Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3Å.
Answers
Solution:
Diameter of an oxygen molecule, d = 3Å
Radius, r = d/2 = 3/2 = 1.5 Å = 1.5 × 10–8 cm
Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3
Molecular volume of oxygen gas, V = (4/3)πr3N
Where, N is Avogadro’s number = 6.023 × 1023 molecules/mole
∴ V = (4/3) × 3.14 × (1.5 × 10-8)3 × 6.023 × 1023 = 8.51 cm3
Ratio of the molecular volume to the actual volume of oxygen = 8.51 / 22400
= 3.8 × 10-4.
Diameter of an oxygen molecule, d = 3Å
Radius, r = d/2 = 3/2 = 1.5 Å = 1.5 × 10–8 cm
Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3
Molecular volume of oxygen gas, V = (4/3)πr3N
Where, N is Avogadro’s number = 6.023 × 1023 molecules/mole
∴ V = (4/3) × 3.14 × (1.5 × 10-8)3 × 6.023 × 1023 = 8.51 cm3
Ratio of the molecular volume to the actual volume of oxygen = 8.51 / 22400
= 3.8 × 10-4.