For a reaction $\Delta H^{\circ }=-40.0\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ and $\Delta S^{\circ }=-100\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$ (temperature independent). Taking $R=8.314\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$, the equilibrium constant at $500\mathrm{K}$ is nearest to

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