Chemistry - Ideal Gas Question with Solution | TestHub
A very long rectangular box is divided into N equal compartments with (N - 1) fixed semipermeable membranes (SPM) numbered from 1 to (N - 1) as shown in the figure. The gases are initially present in only first compartment and they can pass through only those SPM whose number is less than or equal to their subscript. For example, gas A1 can pass through only first SPM, gas A2 can pass only through first and second SPM, and so on. If initially all gases have same moles and after a long time, the ratio of partial pressures of gas A4 in third compartment to that of gas A_(N-1) in first compartment is 3, the value of N is
Answer:
Solution:
Gas Ak passes SPMs 1 to k, so it spreads uniformly over the first (k + 1) compartments. With n moles of each gas and compartment volume v, its uniform partial pressure is p(Ak) = nRT/((k+1)v). Gas A4 occupies 5 compartments: p(A4) = nRT/(5v) (same in the third compartment). Gas A_(N-1) passes all N - 1 membranes, so it fills all N compartments: p(A_(N-1)) = nRT/(Nv) (same in the first compartment). Given ratio: [nRT/(5v)] / [nRT/(Nv)] = N/5 = 3, so N = 15. Hence the answer is 0015.
