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?
[Avogadro constant $\cong 6\times {10}^{23}mo{l}^{-1},\pi \cong 3$]

• A. $0.0216kg.mo{l}^{-1}$
• B. $0.0305kg.mo{l}^{-1}$
• C. $0.4320kg.mo{l}^{-1}$
• D. $0.0432kg.mo{l}^{-1}$

Answer 1

The correct option is B $0.0305kg.mo{l}^{-1}$

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,

$9\times {10}^3=\frac{4\times M}{(200\sqrt{2}\times {10}^{-12}{)}^3\times 6.0\times {10}^{23}}$

$\Rightarrow M=0.0305kg.mo{l}^{-1}$