Colligative Properties Vapour pressure Boiling point Freezing point Osmotic pressure
Learning objectives Describe meaning of colligative property Use Raoult s law to determine vapor pressure of solutions Describe physical basis for vapor pressure lowering Predict magnitude of vapor pressure lowering based on chemical formula Calculate osmotic pressure in solution and use to determine molar mass of solute Predict direction of deviation in non-ideal cases based on intermolecular forces
Physical vs Chemical Mixing is physical process; chemical properties don t change Properties of solutions are similar to those of the pure substances Addition of a foreign substance to water alters the properties slightly
Colligative: particles are particles Colligative comes from colligate to tie together Colligative properties have common origin Colligative properties depend on amount of solute but do not depend on its chemical identity Solute particles exert their effect merely by being rather than doing The effect is the same for all solutes
Colligative properties for nonvolatile solutes: Take it to the bank Vapour pressure is always lower Boiling point is always higher Freezing point is always lower Osmotic pressure drives solvent from lower concentration to higher concentration
Non-volatile solutes and Raoult s law Vapor pressure of solvent in solution containing nonvolatile solute is always lower than vapor pressure of pure solvent at same T At equilibrium rate of vaporization = rate of condensation Solute particles occupy volume reducing rate of evaporationthe number of solvent molecules at the surface The rate of evaporation decreases and so the vapor pressure above the solution must decrease to recover the equilibrium
Molecular view of Raoult s law: Boiling point elevation In solution vapor pressure is reduced compared to pure solvent Liquid boils when vapor pressure = atmospheric pressure Must increase T to make vapor pressure = atmospheric
Molecular view of Raoult s law: Freezing point depression Depends on the solute only being in the liquid phase Fewer water molecules at surface: rate of freezing drops Ice turns into liquid Lower temperature to regain balance Depression of freezing point
Raoult s Law Vapor pressure above solution is vapor pressure of solvent times mole fraction of solvent in solution P =P soln solv X solv Vapour pressure lowering follows: so ln P =P solv X solute
Counting sheep (particles) The influence of the solute depends only on the number of particles Molecular and ionic compounds will produce different numbers of particles per mole of substance 1 mole of a molecular solid 1 mole of particles 1 mole of NaCl 2 moles of particles 1 mole of CaCl 2 3 moles of particles
Solution Deviants Like ideal gas law, Raoult s Law works for an ideal solution Real solutions deviate from the ideal Concentration gets larger Solute solvent interactions are unequal Solvent solvent interactions are stronger than the solute solvent: P vap is higher Solvent solute interactions are stronger than solvent solvent interactions: P vap is lower
Incomplete dissociation Not all ionic substances dissociate completely Van t Hoff factor accounts for this Van t Hoff factor: i = moles of particles in soln/moles of solute dissolved
Riding high on a deep depression Blue curves are phase boundaries for pure solvent Red curves are phase boundaries for solvent in solution Freezing point depression Pure solid separates out at freezing negative T f Boiling point elevation Vapour pressure in solution is lower, so higher temperature is required to reach atmospheric positive T b
Magnitude of elevation Depends on the number of particles present Concentration is measured in molality (independent of T) T K m b = b K b is the molal boiling point elevation constant Note: it is the number of particles
Magnitude of depression Analagous to boiling point, the freezing point depression is proportional to the molal concentration of solute particles T f = m For solutes which are not completely dissociated, the van t Hoff factor is applied to modify m: T f K = f K f m i
Osmosis: molecular discrimination A semi-permeable membrane discriminates on the basis of molecular type Solvent molecules pass through Large molecules or ions are blocked Solvent molecules will pass from a place of lower solute concentration to higher concentration to achieve equilibrium
Osmotic pressure Solvent passes into more conc solution increasing its volume The passage of the solvent can be prevented by application of a pressure The pressure to prevent transport is the osmotic pressure
Calculating osmotic pressure The ideal gas law states But n/v = M and so PV =nrt Π=MRT Where M is the molar concentration of particles and Π is the osmotic pressure Note: molarity is used not molality
Osmotic pressure and molecular mass Molar mass can be computed from any of the colligative properties Osmotic pressure provides the most accurate determination because of the magnitude of Π 0.0200 M solution of glucose exerts an osmotic pressure of 374.2 mm Hg but a freezing point depression of only 0.02ºC
Determining molar mass A solution contains 20.0 mg insulin in 5.00 ml develops an osmotic pressure of 12.5 mm Hg at 300 K M = Π RT M = 12.5mmHg 1 760mmHg L atm 0.0821 300K mol K = 6.68 10 4 M
Moles insulin = MxV = 3.34x10-6 mol Molar mass = mass of insulin/moles of insulin = 0.0200 g/3.34x10-6 mol = 5990 g/mol
Volatile solute: two liquids Total pressure is the sum of the pressures of the two components P = P + total A P B P total = P o A X A + P o B X B
Ideal behaviour of liquid mixture Total pressure in a mixture of toluene (b.p. = 110.6ºC) and benzene (b.p. = 80.1ºC) equals sum of vapor pressures of components P total = P o ben X ben + P o tol X tol
Deviations from ideal Real solutions can deviate from the ideal: Positive (P vap > ideal) solute-solvent interactions weaker Negative (P vap < ideal) solute-solvent interactions stronger
Fractional distillation: separation of liquids with different boiling points The vapour above a liquid is richer in the more volatile component Boiling the mixture will give a distillate more concentrated in the volatile component The residue will be richer in the less volatile component
Purification in stages A 50:50 mixture produces a vapour with a 71:29 composition That mixture boiled produces a vapour with a 86:14 composition That mixture boiled produces a vapour with a composition 94:6
The practice of fractional distillation In practice, it is not necessary to do the distillation in individual steps The vapour rising up the column condenses and re-evaporates continuously, progressively becoming enriched in the volatile component higher up the tube If the column is high enough, pure liquid will be collected in the receiver