Chapter 2
Colligative Properties of Dilute
Solution
Solubility
Boiling-point elevation and freezing-point depression
Vapor pressure and Vapor pressure lowering of solution
Osmosis
2.1 Solubility
NaCl (s) + H2O Na+(aq) + Cl-(aq)
Solubility:
The solubility is defined as the amount that dissolves
in a given quantity of water at a given temperature to
give a saturated solution.
2.1.1 Saturated solution
State,
A solution is in dynamic equilibrium with
respect dissolved substance.
A dynamic equilibrium is reached in which the
rate at which ions leave the crystals equals the rate
at which ions return to the crystals.
2.1.2 Unsaturated solution
A solution not in equilibrium with respect to a
given dissolved substance and in which more
of the substance can dissolve.
2.1.3 Supersaturated solution
A solution that contains more dissolved substance
than a saturated solution does.
2.2 Vapor Pressure Lowering of A Solution
2.2.1 Vapor-pressure
H2O (l) H2O (g)evaporationcondensation
l,liquid phase
g,gas phase
Definition:
When a dynamic equilibrium is reached in the liquid
and gas phase at a given temperature,the saturated
vapor pressure of this system is the vapor-pressure
(symbol p ),The unit is Pa or kPa
Gas phase
Liquid phase
Surface
of water
pA0
34.6 78.5 100
101.3
P/kPa
T/℃
The vapor pressure of Some liquid
Polyglycol
WaterEthanolEther
Essential
1,p,Its unit is Pa or kPa.
2,p related to the quality of solvent,Every kinds
of liquid have different vapor-pressure.
3,p related to the temperature of solvent,When
the temperature is elevated,the p value will
increase,
4,If the p value of a substance is larger,we’ll call
it volatile,And less,nonvolatile.
5,The p value of solid substance is very little,But it
has the ability of sublimation.
2.2.2 Vapor-pressure lowering
If the solute is nonvolatile,pA is the total
vapor pressure of the solution,Because the
mole fraction of solvent in a solution is
always less than that for the pure solvent; the
vapor pressure is lowered.
Gas phase
Liquid phase
Surface
of water
Nonvolatile
of solute
pA
Water
manometer
glucose solution
constant temperature bath
Vapor-Pressure Lowering of Solution
Vapor-pressure lowering of a solvent is a
colligative property equal to the vapor pressure of
the pure solvent minus the vapor pressure of the
solution.
p = pA0 - pA
Consider a solution of volatile solvent,A,and
nonelectrolyte solute,B,which may be volatile or
nonvolatile,According to Raoult’s law,the partial
pressure of solvent,pA,over a solution equals the
vapor pressure of the pure solvent,PA0,times the
mole fraction of solvent,xA,in the solution,So
2.2.3 Raoult’s law
p = pA0 - pA
pA = pA0 ·xA
= pA0 - pA0 · xA = pA0(1- xA)
But the sum of the mole fractions of the components
of a solution must equal 1 ; that is ( xA + xB = 1 ),
So (xB = 1 – xA),Therefore,
p = pA0 · xB
From this equation,we can see that the vapor-pressure
lowering is a colligative property—one that depends
on the concentration,but not on the nature,of the
solution.
2.3 Boiling-point Elevation and
Freezing-point Depression
2.3.1 Boiling-point Elevation
2.3.1.1 Normal boiling point
The normal boiling point of a liquid
is the temperature at which its vapor
pressure equals 101.3 kPa(1 atm).
2.3.1.2 Boiling-point Elevation
The addition of a nonvolatile solute to a liquid
reduces its vapor pressure,the temperature must be
increased to a value greater than the normal boiling
point to achieve a vapor pressure of 101.3 kPa
The boiling-point elevation,ΔTb,is a colligative
property of a solution equal to the boiling point of the
solution minus the boiling point of the pure solvent.
The boiling-point elevation,ΔTb,is found to be
proportional to the molality,bB,of the solution
(for dilute solution).
