Why Is Avogadro's Law Valid for Ideal Gases?

[march1291]

Avogadro's Law states that the same volume of two different gases (at the same temperature and pressure) contains the same number of particles. I understand that this hypothesis was first suggested after Gay-Lussac's experiments with electrolysis showed that the volumes of hydrogen and oxygen related at whole-number ratios.

But I don't understand how Avogadro's Law makes any sense. Could someone please explain why, for an ideal gas, Avogadro's Law is true?

For the sake of progress I'll take a stab at why it works, although I feel like I'm venturing into dangerous territory (I am not at all familiar with the kinetic theory of gases).

So here's goes: Avogadro's Law implies that each particle of gas moves freely through a surrounding volume that is the same for every existing gas molecule or atom, i.e. the amount of space that a hydrogen molecule "occupies" around it through its random movements is the same as the amount of space a nitrogen molecule occupies. This is because the smaller atom, bound less by inertia, moves faster than the larger atoms; the speed with which the particle moves varies inversely with the mass. The varying of the mass stabilizes the collision rate. Since the pressure and temperature are also the same, the same number of particles of two different gases will expand to the same volume.​

Please correct what's wrong with my guess, or tell me if it's completely off.

Thanks in advance,
Zech

 

[mgb_phys]

Avagadros law is an approximation that works because the molecules are very small.
Assuming:
Gas molecules occupy a negligible amount of the volume of the container
The molecules do not collide with each other or have any effect on each other.

If you need more accurate results for gas laws or are working at very high pressueres (where the molecules do interact) or very low temperatures (where the volume of the molecules does matter) there are extra terms to consider

 

[march1291]

Ah, so it's their negligible volume (and the fact that the difference between the volume of smaller atoms and larger ones is negligible) that makes Avogadro's law an apt approximation.

Thanks.

 

[GCT]

If you're interested in this subject research the topic of Vanderwall equation.