Why there is a subtractive volume correction in van der Waals' equation for real gases, both real and ideal gases occupy volume of container in which they are kept, so there shouldn't be any correction?

  • $\begingroup$ Your post is rather unclear at the moment: please edit it for grammar and clarity and be sure to add your thoughts concerning the answer. If this is homework, please be sure to read the site policy on such. $\endgroup$ – Todd Minehardt Sep 8 '15 at 13:21
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    $\begingroup$ This is a wholly different kind of volume. Sure, any gas occupies the volume of container, but here we are talking about the volume of molecules themselves. Ideal gas has none; real gas has some. $\endgroup$ – Ivan Neretin Sep 8 '15 at 13:52
  • $\begingroup$ I don't understand whose volume is talked about of in ideal gas and real gas $\endgroup$ – ashwini abhishek Sep 8 '15 at 13:54
  • $\begingroup$ Is the volume is of container or gas molecules or something else $\endgroup$ – ashwini abhishek Sep 8 '15 at 13:56
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    $\begingroup$ You have two volumes here. The volume of the container V and the volume of the gas molecule, b. Ideal gases are thought of as being points ie zero volume, b=0. Therefore they move about the total volume of the container. Real gases have a volume, b>0. Each gas molecule takes up some space in the container, meaning there is less effective volume for them to move about in. Effective volume is V-nb where n is no of molecules ( or moles depending on units of b). $\endgroup$ – Leeser Sep 8 '15 at 17:11

The van der Waals equation is an attempt to explain the pressure-volume relationship for real gases. For example, what will the pressure be of a given amount of gas in a vessel of a fixed volume.

In ideal gases the size and interactions between the atoms or molecules of the gas don't matter at all. We think of them as point-like entities that don't interact except to bounce elastically off each other and off the walls of the vessel. Their behaviour is described by the ideal gas equation and doesn't depend at all on the nature of the particles making up the gas.

Real molecules and atoms deviate from this ideal behaviour because the particles of the gas both have finite volume and attractive interactions which mean they don't behave exactly as the ideal gas equation describes. The van der Waals equation is a simple attempt to explain those deviations from ideality. The volume correction is one of those factors. It takes into account the fact that real gases are made from particles that actually have a finite size and are not mathematical points. The factor is about the volume of the particles of the gas not about the vessel the gas is in. The result of the correction is that the pressure of a given amount of gas in a vessel of fixed size is slightly different than would be expected from the ideal gas equation.

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One thing that this discussion missed is that the volume occupied by a gas is the volume available for molecular motion. So the volume of a real gas can be given as:

Volume of gas = Volume of the container - Volume not available for molecular motion

While studying ideal gas the volume not available for molecular motion turns out to be zero (due to the assumption of negligible molecular volume).

But for real gasses that is not the case and hence you apply that correction term.

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