Q72 / 200 · NEET 2003 · Chemistry
The pyknometric density of sodium chloride crystal is $2.165 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ while its X-ray density is $2.178 \times 10^3 \mathrm{~kg}$ $\mathrm{m}^{-3}$. The fraction of unoccupied sites in sodium chloride crystal is:
- A5.96
- B$5.96 \times 10^{-2}$
- C$5.96 \times 10^{-1}$
- Correct answerD$5.96 \times 10^{-3}$
Solution
Molar volume from pyknometric density
$=\frac{\mathrm{M}}{2.165 \times 10^3} \mathrm{~m}^3$
Molar volume of X-ray density
$=\frac{\mathrm{M}}{2.178 \times 10^3} \mathrm{~m}^3$
Volume unoccupied
$=\frac{M}{10^3}\left(\frac{1}{2.165}-\frac{1}{2.178}\right) \mathrm{m}^3$
Fraction occupied
$\begin{aligned} & =\frac{0.013 \times 10^{-3}}{2.165 \times 2.178} \times \frac{2.165}{\mathrm{M} \times 10^{-3}} \\ & =5.96 \times 10^{-3}\end{aligned}$
Related Theory
Pyknometric density is the closest approximation to true density calculated from the molecular weight and crystalline lattice of a substance.
Hence, the correct answer is option: 'D'.