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The kinetic theory assumes that, for an ideal gas, the volume taken up by the molecules themselves is entirely negligible compared with the volume of the container. For a real gas, that assumption isn't true. The molecules themselves do take up a proportion of the space in the container. The space in the container available for things to move around in is less than the measured volume of the container.

Gas in a container

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After reading the above, my interpretation of volume of gas is that the space for the molecules to move around. When we consider the volume of molecules, then the space for it to move around reduces. But according to my interpretation the volume of real gas must be lower than the volume of ideal gas which is not true.

When we talk about volume of gas, is it the sum of volume of molecules and space between them?

If that is the case then,

  • When we talk about volume of ideal gas, we are considering the volume of the container which is the sum of volume of molecules and the space in between them. Then what do we take into account when we say volume of molecule is negligible as compared to volume of container?

It might be a basic question, but I didn't get any answer to it till now(from my teachers and other websites). Hope i'll get it cleared in CSE.

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  • $\begingroup$ Molar volume... $\endgroup$ – Mithoron Aug 7 at 22:24
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    $\begingroup$ Your picture has somewhat exaggarated gas particles, and they still only take up $(1/6)^3 = 1/198$th of the volume. The ideal gas law ignores this. Only the the van der Waals approximations claims to make an explicit correction for it, but in the end that's also just an empiric parameter, which needs to be changed for different p/T ranges. vdW is not really a good and useful gas law. $\endgroup$ – Karl Aug 8 at 4:28
  • $\begingroup$ $6^3=180+36=216$ $\endgroup$ – Karl Aug 8 at 20:34
  • $\begingroup$ Consider a substance gaseous and liquid phases just below the critical point, when the density of the former is just slightly lower than the latter. ( for water, it is about 0.2 g/cm3 AFAIK ) . Would you say the volume of liquid is what we are used to be, but gas volume is just the volume of molecules ? $\endgroup$ – Poutnik Aug 14 at 16:13
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Consider a balloon filled with a gas. The volume we mean is the volume of the balloon, whatever is inside. The perfect gas hypothesis will change the properties of a gas. For example, for the same balloon, we would expect a real gas to exert a stronger pressure outward than a perfect gas, since it has less space to move around, like you said.

Assuming the balloon is flexible, the inward and outward pressure will equilibrate by an expansion of the balloon. Thus, the volume of the real gas (molecule + space around) will be greater than the volume of a perfect gas.

You do put the finger on a limitation of the definition of the volume of a gas. A gas will spread to occupy as much volume as it can, unless restricted. For example, think of a molecule in space; what is its volume?

Volume is a macroscopic property which only makes sense in certain conditions.

When we say that the volume of the molecules is negligible, we mean that the total equilibrium volume of a gas is roughly the volume of free space the molecules have to move around. This is a good approximation at low pressures, since the volume of the molecules is a very small percentage of the total volume, and intermolecular collisions are essentially impossible. However, at high pressures, the molecules are rather close together, do occupy a non-negligible fraction of the total volume, and do collide together often.

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  • $\begingroup$ How will we define volume of a real gas? $\endgroup$ – Kaushik Aug 7 at 21:51
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    $\begingroup$ I'd agree with most of this, but you can't really separate the volume the gas molecules occupy and the attractive force between molecules at high pressure. Thus the observed behavior at high pressure depends on both factors. $\endgroup$ – MaxW Aug 7 at 21:53
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    $\begingroup$ @Kaushik - The volume of a gas is the volume of the container. $\endgroup$ – MaxW Aug 7 at 21:53
  • $\begingroup$ @MaxW Doesn't that volume include the volume of the molecules? $\endgroup$ – Kaushik Aug 7 at 22:07
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    $\begingroup$ Molecules aren't big balls either, they're mostly electron clouds and aren't "solid" in any way. $\endgroup$ – Raphaël Aug 7 at 22:11

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