The lattice energy of an ionic compound MO is given by U(r) = -A/r + BN/r12, whe
ID: 1024386 • Letter: T
Question
The lattice energy of an ionic compound MO is given by U(r) = -A/r + BN/r12, where A and B are constants, is the Madelung constant, N is the coordination number, and r is the interionic distance. At equilibrium, it is speculated that this material can crystallize in two structures, NaCl or CsCl. Based on the data in the table below, what is the most probable structure for this compound ? Justify your answer in terms of B only.
NaCl N=6 Radius M2+ = 1.49 Å Radius O2- = 1.26 Å CsCl N=8 Radius M2+ = 1.56 Å Radius O2- = 1.28 ÅExplanation / Answer
value of A for
nacl = 1.7475
cscl = 1.7627
U = N Ae2Z2/r0 (1-1/n) ,z1=z2 = 1
for nacl
n= 6 , e= 1.6 * 10-19 , r0 = 1.49 A0 + 1.56 A0 / 2 = 1.525
U= 6.023 *1023 * 1.7475 * ( 1.6 * 10-19 )2 * (1)2 / 1.525 ( 1 -1/6)
=17.65 * 10-15 (5/6 )
= - 14.78 * 10-15 ergs / mol
similarly
for cscl n= 8 , e= 1.6 * 10-19 , r0 = 1.56 A0 + 1. 28A0 / 2 = 1.42
U= 6.023 *1023 * 1.7627 * ( 1.6 * 10-19 )2 * (1)2 / 1.42 ( 1 -1/8)
= 19.11 * 10-15 (7/8 )
= - 16.72 * 10-15 ergs / mol
as the value of lattice energy for Cscl > Nacl type and we know
greater the lattice enthalpy greater is the stability . hence the ionic compound MO will form the most probable structure for this compound as CsCl .
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