Questions Ā
As shown schematically in the figure, two vessels contain water solutions (at temperature š) of potassium permanganate (KMnO4) of different concentrations š1 and š2 (š1 > š2) molecules per unit volume with . When they are connected by a tube of small length and cross-sectional area S, KMnO4 starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force on each molecule, where is a constant. Neglecting all terms of the order , which of the following is/are correct? (ššµ is the Boltzmann constant)-
detailed solution
Correct option is A
PV=NkBTāP=NVkBT=nkBTn1>>n1ān2=Īn F=P1-P2S=n1ān2kBTS=ĪnkBTSOption (A) is correct.Viscous Force = Total number of molecules ĆĪ²v=n1lSĪ²vIf viscous force is balanced by pressure force, then ĪnkBTS=ān1SĪ²vān1Ī²vā=ĪnkBT Option (B) is correct. Total number of molecules per sec=n1vdtSdt=n1vS=ĪnkBTvSĪ²vā=ĪnākBTĪ²SOption (C) is correct.As ān will decrease with time therefore rate of molecules getting transfer decreases with time.Option (D) is incorrect.Talk to our academic expert!
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