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

[Kaushik]

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 :)

 

[BvU]

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.

 

[Kaushik]

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?

 

[Kaushik]

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]

No: you measure the volume including the volume of the molecules. They are in there !

 

[BvU]

What do you mean by 'free volume'? Do you mean the volume of the container - the volume of molecules?

Correct: the volume available for the molecules to move around in is the container volume minus the volume occupied by the molecules themselves. Of course the 'no go' volume is not a fixed (in time) 3D area, but an average fraction of the container volume where they can't go because of other molecules being there.