Colligative Properties

Vapour pressureBoiling point

Freezing pointOsmotic 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:

solvsolvso XPP ln

solutesolvso XPP ln

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: molality is calculated in terms of particles

mKT bb

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:

mKT ff

imKT ff

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 volume

Passage of solvent can be prevented by applying pressure

Pressure required to prevent transport equals 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

nRTPV

MRT

Osmotic pressure and molecular mass

Molar mass can be determined using 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 osmotic pressure of 374 mm Hg (0.5 atm) but freezing point depression of only 0.02ºC

Determining molar mass A solution contains 20.0 mg insulin in

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

RTM

M

KKmol

atmL

mmHgmmHg

M 41068.6

3000821.0

76015.12

Converting molarity to molar mass:

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

BAtotal PPP

BBAAtotal XPXPP

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

toltolbenbentotal XPXPP

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 rich in hexane

That mixture condensed is about 90:10 hexane

The 90:10 mixture produces vapour about 95:5

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