the vapour pressure of a solvent decreased by 10mm in two columns of mercury when a non volatile solute was added to the solvent.the mole fraction of the solute in the solution is 0.2.what should be the mole fraction of the solvent if the decrease in the vapour pressure is to be 20mm of mercury

The equation governing the change in the vapor pressure when you use a nonvolatile liquid or solid is just a special case of Raoult's Law, P_tot = P_aX_a + P_bX_b. Since the second component has a negligible vapor pressure (nonvolatile), Raoult's law reduces to

P = P⁰X

where P is the vapor pressure of the mixture, P⁰ is the vapor pressure of the pure solvent and X is the mole fraction of the solvent.

Mole fraction of solute = 0.2

so mole fraction of solvent = 0.8 

So

P-10 = 0.8(P)

So P= 10/0.2 = 50

 

In second case

50-20 = x.50

30/50= x

So mole fraction of solvent = 0.6