ΔTb = Tb – Tb0= Kb? bB
Kb,The constant of proportionality,(we called
the boiling-point-elevation constant),it
depends only on the solvent,
Pure solvent
Solution
Solid state of
pure solvent
Phase diagram showing the effect of a nonvolatile solute on
freezing point and boiling point
Solvent Formula Tb0 (℃ ) Kb (℃ /K?kg?mol-1) Tf0 (℃ ) Kf((℃ /K?kg?mol-1)
Acetic acid HC2H3O
2
118.5 3.08 16.60 3.59
Benzene C6H6 80.2 2.61 5.45 5.65
Water H2O 100,512 0.0 1.86
Ethanol C2H5OH 78.4 1.22 -117.3 —
Tetrachloro-
methane CCl4 76.7 5.03 -22.9 32.0
Ether (C2H5)2O 34.7 2.02 -116.2 1.8
Naphthalene C10H8 218 5.80 80.0 6.9
Boiling-point-elevation constants( Kb )and
Freezing-point-depression constants ( Kf )
2.3.1.3 Freezing point of pure solvent
Cooling curve of pure water and solution
Time
T/℃
Time
Tf0
a
b c
d
Ideal cooling curve (1) of pure water
T/℃
Time
Tf0
a
b c
d
b`
Cooling curve of water (2) on condition of experiment
T/℃
Time
Tf0
a
b
c
Tf
Ideal cooling curve (3) of solution
2.3.1.4 Freezing point of solution
T/℃
Time
Tf0
a
b
c
Tf
b`
Cooling curve of solution (4) on experiment condition
The freezing-point depression,ΔTf,is a
colligative property of a solution equal to the
freezing point of the pure solvent minus the
freezing point of the solution.
ΔTf = Tf0 - Tf
Freezing-point depression,ΔTf,like boiling-point
elevation is proportional to the molality,bB(for
dilute solution).
ΔTf = Kf? bB
Here Kf is the freezing-point-depression constant and
depends only on the solvent.
A 0.638 g of urea was dissolved in 250 g of water,
The value of freezing-point depression,by determined,
was 0.079 K,What is the molecular weight of urea?
For example:
Solution:
The freezing-point-depression constant Kf is 1.86 K·kg·mol-1
in the table.
∵ ΔTf = Kf · bB = Kf
∴ MB =
mB
mAMB
Kf ·mB
mA·ΔTf
M(CON2H4) = 1.86K·kg·mol
-1× 0.638g
250g× 0.079K
= 0.060 kg·mol-1
= 60 g·mol-1
So,its molecular weight is 60.
2.3 Osmosis
What is osmosis
Why does an osmosis occur
What is osmotic pressure
Colligative properties of ionic solutions
Osmolarity
The Significance of Osmotic Pressure in
Medicine
Reverse Osmosis
2.3.1 Osmosis and Osmotic Pressure
2.3.1.1 Osmosis
Certain membranes allow solvent molecules to pass
through them but not solute molecules,particularly
not those of large molecular weight.
Such a membrane is called semipermeable and
might be an animal bladder,a vegetable tissue,or a
piece of cellophane.
Osmosis is the phenomenon of solvent flow through
a semipermeable membrane to equalize the solute
concentrations on both sides of the membrane.
Water molecule
Membrane
Glucose molecule
Water
Membrane
Glucose
solution
Funnel
Π
An experiment in osmosis
Water passes through the membrane into
the glucose solution in the inverted funnel,
the liquid level
rises in the stem of
the funnel until the
downward pressure
exerted by the
solution above the
membrane
eventually stops
the upward flow of
water.
pure
solvent solution
net
transform
of solvent
osmotic
pressureΠ
2.3.1.2 Osmotic pressure
Osmotic pressure is defined as the pressure that must be
applied to a solution to prevent any net transfer of pure
solvent into it through a semipermeable membrane.
The osmotic pressure Π of a solution is related to
the molarity of solution,c,(van’t Hoff law),
orΠV = nRT Π = bRT
Here R is the gas constant and T is the absolute temperature,
There is similarity between this equation for osmotic
pressure and the equation for an ideal gas.
