Colligative Properties II
Boiling Point Elevation
• The boiling point of a volatile solvent is elevated
by the addition of a non-volatile solute
ΔTb = Tb - Tb0
ΔTb = boiling point elevation
Tb = boiling point of solution
Tb0= boiling point of pure solvent
But: ΔTb∝ ΔP
∴ ΔTb∝ solute concentration
(molality - moles/kg)
Cannot use molarity (moles/Volume) because
volume changes with temperature
ΔTb = K b Cm
Cm = molal concentration
Kb = molal boiling point elevation constant
e.g. Kb (Water) = 0.52 K / molal
Any aqueous solution with molality 1.0 has a boiling
point of 373.15 + 0.52 = 373.65 K
Colligative Properties III
Freezing Point Depression
• Addition of any solute to a liquid results in a
lowering of its freezing point
ΔTf = Tf0 - Tf
ΔTf = freezing point depression
Tf = freezing point of solution
Tf0= freezing point of pure solvent
ΔTf∝ solute concentration
(molality - moles/kg)
ΔTf = K f Cm
Cm = molal concentration
Kf = molal freezing point depression constant
e.g. Kf (Water) = 1.858 K / molal
Any aqueous solution with molality 1.0 has a
freezing point of 273.15 - 1.858 = 271.292 K
Uses
• spread salt on roads to lower freezing point of H2O
• add ethylene glycol (or methanol) to H2O to form
an anti-freezing agent for car radiators
Ionic Solutions
• Colligative properties of ionic solutions are greater
than those of molecular solutions
e.g. 1.0 molal solutions of NaCl and sucrose in H2O
ΔTf(sucrose) = 1.858 K
ΔTf(NaCl) = 3.716 K
Every unit of NaCl yields 2 particles (Na+ and Cl-) in
solution - colligative properties twice those of sucrose
Ionic Solutions
• Adjust equations for colligative properties
ΔTf = iK f Cm
ΔTb = iK b Cm
i= number of particles in solution after dissociation
number of particles initially dissolved
Solute
sucrose
NaCl
MgSO4
MgCl2
FeCl3
i(calculated)
1.0
2.0
2.0
3.0
4.0
i(measured)
1.0
1.9
1.3
2.7
3.4
Ion-pair formation decreases colligative properties by
reducing the number of particles in solution
Osmosis
• Solvent molecules can diffuse or permeate
through membranes
Osmosis is the net movement of solvent molecules
through a semi-permeable membrane from a low to a
high concentration
Net movement of solvent molecules stops when solute
concentrations on either side of the membrane are
equal
e.g. Responsible for water transplant in plants
Osmosis
Osmotic Pressure
• The pressure (Π) required to stop osmosis
Π V= n R T
But n/V = Molarity (M) and ∴ Π = M R T
Π is a colligative property and depends on i
Π=iMRT
iM = Osmolarity
• Π measurements are used to determine molecular
masses of large molecules (proteins, polymers etc.)
Osmosis in Red Blood Cells
Dialysis
• Dialysis is the net movement of solute molecules
through a semi-permeable membrane from a low to a
high concentration
e.g. Hydrated ions pass through membrane but large
molecules (proteins, etc.) do not
• The kidney relies upon dialysis to remove waste
• Haemodialysis is an artificial process that mimics
the action of the kidney