Question

We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm 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 consider as spheres of radius 1 Å).

Answer 1

Assuming hydrogen molecules as spheres of radius 1 Å.

So, r = 1 Å = radius

The volume of hydrogen molecules = `4/3 pir^3`

= `4/3 (3.14)(10^-10)^3`

= `4 xx 10^-30  m^3`

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

= 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   ......(i)

Now, if the ideal gas law is considered to be constant,

`p_iV_i = p_fV_f`

`V_f = (p_i/p_f)`

`V_i = (1/100)(3 xx 10^-2)^3`

= `(27 xx 10^-6)/10^2`

= 2.7 × 10^–7 m³  ......(ii)

Hence, on compression, the volume of the gas is of the order of the molecular volume [form equation (i) and equation (ii)]. The intermolecular forces will play a role and the gas will deviate from ideal gas behaviour.