can someone please help me with this chem problem?

Question

Given the data below on water, calculate the energy (in kJ) that must be removed to convert 75.0 g of water from a gas at 125. degrees C to a solid at 0.0 degrees C.

heat of vaporization: 40.7 kJ/mol
heat of fusion: 6.02 kJ/mol
specific heat capacities (in J g-1 degrees C-1)
solid: 2.03
liquid: 4.2
gas 2.0

Answer 1

To cool the 75 g of gas H2O from 125 oC to 100 oC you must remove:

Q1 = m*c*ΔT = 75*2*25 = 7500 J = 7.5 kJ of heat.

To convert 75 g of gas H2O 100 oC to 75 g of liquid H2O 100 oC, first find the moles of H2O:

n = m/Mm = 75/18 = 12.5/3 mol where Mm = 18 the molar mass of H2O.

Then find the heat quantity:

Q2 = n*C1 = (12.5/3)*40.7 = 169.583 kJ

To cool the 75 g of liquid H2O from 100 oC to 0 oC you must remove:

Q3 = m*c*ΔT = 75*4.2*100 = 31500 J = 31.5 kJ

To convert the liquid H2O 0 oC to solid H2O 0 oC you must remove:

Q4 = n*C2 = (12.5/3)*6.02 = 25.083 kJ

Total: Q = Q1 + Q2 + Q3 + Q4,

Q = 7.5 + 169.583 + 31.5 + 25.083 = 233.67 kJ of heat.