Question

1 mole of a gas occupies a volume of 400 ml. If the amount of gas is increased to 2.5 moles at the
same temperature and pressure, what will be the new volume?

Answer 1

Answer:

Radius of hydrogen atom, r = 0.5 Å = 0.5 × 10-10 m

Volume of hydrogen atom = (4/3) π r3

                                            = (4/3) × (22/7) × (0.5 × 10-10)3

                                            = 0.524 × 10-30 m3

Now, 1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.

∴ Volume of 1 mole of hydrogen atoms, Va = 6.023 × 1023 × 0.524 × 10–30

                                                                       = 3.16 × 10–7 m3

Molar volume of 1 mole of hydrogen atoms at STP,  

Vm = 22.4 L = 22.4 × 10–3 m3

∴  

V  

a

​  

 

V  

m

​  

 

​  

=  

3.6×10  

−7

 

22.4×10  

−3

 

​  

=7.08×10  

4

 

Hence, the molar volume is 7.08 × 104 times higher than the atomic volume.  

The ratio is so large because inter-atomic separation in hydrogen gas is large.

Explanation: