Volume of a gas

Question

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.

Source

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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.

Answer 1

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.