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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ig050

Two gases A and B have molar masses $M_{A}$ and $M_{B}$ with $M_{A} < M_{B}$ . Which of the following are correct?

AUnder identical conditions A diffuses faster than B
BIf A is at pressure $P$ and B at pressure $2 P$ in separate vessels at the same $T$ , the effusion rate of B is necessarily greater
CIn a mixture of A and B effusing through a pinhole, the gas that remains behind becomes richer in B
DThe rates of effusion of A and B can be made equal by keeping $\frac{p _{A}}{M _{A}} = \frac{p _{B}}{M _{B}}$ at the same temperature

Answer: A, C, D

r \propto p / M

. At equal

p

the lighter gas A is faster (A). Doubling

p_{B}

gives

r_{B} / r_{A} = 2 M_{A} / M_{B}

, which exceeds 1 only if

M_{B} < 4 M_{A}

, so (B) is not necessarily true. A leaves faster, so the residue is enriched in B (C). Equal

p / M

gives equal rates (D).

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