Colligative PropertiesColligative Properties

Vapour pressureVapour pressureBoiling pointBoiling point

Freezing pointFreezing pointOsmotic pressureOsmotic pressure

Learning objectivesLearning objectives

Describe meaning of colligative propertyDescribe meaning of colligative property Use Raoult’s law to determine vapor Use Raoult’s law to determine vapor

pressure of solutionspressure of solutions Describe physical basis for vapor pressure Describe physical basis for vapor pressure

loweringlowering Predict magnitude of vapor pressure Predict magnitude of vapor pressure

lowering based on chemical formulalowering based on chemical formula Calculate osmotic pressure in solution and Calculate osmotic pressure in solution and

use to determine molar mass of soluteuse to determine molar mass of solute Predict direction of deviation in non-ideal Predict direction of deviation in non-ideal

cases based on intermolecular forcescases based on intermolecular forces

Physical vs ChemicalPhysical vs Chemical

Mixing is physical process; chemical Mixing is physical process; chemical properties don’t changeproperties don’t change

Properties of solutions are similar to Properties of solutions are similar to those of the pure substancesthose of the pure substances

Addition of a foreign substance to Addition of a foreign substance to water alters the properties slightlywater alters the properties slightly

Colligative: particles are Colligative: particles are particlesparticles

Colligative comes from colligate – to tie Colligative comes from colligate – to tie togethertogether

Colligative properties have common originColligative properties have common origin Colligative properties depend on Colligative properties depend on amountamount of of

solute but do solute but do notnot depend on its chemical depend on its chemical identity identity

Solute particles exert their effect merely by Solute particles exert their effect merely by being rather than doingbeing rather than doing

The effect is the same for all solutesThe effect is the same for all solutes

Colligative properties for Colligative properties for nonvolatile solutes: nonvolatile solutes: Take it to the bankTake it to the bank

Vapour pressure is Vapour pressure is alwaysalways lower lower Boiling point is Boiling point is alwaysalways higher higher Freezing point is Freezing point is alwaysalways lower lower Osmotic pressure drives solvent from Osmotic pressure drives solvent from

lower concentration to higher lower concentration to higher concentrationconcentration

Non-volatile solutes and Raoult’s Non-volatile solutes and Raoult’s lawlaw

Vapor pressure of solvent in solution containing non-Vapor pressure of solvent in solution containing non-volatile solute is volatile solute is alwaysalways lower than vapor pressure of lower than vapor pressure of pure solvent at same Tpure solvent at same T At equilibrium rate of vaporization = rate of condensationAt equilibrium rate of vaporization = rate of condensation Solute particles occupy volume reducing rate of Solute particles occupy volume reducing rate of

evaporationthe number of solvent molecules at the surfaceevaporationthe number of solvent molecules at the surface The rate of evaporation decreases and so the vapor pressure The rate of evaporation decreases and so the vapor pressure

above the solution must decrease to recover the equilibriumabove the solution must decrease to recover the equilibrium

Molecular view of Raoult’s law:Molecular view of Raoult’s law:Boiling point elevationBoiling point elevation

In solution vapor pressure is reduced In solution vapor pressure is reduced compared to pure solventcompared to pure solvent

Liquid boils when vapor pressure = Liquid boils when vapor pressure = atmospheric pressureatmospheric pressure

Must increase T to make vapor Must increase T to make vapor pressure = atmosphericpressure = atmospheric

Molecular view of Raoult’s law:Molecular view of Raoult’s law:Freezing point depressionFreezing point depression

Depends on the solute only being in the liquid phaseDepends on the solute only being in the liquid phase Fewer water molecules at surface: rate of freezing dropsFewer water molecules at surface: rate of freezing drops Ice turns into liquidIce turns into liquid Lower temperature to regain balanceLower temperature to regain balance Depression of freezing pointDepression of freezing point

Raoult’s LawRaoult’s Law

Vapor pressure above solution is Vapor pressure above solution is vapor pressure of solvent times mole vapor pressure of solvent times mole fraction of solvent in solutionfraction of solvent in solution

