Instant cold packs used to treat athletic injuries contain solid NH_4 NO_3 and a
ID: 976951 • Letter: I
Question
Instant cold packs used to treat athletic injuries contain solid NH_4 NO_3 and a pouch of water. When the pack is squeezed, the pouch breaks and the solid dissolves, lowering the temperature because of the endothermic reaction NH_4 NO_3 (s) + H_2 O(l) rightarrow NH_4 NO_3 (aq) Delta H = +25.7 kJ. What is the final temperature in a squeezed cold pack that contains 43.0 g of NH_4 NO_3 dissolved in 125 mL of water? Assume a specific heat of 4.18J/(g degree C) for the solution an initial temperature of 27.5 degree C, and no heat transfer between the cold pack and the environment.Explanation / Answer
Moles of Nh4NO3 dissolved = mass / Molar mass of Nh4NO3 = 43 /80.043 = 0.5372
heat absorbed = dH x moles = 25.7 KJ x 0.5372 = 13.8063 K = 13806.3 J
This heat is absorbed from solution ,
solution mass = 125 g + 43 g = 168 g ( water has density 1g/ml, hence 125 ml mass is 125 g)
heat lost by solution = specific heat of solution x mass of solution x temp change
13806.3 = 4.18 x 168 x ( 27.5-T)
T = 7.84 C is final temperature of solution