Maxwell’s distribution of molecular speeds/energies

(1) The fraction of molecules possessing very low & very high speeds are very small

(2) The speed which is possessed by very large no. of molecules is called most probable speed.

(3) On increasing temperature the graph is shifted towards right hand side & (V_mp) most probable velocity increases & fraction of molecules possessing (V_mp) also increases

Kinetic Gas equation → Its PV = 1/3 mnu²

If n → 1 mole then

m x n = M (molar mass)

So       PV = 1/3 Mu²

P → Pressure exerted by

Where m → Mass of each molecular of gas

n → n^° of molecules present is volume V

u → Root mean square velocity

Types of speeds → (i) Most probable speed (v_mp)

v_mp = (2RT/M)^1/2

(ii) Root mean square velocity (v_rms) = (v₁² + v₂² + ….v_n²/n)^1/2

Also v_rms = (3RT/M)^1/2

(iii) Average velocity (v_av) v = (v₁ + v₂ + v₃……../n)

Also v_avg = (8RT/πM)

Relation bet there    

V_mp                 :           v_av                   :           v_rms

(2RT/M)^1/2    :           (8RT/ πM)^1/2            :           (3RT/M)^1/2