Question

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 Å.

Answer 1

Diameter of an oxygen molecule, d = 3 Å

 

Radius, r = d / 2

 

r = 3 / 2 = 1.5 Å = 1.5 x 10 -8 cm

 

Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3

 

Molecular volume of oxygen gas, V = 4 / 3 πr3. N

 

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

 

Hence,

 

V = 4 / 3 x 3.14 x (1.5 x 10-8)3 x 6.023 x 1023

 

We get,

 

V = 8.51 cm3

 

Therefore, ratio of the molecular volume to the actual volume of oxygen = 8.51/ 22400 = 3. 8 x 10-4

 

Ratio of molecular volume to actual volume of oxygen = \( 3. 8 \times 10^{-4} \)