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Question

Two liquids 'A' and 'B' have vapour pressure (in pure state) in the ratio pA:pB=1:3 at a certain temperature. Assume 'A' and 'B' form an ideal solution and the ratio of mole fractions of 'A' to 'B' in the vapour phase is 4 : 3. The the mole fraction of 'B' in the solution at the same temperature is:

A
24
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B
15
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C
23
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D
45
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Solution

The correct option is B 15
Given:
pApB=13
where,
pAPure vapour pressure of ApBPure vapour pressure of B

YAYB=43
where,
YAMole fraction of A in vapour phaseYBMole fraction of B in vapour phase

From Dalton's law,
pA=PT×YA
where,
PTTotal pressure of the liquid mixturepAPartial vapour pressure of AYAMole fraction of A in vapour phase

From Raoult's law,
pA=pA×XA
where,
pAVapour pressure of AXAMole fraction of A in liquidpAPure vapour pressure of A
Thus,
YA=pAPTpAXAPT....eqn (i)
Similarly,
YB=pBXBPT.....eqn (ii)
Dividing equation (i) and (ii), we get,
YAYB=pApB×XAXB43=13×XA(1XA)4=XA(1XA)XA=45XB=145XB=15

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