Question

How many times is the forbidden volume compared to actual volume of gas molecules?

• A. double
• B. 3 times
• C. 4 times
• D. 8 times

Answer 1

Answer: (C)

4 times

Volume of the molecules having nonvanishing size, means the space in which the molecules cannot move in a given container is called forbidden volume.

Let us assume molecules are spheres having diameter 'd' or radius 'r'.

Actual volume of the molecule ($V$) = $\frac{4}{3}\times \pi \times r^3$

A bigger circle of radius 'd' shows the volume in which the centers of two molecules cannot move because of each others presence.

where 'd' is the distance between the centers of two molecules.

Then, forbidden volume for one molecule = $\frac{1}{2}\times \frac{4}{3}\times \pi \times d^3$

= $4\times \frac{4}{3}\times \pi \times r^3$

= $4\times V$