Question

We have 0.5 g of H2 gas in a cubic chamber of size 3 cm and kept at NTP. The gas in the chamber is compressed keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?
( Hydrogen molecules can be considered as spheres of radius 1 A)

Answer 1

Hi

Here is your answer,

Assuming hydrogen molecules as spheres of radius 1 A⁰

So, r = 1 A⁰

The volume of hydrogen molecules = 4/3 πr³

                         = 4/3 (3.14) ( 10⁻¹⁰)³

                        = 4 × 10⁻³⁰ m³

 Number of moles of H₂ = Mass/Molecular Mass 

                      = 0.5/2 = 0.25

Molecules of H₂ present = Number of moles of H₂ present × 6.023 × 10²³( Avogadro constant)

                      = 0.25 × 6.023 × 10²³

∴ Volume of molecules present = Molecules number ×  volume of each molecule

                                     = 0.25 × 6.023 × 10²³ × 4 × 10⁻³⁰

                                     = 6.023 × 10²³ × 10⁻³⁰

                                     = 6  × 10⁻⁷ m³-------------------------- (1)

Now, if ideal gas law is considered to be constant 

                →   piVi = pfVf

                →  Vf = (pi/pi)Vi = (1/100) (3 × 10⁻²) ³

                    → 23 × 10⁻⁶/10²

                   →   2.7 × 10⁻⁷ m³ ------------------------------ (2)

Hence, on compression the volume of the gas is of the order of the molecular volume { From (1) and (2) } . The intermolecular forces will play role and the gas will deviate from ideal gas behavior. 


Hope it helps you !