UPSC Civil Services (Mains), Chemistry optional · 2019 · Paper I

Q1(a)(ii). Order of lattice energies: LiCl, KCl, KBr, MgBr₂

Question

Order the following compounds according to their expected lattice energies:
LiCl, KCl, KBr, MgBr₂.
Give reasons to support your answer.

MgBr₂ > LiCl > KCl > KBr

The lattice energy is the electrostatic energy of the ions, U=ν |z₊z₋|d(1-d*d)K, with ν ions per formula, d=r₊+r₋, d*=34.5 pm and K=1.21×10⁵ kJ pm mol⁻¹ (Kapustinskii equation).
MgBr₂ has z₊=2 and ν=3: the numerator is 6 against 2 for the three alkali halides, so it is far ahead, 2360 kJ mol⁻¹.
for the 1:1 salts (same charges): radii Li⁺ 76, K⁺ 138, Cl⁻ 181, Br⁻ 196 pm give d = 257 (LiCl) < 319 (KCl) < 334 pm (KBr). A shorter distance gives a larger energy: LiCl 815 > KCl 677 > KBr 650 kJ mol⁻¹.
MgBr₂ > LiCl > KCl > KBr (experimental KCl: 719 kJ mol⁻¹; the estimate is lower but in the same order).

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

The lattice energy is the electrostatic energy of the ions, U=ν |z₊z₋|d(1-d*d)K, with ν ions per formula, d=r₊+r₋, d*=34.5 pm and K=1.21×10⁵ kJ pm mol⁻¹ (Kapustinskii equation).
Charge first: MgBr₂ has z₊=2 and ν=3: the numerator is 6 against 2 for the three alkali halides, so it is far ahead, 2360 kJ mol⁻¹.
Then size: for the 1:1 salts (same charges): radii Li⁺ 76, K⁺ 138, Cl⁻ 181, Br⁻ 196 pm give d = 257 (LiCl) < 319 (KCl) < 334 pm (KBr). A shorter distance gives a larger energy: LiCl 815 > KCl 677 > KBr 650 kJ mol⁻¹.
The order is fixed by these two factors: MgBr₂ > LiCl > KCl > KBr (experimental KCl: 719 kJ mol⁻¹; the estimate is lower but in the same order).

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