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how do you calculate lattice energy of an ionic compound

The question is "The lattice energies of FeCl3, FeCl2, and Fe2O3 are -2631,-5359, and -14,774 kJ/mol (in no particular order). Match the appropriate formula to the energy and explain. My question is how to do you calculate the lattice energy in order to match it?

I agree with Andre.

Another more qualitative and general way of looking at it is to remember that the lattice energy gets stronger (more negative) as the charges on the ions get larger and as their sizes get smaller.

Fe2+ is has a larger radius than Fe3+, it also has a lower charge, so the lattice energy of FeCl2, with its Fe2+ ion, is less negative than that of FeCl3 and of Fe2O3, both of which contain the Fe3+ ion.

The oxide ions in the Fe2O3 are smaller than the chloride ions in FeCl3, so Fe2O3 should have a more negative (stronger) lattice energy than the FeCl3.

The ranking, in terms of heat released upon formation of the lattice from its ions, will be:
Fe2O3 > FeCl3 > FeCl2

Note that the most negative lattice energy corresponds to the greatest amount of energy released.

If we go strictly by lattice energy, with the most negative lattice energy being the strongest lattice (with the most energy released upon lattice formation, then the order would be reversed, starting with the most negative lattice energy:
Fe2O3 < FeCl3 < FeCl2

You do not need to calculate the lattice energies in order to rank them. You just need to recognize that the lattice energy of ionic compounds becomes larger (more negative) as the charge on the ions becomes larger.

The ionization equations for your three compounds are:

FeCl2 → Fe2+ + 2 Cl-
FeCl3 → Fe3+ + 3 Cl-
Fe2O3 → 2 Fe3+ + 3 O2-

You notice that the sum of the magnitudes of the charges are smallest for the first reaction (2+2*1=4) and largest for the third reaction (2*3+3*2=12), with the second reaction in between (3+3*1=6). Therefore, FeCl2 has lattice energy -2631 kJ/mol (the least negative), FeCl3 has -5359 kJ/mol, and Fe2O3 has -14,774 kJ/mol.