For the dilute solution,the molarity is close to
molality,cB? bB,So,the low of van’t Hoff can
write like as following.
Π? RTbB
Example:
A 2.00 g of sucrose (C12H22O11) was dissolved
in 50.0 ml of water,What is the osmotic pressure
at 37℃?
Solution,
The molar mass of sucrose is 342 g·mol-1.
b(C12H22O11) = nV = 2.00 g342 g·mol-1?0.0500L
= 0.117 mol·L-1
= 0.117 mol·L -1? 8.314 J·K-1·mol-1 × 310K
= 302 kPa
Π = bBRT
Example,
Calculate the molecular weight of hemachrome at
20℃ of an aqueous solution containing 1.00g heme in
100ml of solution,The osmotic pressure of this solution
is 0.366kPa.
Solution:
According to the van’t Hoff equation:
ΠV = nRT = mBM
B
RT
MB = mBRTΠV
Here MB is the molecular weight of heme(g·mol-1),mB
is the mass of heme (g) and V is volume of solution(L).
MB = 1.00g× 8.314J·K
-1·mol-1× 293K
0.366kPa× 0.100L
= 6.66× 104g·mol-1
In most osmotic-pressure experiments,much more dilute
solutions are employed,Often osmosis is used to determine
the molecular weight of macromolecular or polymeric
substances,The freezing-point depression is usually too small
to measure,though the osmotic pressure may be appreciable.
2.3.2 The signification of Osmotic Pressure
in Medicine
2.3.2.1 The colligative property of Ionic solutions
To explain the colligative properties of ionic solutions,we
must realize that it is the total concentration of ions,rather
than the ionic substance,that is important,For instance,
Osmotic pressure is a colligative property of a solution,
Other colligative properties of a solution are vapor pressure
lowering,boiling point elevation and freezing point
depression,
NaCl Na+ + Cl-
Total of concentration = c(Na+) + c(Cl-)
Π= [c(Na+)+c(Cl-)]RT= icBRT
ibBRT
So,the van’t Hoff equation changes like as:
Other colligative properties of solution like as van’t Hoff
equation:
ΔTb = iKbbB
ΔTf = iKfbB
Π? ibBRT
2.3.2.2 Osmolarity
The osmotic pressure of solutions in living systems (such
as plasma,intracellular fluid,etc.),depends on the amount
of solute dissolved in plasma or body fluid.
In body fluids,there are ions,small molecules,large
molecules,and compounds formed by joining ions with
large molecules,All these substances have an osmotic
effect,They are called osmotically active substances.
The osmolarity (cos) is a term to express the total osmotic
pressure of plasma or body fluid,The unit of osmolarity is
mol·L-1 or mmol·L-1,and refers to the total number of
osmotically active substances per unit volume in body
fluids.
Osmolarity of osmotically active substances in body
ofhealth human
2.3.2.3 Osmolarity in biological processes
The osmotic pressure of the hypertonic solution
is greater than that of the cell; the red blood cell
has collapsed.
The osmotic pressure of the isotonic solution
is equal to that of the cell; the cell has it normal
round shape with depressed center,The osmolarity
of a isotonic solution is about 280~320 mmol·L-1.
The osmotic pressure of the hypotonic solution
is less than that of the cell; the cell has a bloated
shape,This phenomena was called hemolysis in
medicine.
Crystalloid osmotic pressure is produced by crystalloid
substances,
The body fluids were formed by electrolytes(NaCl,
KCl,NaHCO3,etc.),small molecules( glucose,amino
acid,urea,etc,),macromolecules ( protein,glucide,
lipide,etc.) dissolved in water.
Colloid osmotic pressure is produced by colloid substances.
In medicine,electrolytes and small molecules are
called crystalloid substances and macromolecules are
called colloid substances.
