Kj of heat needed to convert a liquid to gas

Question

What amount of heat (in kJ) is required to convert 10.1 g of an unknown liquid (MM = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C? (specific heat capacity of liquid = 1.58 J/g･°C; specific heat capacity of gas = 0.932 J/g･°C; ∆Hvap = 22.5 kJ/mol; normal boiling point, Tb = 57.3°C)

Answer 1

(1). heat needed to change temp of liquid from 19.2º to the boiling point of 57.3º

q = mC∆T = (10.1 g)(1.58 J/gº)(38.1º) = 608 J = 0.608 kJ

(2). heat needed to convert the liquid at its boiling point to a gas

q = m∆Hvap and since ∆Hvap is given in kJ/mol, we'll find moles first.

mols = 10.1 g x 1 mol/83.21 g = 0.121 mols

q = (0.121 mols)(22.5 kJ/mol) = 2.72 kJ

(3). heat needed to raise temperature of the gas from 57.3º to 93.5º

q = mC∆T = (10.1 g)(0.932 J/gº)(36.2º) = 341 J = 0.341 kJ

Total energy = 0.608 kJ + 2.72 kJ + 0.341 kJ = 3.70 kJ

Answer 2

4 Steps

1. calculate specific heat to heat the liquid using the values given. q=mc(delta T)
2. (10.1)(1.58)(38.1) --> this answer will be in J so convert to KJ
3. calculate delta h using the number of moles
4. (.121)(22.5) --> this answer will be in KJ
5. same as step 1 but with slightly different values
6. (10.1)(.932)(36.2) --> this will be in J so convert to KJ
7. add all three up together to find the total heat