Question

# At 300 K, the vapour pressure of an ideal solution containing 1 mole of A and 3 moles of B is 500 mm Hg. At the same temperature, 2 moles of B are added to this solution. The vapour pressure of the solution increases by 10% of the original vapour pressure. The correct statement(s) about the vapour pressure are :

A
The vapour pressure of A in the pure state is 1300 mm Hg
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B
The vapour pressure of B in the pure state is 650 mm Hg
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C
The ratio of the final vapour pressure to the initial vapour pressure is 2 : 1
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D
The ratio of the vapour pressure of pure B to the vapour pressure of pure A is 13 : 1
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Solution

## The correct options are B The vapour pressure of B in the pure state is 650 mm Hg D The ratio of the vapour pressure of pure B to the vapour pressure of pure A is 13 : 1 nA = 1; nB = 3; PT = 500 mm Hg When 2 moles of B is added nA = 1; nB = 5 As it is given that vapour pressure increases by 10%, Pâ€²T=500+500Ã—10100=550 500 = Pâˆ˜A(11+3)+Pâˆ˜B(31+3) 2000 = Pâˆ˜A+3Pâˆ˜Bâˆ’âˆ’âˆ’âˆ’âˆ’(1) 550 = Pâˆ˜A(16)+Pâˆ˜B(56) 3300 = Pâˆ˜A+5Pâˆ˜Bâˆ’âˆ’âˆ’âˆ’âˆ’(2) Solving (1) and (2) we get, Pâˆ˜A=50 mm Hg Pâˆ˜B=650 mm Hg Pâˆ˜APâˆ˜B=65050=13:1

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