Let us see how this lowering in vapour pressure is determined mathematically:
Let us assume a binary solution in which the mole fraction of the solvent be x1 and that of the solute be x2 , p1 be the vapour pressure of the solvent and p1o be the vapour pressure of the solvent in a pure state.
According to Raoult’s Law:
The decrease in vapour pressure of the solvent (∆p1) is given by:
=> ∆p1=p1o-p1ox1 [using equation (1)]
=> ∆p1=p1o (1-x1)
Since we have assumed the solution to be binary solution, x2=1-x1
=> x2= ∆p1/p1o
The above equation gives the relative lowering of vapour pressure which is equal to the mole fraction of the solute.