Deduction of Gas Laws from Kinetic Gas equation:

(i) Boyles Law:-

PV = (1/3) Mu²        (Kinetic gas equation)

or PV = (2/2) (1/3) Mu² = 2/3) Kinetic Energy  [∵ (1/2) Mu² = K.E]

so PV = (2/3) K.E —(i) [as Kinetic Energy ∝ Temperature K.E = kT (k → const.)

so PV = (2/3). k.T — (ii)

or PV = constant at const. T (Boyles Law)

(ii) Charles Law →

From equation (ii)

As PV = (2/3) kT so (V/T) = (2/3). (k/P) —(iii)

So at constant pressure V/T = constant at constant P

(iii) Dalton’s law of partial pressure:-

PV = (1/3) mnu² (kinetic gas equation) of two gases are enclosed in same vessel then

P₁V = (1/3) m₁ n₁ u₁² & P₂ V = (1/3) m₂ n₂ u₂²

Or P = P₁ + P₂ = (1/3) (m₁n₁u₁²/V) + (1/3) m₂ n₂ u₂²

Or P = P₁ + P₂