Question

If size of a hydrogen molecule is assumed to be $1 \, \mathring{A} $ then calculate the ratio of molar volume to atomic volume for $1mole$ of hydrogen gas.

• 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 mode of an ideal gas at SIP is known as molar volume.
$\therefore $ Molar volume = $22.4 \, litre=22.4\times 10^{- 3}m^{3}$
Radius of hydrogen atom is r = $0.5 \, A^{0}=0.5\times 10^{- 10}m$
$\therefore $ Atomic volume= $\frac{4}{3}\pi r^{3}N_{A}$
$=\frac{4}{3}\times \frac{22}{7}\times \left(0.5 \times \left(10\right)^{- 10}\right)^{3}\times 6.023\times \left(10\right)^{23}$
$=3.15\times 10^{- 7}m^{3}$
Their corresponding ratio is
$\frac{M o l a r \, v o l u m e}{A t o m i c \, v o l u m e}=\frac{22.4 \times 10^{- 3} m^{3}}{3.15 \times 10^{- 7} m^{3}}=7.1\times 10^{4}$