Remember that the third statement of KMT said “The volume occupied by the particles under normal conditions is so small compared to the volume of the container that the particle volume is negligible.”
When the pressure on a gas is doubled, the volume should be cut in half, but the volume that changes is actually the volume of the empty space between the particles – what is called the ideal volume. If a gas is very dense, that is, if the particles are packed tightly together then cutting the volume of empty space in half will NOT be the same as cutting the entire volume in half.
Putting some numbers to this idea may help.
Lets imagine two gases, one (gas A) is under normal conditions, the other (gas B) is very dense. Both are in 1 liter containers. The difference here is that gas A contains nearly a liter of empty space (lets say for argument's sake, 0.998L, leaving 0.002 L of particles). Gas B contains much less empty space, lets say 0.80 L – still a lot, but it means that one fifth of the volume is taken up by the particles themselves.
Gas A Gas B Total volume 1.000 L 1.000 L Volume of empty space 0.998 L 0.800 L Volume of particles 0.002 L 0.200 L
If the pressure is doubled, that means that gas A's empty space will be cut to 0.499 L (from 0.998 L) for a total volume of 0.501 L. (Remember that the total volume is the sum of the empty space and the particles.) This will be so close to exactly half that the “error” will be un-noticable.
For gas B, the empty space will be cut to 0.40 L, leaving a total volume of 0.60 L. This, of course, is notably “incorrect.” Thus, the denser the gas (the more of the space is occupied by the particles rather than empty space) the less the gas will behave ideally.
Gases are also non-ideal at low temperatures...
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