Question

Which expression of relative lowering of vapour pressure is correct:
delta P/initial vapour pressure of the solvent(P^0)
OR
DeltaP/vapour pressure of solution(Ps)

Answer 1

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 p₁^o be the vapour pressure of the solvent in a pure state.

According to Raoult’s Law:

p₁=x₁p₁^o…………………………..(1)

The decrease in vapour pressure of the solvent (∆p₁) is given by:

=> ∆p₁=p₁^o-p₁

=> ∆p₁=p₁^o-p₁^ox₁ [using equation (1)]

=> ∆p₁=p₁^o (1-x₁)

Since we have assumed the solution to be binary solution, x₂=1-x₁

=> ∆p₁=p₁^ox₂

=> x₂= ∆p₁/p₁^o

The above equation gives the relative lowering of vapour pressure which is equal to the mole fraction of the solute.