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

In summary, at high pressures, the measured volume of real gases is higher than the calculated volume due to the significant volume of the molecules themselves. This is because the ideal gas equation only considers the "free volume" available for the gas to move, while the measured volume includes the volume of the molecules. A good reference for this is PW Atkins: Physical Chemistry, which has a chapter dedicated to this topic.
  • #1
Kaushik
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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 :)
 
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  • #2
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.
 
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  • #3
BvU said:
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?
 
  • #4
BvU said:
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?
 
  • #5
No: you measure the volume including the volume of the molecules. They are in there !
 
  • #6
Kaushik said:
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.
 
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1. What is the van der Waals equation?

The van der Waals equation is a mathematical formula that describes the behavior of real gases, taking into account the intermolecular forces between gas molecules. It is an improvement upon the ideal gas law, which assumes that gas molecules have no volume and do not interact with each other.

2. What is the significance of the 'volume of gas' in the van der Waals equation?

The volume of gas refers to the physical space occupied by gas molecules. In the van der Waals equation, it is taken into account by subtracting the volume occupied by the molecules from the total volume of the gas. This correction factor accounts for the fact that gas molecules have a finite size and take up space.

3. How is the volume of gas determined in the van der Waals equation?

The volume of gas is determined by multiplying the number of moles of gas by the molar volume, which is the volume occupied by one mole of gas at a specific temperature and pressure. It can also be calculated by dividing the mass of the gas by its density.

4. Does the volume of gas change under different conditions?

Yes, the volume of gas can change under different conditions such as temperature and pressure. According to the van der Waals equation, as pressure increases, the volume of gas decreases and as temperature increases, the volume of gas increases. This is due to the changes in the intermolecular forces between gas molecules.

5. How does the volume of gas affect the behavior of real gases?

The volume of gas is an important factor in understanding the behavior of real gases. As mentioned before, the van der Waals equation takes into account the volume of gas and its effect on intermolecular forces. This allows for a more accurate description of gas behavior, especially at high pressures and low temperatures where the ideal gas law fails to accurately predict gas behavior.

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