To understand Gay-Lussac's law, Amedeo Avogadro said
In equal volumes of air under constant temperature and pressure, there are equal number of atoms (or molecules).
Let's take a hydrogen and an oxygen molecule. As the latter is larger in size, when stored in two separate equally-volumed containers, doesn't oxygen increase the pressure inside that container, if the same number of molecules occupied each container? (Does this make Avogadro's statement of constant pressure go wrong?) Again,
$$2mvN\cos\theta = F,$$
where $F$ is the force acting on the walls of the container, $N$ is the number of collisions of the molecules with the walls, $2mv$ is the change of momentum of the molecules, and $\theta$ is the angle of collision of the molecules on the walls.
Therefore, if Avogadro was correct, could anyone give me any reason why $N_\ce{H2} > N_\ce{O2}$ or $v_\ce{H2} > v_\ce{O2}?$
If Avogadro was correct, the above conditions must hold, as $m_\ce{H2} < m_\ce{O2},$ right?
Could you please prove the above phenomena happen when Avogadro's statement above holds?