2.3.2.4 Crystalloid and colloid Osmotic pressure
Brief Summary of Chapter 2
1,Solubility
2,Vapor pressure lowing
3,Raoult’s law and colligative property
4,Boiling point elevation
5,Freezing point depression
6,Osmotic pressure
7,Osmotic pressure of electrolyte
8,Osmotic pressure in Medicine
Colligative Properties of Dilute
Solution
Solubility
Boiling-point elevation and freezing-point depression
Vapor pressure and Vapor pressure lowering of solution
Osmosis
2.1 Solubility
NaCl (s) + H2O Na+(aq) + Cl-(aq)
Solubility:
The solubility is defined as the amount that dissolves
in a given quantity of water at a given temperature to
give a saturated solution.
2.1.1 Saturated solution
State,
A solution is in dynamic equilibrium with
respect dissolved substance.
A dynamic equilibrium is reached in which the
rate at which ions leave the crystals equals the rate
at which ions return to the crystals.
2.1.2 Unsaturated solution
A solution not in equilibrium with respect to a
given dissolved substance and in which more
of the substance can dissolve.
2.1.3 Supersaturated solution
A solution that contains more dissolved substance
than a saturated solution does.
2.2 Vapor Pressure Lowering of A Solution
2.2.1 Vapor-pressure
H2O (l) H2O (g)evaporationcondensation
l,liquid phase
g,gas phase
Definition:
When a dynamic equilibrium is reached in the liquid
and gas phase at a given temperature,the saturated
vapor pressure of this system is the vapor-pressure
(symbol p ),The unit is Pa or kPa
Gas phase
Liquid phase
Surface
of water
pA0
34.6 78.5 100
101.3
P/kPa
T/℃
The vapor pressure of Some liquid
Polyglycol
WaterEthanolEther
Essential
1,p,Its unit is Pa or kPa.
2,p related to the quality of solvent,Every kinds
of liquid have different vapor-pressure.
3,p related to the temperature of solvent,When
the temperature is elevated,the p value will
increase,
4,If the p value of a substance is larger,we’ll call
it volatile,And less,nonvolatile.
5,The p value of solid substance is very little,But it
has the ability of sublimation.
2.2.2 Vapor-pressure lowering
If the solute is nonvolatile,pA is the total
vapor pressure of the solution,Because the
mole fraction of solvent in a solution is
always less than that for the pure solvent; the
vapor pressure is lowered.
Gas phase
Liquid phase
Surface
of water
Nonvolatile
of solute
pA
Water
manometer
glucose solution
constant temperature bath
Vapor-Pressure Lowering of Solution
Vapor-pressure lowering of a solvent is a
colligative property equal to the vapor pressure of
the pure solvent minus the vapor pressure of the
solution.
p = pA0 - pA
Consider a solution of volatile solvent,A,and
nonelectrolyte solute,B,which may be volatile or
nonvolatile,According to Raoult’s law,the partial
pressure of solvent,pA,over a solution equals the
vapor pressure of the pure solvent,PA0,times the
mole fraction of solvent,xA,in the solution,So
2.2.3 Raoult’s law
p = pA0 - pA
pA = pA0 ·xA
= pA0 - pA0 · xA = pA0(1- xA)
But the sum of the mole fractions of the components
of a solution must equal 1 ; that is ( xA + xB = 1 ),
So (xB = 1 – xA),Therefore,
p = pA0 · xB
From this equation,we can see that the vapor-pressure
lowering is a colligative property—one that depends
on the concentration,but not on the nature,of the
solution.
2.3 Boiling-point Elevation and
Freezing-point Depression
2.3.1 Boiling-point Elevation
2.3.1.1 Normal boiling point
The normal boiling point of a liquid
is the temperature at which its vapor
pressure equals 101.3 kPa(1 atm).
2.3.1.2 Boiling-point Elevation
The addition of a nonvolatile solute to a liquid
reduces its vapor pressure,the temperature must be
increased to a value greater than the normal boiling
point to achieve a vapor pressure of 101.3 kPa
The boiling-point elevation,ΔTb,is a colligative
property of a solution equal to the boiling point of the
solution minus the boiling point of the pure solvent.
The boiling-point elevation,ΔTb,is found to be
proportional to the molality,bB,of the solution
(for dilute solution).
