how do you calculate lattice energy of an ionic compound

Question

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?

Answer 1

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

 

 

 

Answer 2

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 O^2-

 

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.