General Chemistry Help - Heat capacity help?

Question

Q: What is the final temperature when 11.5kj of energy is added to 10.0g of ice at 0 degrees C.
specific heat of liquid water: 4.18 j/(C g)
specific heat of steam: 2.10
change of heat of fusion of water=6.01 kJ/mol
change of heat of vaporization= 40.7 kj/mol
Please help me figure out what to use and how to setup
i've done it three ways and i think its so wrong
Thanks

Answer 1

Step 1: At 0 C, ice melts. Determine the amount of heat used to melt the ice.
change of heat of fusion of water=6.01 kJ/mol
10g of ice / 18g/mol for H2O = .5556 mol ice.

6.01 kJ/mol * .5556 mol ice = 3.339 Kj to melt 10g ice.

8.161 KJ left.

Step 2. Determine how much heat is used to heat water from 0C to 100C (boiling point)
10 g * 4.18 j/(C g) * 100 C = 4180 J = 4.180kJ

8.161 - 4.180 = 3.981 kJ left.

Step 3. Determine how much ice can be melted with 3.981 kJ of heat.
40.7 kj/mol for heat of vaporizaton
40.7 kJ/mol * .5556 mol water = 22.6 kJ - not enough heat to boil all the water.

3.981 kJ / 40.7 kJ/mol = 0.0978 mol water boiled * 18 g/mol = 1.76 g boiled.

Answer:
1.76 g of steam at 100C
8.34 g of water at 100C