A 10.0 g sample of ice at -14.0°C is mixed with 124.0 g of water at 81.0°C. Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of H2O(s) and H2O(l) are 2.08 and 4.18 J/g°C, respectively, and the enthalpy of fusion for ice is 6.02 kJ/mol.

Answer 1

q1 = heat to raise T of ice from -14.0 C to zero C.
q1 = mass ice x heat capacity ice x (Tf-Ti) where Tf is 0 and Ti = -14.

q2 = heat to melt ice
q2 = mass iced x heat fusion.

q3 = heat to raise T of melted ice from zero C to Tfinal.
q3 = mass melted H2O x specific heat H2O x (Tf - Ti) where Tf is the unknown and Ti = 0

q4 = heat released by warm water at 81.0C dropping to Tfinal.

q1 + q2 + q3 + q4 = 0.
Substitute and solve for Tf. Post you work if you get stuck.