Instant cold packs used to treat athletic injuries contain solid NH 4 NO 3 and a
ID: 897034 • 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 43.5 g of NH4NO3 dissolved in 125 mL of water? Assume a specific heat of 4.18J/(gC) for the solution, an initial temperature of 30.0 C, and no heat transfer between the cold pack and the environment.
Explanation / Answer
NH4NO3(s)+H2O(l)NH4NO3(aq) H= +25.7 kJ.
Molar mass of NH4NO3 = 80.0434 g/mol
No of moles of NH4NO3 = 43.5/80.0434 = 0.54 mole.
disollution of 1 mole NH4NO3 gives 25.7 kj
so that amount of heat absorbed = 25.7*0.54 = 13.878 kj
q = m*s*DT = 13.878 kj
m = mass of solution = 125+43.5 = 168.5 grams
s = specificheat of solution= 4.18 J/(gC)
DT = (Ti-Tf)
Ti = 30 C
Tf = ?
13.878*10^3 = 168.5*4.18*(30-Tf)
Tf = 10.296 c