Question

The ratio of molar volume to atomic volume for $1$ mole of hydrogen is
(Take size of hydrogen molecule to be $1\,\mathring{A}$)

• A. $7.1 \times 10^{4}$
• B. $7.1 \times 10^{6}$
• C. $7.1 \times 10^{10}$
• D. $7.1 \times 10^{8}$

Answer 1

Answer: (A)

Volume occupied by $1$ mole of an .ideal gas at $STP$ is known as molar volume.
$\therefore $ Molar volume $= 22.4$ litre $= 22.4 \times 10^{-3}\, m^3$
Radius of hydrogen atom is $r=0.5\,\mathring{A}=0.5 \times 10^{-10}\,m$
$\therefore $ Atomic volume $=\frac{4}{3}\,\pi r^{3}\,N_{A}$
$=\frac{4}{3} \times \frac{22}{7} \times\left(0.5\times10^{-10}\right)^{3} \times 6.023 \times10^{23}$
$=3.15 \times10^{-7}\,m^{3}$
Their corresponding ratio is
$\frac{\text{Molar volume}}{\text{Atomic volume}}=\frac{22.4\times10^{-3}\,m^{3}}{3.15\times10^{-7}\,m^{3}}=7.1 \times10^{4}$