ΔTb = Tb – Tb0= Kb? bB
Kb,The constant of proportionality,(we called
the boiling-point-elevation constant),it
depends only on the solvent,
Pure solvent
Solution
Solid state of
pure solvent
Phase diagram showing the effect of a nonvolatile solute on
freezing point and boiling point
Solvent Formula Tb0 (℃ ) Kb (℃ /K?kg?mol-1) Tf0 (℃ ) Kf((℃ /K?kg?mol-1)
Acetic acid HC2H3O
2
118.5 3.08 16.60 3.59
Benzene C6H6 80.2 2.61 5.45 5.65
Water H2O 100,512 0.0 1.86
Ethanol C2H5OH 78.4 1.22 -117.3 —
Tetrachloro-
methane CCl4 76.7 5.03 -22.9 32.0
Ether (C2H5)2O 34.7 2.02 -116.2 1.8
Naphthalene C10H8 218 5.80 80.0 6.9
Boiling-point-elevation constants( Kb )and
Freezing-point-depression constants ( Kf )
2.3.1.3 Freezing point of pure solvent
Cooling curve of pure water and solution
Time
T/℃
Time
Tf0
a
b c
d
Ideal cooling curve (1) of pure water
T/℃
Time
Tf0
a
b c
d
b`
Cooling curve of water (2) on condition of experiment
T/℃
Time
Tf0
a
b
c
Tf
Ideal cooling curve (3) of solution
2.3.1.4 Freezing point of solution
T/℃
Time
Tf0
a
b
c
Tf
b`
Cooling curve of solution (4) on experiment condition
The freezing-point depression,ΔTf,is a
colligative property of a solution equal to the
freezing point of the pure solvent minus the
freezing point of the solution.
ΔTf = Tf0 - Tf
Freezing-point depression,ΔTf,like boiling-point
elevation is proportional to the molality,bB(for
dilute solution).
ΔTf = Kf? bB
Here Kf is the freezing-point-depression constant and
depends only on the solvent.
A 0.638 g of urea was dissolved in 250 g of water,
The value of freezing-point depression,by determined,
was 0.079 K,What is the molecular weight of urea?
For example:
Solution:
The freezing-point-depression constant Kf is 1.86 K·kg·mol-1
in the table.
∵ ΔTf = Kf · bB = Kf
∴ MB =
mB
mAMB
Kf ·mB
mA·ΔTf
M(CON2H4) = 1.86K·kg·mol
-1× 0.638g
250g× 0.079K
= 0.060 kg·mol-1
= 60 g·mol-1
So,its molecular weight is 60.
2.3 Osmosis
What is osmosis
Why does an osmosis occur
What is osmotic pressure
Colligative properties of ionic solutions
Osmolarity
The Significance of Osmotic Pressure in
Medicine
Reverse Osmosis
2.3.1 Osmosis and Osmotic Pressure
2.3.1.1 Osmosis
Certain membranes allow solvent molecules to pass
through them but not solute molecules,particularly
not those of large molecular weight.
Such a membrane is called semipermeable and
might be an animal bladder,a vegetable tissue,or a
piece of cellophane.
Osmosis is the phenomenon of solvent flow through
a semipermeable membrane to equalize the solute
concentrations on both sides of the membrane.
Water molecule
Membrane
Glucose molecule
Water
Membrane
Glucose
solution
Funnel
Π
An experiment in osmosis
Water passes through the membrane into
the glucose solution in the inverted funnel,
the liquid level
rises in the stem of
the funnel until the
downward pressure
exerted by the
solution above the
membrane
eventually stops
the upward flow of
water.
pure
solvent solution
net
transform
of solvent
osmotic
pressureΠ
2.3.1.2 Osmotic pressure
Osmotic pressure is defined as the pressure that must be
applied to a solution to prevent any net transfer of pure
solvent into it through a semipermeable membrane.
The osmotic pressure Π of a solution is related to
the molarity of solution,c,(van’t Hoff law),
orΠV = nRT Π = bRT
Here R is the gas constant and T is the absolute temperature,
There is similarity between this equation for osmotic
pressure and the equation for an ideal gas.
For the dilute solution,the molarity is close to
molality,cB? bB,So,the low of van’t Hoff can
write like as following.
