A diatomic molecule ${\mathrm{X}}_2$ has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is $6.17\mathrm{g}{\mathrm{cm}}^{-3}$. The number of molecules present in 200g of ${\mathrm{X}}_2$  is.

$\left(\text{ Avogadro constant }\left(N_A\right)=6\times {10}^{23}{\mathrm{mol}}^{-1}\right)$

Density expression:

$\mathrm{\rho }=\frac{\mathrm{z}\times \mathrm{M}}{{\mathrm{a}}^3\times {\mathrm{N}}_{\mathrm{A}}}$

Substitute the given values in the above expression:

$$\begin{gathered} 6.17=\frac{2\times \mathrm{M}}{{\left(300\times {10}^{-10}\right)}^3\times {\mathrm{N}}_{\mathrm{A}}} \\ \frac{\mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}}=\frac{6.17\times {\left(300\times {10}^{-10}\right)}^3}{2} \\ \mathrm{M} =8.3\times {10}^{-23} {\mathrm{N}}_{\mathrm{A}}=50 \mathrm{g}/\mathrm{mol} \end{gathered}$$

Number of molecules present in one mole (or molar mass ) is equal to $6\times {10}^{23} \left({\mathrm{N}}_{\mathrm{A}}\right).$ Molecules present in 200 g is:

$\mathrm{Number} \mathrm{of} \mathrm{molecules}=\frac{{\mathrm{N}}_{\mathrm{A}}}{{\displaystyle 50}}\times 200 \mathrm{g}=4 {\mathrm{N}}_{\mathrm{A}}$