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 $=\frac{4}{3}\pi r^3{N}_A$
$=\frac{4}{3}\times \frac{22}{7}\times {\left(0.5\times 10^{-10}\right)}^3\times 6.023\times 10^{23}$
$=3.15\times 10^{-7}{m}^3$
Their corresponding ratio is
$\frac{\text{Molar volume}}{\text{Atomic volume}}=\frac{22.4\times 10^{-3}{m}^3}{3.15\times 10^{-7}{m}^3}=7.1\times 10^4$