Colligative Properties
• Changes in colligative properties depend
only on the number of solute particles
present, not on the identity of the solute
particles.
• Among colligative properties are
– Vapor pressure lowering
– Boiling point elevation
– Melting point depression
– Osmotic pressure
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Colligative Properties:
•Vapor Pressure
•Freezing Point Depression
•Boiling Point Elevation
•Osmotic Pressure
Vapor Pressure
Because of solutesolvent intermolecular
attraction, higher
concentrations of
nonvolatile solutes make
it harder for solvent to
escape to the vapor
phase.
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Raoult’s Law
PA = XAPA
where
– XA is the mole fraction of compound A, and
– PA is the normal vapor pressure of A at that
temperature.
NOTE: This is one of those times when you want
to make sure you have the vapor pressure of
the solvent.
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Vapor Pressure:
• Raoult’s Law: Psolution = XsolventPoH2O
12g Sucrose (C12H22O11)is dissolved in
250.0g water at 90 °C.
What is the vapor pressure of water over
this solution?
(PoH2O = 525.8 mmHg- from data table)
•
Ans. 524 mmHg
Boiling Point Elevation and Freezing
Point Depression
Nonvolatile solutesolvent interactions also
cause solutions to have
higher boiling points
and lower freezing
points than the pure
solvent.
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Boiling Point Elevation
• The change in boiling point
is proportional to the
molality of the solution:
Tb = Kb  m
where Kb is the molal
boiling point elevation
constant, a property of the
solvent.
Tb is added to the normal boiling point
of the solvent.
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Boiling Point Elevation
• The change in freezing
point can be found
similarly:
Tf = Kf  m
• Here Kf is the molal
freezing point depression
constant of the solvent.
Tf is subtracted from the normal boiling point of
the solvent.
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Boiling Point Elevation and Freezing
Point Depression
Note that in both
equations, T does not
depend on what the
solute is, but only on
how many particles are
dissolved.
Tb = Kb  m
Tf = Kf  m
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Freezing Point Depression:
• Freezing Point Depression: ΔTfp = Kfpmsolution
• A solution is prepared by adding 0.50g of caffeine
(C8H10O2N4) to 100g of benzene (C6H6).
• Calculate the freezing point of this solution.
• The freezing point of pure benzene is 5.50°C
• Kfp for benzene = 5.23 °C/m)
Ans.: 0.132 ° C
Tfreezing= 5.37C
Boiling Point Elevation:
• Boiling point elevation: ΔTbp = Kbpmsolute
• A glycerol solution (C3H8O3) in water is prepared by
dissolving glycerol is 500g water. The boiling point of
the solution is 100.42°C at 760mmHg. What mass of
glycerol was dissolved to make this solution?
• Kbp = 0.5121 °C/m
Ans: 38 g glycerol
Colligative Properties of Electrolytes
Since these properties depend on the number of particles
dissolved, solutions of electrolytes (which dissociate in
solution) should show greater changes than those of
nonelectrolytes.
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van’t Hoff Factor
• We modify the
previous equations by
multiplying by the
van’t Hoff factor, i.
Tf = Kf  m  i
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van’t Hoff Factor
• Reassociation is more
likely at higher
concentration.
• Therefore, the
number of particles
present is
concentrationdependent.
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Role of Electrolytes on Colligative
Properties:
• Van’t Hoff Factor: ΔTfp = Kfpmsolutei
• A 0.0711m aqueous solution of Sodium sulfate
freezes at -0.32C. What is the actual value (i) of the
van’t Hoff factor? Kfp = 1.86 °C/m
Ans: i = 2.42
Rank for following:
• Increasing boiling point (ΔTb)
– 0.25 m C6H12O11
– 0.40 m NaCl
– 0.15 m MgCl2
C6H12O11  MgCl2  NaCl
Osmosis
In osmosis, there is net movement of solvent from
the area of higher solvent concentration (lower
solute concentration) to the are of lower solvent
concentration (higher solute concentration).
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Osmotic Pressure
The pressure required to stop osmosis,
known as osmotic pressure, , is
=(
n
)
RT = MRT
V
where M is the molarity of the solution.
If the osmotic pressure is the same on both sides of a membrane (i.e.,
the concentrations are the same), the solutions are isotonic.
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Osmosis in Blood Cells
• If the solute
concentration outside
the cell is greater than
that inside the cell, the
solution is hypertonic.
• Water will flow out of
the cell, and crenation
results.
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Osmosis in Cells
• If the solute
concentration outside
the cell is less than that
inside the cell, the
solution is hypotonic.
• Water will flow into the
cell, and hemolysis
results.
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Osmotic Pressure
• Osmotic Pressure: π= MRT
• What is the osmotic pressure of a 0.1M solution
of sucrose at 25C?
(remember: R= .08206 L-atm/mol-K)
Ans: 2.45 atm
Another Osmotic pressure problem.
• 100. mg of a protein are dissolved in enough
water to make 10.0 mL of a solution.
• If this solution has an osmotic pressure of 13.3
mmHg at 25°C, what is the molar mass of the
protein?
Ans: 1.4 x 104 g/mole
VP problem
• How would you prepare 1.00L of an aqueous
oxalic acid, H2C2O4, solution (d= 1.05 g/mL)
with a vapor pressure of 21.97 mmHg at 24°C
(H20 vp = 22.38 mmHg)?
Ans. Dissolve 89g in 1.0 L solution