Ice added to Water (heats of rxn)

[aqwsde]

Homework Statement

If 24g of ice at -5C is added to a isolated dewar containing 50 mL of water at 10C. What would the temperature of the system be at equilibrium if the heat capacity can be ignored and the system is completely isolated.

Homework Equations

sp ht H2O (l) - 4.18 J/(gC)
sp ht H2O(s) = 2.01 J/(gC)

dHfus = 6.01 kJ/mol
Density H2O = 1g/ml

The Attempt at a Solution

I wasn't sure if the water would start to freeze or the ice would melt or if that is necessary to know. I approached the problem with the assumption that the ice melts and also that the transfer of heat from water to ice during melting is equal and opposite the heat transfer out of the surrounding and thus the terms cancel (I don't know if I can make this assumption). With that in mind

qrxn = -qsurr

qrxn = 24 *2.01 *(0 - (-5)) + 24*4.18*(Tf-0)

-qsurr = -50*4.18*(Tf-10)

Solving for Tf = 5.98C

My main question is if my assumptions are valid and also how would I know without it being said if the ice if going to melt of the water is going to freeze, or does it make a difference?

 

[mgb_phys]

Quick check is how much energy is available before the water gets down to 0C (mcT)
If this is more than the energy to melt the ice then it will be water.