# Does Avogadro's law only apply to ideal gases?

I know the ideal gas law may change a little when for real gases or diatomic ones does Avogadro's law change too or does it stay the same?

• What changes are you specifically interested in? – Aaron Stevens Dec 15 '18 at 13:52
• If the ideal gas law may change why shouldn't the same applies to the Avogadro's law statement? The same V of different gases will contains -strictly speaking - different number of molecules. – Alchimista Dec 15 '18 at 14:50
• @Alchimista You should post that as an answer, not a comment. – Aaron Stevens Dec 15 '18 at 15:00
• @Aaron Stevens. Done in details by another user. Thx. – Alchimista Dec 15 '18 at 17:31
• @Alchimista But it was not at the time. Comments are for clarifications or suggestions if improvement of the question. Even small answers should be posted as an answer and not a comment. – Aaron Stevens Dec 15 '18 at 18:35

Avogadro's law can be stated in the form: equal volumes of all gases, at the same temperature and pressure, have the same number of molecules ( as in wikipedia ). It can justified in the case of the ideal gas, by writing the equation of state in the form: $$\frac{n}{V}= \frac{P}{RT},$$ where $$P,T$$, and $$R$$ are the pressure, temperature and gas constant respectively, and $$n$$ and $$V$$ are the quantity of molecules (in mol) and the volume. Thus, $$\frac{n}{V}$$ represents the density of moles ($$mol/m^3$$). All the perfect gases at the same pressure and temperature, will have th esame density of moles, whatever is their molecular state (mono-atomic, diatomic,tri-,....).
However, if the equation of state (eos) departs from the ideal gas eos, this result is not more valid. For example, at slightly higher pressures and slightly lower temperatures than those which ensure a perfect gas behavior, we know that the equation of state is well represented by a few terms of the so-called virial expansion: $$\frac{P}{RT} = \frac{n}{V} \left(1 + B \frac{n}{V} + C \left(\frac{n}{V}\right)^2 + \dots \right)$$ where the virial coefficients ($$B,C,\dots$$) depend on $$T$$ and on the interaction potential. Thus, the virial coefficients are not the same for different gases and the equality of the left hand side of the previous equations does not imply that $$\frac{n}{V}$$ would be the same. Obviously, if the law does not apply to imperfect gases it does not apply to liquids or solid phases.