QJEEAdv04Ch5390: JEE Advanced 2004 Chemistry - Class 12 JEEAdv04Ch5390 Solution: A compound AB has rock salt type structure. The formula weight…

AB has a rock salt (NaCl) structure. This type of crystal structure possesses fcc unit cell and contains four formula units per unit cell, i.e., Z = 4.

In case of a rock salt structure, the edge-length (a) of the unit cell = 2 $$\times$$ (radius of cation + radius of anion)

Therefore, the edge-length (a) of the unit cell of AB crystal = 2 $$\times$$ Y^1/3 nm = 2Y^1/3 $$\times$$ 10^$$-$$9 m.

We know, $$\rho =\frac{Z\times M}{N\times a^3}$$

Given : M = 6.022 Y g mol^$$-$$1 = 6.022 $$\times$$ 10^$$-$$3 Y kg mol^$$-$$1

$$\therefore$$ $$\rho =\frac{4\times 6.022\times {10}^{-3}Y}{6.022\times {10}^{23}\times {(2Y^{1/3}\times {10}^{-9})}^3}=5.0$$ kg m^$$-$$3

(1) Density of the crystal = 5.0 kg m^$$-$$3

(2) The observed density (= 20 kg m^$$-$$3) is higher than that of the calculated density. This indicates that the crystal structure of AB is likely to have non-stoichiometric defect in the form of metal excess or metal deficiency defect or to have impurity defect in the form of substitutional impurity defect or interstitial impurity defect.