The first step is to calculate the energy required to melt the solid iodine:
Q1 = nΔH_fus
where Q1 is the energy required, n is the number of moles, and ΔH_fus is the molar heat of fusion.
To calculate n, we need to know the molar mass of iodine, which is 126.9 g/mol.
n = m/M
where m is the mass of the sample and M is the molar mass.
n = 352 g / 126.9 g/mol = 2.78 mol
Now we can calculate Q1:
Q1 = 2.78 mol x 16.7 kJ/mol = 46.5 kJ
The second step is to calculate the energy required to heat the liquid iodine from its melting point to 180 oC:
Q2 = mCΔT
where Q2 is the energy required, m is the mass of the sample, C is the specific heat capacity, and ΔT is the temperature change.
ΔT = 180 oC - 114 oC = 66 oC
Now we can calculate Q2:
Q2 = 352 g x 0.054 J/g oC x 66 oC / 1000 = 1.1 kJ
The total energy required is the sum of Q1 and Q2:
Q_total = Q1 + Q2 = 46.5 kJ + 1.1 kJ = 47.6 kJ
Therefore, the amount of energy required to melt 352 g of solid iodine and then heat the liquid to 180 oC is 47.6 kJ.