86600-R \times 298 \ln \left(1.6 \times 10^{12}\right)\right] \ \Delta G _{f _{\left(NO _2\right)}^{\circ}}^{\circ} & =0.5\left[2 \times 86,600-R \times(298) \ln \left(1.6 \times 10^{12}\right)\right] \end{aligned} $$
