Question

A solid having density of $9 \times 10^3\, kg \, m ^{-3}$ forms face centred cubic crystals of edge length $200 \sqrt{2} pm$. What is the molar mass of the solid?
$\left[\right.$ Avogadro constant $\left.\simeq 6 \times 10^{23}\, mol ^{-1}, \pi \simeq 3\right]$

• A. $0.0216 \,kg\, mol ^{-1}$
• B. $0.0305 \,kg\, mol ^{-1}$
• C. $0.4320\, kg \, mol^{-1}$
• D. $0.0432\, kg \, mol^{-1}$

Answer 1

Answer: (B)

Formula for density,
Density, $d =\frac{ Z \times M }{ a ^{3} \times N _{ A }}$
where,
$d =$ density of the unit cell
$M =$ Molar mass of the molecule
$a^{3}=$ volume of the unit cell
$N _{ A }=$ Avogadro number
Here, for FCC unit cell, $Z = 4$
Subsituting the values we get,
$9 \times 10^{3}=\frac{4 \times M }{\left(200 \sqrt{2} \times 10^{-12}\right)^{3} \times 6.0 \times 10^{23}}$
$\Rightarrow M =0.0305 \,kg .mol ^{-1}$