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 the unoccupied sites in sodium chloride crystal is :

• A. $5.96\times {10}^{-4}$
• B. $5.96\times {10}^{-2}$
• C. $5.96\times {10}^{-1}$
• D. $5.96\times {10}^{-3}$

Answer 1

The correct option is D $5.96\times {10}^{-3}$

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