Deduce Avogadro's law based on kinetic theory.

Explanation

Avogadro's law:
(i) This law states that at constant temperature and pressure, equal volumes of all gases contain the same number of molecules. For two different gases at the same temperature and pressure, according to kinetic theory of gases,
From equation
`P=(1)/(3)(N_(1))/(V)m_(1)bar(v_(1)^(2))=(1)/(3)(N_(2))/(V)m_(2)bar(v_(2)^(2))" "...(1)`
where `bar(v_(1)^(2))` and `bar(v_(2)^(2))` are the mean square speed for two gases and `N_(1)andN_(2)` are the number of gas molecules in two different gases.
(ii) At the same temperature, average kinetic energy per molecules is the same for two gases.
`(1)/(2)m_(1)bar(v_(1)^(2))=(1)/(2)m_(1)bar(v_(2)^(2))" "...(2)`
Dividing equation (1) by (2) we get `N_(1)=N_(2)`
(iii) This is Avogadro's law. It is sometimes referred to as Avogadro's hypothesis or Avogadro's Principle.