Question

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

• A. 2 × 10–4
• B. 1 × 10–4
• C. 1.5 × 10–4
• D. 4 × 10–4

Answer 1

Answer: (D)

4 × 10–4

Answer 2

Here, diameter, d = 3Å

$\therefore r = \frac{d}{2} = \frac{3}{2} \times 10^{- 10}m = \frac{3}{2} \times 10^{- 8}cm = 1.5 \times 10^{- 8}cm$Molecular volume of oxygen gas,

$V = \frac{4}{3}\pi r^{3} \times N$

N $\rightarrow$Avogadros number

Actual volume occupied by 1 mol of oxygen gas at STP

= 22,400 $cm^{2}$

$\therefore V = \frac{4}{3} \times 3.14 \times (1.5 \times 10^{- 8})^{3} \times 6.023 \times 10^{23} = 8.51cm^{3}$

Therefore, ratio of the molecular volume in the actual volume of oxygen.

$\frac{V}{V_{1}} = \frac{8.51}{22,400} = 3.8 \times 10^{- 4} = 4 \times 10^{- 4}$