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Equilibrium constants are given (in atm) for the following reactions at \( 0^{\circ} \mathrm{C} \) : \( \begin{array}{ll}\mathrm{SrCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{SrCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & \mathrm{K}_{\mathrm{p}}=5 \times 10^{-12} \\ \mathrm{Na}_{2} \mathrm{HPO}_{4} \cdot 12 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{HPO}+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & \mathrm{K}_{\mathrm{p}}=2.43 \times 10^{-13} \\ \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{~s})+10 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & \mathrm{K}_{\mathrm{p}}=1.024 \times 10^{-27} \\ \text { The vapor pressure of water at } 0^{\circ} \mathrm{C} \text { is } 4.56 \text { torr. } & \end{array} \)
\( \mathrm{P} \)
At what relative humidities will \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) be deliquescent (i.e. absorb moisture) when exposed to the air at \( 0^{\circ} \mathrm{C} \) ?
(A) above \( 33.33 \% \)
(B) below \( 33.33 \% \)
(C) above \( 66.66 \% \)
(D) below \( 66.66 \% \)
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