Colligative Properties

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 non-volatile 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 • Vapour pressure lowering follows:

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 CaCl2 → 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: Pvap is higher • Solvent – solute interactions are stronger than solvent – solvent interactions: Pvap 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 ΔTf • Boiling point elevation • Vapour pressure in solution is lower, so higher temperature is required to reach atmospheric – positive ΔTb

Magnitude of elevation • Depends on the number of particles present • Concentration is measured in molality (independent of T) • Kb 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 • For solutes which are not completely dissociated, the van’t Hoff factor is applied to modify m:

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 • 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

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

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

Deviations from ideal • Real solutions can deviate from the ideal: • Positive (Pvap > ideal) solute-solvent interactions weaker • Negative (Pvap < 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

Colligative Properties