N2O4(g) ⇌ 2NO2(g)
If N2O4 is 50% dissociated, the mole fraction of both the substances is given by,
\(X_{N_2O_4}\) = \(\frac{1-0.5}{1+0.5}\)
\(X_{NO_2}\) = \(\frac{2\times0.5}{1+0.5}\)
\(P_{N_2O_4}\) = \(\frac{0.5}{0.5}\)x 1 atm
\(P_{NO_2}\) = \(\frac{1}{1.5}\) x 1 atm
The equilibrium constant Kp is given by,
Kp = \(\frac{(P_{NO_2})^2}{P_{N_2O_4}}\)
= \(\frac{\big(\frac{1}{1.5}\big)^2}{\frac{0.5}{1.5}}\)
= 1.33
\(\therefore\) ∆fGΘ = −RT In Kp
= −2.303 RT logKp
= −2.303 × (8.314 J K−1 mol−1) × (333K) log 1.33
= −2.303 × 8.14 JK−1 mol−1 × 333K × 0.1239
= −763.8 kJ mol−1