Question

The excluded volume of one molecule in comparison to actual volume is ______ times.

Answer 1

The excluded volume of molecule in motion is 4 times the actual volume of a molecule at rest.

Explanation:

Consider 1 mole of a gas is satisfying ideal gas law,

$P=\frac{RT}{V_m}=\frac{RT}{V}$

Assuming all particles are hard spheres of the same finite radius $r$. Replacing $V$ with $V_m-b$

where b is the excluded volume,

$P=\frac{RT}{V_m-b}$

We must realise that a particle is surrounded by a sphere of radius $2r$ that is forbidden for the centres of other particles.

The excluded volume for 2 particles,

$b\frac{1}{2}=4\pi \frac{d^3}{3}=8\frac{4\pi r^3}{3}$

which divided by 2 gives the excluded volume per particle.

$b^1=\frac{b\frac{1}{2}}{2}=b^1=4\left[\frac{4\pi r^3}{3}\right]$