Finding mass from an enthalpy change.

Question

Dissolving an unknown quantity of NH₄No₃ (molar mass = 80.05 g/mol) to 505g of solution, for which we can assume the same specific heat capacity as water, in a coffee cup calorimeter causes the temperature of the solution to decrease by 13.3^o C (ΔT_H2O = -13.3^o C). The enthalpy change that accompanies the dissolution process, ΔH_soln = +28. kJ/mol. What was the mass (in g) of the ammonium nitrate dissolved?

Answer 1

So, the equation we'll use for this problem is

q = mC∆T

q = heat = ?

m = mass = 505 g

C = specific heat = 4.184 J/gº

∆T = change in temperature = -13.3º

Solve for q:

q = (505 g)(4.184 J/gº)(13º) = 27,468 J = 27.468 kJ (note there should be a - sign, but for the calculations, it doesn't matter since we can't end up with negative mass)

Since we know the ∆H_soln we can now calculate moles of NH₄NO₃ and then grams.

27.468 kJ x 1 mol NH₄NO₃ / 28 kJ = 0.981 mol NH₄NO₃

grams NH₄NO₃ = 0.981 mol x 80.05 g/mol = 78.5 g NH₄NO₃