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Two liquids A and B have vapour pressure...

Two liquids A and B have vapour pressure in the ratio `P_A^@ : P_B^@=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. Then the mole fraction of B in the solution at the same temperature is :-

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The correct Answer is:
a
`Y_(A)=P_(A)/P=(P_(A)^(@)X_(A))/P,Y_(B)=P_(B)/P=(P_(B)^(@)X_(B))/P`
`Y_(A)/Y_(B)=P_(A)^(@)/P_(B)xxX_(A)/X_(B)`
Mole fraction in V.P. `prop` vapour phase in vapour phase (Y).
`4/3=1/3xxX_(A)/((1-X_(A)))`
`X_(A)/((1-X_(A)))=4 or (1-X_(A))/X_(A)=1/4`
`X_(A)=4/5 or X_(B)=1/5`
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