Question

A 459.1-g sample of an element at 187°C is dropped into an ice–water mixture; 102.5 g of ice melts and an ice–water mixture remains. Calculate the specific heat of the element. ΔHfusion = 6.02 kJ/mol (for liquid water at 0°C).

Answer 1

heat lost by metal is
mass metal x specific heat x (Tfinal-Tinitial). Tf = 0; Ti = 187

heat gained by ice is
mass ice x heat fusion. I used 333.5 J/g for heat fusion

Put those together.

(mass metal x specific heat metal x (Tf-Ti) - (mass ice x heat fusion ice) = 0

Solve for specific heat metal. Something like 0.4 or so I think. That's an estimate.

Answer 2

I added those together but put a - sign. Arrrgh!. The following corrects that.
(mass metal x specific heat metal x (Tf-Ti) + (mass ice x heat fusion ice) = 0