Chemistry - Ideal Gas Question with Solution | TestHub
A 50 litre vessel is equally divided into three parts with the help of two stationary (fixed) semi-permeable membranes (SPM). The vessel contains 60 g H2 in the left chamber, 160 g O2 in the middle and 140 g N2 in the right chamber. The left SPM allows transfer of only H2 gas while the right SPM allows the transfer of both H2 and N2. If the ratio of final total pressures in the three chambers is x:y:5, then the value of (5 x x x y) is
Answer:
Solution:
Each chamber has volume V = 50/3 L. Moles: n(H2) = 60/2 = 30, n(O2) = 160/32 = 5, n(N2) = 140/28 = 5. At equilibrium: H2 crosses both SPMs, so it fills all three chambers (total volume 50 L) at uniform partial pressure p(H2) = 30RT/50 = 0.6 RT. N2 crosses only the right SPM, so it occupies the middle + right chambers (100/3 L): p(N2) = 5RT/(100/3) = 0.15 RT. O2 crosses neither membrane and stays in the middle: p(O2) = 5RT/(50/3) = 0.3 RT. Total pressures: left = 0.6 RT; middle = 0.6 + 0.3 + 0.15 = 1.05 RT; right = 0.6 + 0.15 = 0.75 RT. Ratio 0.6 : 1.05 : 0.75 = 12 : 21 : 15 = 4 : 7 : 5, so x = 4, y = 7 and 5xy = 5 × 4 × 7 = 140. Hence the answer is 0140.
