Question

The diameter of an oxygen molecule is $3\stackrel{o}{A}$. The ratio of molecular volume to the actual volume occupied by the oxygen gas at STP is?

• A. $2\times {10}^{-4}$
• B. $1\times {10}^{-4}$
• C. $1.5\times {10}^{-4}$
• D. $4\times {10}^{-4}$

Answer 1

The correct option is D $4\times {10}^{-4}$

Here, diameter, $d=3\stackrel{o}{A}$
$\therefore r=\frac{d}{2}=\frac{3}{2}\times {10}^{-10}m=\frac{3}{2}\times {10}^{-8}$cm $=1.5\times {10}^{-8}$cm
Molecular volume of oxygen gas, $V=\frac{4}{3}\pi r^3\times N$
N$\to$ Avogadros number
Actual volume occupied by $1$ mol of oxygen gas at STP$=22,400$ $c{m}^3$.
$\therefore V=\frac{4}{3}\times 3.14\times (1.5\times {10}^{-8}{)}^3\times 6.023\times {10}^{23}=8.51c{m}^3$
Therefore, ratio of the molecular volume to the actual volume of oxygen.
$\frac{V}{V_1}=\frac{8.51}{22,400}=3.8\times {10}^{-4}=4\times {10}^{-4}$