Π? RTbB
Example:
A 2.00 g of sucrose (C12H22O11) was dissolved
in 50.0 ml of water,What is the osmotic pressure
at 37℃?
Solution,
The molar mass of sucrose is 342 g·mol-1.
b(C12H22O11) = nV = 2.00 g342 g·mol-1?0.0500L
= 0.117 mol·L-1
= 0.117 mol·L -1? 8.314 J·K-1·mol-1 × 310K
= 302 kPa
Π = bBRT
Example,
Calculate the molecular weight of hemachrome at
20℃ of an aqueous solution containing 1.00g heme in
100ml of solution,The osmotic pressure of this solution
is 0.366kPa.
Solution:
According to the van’t Hoff equation:
ΠV = nRT = mBM
B
RT
MB = mBRTΠV
Here MB is the molecular weight of heme(g·mol-1),mB
is the mass of heme (g) and V is volume of solution(L).
MB = 1.00g× 8.314J·K
-1·mol-1× 293K
0.366kPa× 0.100L
= 6.66× 104g·mol-1
In most osmotic-pressure experiments,much more dilute
solutions are employed,Often osmosis is used to determine
the molecular weight of macromolecular or polymeric
substances,The freezing-point depression is usually too small
to measure,though the osmotic pressure may be appreciable.
2.3.2 The signification of Osmotic Pressure
in Medicine
2.3.2.1 The colligative property of Ionic solutions
To explain the colligative properties of ionic solutions,we
must realize that it is the total concentration of ions,rather
than the ionic substance,that is important,For instance,
Osmotic pressure is a colligative property of a solution,
Other colligative properties of a solution are vapor pressure
lowering,boiling point elevation and freezing point
depression,
NaCl Na+ + Cl-
Total of concentration = c(Na+) + c(Cl-)
Π= [c(Na+)+c(Cl-)]RT= icBRT
ibBRT
So,the van’t Hoff equation changes like as:
Other colligative properties of solution like as van’t Hoff
equation:
ΔTb = iKbbB
ΔTf = iKfbB
Π? ibBRT
2.3.2.2 Osmolarity
The osmotic pressure of solutions in living systems (such
as plasma,intracellular fluid,etc.),depends on the amount
of solute dissolved in plasma or body fluid.
In body fluids,there are ions,small molecules,large
molecules,and compounds formed by joining ions with
large molecules,All these substances have an osmotic
effect,They are called osmotically active substances.
The osmolarity (cos) is a term to express the total osmotic
pressure of plasma or body fluid,The unit of osmolarity is
mol·L-1 or mmol·L-1,and refers to the total number of
osmotically active substances per unit volume in body
fluids.
Osmolarity of osmotically active substances in body
ofhealth human
2.3.2.3 Osmolarity in biological processes
The osmotic pressure of the hypertonic solution
is greater than that of the cell; the red blood cell
has collapsed.
The osmotic pressure of the isotonic solution
is equal to that of the cell; the cell has it normal
round shape with depressed center,The osmolarity
of a isotonic solution is about 280~320 mmol·L-1.
The osmotic pressure of the hypotonic solution
is less than that of the cell; the cell has a bloated
shape,This phenomena was called hemolysis in
medicine.
Crystalloid osmotic pressure is produced by crystalloid
substances,
The body fluids were formed by electrolytes(NaCl,
KCl,NaHCO3,etc.),small molecules( glucose,amino
acid,urea,etc,),macromolecules ( protein,glucide,
lipide,etc.) dissolved in water.
Colloid osmotic pressure is produced by colloid substances.
In medicine,electrolytes and small molecules are
called crystalloid substances and macromolecules are
called colloid substances.
2.3.2.4 Crystalloid and colloid Osmotic pressure
Brief Summary of Chapter 2
1,Solubility
2,Vapor pressure lowing
3,Raoult’s law and colligative property
4,Boiling point elevation
5,Freezing point depression
6,Osmotic pressure
7,Osmotic pressure of electrolyte
8,Osmotic pressure in Medicine
