Question

A diatomic molecule $X_{2}$ has a body-centred cubic (bcc) structure with a cell edge of $300\, pm$. The density of the molecule is $6.17 \,g \,cm ^{-3}$. The number of molecules present in $200\, g$ of $X _{2}$ is (Avogadro constant $\left.\left( N _{ A }\right)=6 \times 10^{23} \,mol ^{-1}\right)$

• A. $8\, N _{ A }$
• B. $40\, N _{ A }$
• C. $4 \,N _{ A }$
• D. $2 \,N _{ A }$

Answer 1

Answer: (C)

$4 \,N _{ A }$

Answer 2

$p =\frac{2 \times \frac{ M }{ N _{ A }}}{ a ^{3}}$
$\Rightarrow 6.17=\frac{2 \times \frac{ M }{ N _{ A }}}{\left(3 \times 10^{-8} cm \right)^{3}}$
$\Rightarrow M \simeq 50 gm / mol$

No $=\frac{ w }{ M } \times N _{ A }=\frac{200}{50} \times N _{ A }=4 N _{ A }$