Biphenyl, C12H10, is a nonvolatile, nonionizing solute that is soluble in benzene, C6H6.

Question

At 25 ∘C, the vapor pressure of pure benzene is 100.84 Torr. What is the vapor pressure of a solution made from dissolving 19.7 g of biphenyl in 30.3 g of benzene?

Answer 1

When a solute (biphenyl) is dissolved in a solvent (benzene), the vapor pressure of the pure solvent is going to be reduced. The amount it is reduced depends on the amount of solute added, and hence on the amount of pure solvent left. This is Raoult's Law.

This law essentially says that the vapor pressure of the new solution will be the vapor pressure of the pure solvent times the mole fraction of the solvent. It often looks like this...

P_x = X_xP_xº where P_x = vapor pressure of solution; X_x = mol fraction of solvent; P_xº = vapor pressure pure

In this problem, we will first find the mol fraction of the solvent, benzene.

moles biphenyl = 19.7 g x 1 mol/154 g = 0.1279 moles

moles benzene = 30.3 g x 1 mol/78 g = 0.4280 moles

Total moles = 0.5559 moles

Mole fraction of benzene = 0.4280 / 0.5559 = 0.7699

Now we can find the vapor pressure of the solution...

vapor pressure of solution = vapor pressure of pure benzene x mol fraction of benzene

vapor pressure of solution = 100.84 torr x 0.7699 = 77.6 torr (3 sig. figs.)