For a reaction to be spontaneous, the change in Gibbs free energy ($\Delta G$) must be negative ($\Delta G < 0$). According to the Gibbs equation, $\Delta G = \Delta H - T\Delta S$. Therefore, for spontaneity: $\Delta H - T\Delta S < 0$, which implies $T\Delta S > \Delta H$ or $\Delta S > \frac{\Delta H}{T}$. Given: $\Delta H = 30\text{ kJ mol}^{-1} = 30000\text{ J mol}^{-1}$ $T = 450\text{ K}$ Substituting the given values: $\Delta S > \frac{30000\text{ J mol}^{-1}}{450\text{ K}}$ $\Delta S > 66.67\text{ J K}^{-1}\text{ mol}^{-1}$ Among the given options, $70$ is the only value strictly greater than $66.67$. Therefore, the value of $\Delta_r S$ must be $70\text{ J K}^{-1}\text{ mol}^{-1}$ for the reaction to be spontaneous.