Glauber's salt, sodium sulfate decahydrate \(\left(\mathrm{Na}_{2}
\mathrm{SO}_{4} .\right.\) \(\left.10 \mathrm{H}_{2} \mathrm{O}\right),\)
undergoes a phase transition (i.e., melting or freezing) at a convenient
temperature of about \(32^{\circ} \mathrm{C}\) :
\(\begin{aligned}{\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2}
\mathrm{O}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10
\mathrm{H}_{2} \mathrm{O}(l)}{\Delta H^{\circ}} &=74.4 \mathrm{~kJ} /
\mathrm{mol} \end{aligned}\) As a result, this compound is used to regulate the
temperature in homes. It is placed in plastic bags in the ceiling of a room.
During the day, the endothermic melting process absorbs heat from the
surroundings, cooling the room. At night, it gives off heat as it freezes.
Calculate the mass of Glauber's salt in kilograms needed to lower the
temperature of air in a room by \(8.2^{\circ} \mathrm{C}\). The mass of air in
the room is \(605.4 \mathrm{~kg} ;\) the specific heat of air is \(1.2
\mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).