Vapour pressure lowering follows:Vapour pressure lowering follows:solvsolvso XPP ln

solutesolvso XPP ln

Counting sheep (particles)Counting sheep (particles)

The influence of the solute depends only The influence of the solute depends only on the number of particleson the number of particles

Molecular and ionic compounds will Molecular and ionic compounds will produce produce differentdifferent numbers of particles per numbers of particles per mole of substancemole of substance 1 mole of a molecular solid 1 mole of a molecular solid → 1 mole of particles→ 1 mole of particles 1 mole of NaCl 1 mole of NaCl → 2 moles of particles→ 2 moles of particles 1 mole of CaCl1 mole of CaCl22 → 3 moles of particles → 3 moles of particles

Solution DeviantsSolution Deviants

Like ideal gas law, Raoult’s Law works for Like ideal gas law, Raoult’s Law works for an an idealideal solution solution

Real solutions deviate from the idealReal solutions deviate from the ideal Concentration gets largerConcentration gets larger Solute – solvent interactions are unequalSolute – solvent interactions are unequal

Solvent – solvent interactions are stronger Solvent – solvent interactions are stronger than the solute – solvent: Pthan the solute – solvent: Pvapvap is higher is higher

Solvent – solute interactions are stronger Solvent – solute interactions are stronger than solvent – solvent interactions: Pthan solvent – solvent interactions: Pvapvap is is lowerlower

Incomplete dissociationIncomplete dissociation

Not all ionic substances dissociate Not all ionic substances dissociate completelycompletely

Van’t Hoff factor accounts for thisVan’t Hoff factor accounts for this

Van’ t Hoff factor:Van’ t Hoff factor:

i i = moles of particles in soln/moles of = moles of particles in soln/moles of solute dissolvedsolute dissolved

Riding high on a deep Riding high on a deep depressiondepression

Blue curves are phase boundaries for pure Blue curves are phase boundaries for pure solventsolvent

Red curves are phase boundaries for solvent Red curves are phase boundaries for solvent in solutionin solution

Freezing point depressionFreezing point depression Pure solid separates out at freezing – negative Pure solid separates out at freezing – negative ΔΔTTff

Boiling point elevationBoiling point elevation Vapour pressure in solution is lower, so higher Vapour pressure in solution is lower, so higher

temperature is required to reach atmospheric – temperature is required to reach atmospheric – positive positive ΔΔTTbb

Magnitude of elevationMagnitude of elevation

Depends on the number of particles Depends on the number of particles presentpresent

Concentration is measured in Concentration is measured in molality (independent of T)molality (independent of T)

KKbb is the molal boiling point elevation is the molal boiling point elevation constantconstant

Note: it is the number of Note: it is the number of particlesparticles

mKT bb

Magnitude of depressionMagnitude of depression

Analagous to boiling point, the Analagous to boiling point, the freezing point depression is freezing point depression is proportional to the molal proportional to the molal concentration of solute particlesconcentration of solute particles

For solutes which are not completely For solutes which are not completely dissociated, the van’t Hoff factor is dissociated, the van’t Hoff factor is applied to modify applied to modify mm::

mKT ff

imKT ff

Osmosis: molecular Osmosis: molecular discriminationdiscrimination

A A semi-permeablesemi-permeable membrane membrane discriminates on the basis of discriminates on the basis of molecular typemolecular type Solvent molecules pass throughSolvent molecules pass through Large molecules or ions are blockedLarge molecules or ions are blocked

Solvent molecules will pass from a Solvent molecules will pass from a place of lower solute concentration place of lower solute concentration to higher concentration to achieve to higher concentration to achieve equilibriumequilibrium

Osmotic pressureOsmotic pressure

Solvent passes into more conc Solvent passes into more conc solution increasing its volumesolution increasing its volume

The passage of the solvent can be The passage of the solvent can be prevented by application of a prevented by application of a pressurepressure

The pressure to prevent transport is The pressure to prevent transport is the the osmotic pressureosmotic pressure

