Question

How much energy (in kilojoules) is needed to heat 4.00g of ice from -11.0∘C to 21.5∘C? The heat of fusion of water is 6.01kJ/mol, and the molar heat capacity is 36.6 J/(K⋅mol) for ice and 75.3 J/(K⋅mol) for liquid water.

Answer 1

Three equations will work most of the heat problems.
When you are heating WITHIN a phase (raising a liquid @ one T to liquid at another T; solid at one T to solid at another T; gas at one T to gas at another T) use
q = mass x specific heat in that phase x (Tfinal-Tintitial)

When you are at a phase change use one of these two.
For phase change from solid to liquid (the melting point is where you change from solid phase to liquid phase) use
q = mass x heat fusion.

For phase change from liquid to gas (the boiling point is where you change from the liquid phase to the gas phase) use
q = mass x heat vaporization.

For the above problem you have
solid ice moving from -11 C to zero C (that's within a phase).
Then you have ice melting (phase change)
Then you have liquid water going from zero C to 21.5 C.(another within a phase)
Total q is the sum of q1 + q2 + q3