How does kinetic throry justify Avogadro's hypothesis and show that Avogadro Number in different gases is same?

How does kinetic throry justify Avogadro's hypothesis and show that Av

1.	How does kinetic throry justify Avogadro's hypothesis and show that Avogadro Number in different gases is same?
Answer» Solution :Avogadro.s law or Avogadro.s hypothesis: It STATES that "equal VOLUMES of all gases under similar conditions of temperature and pressure contain equal number of molecules". Consider two gases distinguished by subscripts 1 and 2. LET `m_(1)` and `m_(2)` =masses of molecules of 1 and 2 respectively. `N_(1) and N_(2)` = no. of molecules of 1 and 2 respectively `P_(1) and P_(2)` = pressure of 1 and 3 respectively `V_(1) and V_(2)` = volumes of 1 and 2 respectively. `P_(1) V_(1) = 1/3 m_(1)N_(1) bar(V_(1)^(2)) and P_(2) V_(2) = 1/3 m_(2)N_(2) bar(V_(2)^(2))` For equal volumes at the same pressure, `P_(1) V_(1) = P_(2) V_(2)` `:. 1/3 m_(1)N_(1) bar(V_(1)^(2)) =1/3 m_(2)N_(2) bar(V_(2)^(2))`_______ (1) If the gases are at the same temperature the average kinetic energies of their molecules are equal. i.e., `1/2 m_(1)bar(V_(1)^(2)) = 1/2 m_(2)bar(V_(1)^(2)) implies m_(1) bar(V_(1)^(2)) = m_(2) bar(V_(1)^(2))` `:.` equation (1) becomes : `N_(1) = N_(2)` Hence, equal volumes of all gases under similar conditions of temperature and pressure have the same number of molecules.