Question

The crystal `AB`(rock salt structure) has molecular weight `6.023Y u`, where `Y` is an arbitrary number in `u`. If the minimum distance between cation and anion is `Y^(1)/(3) nm` and the observed density is `20 kg m^(-3)`. Find
a. The density in `kg m^(-3)`. and
b. The type of defect

Answer 1

a. Density, `rho = (Z_(eff) xx Mw)/(a^(3) xx N_(A))`
Edge length
`a = 2Y^(1)//(3) xx 10^(-9) m`
For rock salt structure, `Z_(eff) = 4`
`M = 6.023 Y u = (6.023)/(1000) Y kg`
Density, `rho`
`(4 xx (6.023)/(1000) xx10^(-3) xx Y)/(6.023 xx 10^(23) xx (2Y^(1//3) xx 10^(-9))^(3))`
`= (40)/(8) = 5 kg m^(-3)`
b. Observed density `= 20 kg m^(-3)`
Calculated density `= 5 kg m^(-3)`
The observed density is higher than the calculated density, hence, the solid must have non-stoichiometric defect.