Colligative Properties Vapour pressure Boiling point Freezing point Osmotic pressure

Learning objectives Describe meaning of colligative property Describe meaning of colligative property Use Raoult’s law to determine vapor pressure of solutions Use Raoult’s law to determine vapor pressure of solutions Describe physical basis for vapor pressure lowering Describe physical basis for vapor pressure lowering Predict magnitude of vapor pressure lowering based on chemical formula Predict magnitude of vapor pressure lowering based on chemical formula Calculate osmotic pressure in solution and use to determine molar mass of solute 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 Predict direction of deviation in non-ideal cases based on intermolecular forces

Physical vs Chemical Mixing is physical process; chemical properties don’t change Mixing is physical process; chemical properties don’t change Properties of solutions are similar to those of the pure substances Properties of solutions are similar to those of the pure substances Addition of a foreign substance to water alters the properties slightly Addition of a foreign substance to water alters the properties slightly

Colligative: particles are particles Colligative comes from colligate – to tie together Colligative comes from colligate – to tie together Colligative properties have common origin Colligative properties have common origin Colligative properties depend on amount of solute but do not depend on its chemical identity 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 Solute particles exert their effect merely by being rather than doing The effect is the same for all solutes The effect is the same for all solutes

Colligative properties for nonvolatile solutes: Take it to the bank Vapour pressure is always lower Vapour pressure is always lower Boiling point is always higher Boiling point is always higher Freezing point is always lower Freezing point is always lower Osmotic pressure drives solvent from lower concentration to higher concentration 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 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 At equilibrium rate of vaporization = rate of condensation Solute particles occupy volume reducing rate of evaporationthe number of solvent molecules at the surface 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 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 In solution vapor pressure is reduced compared to pure solvent Liquid boils when vapor pressure = atmospheric pressure Liquid boils when vapor pressure = atmospheric pressure Must increase T to make vapor pressure = atmospheric 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 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 Vapor pressure above solution is vapor pressure of solvent times mole fraction of solvent in solution Vapour pressure lowering follows: Vapour pressure lowering follows:

Counting sheep (particles) The influence of the solute depends only on the number of 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 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 a molecular solid → 1 mole of particles 1 mole of NaCl → 2 moles of particles 1 mole of NaCl → 2 moles of particles 1 mole of CaCl 2 → 3 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 Like ideal gas law, Raoult’s Law works for an ideal solution Real solutions deviate from the ideal Real solutions deviate from the ideal Concentration gets larger Concentration gets larger Solute – solvent interactions are unequal Solute – solvent interactions are unequal Solvent – solvent interactions are stronger than the solute – solvent: P vap is higher 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 Solvent – solute interactions are stronger than solvent – solvent interactions: P vap is lower

Incomplete dissociation Not all ionic substances dissociate completely Not all ionic substances dissociate completely Van’t Hoff factor accounts for this Van’t Hoff factor accounts for this Van’ t Hoff factor: i = moles of particles in soln/moles of solute dissolved i = moles of particles in soln/moles of solute dissolved

Riding high on a deep depression Blue curves are phase boundaries for pure solvent Blue curves are phase boundaries for pure solvent Red curves are phase boundaries for solvent in solution Red curves are phase boundaries for solvent in solution Freezing point depression Freezing point depression Pure solid separates out at freezing – negative ΔT f Pure solid separates out at freezing – negative ΔT f Boiling point elevation Boiling point elevation Vapour pressure in solution is lower, so higher temperature is required to reach atmospheric – positive ΔT b Vapour pressure in solution is lower, so higher temperature is required to reach atmospheric – positive ΔT b

Magnitude of elevation Depends on the number of particles present Depends on the number of particles present Concentration is measured in molality (independent of T) Concentration is measured in molality (independent of T) K b is the molal boiling point elevation constant K b is the molal boiling point elevation constant Note: it is the number of particles 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 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: 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 A semi-permeable membrane discriminates on the basis of molecular type Solvent molecules pass through Solvent molecules pass through Large molecules or ions are blocked Large molecules or ions are blocked Solvent molecules will pass from a place of lower solute concentration to higher concentration to achieve equilibrium 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 Solvent passes into more conc solution increasing its volume The passage of the solvent can be prevented by application of a pressure The passage of the solvent can be prevented by application of a pressure The pressure to prevent transport is the osmotic pressure The pressure to prevent transport is the osmotic pressure

Calculating osmotic pressure The ideal gas law states The ideal gas law states But n/V = M and so But n/V = M and so Where M is the molar concentration of particles and Π is the osmotic pressure Where M is the molar concentration of particles and Π is the osmotic pressure Note: molarity is used not molality Note: molarity is used not molality

Osmotic pressure and molecular mass Molar mass can be computed from any of the colligative properties Molar mass can be computed from any of the colligative properties Osmotic pressure provides the most accurate determination because of the magnitude of Π Osmotic pressure provides the most accurate determination because of the magnitude of Π M solution of glucose exerts an osmotic pressure of mm Hg but a freezing point depression of only 0.02ºC M solution of glucose exerts an osmotic pressure of 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 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 Moles insulin = MxV = 3.34x10 -6 mol Molar mass = mass of insulin/moles of insulin Molar mass = mass of insulin/moles of insulin = g/3.34x10 -6 mol = g/3.34x10 -6 mol = 5990 g/mol = 5990 g/mol

Volatile solute: two liquids Total pressure is the sum of the pressures of the two components 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 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: Real solutions can deviate from the ideal: Positive (P vap > ideal) solute-solvent interactions weaker Positive (P vap > ideal) solute-solvent interactions weaker Negative (P vap < ideal) solute-solvent interactions stronger 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 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 Boiling the mixture will give a distillate more concentrated in the volatile component The residue will be richer in the less 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 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 86:14 composition That mixture boiled produces a vapour with a composition 94:6 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 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 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 If the column is high enough, pure liquid will be collected in the receiver