Colligative Properties
• Consider three beakers:
– 50.0 g of ice
– 50.0 g of ice + 0.15 moles NaCl
– 50.0 g of ice + 0.15 moles sugar (sucrose)
• What will the temperature of each
beaker be?
– Beaker 1:
– Beaker 2:
– Beaker 3:
Colligative Properties
• The reduction of the freezing point
of a substance is an example of a
colligative property:
–
A property of a solvent that depends
on the total number of solute particles
present
• There are four colligative properties
to consider:
–
–
–
–
Vapor pressure lowering (Raoult’s
Law)
Freezing point depression
Boiling point elevation
Osmotic pressure
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:
•
•
•
•
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
How Does a Solution Form
If an ionic salt is
soluble in water, it is
because the iondipole interactions
are strong enough
to overcome the
lattice energy of the
salt crystal.
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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
Energy Changes in Solution
• Simply put, three
processes affect the
energetics of solution:
– separation of solute
particles,
– separation of solvent
particles,
– new interactions
between solute and
solvent.
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Energy Changes in Solution
The enthalpy
change of the
overall process
depends on H for
each of these steps.
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Endothermic Processes?
Factors Affecting Solubility
• Chemists use the axiom “like dissolves like."
– Polar substances tend to dissolve in polar solvents.
– Nonpolar substances tend to dissolve in nonpolar
solvents.
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Factors Affecting Solubility
The more similar the
intermolecular
attractions, the more
likely one substance
is to be soluble in
another.
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Factors Affecting Solubility
Glucose (which has
hydrogen bonding)
is very soluble in
water, while
cyclohexane (which
only has dispersion
forces) is not.
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Factors Affecting Solubility
• Vitamin A is soluble in nonpolar compounds
(like fats).
• Vitamin C is soluble in water.
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Gases in Solution
• The solubility of
liquids and solids
does not change
appreciably with
pressure.
• The solubility of a
gas in a liquid is
directly proportional
to its pressure.
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Henry’s Law
Sg = kPg
where
• Sg is the solubility of
the gas,
• k is the Henry’s Law
constant for that gas in
that solvent, and
• Pg is the partial
pressure of the gas
above the liquid.
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Temperature
Generally, the
solubility of solid
solutes in liquid
solvents increases
with increasing
temperature.
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Temperature
• The opposite is true
of gases.
– Carbonated soft
drinks are more
“bubbly” if stored in
the refrigerator.
– Warm lakes have
less O2 dissolved in
them than cool lakes.
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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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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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Colligative Properties – Vapor
Pressure
• A solvent in a closed container reaches a
state of dynamic equilibrium.
• The pressure exerted by the vapor in the
headspace is referred to as the vapor
pressure of the solvent.
• The addition of any nonvolatile solute
(one with no measurable vapor pressure)
to any solvent reduces the vapor
pressure of the solvent.
Colligative Properties – Vapor
Pressure
• Nonvolatile solutes reduce the ability
of the surface solvent molecules to
escape the liquid.
– Vapor pressure is reduced.
• The extent of vapor pressure
lowering depends on the amount of
solute.
– Raoult’s Law quantifies the amount of
vapor pressure lowering that is observed.
Non-volatile solutes and Raoult’s
law
• Vapor pressure of solvent in solution containing nonvolatile 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
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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Colligative Properties – Vapor
Pressure
Example: The vapor pressure of water at
20oC is 17.5 torr. Calculate the vapor
pressure of an aqueous solution prepared
by adding 36.0 g of glucose (C6H12O6) to
14.4 g of water.
Colligative Properties – Vapor
Pressure
Answer: 14.0 torr
Colligative Properties – Vapor
Pressure
Example: The vapor pressure of pure
water at 110oC is 1070 torr. A solution of
ethylene glycol and water has a vapor
pressure of 1.10 atm at the same
temperature. What is the mole fraction
of ethylene glycol in the solution?
Both ethylene glycol and water are liquids. How
do you know which one is the solvent and which
one is the solute?
Colligative Properties – Vapor
Pressure
Answer: XEG = 0.20
Colligative Properties – Vapor
Pressure
• Ideal solutions are those that obey
Raoult’s Law.
• Real solutions show approximately
ideal behavior when:
– The solution concentration is low
– The solute and solvent have similarly
sized molecules
– The solute and solvent have similar types
of intermolecular forces.
Colligative Properties – Vapor
Pressure
• Raoult’s Law breaks down when
solvent-solvent and solute-solute
intermolecular forces of attraction
are much stronger or weaker than
solute-solvent intermolecular forces.
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
Tb is added to the normal
boiling point of the solvent.
where Kb is the molal
boiling point elevation
constant, a property of
the solvent.
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Colligative Properties – BP
Elevation
• The addition of a
nonvolatile solute
causes solutions to
have higher boiling
points than the
pure solvent.

