Question

Calculate average kinetic energy of oxygen gas molecules at 0°C. (Given kb = 1.38 *10-23)

Answer 1

(a) n = P/kT

where k = Boltzmann constant =

1.38 x 10-23 J/mol/K

P = 1 atmosphere = 1.01 x 105

n/m²,

T = 27°C = 300°K

5

25 3

23

1.01x10

n 2.44x10 m

1.38x10 x300

−

− = =

The root mean square velocity rms V is given by

A

rms A

m m

3RT 3N kT

V ( R N k)

M M

    = =     =      



NA= Avogadro number = 6.02 × 1023 molecule/mole

Mm = 32gm = 32 × 10-3 kg.

23 -23

rms -3

36.02x10 x1.38x10 x300 V = =483.4m/s.

32x10

   

 

Since each molecule may be moving at a given instant,

along any of the six directions (i.e. +X, +Y and +Z) only

(1/6)th of the total molecules contained in the volume

along positive and negative x, y, z directions, move

towards the wall. The number of collisions per second

with one square meter area of the vessel wall will be

25

rms

1 1 xn V 2.44 10 483.4

6 6 = × =× × × = 1.97 × 1027.