10. Most first aid cold packs are based on the endothermic dissolution of ammoni
ID: 871738 • Letter: 1
Question
10. Most first aid cold packs are based on the endothermic dissolution of ammonium nitrate in water. A particular cold pack contains 50.0 g of NH4NO3 and 125.0 g of water. When the pack is squeezed. all of the NH4NO3 dissolves in the water. If the pack and its contents are initially at 24.0C, what is the lowest temperature that this bag could reach? (Assume that the ammonium nitrate solution has a specific heat of 4.20 J g^-1 K^-1, and that the heat capacity of the bag itself is small enough to be neglected.)Explanation / Answer
According to the equation , 1 mole of NH4NO3 requires 25.69 kJ of heat
MOlar mass of NH4NO3 is = 14+(4x1) + 14 + (3x16) = 80 g/mol
So 80 g of NH4NO3 requires 25.69 kJ of heat
50 g of NH4NO3 requires Z kJ of heat
Z = ( 25.69 / 80 ) x 50
= 16.056 kJ of heat
= 16056 J
This amount of heat must be taken from solution
heat = mcdt
where m = mass of bag = 125.0+ 50.0 = 175.0 g
c = specific heat capacity of solution = 4.20 J/g-K
dt = change in temperature = initial - final
= 24.0 - t
Plug the values we get 16056 = 175.0 x 4.20 x (24.0 -t )
24.0 -t = 21.845
t = 2.17 oC
Therefore the lowest temperature attained by bag is 2.17 oC
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