Colligative Properties

Colligative Properties

 Colligative properties depend on quantity of solute molecules.  Vapor pressure lowering  Boiling point elevation  Freezing point depression  Osmotic pressure

Colligative Properties of Solutions

Definition:

Properties, that depend on the NUMBER particles present in solution of solute

Concentration:

Osmol per liter

or osmolarity An OSMOL is a mole of solute particle

C 6 H 12 O 6

does not dissociate

1 M (6 x 10 23 ) C 6 H 12 O 6 1 osmol/L NaCl

does dissociate

Na + + Cl 1 M 1 osmol/L 1 osmol/L 2 osmol/L 2 x (6 x 10 23 )

Lowering the Vapor Pressure

  Non-volatile solvents reduce the ability of the surface solvent molecules to escape the liquid.

 Therefore, vapor pressure is lowered.

The amount of vapor pressure lowering depends on the amount of solute.

solvent solution

Vapor pressure lowering

   

Raoult’s Law – a nonvolatile water.

law.

solute will lower the vapor pressure of a solvent Pure water will have a higher vapor pressure than salt Ideal solution: one that obeys Raoult’s Raoult’s law breaks down when the solvent-solvent and solute-solute intermolecular forces are greater than solute-solvent intermolecular forces.

P solution  Χ solvent P  solvent P solution  vapor pressure of the solution Χ solvent  mole fraction of the solvent Χ solvent 

n n solvent solvent



n solute i

P  solvent 

vapor

pressure of pure solvent i  van ' t Hoff factor

Phase Diagram Analysis

760 torr

Liquid Solid ΔT m Gas

Temperature

ΔT b

Boiling-Point Elevation

Interpret the phase diagram for a solution.

Non-volatile solute lowers the vapor pressure.

At 1 atm (normal bp of pure liquid) there is a lower vapor pressure of the solution.  a higher bp is required to reach a vapor pressure of 1 atm for the solution.

ΔTb = Kbmi

Freezing-Point Depression

Solvent Water Acetic acid Benzene Chloroform Camphor Cyclohexane Bp (°C) Kb (°C m–1) Mp (°C) Km (°C m–1) 100 118 80 61 – 81 0.51

3.07

2.53

3.63

– 2.69

0 17 5.5

– 178 6.5

1.86

3.57

5.07

– 37.7

20.0

 ΔT b  K b = change in bp = bp constant for solvent  m = molality of solute  i = van ‘t Hoff factor

Freezing-Point Depression

  At 1 atm (normal boiling point of pure liquid) there is no depression by definition The solution freezes at a lower temperature (ΔT f ) than the pure solvent.

 Decrease in freezing point (ΔT f ) is directly is the molal freezing-point proportional to molality (K f depression constant):  ΔT f = K f mi  Colligative properties can be used to determine the MW of an unknown compound.

1. Vapor pressure lowering

Raoult’s law P soln = X solv P 0 P soln = vapor pressure of solution X solv = mole fraction of solvent P 0 = vapor pressure of pure solvent

2. Freezing point depression

D

T f = K f m

D

T f = freezing point depression K f = cryoscopic constant m= molality

3. Boiling point elevation

D

T b = K b m

D

T= boiling point elevation K b = ebullioscopic constant m= mola l ity

Cryoscopic and ebullioscopic constants

Solvent

Water

K f

1.86

K b

0.52

Benzene Phenol 5.12

2.53

7.40

3.56

°C kg solvent (mol solute) -1

4. Osmotic pressure

p

= M



RT

p

= osmotic pressure M = mola r ity R = 8.314 JK -1 mol -1

Osmotic Pressure



Semipermeable membrane: permits passage of some components of a solution. Example: cell membranes and cellophane.



Osmosis: the movement of a solvent from low solute concentration to high solute concentration.



There is movement in both directions across a semipermeable membrane.



As solvent moves across the membrane, the fluid levels in the arms becomes uneven.



Eventually the pressure difference between the arms stops osmosis.

Concentrated solution Membrane Dilute solution

Osmotic Pressure

 Osmotic pressure, P, is the pressure required to stop osmosis.

 Isotonic solutions: two solutions with the same P separated by a semipermeable membrane.

 Hypotonic solutions: a solution of lower P than a hypertonic solution.

 Osmosis is spontaneous.



V



nRTi

    

n V

   

RTi MRTi

Osmotic Pressure & Biology

 Red blood cells are surrounded by semipermeable membranes.

 Crenation:   red blood cells placed in hypertonic solution (a lower solute concentration exists in the cell) osmosis occurs and water passes out of the cell causing the cell to shrivel up.

 Hemolysis is opposite   red blood cells placed in a hypotonic solution (a higher solute concentration in the cell) water moves into the cell causing the cell to burst.

 To prevent crenation or hemolysis, IV (intravenous) solutions must be isotonic.

Osmotic Pressure Applications



Pickling food by placing in salty solutions.



Water moves into plants through osmosis.

 

Salt added to meat or sugar to fruit prevents bacterial infection (a bacterium placed on the salt will lose water through osmosis and die).

Dialysis machines work by osmosis.



Reverse osmosis is used in desert countries to produce drinking water from the sea.

P > P

Salty sea water would normally draw in more water to this side Drinking water is produced by applying a pressure that exceeds P .

Electrolytes

‘Anomalous’ behavior: 1.

2.

Ability to conduct electric current Greater effect on colligative properties

D

T f values: (k f = 1.86

°C for H 2 O) Sucrose NaCl 0.001 m 0.00186

0.00366

K2SO4 0.00528

K3[Fe(CN)6] 0.00710

0.01 m 0.0186

0.0360

0.0501

.0626

0.1 m 0.188

0.348

0.432

0.530

van’t Hoff factor: i i = measured value expected value

D

T f = K f m i =

D

T f K f m

D

T f = i K f m

D

T b = i K b m

p

= i MRT

i values:

Sucrose HCl KCl MgSO 4 K 2 SO 4 0.1

1.01

1.89

1.85

1.21

2.32

0.01 m 1.00

1.94

1.94

1.53

2.70

0.001 m 1.00

Infinite dilution 1.00

1.98

1.98

2.00

2,00 1.82

2.84

2,00 3.00