Question

Estimate the fraction of molecular volume to the actual volume occupied by oxygenm gas at STP. Take the diameter of an oxygen molecule to be 3 Å.

Answer 1

Given, the diameter of oxygen molecule is 3× 10 −10  m.

Let V actual be the actual volume occupied by the gas and d be the diameter of the oxygen molecule, then

V actual = 4 3 π ( d 2 ) 3 ⋅N

Here, N is the Avogadro number.

Substitute the values in the above expression.

V actual = 4 3 ×3.14× ( 3 2 × 10 −10 ) 3 ×6.023× 10 23 =8.51  cm 3  or 8.51× 10 −3  litre

Let V molar be the molecular volume of one mole of oxygen, then at standard pressure and temperature,

V molar =22.4 litre

Hence, the fraction F of molecular volume to the actual volume occupied by the oxygen gas is,

F= V actual V molar

Substitute the values in the above expression.

F= 8.51× 10 −3 22.4 ≈4× 10 −4

Hence, the fraction of molecular volume to the actual volume occupied by the oxygen gas is 4× 10 −4 .