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(D) Lattice energy is directly proportional to the product of the charges of the ions and inversely proportional to the sum of the ionic radii $(U \pr

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$MgO, \, LiF, \, Mg_3N_2$

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(D) Lattice energy is directly proportional to the product of the charges of the ions and inversely proportional to the sum of the ionic radii $(U \propto \frac{q_1 q_2}{r_+ + r_-})$.$(i)$ Between $KCl$ $(K^+, Cl^-)$ and $MgO$ $(Mg^{2+}, O^{2-})$,$MgO$ has higher charges $(+2, -2)$ and smaller ionic radii,so $MgO$ has higher lattice energy.$(ii)$ Between $LiF$ $(Li^+, F^-)$ and $LiBr$ $(Li^+, Br^-)$,the charges are the same. Since $F^-$ is smaller than $Br^-$,$LiF$ has higher lattice energy.$(iii)$ Between $Mg_3N_2$ $(Mg^{2+}, N^{3-})$ and $NaCl$ $(Na^+, Cl^-)$,$Mg_3N_2$ has much higher ionic charges,resulting in significantly higher lattice energy.Therefore,the set with higher lattice energy is $MgO, \, LiF, \, Mg_3N_2$.

Which set of compounds in the following pairs of ionic compounds has the higher lattice energy?
$(i) \, KCl$ and $MgO$
$(ii) \, LiF$ and $LiBr$
$(iii) \, Mg_3N_2$ and $NaCl$

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Which set of compounds in the following pairs of ionic compounds has the higher lattice energy?$(i) \, KCl$ and $MgO$$(ii) \, LiF$ and $LiBr$$(iii) \, Mg_3N_2$ and $NaCl$