Question

Under what conditions do the assumptions associated with the application of the ideal gas start to break down? Why?

Answer 1

The essential assumptions of an ideal gas are that the particles be very small, compared to the average distance between them, and that there is no attractive force acting between them. In short, the only way they interact is by colliding and bouncing off each other, and they spend most of their time between collisions, just drifting along.

When would this be no longer true? When the average space between the particles becomes comparable to their size. That is, when the density becomes high, which will happen for a gas held at a constant pressure when the pressure is increased or the temperature is decreased.

Two factors become important then: the fact that the size of the particles is comparable to the distance between them, which means, roughly speaking, they collide more often than in the ideal-gas situation, which tends to raise the pressure higher than the ideal gas. Also, short-range attractive forces (van der Waals forces) start to act, which tends to reduce the pressure below the ideal gas. At high temperature the first effect is more important (so at high pressure and high temperature, real gases tend to have higher pressure than ideal gases), and at low temperature the second is more important (so at low temperature real gases tend to have lower pressure than ideal gases).

There's one other much more unusual situationin which real gases stop being ideal: when the density becomes very low, so low that the particle no longer collide very often, relative to how long a macroscopic measurement takes. Under these odd conditions, which might prevail in a very good vacuum, e.g. on the surface of the Moon, the system won't exhibit many of the typical properties of a gas, for example having pressure proportional to temperature.

Answer 2

Great answer. Carl! Keep up the good work!