Question

Vapour pressure of a solution containing 6 g of a non-volatile solute in 180gm of water is 20.0 torr. If 1 mole of water is added now, the vapor pressure increases by 0.02 torr..

explain which of the following is true/false.

1) Molecular mass of solute = 54 g/mol
2 Vapor pressure of pure water = 20.22 torr
3) Addition of more water will increase the vapor pressure
4) Vapor pressure of pure water = 22.22 torr

Answer 1

the options 1,  2, 3 are true...

vapour pressure of a substance above a solution is proportional to the partial fraction (of total moles) of the substance in the solution.    180 gm = 10 moles of water.  Let M be molar mass of solute.    Let k be proportionality constant  in  Torr.

10/[10+6/M]  = k 20                      =>   10 = k 20  [10+6/M]

11/[11+6/M] = k 20.02                  =>   11 = k 20.02 [11+6/M]

     200.2*11 + 200.2*6/M   =   2200 + 220*6/M

     2.2 = 19.8*6/M                 => M = 54

     4.5 / 91 = k  =>            1/k = 910/45 = 20.2222

for pure water the vapoour pressure will be 20.22 torr...

Another way,   when mole fraction of water is increased by 0.001 from 0.989 to 0.990 above, the vapor pressure increased by 0.02 torr.    If mole fraction is increased by 0.01 to make that pure water,  the pressure increases by  0.02*10 = 0.2 torr.  So pressure will be 20.2 torr