Calculate Mass Needed to Freeze 2 Mol Water at 20°C

[Qube]

Homework Statement

The chlorofluorocarbon CCl2F2 was once used as a refrigerant. What mass of this substance must
evaporate to freeze 2 mol water initially at 20°C? (ΔHvap for CCl2F2 is 289 J/g; ΔHfus for solid ice is 6.02 kJ/mol; specific heat capacity for liquid water is 4.184 J/g•°C)

Homework Equations

Heat of fusion is the energy needed to transform solid water into liquid water.

Hess's Law.

The Attempt at a Solution

1) Liquid water to liquid water. 20 degrees C --> 0 degrees C. The heat needed for this transformation is 4.184 J/(g*C) * (36 grams of water) * 20 degrees C. Units cancel and leave us with 3012 joules of energy.

2) Liquid water to solid water. 0 degrees C --> 0 degrees C. The heat needed for this is 6.02 kJ/mol * 2 moles of water = 12.04 kJ = 12040 joules of energy.

Summing the energies, we now have a total energy is 15052 joules.

15052 joules = H(vap of CCl2F2) * grams of CCl2F2 needed

= 289 J/g * x grams

15052 / 289 = 52.08 grams needed.

Questions:

1) I'm fairly certain my work is correct. I'd appreciate a second opinion though.

2) Why is there no change in temperature as liquid water changes state and forms solid water? Why are there horizontal lines on the phase change diagram in which temperature remains constant as substances change state? Does this have to do with the fact that temperature is average kinetic energy while heat is total kinetic energy?

 

[nate808]

1) Your work looks correct to me. I would suggest double checking your calculations to ensure accuracy.

2) There is no change in temperature during a phase change because the energy being added or removed is being used to break or form intermolecular bonds, rather than increase or decrease the temperature. The horizontal lines on the phase change diagram represent the energy being used for the phase change, while the diagonal lines represent the change in temperature. This is because during a phase change, the average kinetic energy of the particles remains the same, but the arrangement of the particles changes.