The value of ${\mathrm{\Delta }}_{\mathrm{r}}G-{\mathrm{\Delta }}_{\mathrm{r}}{G}^{\circ }$ of the reaction ${\mathrm{N}}_2(\mathrm{g},0.2\text{ bar })+2{\mathrm{O}}_2(\mathrm{g},0.2\text{ bar })⟶2{\mathrm{NO}}_2(\mathrm{g},0.2\text{ bar })$ at $300 \mathrm{K}$ is $\text{ (Given: }\log 0.2=-0.699)$

We have    ${\mathrm{\Delta }}_{\mathrm{r}}G={\mathrm{\Delta }}_{\mathrm{r}}{G}^{\circ }+RT\ln \frac{\left(p_{{\mathrm{NO}}_2}/p^{\circ }\right)}{\left(p_{{\mathrm{N}}_2}/p^{\circ }\right){\left(p_{{\mathrm{O}}_2}/p^{\circ }\right)}^2}$

Hence    $\begin{array}{r}{\mathrm{\Delta }}_{\mathrm{r}}G-{\mathrm{\Delta }}_{\mathrm{r}}{G}^{\circ }=RT\ln \frac{(0.2{)}^2}{\left(0.2\right)(0.2{)}^2}=-RT\ln \left(0.2\right)\\ =\left(2.303\right)\left(8.314 {\mathrm{JK}}^{-1 }{\mathrm{mol}}^{-1}\right)(300 \mathrm{kJ})\left(0.699\right)\\ =4015.2 \mathrm{J} {\mathrm{mol}}^{-1}\end{array}$