Question

The pyknometric density of sodium chloride crystal is $2.165\times {10}^3$ kg $m^{-3}$ while its X - ray density is $2.178\times {10}^3$ kg $m^{-3}$. The fraction of unoccupied sites in sodium chloride crystal is:-
AIPMT-2003

Answer 1

Molar volume from pyknometric density:
$\frac{M}{d}=\frac{M}{2.165\times {10}^3}{m}^3\text{(M in kg)}$
Molar volume from X-ray density:
$\frac{M}{d}=\frac{M}{2.178\times {10}^3}{m}^3$
Volume unoccupied:
$\frac{M}{{10}^3}(\frac{1}{2.165}-\frac{1}{2.178})m^3$

Fraction unoccupied :
$\frac{\left(\frac{0.013M\times {10}^{-3}}{2.165\times 2.178}\right)}{\left(\frac{M\times {10}^{-3}}{2.165}\right)}=5.96\times {10}^{-3}$
Hence, option (d) is correct.