Calculating osmotic Calculating osmotic pressurepressure

The ideal gas law statesThe ideal gas law states

But n/V = M and soBut n/V = M and so

Where M is the molar concentration of Where M is the molar concentration of particles and particles and ΠΠ is the osmotic pressure is the osmotic pressure

Note: Note: molaritymolarity is used not is used not molalitymolality

nRTPV

MRT

Osmotic pressure and Osmotic pressure and molecular massmolecular mass

Molar mass can be computed from Molar mass can be computed from any of the colligative propertiesany of the colligative properties

Osmotic pressure provides the most Osmotic pressure provides the most accurate determination because of accurate determination because of the magnitude of the magnitude of ΠΠ 0.0200 M solution of glucose exerts an 0.0200 M solution of glucose exerts an

osmotic pressure of 374.2 mm Hg but a osmotic pressure of 374.2 mm Hg but a freezing point depression of only 0.02ºCfreezing point depression of only 0.02ºC

Determining molar massDetermining molar mass A solution contains 20.0 mg insulin A solution contains 20.0 mg insulin

in 5.00 ml develops an osmotic in 5.00 ml develops an osmotic pressure of 12.5 mm Hg at 300 Kpressure of 12.5 mm Hg at 300 K

RTM

MK

KmolatmL

mmHgmmHgM 41068.6

3000821.0

76015.12

Moles insulin = MxV = 3.34x10Moles insulin = MxV = 3.34x10-6-6 mol mol

Molar mass = mass of insulin/moles Molar mass = mass of insulin/moles of insulinof insulin

= 0.0200 g/3.34x10= 0.0200 g/3.34x10-6-6 mol mol

= 5990 g/mol= 5990 g/mol

Volatile solute: two liquidsVolatile solute: two liquids

Total pressure is the sum of the Total pressure is the sum of the pressures of the two componentspressures of the two components

BAtotal PPP

BBAAtotal XPXPP

Ideal behaviour of liquid Ideal behaviour of liquid mixturemixture

Total pressure in a mixture of toluene Total pressure in a mixture of toluene (b.p. = 110.6(b.p. = 110.6ºC)ºC) and benzene (b.p. = and benzene (b.p. = 80.180.1ºC) equals sum of vapor ºC) equals sum of vapor pressures of componentspressures of components

toltolbenbentotal XPXPP

Deviations from idealDeviations from ideal

Real solutions can deviate from the Real solutions can deviate from the ideal:ideal: Positive (PPositive (Pvapvap > ideal) solute-solvent > ideal) solute-solvent

interactions weakerinteractions weaker Negative (PNegative (Pvapvap < ideal) solute-solvent < ideal) solute-solvent

interactions strongerinteractions stronger

Fractional distillation: Fractional distillation: separation of liquids with separation of liquids with

different boiling pointsdifferent boiling points The vapour above a liquid is richer in The vapour above a liquid is richer in

the more volatile componentthe more volatile component Boiling the mixture will give a Boiling the mixture will give a

distillate more concentrated in the distillate more concentrated in the volatile componentvolatile component

The residue will be richer in the less The residue will be richer in the less volatile componentvolatile component

Purification in stagesPurification in stages

A 50:50 mixture produces a vapour A 50:50 mixture produces a vapour with a 71:29 compositionwith a 71:29 composition

That mixture boiled produces a That mixture boiled produces a vapour with a 86:14 compositionvapour with a 86:14 composition

That mixture boiled produces a That mixture boiled produces a vapour with a composition 94:6vapour with a composition 94:6

The practice of fractional The practice of fractional distillationdistillation

In practice, it is not necessary to do the In practice, it is not necessary to do the distillation in individual stepsdistillation in individual steps

The vapour rising up the column The vapour rising up the column condenses and re-evaporates condenses and re-evaporates continuously, progressively becoming continuously, progressively becoming enriched in the volatile component higher enriched in the volatile component higher up the tubeup the tube

If the column is high enough, pure liquid If the column is high enough, pure liquid will be collected in the receiverwill be collected in the receiver