Metal oxide (MO) crystallises in NaCl type structure. The compound is however non-stoichiometric with the formula MO 0.95 . The defect arises due to some cationic positions occupied by neutral Metal

Question

Metal oxide (MO) crystallises in NaCl type structure. The compound is however non-stoichiometric with the formula $MO_{0.95}$ . The defect arises due to some cationic positions occupied by neutral Metal atom in place of $M^{2 +}$ ions and equivalent numbers of anion sites are vacant. Calculate density (in gm/ml) of solid.

(Atomic mass of M = 48, $N_{A} = 6 \times 1 0^{23}$ , $r_{M^{2 +}} = 0.6 \overset{˚}{A}$ , $r_{O^{2 -}} = 1.4 \overset{˚}{A}$ )

TestHub · Accepted Answer

For 1 M-atom, there should be 1 O-atom, but the actual number is 0.95. Hence, the percentage of anion sites:

$v a c an t = \frac{1 - 0.95}{1} \times 100 = 5%$

The density $d$ can be calculated as:

$d = \frac{4 \times 48 \times 4 \times 16 \times 0.95}{6 \times 1 0 ^{23} \times ( 4 \times 1 0 ^{- 8} ) ^{3}}$

Another calculation for $d$ is:

$d = \frac{3 + 0.95}{6 \times 1 0 ^{- 1}} = \frac{39.5}{6}$

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