Question

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO₄) of diffrent concentrations n₁ and n₂ (n_1>n₂) molecules per unit volume with Δn = (n₁ - n₂)<< n₁. When they are connected by a tube of small length l and cross- sectional area S, KMnO₄ starts of diffuse from the left to the right vessel through the tube partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force - βv on each molecule, where β is a constant. Neglecting all terms of the order (Δn²), which of the following is/are correct? (k_B is the boltzmann constant)-

(A) the force causing the molecules to move across the tube is Δnk_BTS

(B) force balance implies n₁βvl = Δnk_BT 

(C) total number of molecules going across the tube per sec is (\(\frac {Δn}{l}\)) (\(\frac{k_BT}{β}\))S

(D) rate of molecules getting transferred through the tube does not change with time

Answer 1

Correct answer is (A,B,C)

n₁ >>(n₁- n₂) = Δn

As Δn will decrease with time therefore rate of molecules getting transfer decreases with time.