Given:
Diameter of O2 molecule = 3 Å
Radius, r = 1.5 Å = 1.5 × 10−10 m
Avogadro’s number, NA = 6.022 × 1023 mol−1
Molar volume at STP = 22.4 L = 22.4 × 10−3 m3
Step 1: Volume of one oxygen molecule
Assuming the molecule to be spherical:
Volume of one molecule,
V = (4/3)πr3
V = (4/3)π(1.5 × 10−10)3
V = 1.41 × 10−29 m3
Step 2: Total molecular volume of 1 mole of O2
Total molecular volume = NA × volume of one molecule
= 6.022 × 1023 × 1.41 × 10−29
= 8.49 × 10−6 m3
Step 3: Calculate the fraction of molecular volume to actual volume
Fraction = (Total molecular volume) / (Actual volume at STP)
Fraction = (8.49 × 10−6) / (22.4 × 10−3)
Fraction = 3.8 × 10−4
Final Answer:
The fraction of molecular volume to the actual volume occupied by oxygen gas at STP is:
≈ 3.8 × 10−4