Why isn't the volume of the individual gas particles relevant to the total pressure in Dalton's Law of Partial Pressures?

Question

I was reading about Dalton's Law of Partial Pressures in a textbook and the proposition is that under ideal conditions, the relevant factors are the pressures of the individual gases and their number of moles. The identity of the gas particles, however, does not matter, and the amount of volume each gas takes up is irrelevant.

But why isn't it relevant? Isn't pressure inversely proportional to volume? I'm missing something here, and I would appreciate help.

Answer 1

That law is an approximation that works just fine at pressures that are not extremely high. Once you get to such high pressures & densities that the actual volumes of the gas atoms (or molecules) themselves cannot be ignored any longer, you have to use a different set of (approximate) laws that take this into account.