The standard free energy change (Δ G °) for 50 % dissociation of N...

${N}_{2}{O}_{4}\left(g\right) ⇌ 2{NO}_{2}\left(g\right)$

$1 - \alpha2\alpha$

${K}_{p} = \dfrac{4{\alpha}^{2}p}{1 - {\alpha}^{2}} = \dfrac{4 \times {\left(0 . 5\right)}^{2} \times 1}{1 - {\left(0 . 5\right)}^{2}} = \dfrac{1}{0 . 75}$

${K}_{p} = \dfrac{4}{3}$

${\Delta G}^{o} = - 2 . 303RTlog{K}_{p}$

$= - 2 . 3 \times 8 . 31 \times 300\left[log\dfrac{4}{3}\right] = - 2 . 3 \times 8 . 31 \times 300 \times 0 . 1239$

$= - 710J$