As shown schematically in the figure , two vessels contain water solutions (at temperature T) of potassium permanganate `(KMnO_(4))` of different concentrations `n_(1)andn_(2)(n_(1)gtn_(2))` molecules per unit volume with `Deltan=(n_(1)-n_(2)ltltn_(1)`. When they are connected by a tube of small length and cross - sectional area s, `KMnO_(4)` starts to diffuse from the left to the right vassel through the tibe Consider the two collection of molecules to between as dilute ideal gases and the difference in their partial pressure in the two vassels causing the diffusion . The speed v of the molecules is limited by the viscous force `-betav` on each molecule, where `beta` is a constant . neglecting all terms of the order `(Deltan)^(2)` which of the following is / are correct ? (`k_(B)` is the Boltzmann constant)

Options

A. the force causing the molecules to move across the tube is `Deltank_(a)TS`
B. force balance implies `n_(1)betavl=Deltank_(B)T`
C. total number of molecues going across the tube per sec is `((Deltan)/(l))((k_(B)T)/(beta))S`
D. rate of molecules getting transferred through the tube does not change with time

Answer

A, B, C

Explanation

(A)
`F=DeltaP.A=(P_(1)-P_(2))A`
`=n_(1)xx"RTA"-n_(2)"RT.A"`
`F=Deltan."RT.A"`
(B) `betavxx(n_(1)xxAxxl)=Delta.T.A`
`beta.v.n_(1).l=Deltan.k.T`
(C ) `(dN)/(dt)=sxxvxxn_(1)`
`=s.n_(1)xx(Deltan,K,T)/(beta.n_(1)l)=(SxxDeltan.K.TS)/(beta.l)`
(D) `Deltan to` decreasing then `(dN)/(dt) to` decreasing