Calculate the amount of salt in a commercial cold-pack containing ammonium nitrate (ΔHsol = + 25.7 kJ/mol) if the final temperature of the cold-pack is 0ºC.

Question

Calculate the amount of salt in a commercial cold-pack containing ammonium nitrate (ΔHsol = + 25.7 kJ/mol) if the final temperature of the cold-pack is 0ºC. Assume that the initial temperature of water is 25ºC, mass of solution is 25 g and the specific heat of the solution is 4.184 J/g.K.

a. 8.1 g

b. 7.5 g

c. 7.8 g

d. 0.79 g

Answer 1

q = mC∆T

q = heat = ?

m = mass = 25 g

C = specific heat = 4.184 J/gº

∆T = change in temperature = 25º (it went from 25º to 0º)

q = (25 g)(4.184 J/gº)(25º)

q = 2615 J = 2.62 kJ

We can find the moles of NH₄NO₃ from the ∆Hsoln as follows:

2.62 kJ x 1 mole/25.7 kJ = 0.102 moles NH₄NO₃ must have been present

Converting this to grams, we have... 0.102 mole NH₄NO₃ x 80.1 g/mol = 8.17 g NH₄NO₃