Question

# Two liquids A and B form ideal solutions. At 300 K, the vapour pressure of a solution containing 1 mole of A and 3 moles of B is 550 mm Hg. At the same temperature, if one more mole of B is added to this solution, the vapour pressure of the solution increases by 10 mm Hg. The vapour pressure of A and B in their pure states are respectively:

A
poA=600 mm Hg and poB=400 mm Hg
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B
poA=500 mm Hg and poB=560 mm Hg
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C
poA=450 mm Hg and poB=650 mm Hg
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D
poA=400 mm Hg and poB=600 mm Hg
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Solution

## The correct option is D poA=400 mm Hg and poB=600 mm HgLet, PoA and PoB be the pure liquid pressure of A and B respectively.Case - I:nA=1 mol;nB=3 mol;P1=550So, xA=nAnA+nB=11+3=0.25 xB=1−xA=1−0.25=0.75Now,PT=xAPoA+xBPoB550=0.25PoA+0.75PoB ------- eqn. 1Case - II:nA=1 mol;nB=4 mol;P1=560So, xA=nAnA+nB=11+4=0.20 xB=1−xA=1−0.20=0.80Now,PT=xAPoA+xBPoB560=0.20PoA+0.80PoB ------- eqn. 2Solving eqn. 1 and eqn. 2 we getPoA=400 mm and PoB=600 mm

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