The equilibrium constant, $K_{\mathrm{p}},$ for $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftarrows$ $2 \mathrm{NO}_{2}(\mathrm{g})$ is 0.14 at $25^{\circ} \mathrm{C} .$ Calculate $\Delta_{r} G^{\circ}$ for the conversion of $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})$ to $\mathrm{NO}_{2}(\mathrm{g})$ from this constant, and compare this value with that determined from the $\Delta_{f} G^{\circ}$ values in Appendix L.