Enthalpy of fusion/Molar heat capacity question

[lbk]

I really need help on this question. I can't just do the M1C1DT = M2C2DT equation, because I don't know how the enthalpy of fusion fits in. The answer in the back of the book is 10.4 degrees celsius but I don't know how to get there. Thanks in advance for your help!

Suppose an ice cube weighing 36.0g at a temperature of -10.0 degrees celsius is placed in 360 g of water at a temperature of 20 degrees celsius. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings. The enthalpy of fusion of ice is (DHfus) 6.007 kJ/mol. The molar heat capacity (cp) of ice is 38 J K- mol- and cp of water is 75 J K- mol-.

[adrian]

2 moles of ice at -10°C and 20 moles of water at 20°C.
you have 3 steps for ice:
1. ice heating from -10° to 0°; DHi=38*10*2= ... calculate yourself
2. ice melting at 0°C ; DHm=2* 6007= ...
Now, you must find if the water is enough to melt all ice:
DHw=75*20*10= ...

if DHw>DHm+DHi, then all ice will melt, and you can calculate the temperature for total melting and after that the final temp.
if not, then means you'll have a mixture ice-water at 0°C.

Good luck!