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

Question

$\begin{array}{1 1}5.96\times 10^{-3}\\4.96\times 10^{-3}\\3.96\times 10^{-3}\\2.96\times 10^{-3}\end{array} $

Answer 1

Molar volume from pycnometric density =$\large\frac{M}{2.165\times 10^3}$$m^3$

Molar volume from X-ray density =$\large\frac{M}{2.178\times 10^3}$$m^3$

$\therefore$ Volume occupied =$\large\frac{M}{10^3}\big(\frac{1}{2.165}-\frac{1}{2.178}\big)$$m^3$

$\Rightarrow \large\frac{M}{10^3}\big(\large\frac{0.013}{2.165\times 2.178}\big)$$m^3$

Fraction unoccupied =$\large\frac{\big(\Large\frac{0.013M\times 10^{-3}}{2.165\times 2.178}\big)}{\Large\frac{M\times 10^{-3}}{2.165}}$

$\Rightarrow 5.96\times 10^{-3}$