Mass of solid water and gaseous water?

[tacloban87]

Homework Statement

a 1kg of Water at 25 degrees celsius is in a container. A solid block of 1kg Carbon Dioxide at its sublimation temp of -80 degrees celcious is placed into the container, with the lid then closed.
Final temperature of entire system = 0 degrees celcius
Final phase of the Carbon Dioxide is gas

*What is the final mass of the liquid H20, solid H20, and gaseous H20?

Homework Equations

Heat of Vap of Water = 2000 kj/kg
Heat of Melt of Water = 300 kj/kg
Csp of Water = 4 kj/kg
Csp of CO2 gas = 1 kj/kg
Heat of Sub of CO2 = 200 kj/kg

[delta]Ethermal = mc[delta]T
[delta]Ebond = ([delta]m)([delta]Heat of...)

The Attempt at a Solution

From what I understand, the H20's conditions change as follows:
Temp Initial = 25 degrees celcius
Temp Final = 0 degrees celcious
Phase Initial = Liquid
Phase Final = Solid

Thus, the H20 will have its thermal energy increasing and its bond energy increasing as well.

As for the CO2's conditions:
Temp Initial = -80 degrees celcius
Temp Final = 0 degrees celcius
Phase Intial = Solid
Phase Final = Gas

Since it is at it's sublimation temperature, it will skip over its intermediate state as a liquid and its thermal energy is increasing and its bond energy decreasing.

So, to find the final mass of the liquid water, do I just use:
[delta]Ethermal = Q
mc[delta]t = Q
(1kg)(4kj/kg K)(0celcius-25celcius) = Q
-100 kj = Q

[delta]m = Q/[delta]Heat of...
[delta]m = -100/300 kg/kg <-- do I use Heat of melting for the liquid phase?

What should be the next step I take in finding the mass of solid water and gaseous water?

 

[Andrew Mason]

Assume that a portion of the H₂O is in the form of liquid. Work out an algebraic formula for the heat flow in terms of the quantity of liquid and solid H₂O. You know that they sum to 1 kg. Use the specific heat of liquid water for the entire mass of H₂O but use the specific heat of fusion only for the portion that ends up as ice.

AM