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Question

Liquids A and B form ideal solution over the entire range of composition. At temperature, T, an equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions XA and XB, respectively, has a vapour pressure of 22.5 Torr. The value of XA/XB in the new solution is __________.
(Given that the vapour pressure of pure liquid A is 20 Torr at temperature T).

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Solution

At a certain temperature, vapour pressure of equimolar binary solution =45 Torr. 12PA+12PB=45( Raoult's Law)

(where PA and PB are vapour pressure of pure liquids A and B at temperature T )

It is given,PA=20Torr.

PB=70 Torr (From eqn-(i))

Now, for another solution described, we may write by Raoult's Law: PAXA+PBXB=PT=22.5 Torr.

(where XA and XB are mole fraction A and B in solution)

20XA+70(1XA)=22.5(XA+XB=1)

XA=0.95 and XB=0.05

Hence, XAXB=0.950.05=19

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