Using the data provided, find the value of the equilibrium constant for the following reaction at 298 K and 1 atm pressure.

$\text{NO}(g) + \frac{1}{2}\text{O}_2(g) \rightleftharpoons \text{NO}_2(g)$

$\Delta_f H^\circ (\text{NO}(g)) = 90.4$ kJ mol$^{-1}$

$\Delta_f H^\circ (\text{NO}_2(g)) = 32.48$ kJ mol$^{-1}$

$\Delta S^\circ$ at 298 K = $-70.8$ J K$^{-1}$ mol$^{-1}$

[Given: antilog$(0.50) = 3.162$]