$G_{N O_{2}(g)}^{\circ}=x\, J / m o l$

$T=298, K_{p}=1.6 \times 10^{12}$

$\Delta G^{\circ}=-R T \ln K_{p}$

Given equation,

$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$

$2 \Delta G_{N O_{2}}^{\circ}-2 \Delta G_{N O}^{\circ}=-R(298) \ln \left(1.6 \times 10^{12}\right)$

$2 \Delta G_{N O_{2}}^{\circ}-2 \times 86600=-R(298) \ln \left(1.6 \times 10^{12}\right)$

$2 \Delta G_{N O_{2}}^{\circ}=2 \times 86600-R(298) \ln \left(1.6 \times 10^{12}\right)$

$\Delta G^{\circ}_{N O_{2}}=\frac{1}{2}\left[2 \times 86600-R(298) \ln \left(1.6 \times 10^{12}\right)\right]$

$=0.5\left[2 \times 86600-R(298) \ln \left(1.6 \times 10^{12}\right)\right]$