Kinetic Theory of Gases

Question 1

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27 °C. The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, R = 100/12 J mol⁻¹ K⁻¹, molecular mass of O₂ = 32, and 1 atm pressure = 1.01 x 10⁵ N m⁻²]

Accepted Answer

0.116 kg. Gauge pressure is measured above atmospheric, so the absolute pressure is 11 + 1 = 12 atm — missing this is the usual error here. Then n = PV/RT = (12 x 1.01 x 10⁵ x 30 x 10⁻³)/((100/12) x 300) ≈ 14.54 mol, so (18.20 − 14.54) x 32 g ≈ 0.116 kg was withdrawn.

Answer

0.125 kg

Answer

0.144 kg

Answer

0.156 kg

Question 2

A container has two chambers of volumes V₁ = 2 litres and V₂ = 3 litres separated by a partition made of a thermal insulator. The chambers contain n₁ = 5 and n₂ = 4 moles of ideal gas at pressures p₁ = 1 atm and p₂ = 2 atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

Accepted Answer

1.6 atm. The container is insulated, so the total internal energy is unchanged. Since U is proportional to PV for an ideal gas, this reduces to P(V₁ + V₂) = P₁V₁ + P₂V₂, giving P = (1 x 2 + 2 x 3)/5 = 1.6 atm — and note the mole counts are not needed at all.

Answer

1.3 atm

Answer

1.4 atm

Answer

1.8 atm

Question 3

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are nA and nB, respectively, the correct option is:

Accepted Answer

nA = (1/2) nB. The mean free path is λ = 1/(√2 π d² n), so λ is inversely proportional to d²n. Halving λ means doubling the product d²n — but doubling the diameter has already multiplied d² by four, so the number density must fall by a factor of two, giving nA = nB/2.

Answer

nA = nB

Answer

nA = 2nB

Answer

nA = (1/4) nB

Q3.The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are nA and nB, respectively, the correct option is: