Question

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

• 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)

$7.1\times {10}^4$

Volume occupied by 1 mole of an ideal gas at STP is known as molar volume.
Molar volume = 22.4 litre = $22.4\times {10}^{-3}{m}^3$
Radius of hydrogen atom is r = 0.5 $\stackrel{o}{A}$ = $0.5\times {10}^{-10}$m
Atomic volume = $\frac{4}{3}\pi r^3{N}_A$
$=\frac{4}{3}\times \frac{22}{7}\times (0.5\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}$
$=3.15\times {10}^{-7}{m}^3$
Their corresponding ratio is
$\frac{Molarvolume}{Atomicvolume}=\frac{22.4\times {10}^{-3}{m}^3}{3.15\times {10}^{-7}{m}^3}=7.1\times {10}^4$