Is the Avogadro hypothesis ambiguous?

[Hamiltonian]

Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules."

but will this apply to gases that are not neutral i.e if the molecules are ions? won't there be a large repulsion between molecules compared to a neutral gas? Or maybe if the nuclei of the atoms are very heavy and have more protons hence leading to a large repulsion between molecules of that gas? My point being the repulsion between molecules is different for different gasses then shouldn't they occupy different volumes.

Is the proof/derivation for the Avogadros law strictly empirical?
a proof that I came across was using the ideal gas equation $PV = nRT$ it stated since the pressure, number of moles, and temperature are constant hence the volume of the gases(V) will be constant. is this proof correct(and is it the only proof of the Avogadro hypothesis?) as it does not account for the repulsions between molecules.

 

[Borek]

Ionized gas is called plasma and has completely different properties.

Besides, Avogadro's law works OK for gases which can be considered ideal, it is not that good for real gases, especially at high pressure and low temperature.

That being said, no, neutral atoms/molecules of the gas don't repel each other stronger when they get large. Quite the opposite, they are more and more attracted to each other (which is why heavier elements have higher boiling points).