Chapter 9, Problem 9.96PAE

9.96 Most first aid "cold packs" are based on the endothermic dissolution of ammonium nitrate in water:

   ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}\left(\text{s}\right)\to {\text{NH}}_{\text{4}}{}^{+}\left(\text{aq}\right)+{\text{NO}}_{\text{3}}{}^{-}\left(\text{aq}\right)$

   $\Delta \text{H}°$= 25.69 kJ

A particular cold pack contains 50.0 g of NH₄NO₃ and 125.0 g of water. When the pack is squeezed, the NH₄NO₃dissolves in the water. If the pack and its contents are initially at 24.0°C, what is the lowest temperature that this bag could reach? (Assume that the ammonium nitrate solution has a specific heat of 4.25J g-l K-l, and that the heat capacity of the bag itself is small enough to be neglected.)