Ammonium nitrate sometimes is used in cold packs because its enthalpy of solvation in water is +21 kJ/mol. What is the minimum amount of ammonium nitrate (80.05 g/mol) that is needed to cool a 1.0 L soft drink (d = 1.0 g/mL, specific heat 4.5 J g^-¹ °C^-¹) and its plastic bottle (heat capacity 50 J/K) from 30°C to 5°C.

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat that needs to be removed from the soft drink and its container:

q = mcdeltaT

q_soft drink = (1000 g)(4.5 J/g°C)(30-5) = 112,500 J
q_container = (100 g)(50 J/K)(30-5) = 47,500 J
q_total = 160,000 J

Next, we need to calculate the number of moles of ammonium nitrate needed to release this amount of heat:

q = nΔHsol
n = q/ΔHsol

n = (160,000 J)/(21,000 J/mol) = 7.62 mol

Finally, we can calculate the mass of ammonium nitrate needed:

mass = n x molar mass
mass = 7.62 mol x 80.05 g/mol = 609 g

However, we need to choose the minimum amount of ammonium nitrate needed, so we round up to the nearest multiple of 80 g/mol:

mass = 8 mol x 80.05 g/mol = 640 g

Therefore, the minimum amount of ammonium nitrate needed is 640 g, which corresponds to answer choice D.

Ammonium Nitrate Sometimes Is Used in Cold Packs Because Its