Topic Five: Colligative Properties
- Origin of Colligative Properties
- Boiling Point Elevation
- Freezing Point Lowering
- Osmotic Pressure
- Determination of Molecular Weight
Colligative Properties of Solutions
Colligative properties represent shifts in fundamental properties of solvents:
(a) by virtue of the presence of an involatile solute
(b) they include lowering of vapour pressure (and thereby elevation of boiling point) and lowering of freezing point
(c) give rise to osmotic pressure - very important in biology
These shifts rise as a result of the entropy of mixing in the liquid solution phase which is absent in the pure solvent phase.
The extend of the effect depends only on the mole fraction of the solute - not on their identities!
Hence the name Colligative properties - "collection"
There are two assumptions
(1) The solute is not volatile
(2) The solute does not dissolve in the solid solvent after frozen
Colligative properties represent shifts in fundamental properties of solvents:
(a) by virtue of the presence of an involatile solute
(b) they include lowering of vapour pressure (and thereby elevation of boiling point) and lowering of freezing point
(c) give rise to osmotic pressure - very important in biology
These shifts rise as a result of the entropy of mixing in the liquid solution phase which is absent in the pure solvent phase.
The extend of the effect depends only on the mole fraction of the solute - not on their identities!
Hence the name Colligative properties - "collection"
There are two assumptions
(1) The solute is not volatile
(2) The solute does not dissolve in the solid solvent after frozen
Solutions
Solute + Solvent --> Solution
(i) Ionic solute in water
Each ion counts as a separate entity for colligative properties - i.e. they are all equivalent
(ii) Polymers - distribution of molecular weight - polydisperse
Biopolymers - single molecular weight 'monodisperse' e.g. enzymes
Solute + Solvent --> Solution
(i) Ionic solute in water
Each ion counts as a separate entity for colligative properties - i.e. they are all equivalent
(ii) Polymers - distribution of molecular weight - polydisperse
Biopolymers - single molecular weight 'monodisperse' e.g. enzymes
Go Back To Topic One And Revisit Chemical Potential If Required
Colligative Properties and Chemical Potential
The common feature of colligative properties is the reduction of the chemical potential of the liquid solvent as a result of the presence of solute.
The reduction form is:
The common feature of colligative properties is the reduction of the chemical potential of the liquid solvent as a result of the presence of solute.
The reduction form is:
µsolvent liquid --> µsolvent liquid + RTlnxsolvent
0 < xsolvent < 1
lnxsolvent < 0
0 < xsolvent < 1
lnxsolvent < 0
From the previous assumptions - there is no influence of the solute on the chemical potential of the solvent vapour (solute not volatile) or solvent solid (solute does not dissolve in the solid solvent after frozen)!
The physical basis of the reduction of µ
In this case, the change is not due to the interaction of the solute and solvent particles (unlike departure from ideal mixing). This occurs even for ideal solutions. Therefore the effects are entropic!!
For a pure solvent - vapour pressure reflects disorder. That is, evaporation involves molecules moving from the more organised liquid phase into the more random gas phase.
Introducing the solute increases disorder of the liquid, thereby increasing the entropy. Now its desire to form vapour is lowered, hence vapour pressure lowered and boiling point is increased.
Similarly, the more disordered liquid has a lower tendency to form solid, hence freezing point lowering.
In this case, the change is not due to the interaction of the solute and solvent particles (unlike departure from ideal mixing). This occurs even for ideal solutions. Therefore the effects are entropic!!
For a pure solvent - vapour pressure reflects disorder. That is, evaporation involves molecules moving from the more organised liquid phase into the more random gas phase.
Introducing the solute increases disorder of the liquid, thereby increasing the entropy. Now its desire to form vapour is lowered, hence vapour pressure lowered and boiling point is increased.
Similarly, the more disordered liquid has a lower tendency to form solid, hence freezing point lowering.
Concentration Units
Unit
Molarity Mole Fraction Molality |
Symbol
C or [ ] x m |
Definition
Moles of solute per unit volume (V) of solution Fraction of moles of solute in solution Moles of solute per unit mass of solvent |
Mathematical Definition
n (solute) / {V (solute) + V (solvent)} n (solute) / {n (solute) + n (solvent)} n (solute) / mass (solvent) |
Units
mol dm^-3 dimensionless mol kg^-1 |
Dilute Solutions - Elevation of a Boiling Point and Freezing Point Lowering
For dilute solutions the boiling point and freezing point shifts are given by similar equations:
For dilute solutions the boiling point and freezing point shifts are given by similar equations:
Vapour Pressure Osometry
The vapour pressure of a solvent is lowered by the presence of a solute (hence boiling point elevation)
Lowering of vapour pressure
The vapour pressure of a solvent is lowered by the presence of a solute (hence boiling point elevation)
Lowering of vapour pressure
ΔP = xsolute Psolvent*
ΔP = depression of vapour pressure
P*solvent = vapour pressure of pure solvent
xsolute = mole fraction of solute
P*solvent = vapour pressure of pure solvent
xsolute = mole fraction of solute
Dilute Solution Approximation
We seek to find a relationship between the changes in boiling point elevation and freezing point lowering:
We seek to find a relationship between the changes in boiling point elevation and freezing point lowering:
ΔTb = Kbmsolute
|
ΔTf = Kfmsolute
|
MMsolute = (Kf x masssolute) / (ΔTf x masssolvent)
Osmotic Pressure
Osmotic pressure is the spontaneous passage of pure solvent through a semi-permeable membrane into a solution.
The membrane is permeable to the solvent, but not to the solute.
The osmotic pressure, π, is the pressure that must be applied to stop the influx of the solvent.
Important in biology (cell membranes), medicine (dialysis), and engineering (reverse osmosis).
Osmotic pressure is the spontaneous passage of pure solvent through a semi-permeable membrane into a solution.
The membrane is permeable to the solvent, but not to the solute.
The osmotic pressure, π, is the pressure that must be applied to stop the influx of the solvent.
Important in biology (cell membranes), medicine (dialysis), and engineering (reverse osmosis).
Osmotic Pressure, π
This arises from net flux of solvent into solution when separated be a semi-permeable membrane (SPM).
Solvent flow creates a pressure difference P(A) < P(B)
P(A) - P(B) = π = ρgh
We can prevent osmotic flow by application of a pressure π to the solution. π is required to prevent the flow.
This arises from net flux of solvent into solution when separated be a semi-permeable membrane (SPM).
Solvent flow creates a pressure difference P(A) < P(B)
P(A) - P(B) = π = ρgh
We can prevent osmotic flow by application of a pressure π to the solution. π is required to prevent the flow.
π = (RT / (Vm)solvent)xsolvent
Reverse Osmosis - Desalination
When the pressure is greater than π the solution (water) flows against the osmotic pressure. Wide application of desalination of sea water.
P + π + ΔP
When the pressure is greater than π the solution (water) flows against the osmotic pressure. Wide application of desalination of sea water.
P + π + ΔP
π = RTcsolute (csolute = molar concentration (mol m^-3))
Topic One: Single Component Mixtures
Topic 2: Thermodynamics of Liquid Mixtures Topic 3: Thermodynamics of Non Ideal Mixtures Topic 4: Two and Three Component Mixtures Topic 5: Colligative Properties |