– Vapor pressure
decreases with
addition of non-
Higher temperature is
needed in order for vapor
pressure to equal 1 atm.
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
Freezing Point Depression
• 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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Colligative Properties - Freezing Pt Depression
• The addition of a
nonvolatile solute causes
solutions to have lower
freezing points than the
pure solvent.
• Solid-liquid equilibrium line
rises ~ vertically from the
triple point, which is lower
than that of pure solvent.

Freezing point of
the solution is lower
than that of the
pure solvent.
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
Colligative Properties - Freezing Pt Depression
• Reminder: You should be able to do
the following as well:
– Calculate the freezing point of any
solution given enough information to
calculate the molality of the solution and
the value of Kf
– Calculate the molar mass of a solution
given the value of Kf and the freezing
point depression (or the freezing points
of the solution and the pure solvent).
Deviations from ideal
• Real solutions can deviate from the
ideal:
– Positive (Pvap > ideal) solute-solvent
interactions weaker
– Negative (Pvap < ideal) solute-solvent
interactions stronger
Colligative Properties - Osmosis
• Some substances form semipermeable
membranes, allowing some smaller particles
to pass through, but blocking other larger
particles.
• In biological systems, most semipermeable
membranes allow water to pass through,
but solutes are not free to do so.
• If two solutions with identical
concentration (isotonic solutions) are
separated by a semipermeable membrane,
no net movement of solvent occurs.
Colligative Properties - Osmosis
• Osmosis: the net movement of a
solvent through a semipermeable
membrane toward the solution with
greater solute concentration.
• In osmosis, there is net movement of
solvent from the area of lower solute
concentration to the area of higher
solute concentration.
– Movement of solvent from high
solvent concentration to low solvent
concentration
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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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 its volume
• The passage of the solvent can be
prevented by application of a pressure
• The pressure to prevent transport is the
osmotic pressure
Calculating osmotic pressure
• The ideal gas law states
PV  nRT
• But n/V = M and so
  MRT
• Where M is the molar concentration of
particles and Π is the osmotic pressure
• Note: molarity is used not molality
Colligative Properties Osmosis
• Osmosis plays an important role
in living systems:
– Membranes of red blood cells
are semipermeable.
• Placing a red blood cell in a
hypertonic solution (solute
concentration outside the cell is
greater than inside the cell)
causes water to flow out of the
cell in a process called
crenation.
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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Colligative Properties
• Placing a red blood cell in a hypotonic
solution (solute concentration outside
the cell is less than that inside the
cell) causes water to flow into the
cell.
– The cell ruptures in a process called
hemolysis.
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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Colligative Properties - Osmosis
• Other everyday examples of osmosis:
– A cucumber placed in brine solution loses
water and becomes a pickle.
– A limp carrot placed in water becomes
firm because water enters by osmosis.
– Eating large quantities of salty food
causes retention of water and swelling of
tissues (edema).
Osmotic pressure and molecular
mass
• Molar mass can be computed from 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 an
osmotic pressure of 374.2 mm Hg but a
freezing point depression of only 0.02ºC
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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Determining molar mass
• A solution contains 20.0 mg insulin in 5.00
ml develops an osmotic pressure of 12.5
mm Hg at 300 K

M
12.5mmHg 1
RT
760mmHg
M
 6.68 10  4 M
L  atm
0.0821
300 K
mol  K
Mass Percentage
mass of A in solution
 100
Mass % of A =
total mass of solution
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Parts per Million and
Parts per Billion
Parts per Million (ppm)
mass of A in solution
 106
ppm =
total mass of solution
Parts per Billion (ppb)
mass of A in solution
 109
ppb =
total mass of solution
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Mole Fraction (X)
moles of A
XA =
total moles in solution
• In some applications, one needs the
mole fraction of solvent, not solute —
make sure you find the quantity you
need!
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Molarity (M)
M=
mol of solute
L of solution
• You will recall this concentration
measure from Chapter 4.
• Since volume is temperaturedependent, molarity can change with
temperature.
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Molality (m)
m=
mol of solute
kg of solvent
Since both moles and mass do not
change with temperature, molality
(unlike molarity) is not temperaturedependent.
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Changing Molarity to Molality
If we know the
density of the
solution, we can
calculate the
molality from the
molarity and vice
versa.
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