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Two liquids Aand B have vapour pressures...

Two liquids `A`and `B` have vapour pressures in the ratio of `p_(A)@,p_(B)@` = 1 : 2 at a certain temperature. Suppose we have an ideal solution of `A` and `B` in the mole fraction ratio `A:B = 1:2`. What would be the mole fraction of `A` in the vapour in equilibrium with the solution at a given temperature?
a.`0.25` , b.`0.2` , c.`0.5` d.`0.33`

Text Solution

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b. `p_(A)@ : p_(B)@ = 1:2`
`p_(A) : chi_(A) xx p_(A)@ = A xx chi_(A)`
`p_(B) : chi_(B) xx p_(B)@ = 2A xx 2chi_(A)`
`p_("total") = A chi_(A) + 4 Achi_(A) = 5 Achi_(A)`
`chi_(A("vapour phase"))= (P_(A))/(P_("total")) =( A chi_(A))/( 5 Achi_(A)) = 1/5 = 0.2`
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