Question

Deduce Avogadro’s law based on kinetic theory.

Answer 1

Avogadro’s law: 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 the kinetic theory of gases,

From P = `1/3 "N"/"V""m"bar("v"^2)`

P = `1/3 "N"_1/"V""m"_1bar("v"_1^2) = 1/3 "N"_2/"V""m"_2bar("v"_2^2)` ............(1)

At the same temperature, the average kinetic energy per molecule is the same for two gases.

`1/2 "m"_1bar("v"_1^2) = 1/2 "m"_2bar("v"_2^2)` ..........(2)

Dividing the equation (1) by (2) we get N₁ = N₂ This is Avogadro’s law. It is sometimes referred to as Avogadro’s hypothesis or Avogadro’s Principle.