Consider the following reaction at 298 K. . for the reaction is __________ kJ.

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Solution

Q.
Consider the following reaction at 298 K. $\frac{3}{2} O_{2 (g)} ⇌ O_{3 (g)}$ . $K_{p} = 2.47 \times 10^{- 29}, Δ_{r} G^{Θ}$ for the reaction is __________ kJ.

(Given R $= 8.314$ ${JK}^{- 1}$ ${mol}^{- 1}$ ) [2024]

Ans.
(163)

$\log (K) = \log_{10} (2.47 \times 10^{- 29}) \approx \log_{10} (25 \times 10^{- 30})$

$= \log_{10} (5^{2} \times 10^{- 30}) = 2 \log_{10} 5 - 30$ $\log$ $10$

$= 2 \times 0.7 - 30 \times 1 = - 28.6$

$Δ G ° = - 2.303$ $RT$ $\log_{10} K$

$Δ G ° = - 2.303 \times 8.314 \frac{J}{K mol} \times 298 K \times \log_{10} (2.47 \times 10^{- 29})$

$= - 2.303 \times 8.314 \times 298 \times (- 28.6) J m o l^{- 1} = 163.2 k J m o l^{- 1}$

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