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Fundamentals of thermodynamics

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Question

Calculate $Δ, G^{\circ}$ for the conversion of oxygen to ozone, $\frac{3}{2} O_{2} (g) ⟶ O_{\hat{3}} (g)$ at $298 K$ if $K_{p}$ for the conversion is $2.47 \times 10^{- 29}$

Moderate

Solution

$\begin{array}{l} T = 298 K, K_{n} = 2.47 \times 10^{- 29} \\ R = 8.314 {JK}^{-} {mol}^{- 29}; Δ_{i} G^{\circ} = ? \end{array}$
We know, $Δ, G^{\circ} = - 2.303 RTlog K_{p}$
Substituting the values, we get,
$\begin{array}{l} Δ_{r} G^{\circ} = - 2 .303 \times 8 .314 {JK}^{-} {mol}^{-} \\ \times 298 Klog 2 .47 \times 10^{- 29} \\ = - 5705 .8 [\log 2 .47 - 29 \log 10] \\ = - 5705 .8 [0 .3927 - 29] \\ = - 5705 .8 \times - 28 .6 = 163185 J \\ = 163.185 kJ \end{array}$

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