# The van der Waals Equation: What is the exact meaning of 'volume of gas'?

## Main Question or Discussion Point

It is said that, for real gases at high pressure, the measured volume is higher than the calculated volume.

My perception of the volume of the gas, as of now, is the following: The free space available for the gas to move. It excludes the volume of the molecules. So on increasing the pressure, the volume of the molecules becomes significant. So the measured volume should be less than the calculated volume. (Calculated volume is the volume obtained from the ideal gas equation).

I reckon that the confusion of mine arose due to the misconception of "volume". Please correct me :)

## Answers and Replies

BvU
Homework Helper
2019 Award
If you simply look at the vdW equation you can see there is a factor $V - nb$. This means V is the occupied volume including the volume of the molecules themselves.

Your perception seems right to me. The conclusion not: ideal gas equation has 'free volume'; occupied (= measured) volume is larger by $nb$ .

A good reference is PW Atkins: Physical chemistry. He has a whole chapter on this.

If you simply look at the vdW equation you can see there is a factor $V - nb$. This means V is the occupied volume including the volume of the molecules themselves.

Your perception seems right to me. The conclusion not: ideal gas equation has 'free volume'; occupied (= measured) volume is larger by $nb$ .

A good reference is PW Atkins: Physical chemistry. He has a whole chapter on this.
What do you mean by 'free volume'? Do you mean the volume of the container - the volume of molecules?

A good reference is PW Atkins: Physical chemistry. He has a whole chapter on this.
It says that instead of moving in volume V, it is restricted to move in V-nb. So the measured volume is V - nb?

BvU
Homework Helper
2019 Award
No: you measure the volume including the volume of the molecules. They are in there !

BvU