# The vapor pressure of water at 338 K is 187.5 torr. Calculate the vapor pressure of water above a solution prepared by adding 16.2 g of lactose (C12H22O11) to 105.7 g of water at 338 K.

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### 1 Answer

The molar mass of lactulose is =(12*12+22*1+16*11) = 342

From Rauolt’s law, we know, relative lowering of vapour pressure is equal to the mole fraction of the solute.

Mathematically, `(P_1 - P_1^o)/P_1^o = x_2 `

Here, p1(o) = 187.5 torr,

P1 has to be determined.

x2 = mole fraction of the solute = `(16.2/342)/(16.2/342+105.7/18)`

=0.047368/(0.047368+5.87222) = 0.008

Putting these values, in the vapour pressure equation, (p1-187.5)/187.5 = 0.008

or, p1 - 187.5 = 1.5

or, p1 = 187.5 + 1.5

=189 torr.

So, the vapour pressure over of water above lactulose solution is 189 torr.

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