Calculate the lattice energy (in Units kJ mol-1) for ZnO crystal using Eq. 3.4 based on electrostatic model and using a Born-Haber cycle. Compare the two answers and comment on any difference.
Useful data:
Medelung constant (A) = 1.6411
Born Constant (n) = 8
Internuclear distance (a) = 199 pm
Zn(s) + ½ O2(g) → ZnO(s) ∆Hf = - 350.5 kJ mol-1
Zn(s) → Zn(g) ∆HS = 130.4 kJ mol-1
Zn(g) → Zn+(g) I(Zn) = 906.3 kJ mol-1
Zn+(s) → Zn2+(g) I(Zn+) = 1733 kJ mol-1
½ O2(g) → O(g) ½ ∆Hd = 248.5 kJ mol-1
O(g) → O- (g) EA(O) = 141 kJ mol-1
O-(g) → O2-(g) EA(O-) = - 780 kJ mol-1
For the theoretical calculation using the Born-Landé equation:
Elat = –[(N0Z+Z–e2A)/(4πε0d0)](1 – 1/n)
N0 = 6.022×1023
Z+ = +2
Z– = –2
e = 1.602×10–19
A = 1.641 for the wurtzite structure
4πε0 = 1.113×10–10
d0 = 75 + 124 = 199 pm (for coordination number = 4) = 1.99×10–10 m
n = 8
Elat = –[(6.022×1023)(2)(–2)(1.602×10–19)2(1.641)/(1.113×10–10)(1.99×10–10)](1
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