The correct relation is:

The free energy change for a reversible reaction at equilibrium is

Identify the relation between the standard Gibbs free energy change $\Delta G^{\circ}$ and the equilibrium constant $K_c$ for a chemical reaction.

At $298 \ K$,for the reaction $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,the $K_p$ value is $0.98$. Predict whether the reaction is spontaneous or not.

The value of $\log _{10} K$ for a reaction $A \rightleftharpoons B$ is
(Given : $\Delta _{r} H_{298 K}^{\circ} = -54.07 \ kJ \ mol^{-1}$,$\Delta _{r} S_{298 K}^{\circ} = 10 \ J \ K^{-1} \ mol^{-1}$ and $R = 8.314 \ J \ K^{-1} \ mol^{-1}$; $2.303 \times 8.314 \times 298 = 5705$)

For a hypothetical reversible reaction $\frac{1}{2} A_{2(g)} + \frac{3}{2} B_{2(g)} \rightarrow AB_{3(g)}$; $\Delta H = -20 \, kJ$. If the standard entropies of $A_2, B_2$ and $AB_3$ are $60, 40$ and $50 \, J K^{-1} mol^{-1}$ respectively,at what temperature $(K)$ will the reaction be in equilibrium?