2O₃(g) $?$ 3O₂(g)

At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is (-)________. J mol^?1. (Nearest integer)

[Given: In 1.35 = 0.3 and R=8.3 J K^-1 mol^-1]

2O₃(g) -> 3O₂

t = 0      a moles               0

-0.5a mole     +0.75a mole

At Eq.    0.5a mole         0.75a mole

Total moles at eq = 0.5a + 0.75 a = 1.25a

$P_{O_3}=x_{O_3}*P_T=\frac{0.5a}{1.25a}*1=\frac{2}{5}atm$

$P_{O_2}=x_{O_2}*p_T=\frac{0.75a}{1.25a}*1=\frac{3}{5}atm$

$K_p=\frac{{\left(P_{O_2}\right)}_{eq}^3}{{\left(P_{O_3}\right)}_{eq}^3}=\frac{{\left(\frac{3}{5}\right)}^3}{{\left(2/5\right)}^2}=1.35atm$

$\Delta G^{°}=-RT\mathcal{l}nKP$

$\begin{array}{l}=-8.3*300\mathcal{l}n1.35\\ =-747J/mole\end{array}$