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. Gases A₁, A₂, ..., AN-1 are initially present in only the first compartment, and each gas can pass through only those SPM whose number is less than or equal to its subscript. If initially all gases have the same number of moles and after a long time the ratio of partial pressures of gas A₃ in the second compartment to that of gas AN-1 in the first compartment is 2, the value of N is
Answer:
Solution:
Gas Aₖ crosses SPMs 1 to k, so it fills the first (k + 1) compartments uniformly: with n moles and compartment volume v, p(Aₖ) = nRT/((k+1)v). Gas A₃ occupies 4 compartments: p(A₃) = nRT/(4v) (same in the second compartment). Gas AN-1 fills all N compartments: p(AN-1) = nRT/(Nv). Given ratio: [nRT/(4v)] / [nRT/(Nv)] = N/4 = 2, so N = 8. Hence the answer is 0008.
