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.

Fe

^{2+}is has a larger radius than Fe^{3+}, it also has a lower charge, so the lattice energy of FeCl_{2}, with its Fe^{2+}ion, is less negative than that of FeCl_{3}and of Fe_{2}O_{3}, both of which contain the Fe^{3+}ion.The oxide ions in the Fe

_{2}O_{3}are smaller than the chloride ions in FeCl_{3}, so Fe_{2}O_{3}should have a more negative (stronger) lattice energy than the FeCl_{3}.The ranking, in terms of heat released upon formation of the lattice from its ions, will be:

Fe

_{2}O_{3}> FeCl_{3}> FeCl_{2}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:

Fe

_{2}O_{3}< FeCl_{3}< FeCl_{2}