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Question

# Two containers C1 and C2 are kept at a constant temperature T=300 K. Container C1 has a volume of 2 litres and it contains Helium gas at a pressure of 10 atm while container C2 has a volume of 8 litres and that contains Methane (CH4) gas at a pressure of 5 atm. Assume the effective radius of CH4 gas molecule is 4 times that of a He gas molecule. List-I contains questions related to gases in containers C1 and C2 and List-II contains their answer(s). List - IList - II(I) When both the containers are connected with(P) 4 a thin tube, the final pressure will be (in atm)(II) The mole fraction of He gas when both(Q) 14 containers are connected with the thin tube(III) The ratio of the mean fee path of CH4 to He(R) 18 before connecting the containers(IV) The ratio of collision frequency of He to CH4(S) 23 before connecting the containers(T) 13(U) 6 Which of the following options has the correct combination considering questions of List-I and answers of List-II

A
(I), (P) and (III), (Q)
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B
(II), (S) and (I), (P)
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C
(I), (U) and (III), (R)
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D
(IV), (R) and (II), (T)
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Solution

## The correct option is C (I), (U) and (III), (R)Partial pressure of He after connecting both containers, =P1V1V2=10×210=2 atm Partial pressure of CH4 after connecting both containers, =P1V1V2=5×810=4 atm (I) Total pressure after connecting both the containers = 2 + 4 = 6 atm (II) Mole fraction of He, when both the containers are connected, =Partial pressure of HeTotal pressure=26=13 (III) The ratio of mean free path of CH4 to He before connecting the containers,λCH4λHe=RT√2πd2CH4NAPCH4RT√2πd2HeNAPHe=1042×5=18 (d = molecular diameter, NA = Avogadro no.) (IV) The ratio of collision frequency of He to CH4 before connecting the containers ZHeZCH4=Vav(He)λHeVav(CH4)λCH4=λCH4λHe×Vav(He)Vav(CH4)=18×√MCH4MHe=18×√164=14

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