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 = $22.4litre=22.4\times 10^{-3}{m}^3$
Radius of hydrogen atom is r = $0.5A^0=0.5\times 10^{-10}m$
$\therefore$ 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
$\frac{Molarvolume}{Atomicvolume}=\frac{22.4\times 10^{-3}{m}^3}{3.15\times 10^{-7}{m}^3}=7.1\times 10^4$