Q. 14.0( 25 Votes )

# 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.

Answer :

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(V_{molecular})

V_{molecular} = πr^{3} × N_{A} ---(1)

The actual volume occupied by oxygen gas at STP (V_{actual})

V_{actual} = 22.4 litres = 0.0224 m^{3}

V_{actual} = 0.0224 m^{3} ---(2)

(Where N_{A} = 6.02214086 × 10^{23} mol^{-1} is Avogadro's constant.)

Substituting for ‘r’ and ‘N_{A}’ in equation (1) we get

V_{molecular} = πr^{3} × N_{A} = π(1.5 × 10^{-10})^{3} × ( 6.02214086 × 10^{23})

= 0.000008513≈ 8.51 × 10^{-6} m^{3}

(∵ 1 Å = 1 × 10^{-10} m)

∴ V_{molecular} = 8.52 × 10^{-6} m^{3} ---(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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