Chapter 9, Problem 9.85PAE

9.85 The figure below shows a "self-cooling" beverage can.

The can is equipped with an outer jacket containing sodium carbonate (Na₂CO₃), which dissolves in water rapidly and endothermically:

   ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\left(\text{s}\right)\to {\text{2Na}}^{+}\text{(aq)}+{\text{CO}}_{\text{3}}{}^{\text{2}-}\text{(aq)}$

   $\Delta \text{H}°$= 67.7 kJ

The user adds water to the outer jacket, and the heat absorbed in the chemical reaction chills the drink. The can contains 200 g of drink, the jacket contains 55 g of Na₂CO₃, and 100 g of water is to be added. If the initial temperatures of the can and the water are both 32°C on a summer day, what is the coldest temperature that the drink

can reach? The can itself has a heat capacity of 40 J/C Assume that the Na₂CO₃ solution and the drink both have the same heat capacity as pure water, 4.184 J g-l C-l, (HINT: Treat this like a calorimetry problem.)