# Vapor Pressure Lowering

The vapor pressure of a solvent in a solution is always lower than the vapor pressure of the pure solvent. The vapor pressure lowering is directly proportional to the mole fraction of the solute.

$P_{solvent} = X_{solvent} P^o_{solvent}$

or

$\Delta P = X_{solute} P^o_{solvent}$

where Psolvent  is the vapor pressure of the solvent on the solution, $$X_{solvent}$$ and $$X_{solute}$$ is the mole fraction of the solvent or solute, respectively. (Xsolvent + Xsolute = 1). Posolvent is the vapor pressure of the pure solvent, and $$\Delta P$$ is amplitude of the vapor pressure lowering .

Exercise

At 25oC the vapor pressure of pure benzene is 93.9 torr. When a non-volatile solvent is dissolved in benzene, the vapor pressure of benzene is lowered to 91.5 torr. What is the concentration of the solute and the solvent, expressed in mole fraction?

Vapor pressure lowering $$\Delta P= 2.4\; torr$$ with $$X_{solute} = 0.026$$.