The vapour pressures of pure liquids A and B are 400 and 600   mm   Hg respectively at 298  …

The vapour pressures of pure liquids A and Bare 400 and 600 mm Hg respectively at 298 K. On mixing the two liquids, the sum of their volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in the vapour phase, respectively are 
  1.  500 mm Hg, 0.5, 0.5
  2.  450 mm Hg, 0.4, 0.6
  3. 450 mm Hg, 0.5, 0.5
  4. 500 mm Hg, 0.4, 0.6

Solution

Raoult’s law for ideal solution,

PTotal=PA+ PB

PTotal=xA×PA∘+ xB×PB∘

PTotal=12×400+12×600=500 mm of Hg

Dalton’s law,

yA×PTotal=PA 

yA=xA×PA0PTotal=12×400500=0.4

yB=1-0.4=0.6 

Asked in: JEE Main 2019 (08 Apr Shift 1)

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