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Chemistry Question on Gibbs Free Energy

Calculate ΔGo\Delta G^{o} for conversion of oxygen? To ozone 3/2O2(g)→O3(g)3 / 2 O _{2}(g) \rightarrow O _{3}(g) at 298 K298 \,K, if KpK_{p} for this conversion is 2.47×10−292.47 \times 10^{-29} :

A

163 kJ mol−1163\, kJ \,mol ^{-1}

B

2.4×102 kJ mol−12.4 \times 10^{2} \,k J\, mol ^{-1}

C

1.63 kJ mol−11.63\,kJ\, mol ^{-1}

D

2.38×106 kJ mol−12.38 \times 10^{6}\, kJ \,mol ^{-1}

Answer

163 kJ mol−1163\, kJ \,mol ^{-1}

Explanation

Solution

Use the following formula to find ΔG∘\Delta G^{\circ}. ΔG∘=−2.303RTlog⁡Kp\Delta G^{\circ}=-2.303 R T \log K_{p} Given, Kp=2.47×10−29K_{p}=2.47 \times 10^{-29} ∴ΔG∘=2.303×8.314×298×log⁡2.47×10−29\therefore \Delta G^{\circ}=2.303 \times 8.314 \times 298 \times \log 2.47 \times 10^{-29} =163000 J mol−1=163000\, J\,mol ^{-1} =163 kJ mol−1=163\, kJ\,mol ^{-1}