Density of ideal gas molecules

Question

From Boyle's Law, in very low pressure ($P \rightarrow 0$), it is a good approximation for real gases to behave as ideal gases. (refer to the graph)

Boyle's Law stated that $ P \propto \frac{1}{V} $

So I am thinking that when $P \rightarrow 0$, $V \rightarrow \infty$, then by $\mathrm{density} = m / V $, supposedly density of ideal gas molecules should be indefinitely small ($\mathrm{density} \rightarrow 0$)

However, it seems density is a measurable value and is involved in calculations of ideal gases. Then may I ask why it is not indefinitely small but a measurable value?

Answer 1

I think the problem may be that you are conflating the density of gas molecules vs the density of the substance.

The ideal gas molecules themself are considered as point particles with no dimensions, while if we take a volume element inside the ideal gas container, it has an average density. Essentially, the density we use with the ideal gas law is not the density of the actual molecule but the total mass of all these point particles in the container is divided by the total volume of the container.

It's sort of a weird idea to think about because they are point but at the same time, we say they are distributed in some way in space and also give a mass to the region they are spread out in (the whole container).

Answer 2

Boyle’s law applies only if the temperature and the mass of the gas is constant. So clearly when pressure decreases and volume increases with the same mass (same number of particles) the density will decrease.

But as a practical matter when applying the gas laws one doesn’t deal with combinations of zero pressures and infinite volumes. Whether or not the density is measurable is a matter involving sensitivity of instrumentation and the test methodology.

Hope this helps.