Question

The unit cell length of $NaCl$ is observed to be $0.5627nm$ by X-ray diffraction studies; the measured density of $NaCl$ is $2.164gc{m}^{-3}$. Correlate the difference of observed and calculated densities and calculate % of missing $N{a}^{+}$ and $C{l}^{-}$ ions.

Answer 1

$Z=\frac{a^3\times \rho \times N}{M}$

where,

$Z=$ number of constituent units per unit cell$=4$ in fcc

$a=$ edge length $=0.5627\times {10}^{-7}$ cm

$\rho =$ density
$N=$ Avogadro's number
$M=$ molar mass

$\frac{(0.5627\times {10}^{-7}{)}^3\times \rho \times 6.023\times {10}^{23}}{58.5}=4$

$\rho =2.1805g/c{m}^3$

Observed density $=2.164g/c{m}^3$ which is less than calculated density because some places are missing.

Actual constituent units per unit cell can be calculated as:

$Z=\frac{(0.5627\times {10}^{-7}{)}^3\times 2.164\times 6.023\times {10}^{23}}{58.5}=3.969$

Missing units $=4-3.969=0.031$

% missing $=\frac{0.031}{4}\times 100=0.775$%