# 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 3 Å.

Given:

Diameter of an oxygen molecule (D) = 3 Å

the radius of an oxygen molecule (r) = 1.5 Å ( r = D/2)

Fraction = ?

Explanation: We know that the volume occupied by 1 mole of oxygen gas at STP = 22.4 litres. The molecular volume occupied 1 mole of oxygen molecules can be found by multiplying the volume of a single oxygen molecule (considering it to be a sphere) with the

Avogadro's constant. Then dividing the latter by the former the required result is obtained.

Volume of 1 mole of oxygen gas at S.T.P(Vmolecular)

Vmolecular = πr3 × NA ---(1)

The actual volume occupied by oxygen gas at STP (Vactual)

Vactual = 22.4 litres = 0.0224 m3

Vactual = 0.0224 m3 ---(2)

(Where NA = 6.02214086 × 1023 mol-1 is Avogadro's constant.)

Substituting for ‘r’ and ‘NA’ in equation (1) we get

Vmolecular = πr3 × NA = π(1.5 × 10-10)3 × ( 6.02214086 × 1023)

= 0.000008513≈ 8.51 × 10-6 m3

( 1 Å = 1 × 10-10 m)

Vmolecular = 8.52 × 10-6 m3 ---(3)

Fraction = = = 0.00038007 ≈ 3.8 × 10-4

Fraction = 3.8 × 10-4

The required ratio/fraction is 3.8 × 10-4.

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