The following reaction is performed at 298 K.2NO(g)+O2(g)⇌2NO2(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 NO2(g) at 298K? (Given: Kp0=1.6×1012)

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The following reaction is performed at 298 K.

$2 NO (g) + O_{2} (g) ⇌ 2 {NO}_{2} (g)$

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 ${NO}_{2} (g) at 298 K ?$ (Given: $K_{p}^{0} = 1.6 \times 10^{12}$ )

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$86600 J {mol}^{- 1} + R (298 K) \ln (1.6 \times 10^{12})$

$R (298 K) \ln (1.6 \times 10^{12}) - 86600 J {mol}^{- 1}$

$86600 J {mol}^{- 1} - \frac{\ln (1.6 \times 10^{12})}{R (298 K)}$

$0.5 [2 \times 86600 J {mol}^{- 1} - R (298 K) \ln (1.6 \times 10^{12})]$

answer is D.

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Detailed Solution

The free energy change of the given reaction is $Δ_{r} G^{o} = - R T \ln K_{p}^{o} = - R (298 K) \ln (1.6 \times 10^{12})$

also, $Δ_{r} G^{o} = 2 Δ_{f} G^{\circ} ({NO}_{2}, g) - 2 Δ_{f} G^{o} (NO, g)$

hence

$Δ_{f} G^{o} ({NO}_{2}, g) = \frac{1}{2} [Δ_{r} G^{o} + 2 Δ_{f} G^{o} (NO, g) = \frac{1}{2} [- R (298 K) \ln (1.6 \times 10^{12}) + 2 \times 86600 J {mol}^{- 1}]$