Chapter 6, Problem 6.111QP

Glauber’s salt, sodium sulfate decahydrate (Na₂SO₄ · 10H₂O), undergoes a phase transition (that is, melting or freezing) at a convenient temperature of about 32°C:

$\begin{array}{l}{\text{Na}}_2{\text{SO}}_4\cdot 10{\text{H}}_2\text{O}(s)\stackrel{}{\to }{\text{NaSO}}_4\cdot 10{\text{H}}_2\text{O}(l)\hfill \\ \Delta H^{\text{o}}=74.4\text{kJ/mol}\hfill \end{array}$

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°C at 1.0 atm. The dimensions of the room are 2.80 m × 10.6 m × 17.2 m, the specific heat of air is 1.2 J/g · °C, and the molar mass of air may be taken as 29.0 g/mol.