Question

Two liquids A and B are mixed In such a promotion that they form an ideal solution whose total vapour pressure is three times the partial pressure of A . if PA and PB are vapour pressures of pure A and B respectively , then the total vapour pressure of solution is given by .......
1 - 2 PA PB/3 PA+PB
2 - 3 PA PB/2PA+PB
3 - 2 PA/2PA+PB
4 - 2PB/PA+2PB

Answer 1

Two liquids A and B are mixed in such a way that they form an ideal solution whose total vapor pressure is three times the partial pressure of A.

here PA and PB are vapor pressures of pure A and B respectively.

To find : total vapor pressure of solution.

solution : we know, partial vapor pressure of A, P'A = xA PA .....(1)

total vapor pressure of the solution is given by,

P = PB + xA(PA - PB)

given, P = 3P'A .....(2)

from equations (1) and (2) we get,

PB + xA(PA - PB) = 3xA PA

⇒PB = 3xA PA - xA(PA - PB)

⇒PB = 3xA PA - xA PA + xA PB

⇒PB = xA (2PA + PB)

⇒xA = PB/(2PA + PB) .......(3)

now putting equation (3) in equation (2) we get,

P = PB + PB/(2PA + PB) × (PA - PB)

= {2PA PB + PB² + PA PB - PB²}/(2PA + PB)

= 3PA PB/(2PA + PB)

Therefore the total vapor pressure of solution is 3PA PB/(2PA + PB) i.e., option (2) is correct choice.