Chemistry - Ideal Gas Question with Solution | TestHub
A container is divided into two parts in the ratio 1:2 by a fixed semi-permeable membrane (SPM) which permits movement of NO₂ gas only. At T K, compartment - I contains only N₂O₄ gas at 40 mm Hg pressure and compartment - II contains a small amount of liquid water, sufficient to maintain equilibrium with its vapour at any temperature. Both compartments are heated to '1.5T' K, at which 50% of the N₂O₄ dissociates into NO₂. The vapour pressure of water at T K and '1.5T' K are 20 and 30 mm Hg, respectively. If ab and cd are the final pressures (in mm Hg) of gases in compartments I and II, respectively, then the value of abcd is
Answer:
Solution:
Let the volumes be V (I) and 2V (II). Initial moles of N₂O₄ in I: n₀ = 40V/RT. At 1.5T with 50% dissociation: N₂O₄ left = 0.5 n₀, confined to compartment I: p(N₂O₄) = 0.5 × 40 × 1.5 = 30 mm Hg. NO₂ formed = n₀ moles, spreading uniformly over V + 2V = 3V at 1.5T: p(NO₂) = n₀ R(1.5T)/(3V) = 40 × 1.5/3 = 20 mm Hg on both sides. Compartment I total = 30 + 20 = 50 mm Hg, so ab = 50. Compartment II = water vapour (saturated, 30 mm) + NO₂ (20 mm) = 50 mm Hg, so cd = 50. Hence abcd = 5050.
