Instant cold packs used to treat athletic injuries contain solid N H 4 N O 3 and
ID: 801253 • Letter: I
Question
Instant cold packs used to treat athletic injuries contain solid NH4NO3 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
NH4NO3(s)+H2O(l)?NH4NO3(aq) ?H = +25.7 kJ.
What is the final temperature in a squeezed cold pack that contains 41.0g of NH4NO3 dissolved in 125 mL of water? Assume a specific heat of 4.18J/(g??C) for the solution, an initial temperature of 25.0?C, and no heat transfer between the cold pack and the environment
Explanation / Answer
Let T be the final temperature
Moles of NH4NO3 = mass/molar mass of NH4NO3 = 41.0/80.04 = 0.51224 mol
Heat absorbed by reaction = moles x heat of solution of NH4NO3
= 0.51224 x 25.7 = 13.165 kJ = 13165 J
Mass of water = volume x density = 125 x 1.00 = 125 g
Mass of solution = mass of water + mass of NH4NO3
= 125 + 41.0 = 166 g
Heat released by solution = mass x specific heat x temperature change of solution
= 166 x 4.18 x (25.0 - T)
Heat released = heat absorbed
166 x 4.18 x (25.0 - T) = 13165
693.88T = 4182
Final temperature T = 6.03 deg C = 6.0 deg C