Question

Use the Born-Haber Cycle to calculate the lattice energy of an ionic solid which includes a polyatomic ion.

Answer 1

Consider the case of CaCl2:

Ca(s) + Cl2(g)    CaCl2(s)

Using Born-Haber Cycle:

Ca (s) Ca (g) ............Hsub = 178.2 kJ

Ca (g) Ca+ (g) + e- ...........H_I.E.1 = 590 kJ

Ca+ (g) Ca2+(g) + e- .......H_I.E.2 = 1145 kJ

Cl2 (g) 2Cl (g) ..............B.E. Cl2 =  244 kJ

2Cl (g) + 2e- 2Cl- ...........H_{E.A. 2Cl} = 2(−349 kJ)

Ca2+ (g) + 2Cl- (g) CaCl2 (s) ......L.E. = ?

Ca (s) + Cl2 (g) CaCl2 (s) ......Hf =  -795.8 kJ

Now,

Hf = L.E. + Hsub + H_I.E.1 + H_I.E.2 + B.E. Cl2 + H_{E.A. 2Cl}

-795 kJ =  = LE + 2(-349 kJ) + 244 kJ + 1145 kJ + 590 kJ + 178.2 kJ

L.E. = 2254.2 kJ

Hence, Lattice Energy for CaCl2 (s) = 2254.2 kJ