Question

A diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of $300pm$. The density of the molecule is $6.17g/c{m}^3$. The number of molecules present in $200g$ of $X_2$ is:
$\text{Avogadro constant}\left(N_A\right)=6\times {10}^{23}mo{l}^{-1})$

• A. $40N_A$
• B. $2N_A$
• C. $4N_A$
• D. $8N_A$

Answer 1

The correct option is C $4N_A$

A diatomic molecule $X_2$ has $bcc$ structure.

$a=300pm$

$d=6.17g/c{m}^3=\frac{2\times MM}{6\times {10}^{23}\times (300\times {10}^{-10}{)}^3}$

$\text{MM}=\frac{6.17\times 6\times 9\times 3\times {10}^{-1}}{2}$

$\text{MM}=81\times 6.17\times {10}^{-1}=49.97g/mol$

$\text{Number of moles}=\frac{200g}{49.97g/mol}=4mol$

$\text{Number of molecules}=4N_A$