Calorimetry problem (been stuck for an hour or so)

[calrimetryftl]

A 25.0g ice cube at its melting point is added to a calorimeter water at 25.4ºC. When thermal equilibrium is reached, the final temperature of the mixture is at 15.0ºC. The original volume of water in the calorimeter was?
This is all the data given.
A. 93.4mL
B. 136mL
C. 209mL
D. 228mL


I used the mcΔt = mcΔt formula, but the answer didn't seem to match the options given in my assignment.

I've been trying to figure this out for more than an hour now...please someone help, if I am using the wrong formula correct me.

 

[burningbend]

you have probably forgotten to incorporate phase change of the ice

 

[calrimetryftl]

How would I do that? sorry I'm a little lost

 

[burningbend]

no prob.

when you put ice in water, the ice absorbs heat from its surroundings to change from a solid to a liquid. that change is mΔH where ΔH is the heat of fusion (and can be looked up in a table).

so while the water releases heat at mcΔT because there is a temperature change, the ice absorbs the heat the water released, does not change temperature, but instead changes phase. make sense?

 

[burningbend]

oh and don't forget you still have to account for the change in temperature of that now 25g of water up to 15 C, so you have both melting and heating on one side and cooling on the other side of the equation.