Kinetic Theory – Solutions

1) Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 A.

Solution:

Radius ‘r’ of an oxygen molecule, r = d/2 = (3/2) A = 1.5 x 10^-8 cm

Volume occupied by 1 mole of oxygen gas at STP = 22.4 litres = 22400 cm³

Molecular volume of one mole of oxygen gas, V =  πr³ N

Where, N is Avagadro’s number = 6.023 x 10²³ molecules/mole

So, V =  x 3.14 x (1.5 x 10^-8)³ x 6.023 x 10²³= 8.51 cm³

Ratio of the molecular volume to the actual volume of oxygen =  = 3.8 x 10^-4

2) Molar volume is the volume occupied by 1 mole of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0⁰C). Show that it is 22.4 litres.