phase change energetics

Question

The following information is given for iron at 1 atm:

boiling point = 2750 °C	Hvap(2750 °C) = 354 kJ/mol
melting point = 1535 °C	Hfus(1535 °C) = 16.2 kJ/mol
specific heat solid = 0.452 J/g°C
specific heat liquid = 0.824 J/g°C

 kJ are required to melt a 34.4 g sample of solid iron, Fe, at its normal melting point.

Answer 1

Fusion is another word for melting, so from the data given, the ΔH_fus represents the amount of heat (or energy) needed to melt iron. The units are kJ/mol, so this value means that 16.2 kJ of heat are required to melt 1 mole of iron.

We don't have 1 mole of iron though, we have 34.4 g of iron. So we need to convert this to moles:

(34.4 g Fe) * (1 mol Fe / 55.85 g Fe) = 0.616 mol Fe

Now we can use the ΔH_fus for iron to calculate the heat needed. Since we are already at the melting point of iron, we do not need to raise the temperature at all, we just need to add heat to melt it! So,

(0.616 mol Fe) * (16.2 kJ / 1 mol Fe) = 9.98 kJ needed to melt 34.4 g of iron.

The rest of the information in this question would be useful for other calculations (like raising the temperature of iron from room temperature to the melting point, for example), but are not needed for this question.

Hope this helps!