Question

PA and PB are the vapour pressure of pure liquid components,
A and B, respectively of an ideal binary solution. If XA
represents the mole fraction of component A, the total
pressure of the solution will be.
(a) PA + XA (PB – PA) (b) PA + XA (PA – PB)
(c) PB + XA (PB – PA) (d) PB + XA (PA – PB)

Answer 1

The total pressure of the solution is PB + XA (PA – PB).

Total liquids = 2 = A and B (GIven)

Vapour pressure = PA and PB (GIven)

Therefore,

Vapour pressure of A = XaPa

Vapour pressure of B = XbPb

= ( 1 - Xa) Pb

Total pressure = Vapour pressure of A + Vapour pressure of B

= XaXa + ( 1 - Xa)Pb

= Pb + Xa ( Pa - Pb)

Therefore, the total pressure of the solution is  Pb + Xa ( Pa - Pb).