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Which compound has largest amount of lattice energy among $\ce{AlF3}$ and $\ce{AlN}$. I think it should be $\ce{AlF3}$ because lattice energy in inversely proportional to radius and size of flourine is quite small as compared to nitrogen. Talking about charge then both have charge of magnitude 3 but my textbook says $\ce{AlN}$ has higher lattice energy could you explain

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In my opinion the difference in charge always prevail over atomic radius. Additionally, according to the Born-Lande equation says the lattice energy is proportional to the charges on each ion, not the charge difference. The fluoride ion has a 1- charge which is smaller than the nitride which is 3-. Anyways these ionic solids have different structures and thus different Madelung constants, it does contribute to the lattice energy difference as well.

You can also refer to the Kapustinskii equation (search on Wikipedia). If you can assume that the radius of the nitride and fluoride ions are roughly the same (in fact the nitride is larger, but as I said the difference in charge always prevail over atomic radius), then the lattice energy is proportional to the total number of ions in the empirical formula and the absolute value of the ion charges. For AlF3, it is 4*3*1=12 and AlN is 2*3*3=18. So the aluminium nitride should has larger lattice energy.

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