Show that, ratio of the masses of equal volumes of two gases at the same temperature and pressure is equal to the ratio of their molecular masses.

Explanation

Let the molecular masses of two gases, A and B be `M_(A) and M_(B)` respectively and `W_(A),W_(B)` be their respective masses.
Now, number of moles of gas `A=W_(A)//M_(A)`
`therefore`Number of molecules in gas `A=(W_(A))/(M_(A))xx6.022xx10^(23)`
Again, number of moles of gas `B=W_(B)//M_(B)`
`therefore` Number of molecules in gas `B=(W_(B))/(M_(B)) xx6.022xx10^(23)`
Since the gases (having equal volumes) are at same temperature and pressure, accordinng to Avogadro's hypothesis they will contain the same numbe of molecules.
`therefore (W_(A))/(M_(A)) xx6.022xx10^(23)=(W_(B))/(M_(A))xx6.022xx10^(23)` i.e., `(W_(A))/(W_(B))=(M_(A))/(M_(B))`.