Question

How was the Avogadro’s law discovered$?$

Answer 1

Avogadro's law is an experimental gas law discovered by Amedeo Avogadro in $1811$ relating the volume of a gas to the amount of substance of gas present and is a specific case of the ideal gas law. The law relate to the work of two of his contemporaries, Joseph Louis Gay-Lussac and John Dalton.

Complete step-by-step answer: Avogadro's law is an experimental gas law discovered by Amedeo Avogadro in $1811$ relating the volume of a gas to the amount of substance of gas present and is a specific case of the ideal gas law.
Gay-Lussac noticed that when $2\,L$ of ${H_2}$ gas react with $1\,L$ of ${O_2}$ gas, they form $2\,L$ of gaseous ${H_2}O$. He observed all gases seemed to react in simple volume ratios.
In $1811$ Avogadro published a paper in Journal de Physique, the French Journal of Physics, where he gave the explanation to Gay-Lussac’s observations of gas reactions and said that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules provided they follow ideal gas behaviour and this law is now called Avogadro’s law. In practice, real gases show small deviations from the ideal behaviour and the law holds only approximately, but is still a useful approximation
In Avogadro’s view, the reason that $2\,L$ of ${H_2}$ gas react with $1\,L$ of ${O_2}$ gas, they form $2\,L$ of gaseous ${H_2}O$ is that the volume decreases because the number of particles present decreases. Therefore the chemical reaction must be: $2{H_2}\left( g \right) + {O_2}\left( g \right) \to 2{H_2}O\left( g \right)$.
Note: According to Avogadro’s law we can write that $V$is directly proportional to $n$ which can be represented as: $V = nk$, where $V$is the volume of a given gas, $n$is the amount of substance of the has in $moles$ and $k$ is a constant for a given temperature and pressure.