property = solute concentration x constant
|Property||Symbol||Solute Concentration||Proportionality Constant|
|Vapor pressure||DP||mole fraction||Po (vapor pressure of pure solvent)|
|Boiling Point||DTb||molal||Kb (bpoilng point constant)|
|Freezing Point||DTf||molal||Kf (freezing point constant)|
The determination of colligative properties allows us to
Psolvent = Xsolvent Posolventor DP = Xsolute Posolvent
where Psolvent is the vapor pressure of the solvent
on the solution, Xsolvent and Xsolute is the
mole fraction of the solvent or solute, respectively. (Xsolvent
+ Xsolute = 1). Posolvent is the vapor
pressure of the pure solvent, and DP is the
lowering in vapor pressure.
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? (answer: vapor pressure lowering DP= 2.4 torr; X solute = 0.026)
The boiling points of solutions are all higher than that of the pure solvent. Difference between the boiling points of the pure solvent and the solution is proportional to the concentration of the solute particles:
DTb = Tb (solution) - Tb (solvent) = Kb x mwhere DTb is the boiling point elevation, Kb is the boiling point elevation constant, and m is the molality (mol/kg solvent) of the solute.
Exercise: A solution is prepared when 1.20 g of a compound is dissolved in 20.0 g of benzene. The boiling point of the solution is 80.94 oC.
Freezing Point Depression:
The freezing points of solutions are all lower than that of the pure solvent. The freezing point depression is directly proportional to the molality of the solute.
DTf = Tf(solvent) - Tf (solution) = Kf x mwhere DTf is the freezing point depression,Tf (solution) is the freezing point of the solution, Tf(solvent) is the freezing point of the solvent,Kf is the freezing point depression constant, and m is the molality.
Osmosis is the diffusion of a fluid through a semipermeable membrane. When a semipermeable membrane (animal bladders, skins of fruits and vegetables) separates a solution from a solvent, then only solvent molecules are able to pass through the membrane. The osmotic pressure of a solution is the pressure difference needed to stop the flow of solvent across a semipermeable membrane. The osmotic pressure of a solution is proportional to the molar concentration of the solute particles in solution.
P = nRT/V = MM RT
where is the osmotic pressure, R is the ideal gas constant (0.0821 L
atm / mol K), T is the temperature in Kelvin, n is the number of moles
of solute present, and V is the volume of the solution (n/V is then the
molar concentration of the solute), and MM is the molar mass of
Exercise:Hemoglobin is a large molecule that carries oxygen in human blood. A water solution that contains 0.263 g of hemoglobin (Hb) in 10.0 mL of solution has an osmotic pressure of 7.51 torr at 25oC. What is the molar mass of the hemoglobin? (answ.: 6.51 x 104 g/mol)