Answer:
Qtotal = 90.004 kJ
Explanation:
To start resolving the problem we need to first convert the kJ/mol units from the thermodynamic values to J/g, so that we can work with the units of the heat capacity values. We know that the molar mass of water is 18.015 g/mol, so with this we do the respective conversion:
ΔH°fus of H2O = (6.02 kJ/mol) (1 mol/18.015g) (1000J/kJ) = 334.165 J/g
ΔH°vap of H2O = (40.7 kJ/mol) (1mol/18.015g) (1000J/kJ) = 2259.228 J/g
Now we need to find out the heat energy required to rise the temperature (specific heat capacity) and the energy required for each change of phase (specific latent heat), and add everything up. For this we will require the specific heat capacity and latent heat equations:
Q = mCΔT ; where m = mass, C = Hear capacity, ΔT = change of temperature
Q = mL ; where m = mass, L = specific latent heat
<u />
<u>First change of phase (solid to liquid - fusion)</u>
Q1 = (25g) (2.09 J/g°C) (0°C - (-129°C) = 6740.25 J
Q2 = (25g) (334.165 J/g) = 8354.125 J
<u>Second change of phase (liquid to gas - vaporization)</u>
Q3 = (25g) (4.18 J/g°C) (100°C - 0°C = 10450 J
Q4 = (25g) (2259.228 J/g) = 56480.7 J
<u>Rise of temperature of the gaseous water</u>
Q5 = (25g) (1.97 J/g°C) (262°C - 100°C = 7978.5 J
Finally we add everything up:
Qtotal = Q1 + Q2 + Q3 + Q4 + Q5 = 6740.25 J + 8354.125 J + 10450 J + 56480.7 J + 7978.5 J = 90003.575 J = 90.004 kJ
