Most first aid \"cold packs \" are based on the endothemic dissolution of ammoni

Question

Most first aid "cold packs " are based on the endothemic dissolution of ammonium nitrate in water: NH_4NO_3 (s) rightarrow NH_4^+ (aq) + NO_3^- (aq) delta H^degree = 25.69 kJ A particular cold pack contains 55.0 g of NH_4NO_3 and 145.0 g of water. When the pack is squeezed, the NH_4NO_=3 dissolves in the water. If the pack and its contents are initially at 24.0 degree C. what is the lowest temperature that this bag could reach0 (Assume that the ammonium nitrate solution has a specific heat of 4.25 J g^-1K^-1, and that the heat capacity of the bag itself is small enough to be neglected.) Temperature = _________ degree C

Explanation / Answer

number of moles of NH4NO3 = mass of NH4NO3 / molar mass of NH4NO3
= 55.0 g/ 80 g/mol
=0.6875 mol

max heat absorbed = number of mol * H
= 0.6875 mol * 25.69 KJ/mol
= 17.662 KJ
= 17662 J

use:
Q = (ms*Cs + mw*Cw)*delta T
17662 = (55*4.25 + 145*4.184)*delta T
delta T = 21 oC

Tf = 24 - 21 = 3 oC

Answer: 3 oC

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