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.

Solution

Given,
Diameter of an oxygen molecule, d = 3Å
Radius, r =

straight d over 2 space equals space 3 over 2 space equals space 1.5 space A with o on top space space space space space space space equals space 1.5 space cross times space 10 to the power of negative 8 end exponent space c m

Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm³
Molecular volume of oxygen gas, V =

4 over 3

πr³N
where,

N is Avogadro’s number = 6.023 x 10²³ molecules/mole
∴ V =

4 over 3

× 3.14 × (1.5 × 10⁸)³ × 6.023 × 10²³
= 8.51 cm³
Ratio of the molecular volume to the actual volume of oxygen =

fraction numerator 8.51 over denominator 22400 end fraction

= 3.8 × 10^-4.

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