SAPTARSHI
Solutions and Colligative Properties
Introduction:
Solutions: Mix ture of two or more components.
Depending on size of components, mix tures are classified into 3 types.
a) Coarse mixture:
Definition: The mix ture which contains components having relati vely bigger size is called as
coarse mix ture. E.g. Mix ture of sal t and sugar.
b) Colloidal dispersion:
Definition: The mix ture which is formed when the size of particles dispersed in solvent are in
the range of
107 cm to 104 cm is called as colloidal dispersion.
Properties of colloidal particles/solutions.
1)
Colloidal particles carry posi tive or nega tive c harge which stabilizes colloidal dispersion. E.g.
Ferric hydroxide sol, arsenic sulphide sol.
2) Colloidal solutions are heterogeneous and can be easily separa ted.
c) True solution:
Definition: It is defined as the homogeneous mix ture of two or more substances, the
composi tion of which is not fixed and may be varied within certain li mi ts.
Properties of true solution:
1)
Size of particles dissolved in the solvent are very small of the order of
108 cm
2) It is homogenous.
3) It cannot be separa ted into components by si mple mechanical method.
Composition of solution –
a) Solute: The component which consti tutes smaller part of solution is called as solute.
b) Solvent: The component which consti tutes larger pa rt of solution is called as solvent.
Homogeneous solution:
Definition- The solution whose composi tion is uniform throughout the body of the solution is called
as homogeneous solution.
Formation/Preparation: The homogeneous solution is formed due to force of a ttrac tion between
the molecules or pa rticles of solute and solvent.
Heterogeneous solution: It i s defined as the mix ture of two or more pha ses.
Solvation: It i s defined as the process of interac tion of solvent molecules with solute particles to
form aggrega tes. When wa ter i s used as solvent, i t i s called as hydra tion or aqua tion.
Remember:
Extent of dissolution of solute in solvent to form homogenous solution depends on na ture of solute
and solvent.
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General rule for solubility is “Like dissolves like” i.e. polar solutes are soluble in polar solvents.
E.g. NaCl in water.
or non-polar solutes are soluble in non-polar sol vents. E.g. Iodine in CCl 4
Explain: Water is called universal sol vent.
1)
It is polar in na ture hence i t dissolves most of polar solutes.
2) It has high –dielectric constant. Hence, it reduces the force of attrac tion between ions of
solute and offers them to remain apart.
3) Thus, i t acts as good medium for grea ter ionization of the solutes hence i t is called as universal
solvent.
Types of solution:
No.
Solute
Solvent
Examples
1
Solid
Solid
Alloys like brass, bronze, copper in gold etc .
2
Liquid
Solid
Amalga ms of mercury with metal
3
Gas
Solid
Hydrogen gas in palladium metal, pumice stone
4
Solid
Liquid
Iodine in CCl 4 benzoic acid in C 6 H6 , sugar in
water
5
Liquid
Liquid
Ethanol in water
6
Gas
Liquid
Oxygen, carbon dioxide in water
7
Solid
Gas
Iodine in air
8
Liquid
Gas
Chloroform in ni trogen
9
Gas
Gas
Air, mix tures of non reac ting ga ses
Aqueous solution: The solution in which water is used as solvent is called as aqueous solutions.
Non-aqueous solutions: The solution in which solvent other than water is used is called as non-aqueous
solution.
Concentration of solutions: It is defined as the a mount of solute dissolved in specific a mount of
solvent.
Dilute solutions: The solutions containing relati vely less a mount of solute are called as dilute solutions.
Concentrated solution: The solution containing relati vely more a mount of solute is called as
concentra ted solution.
Different methods of expressing the concentration of solution1)
Percentage by mass or weight (W/W) – The ma ss of solute in gram dissolved in solvent to
form 100 gra m of solution is called as Mass perc entage.
Formula:
%by mass of solute 
Mass of solute
100
Mass of solution
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SAPTARSHI
Where
Mass of solution  Mass of solute  Mass of solvent
It is independent of tempera ture as i t does not contain term volume.
2) Percentage by volume (v/ v) : It is defined as the ra tio of number of parts by volume of the
solute to one hundred pa rts by volume of the solution.
Formula:
%by volume of solute 
volume of solute
100
Volume of solution
Note:

Used when both the components of solution are in liquid phase.

Total volume of solutions is not equal to sum of volumes of solute and solvent as sa me
solute particles occupy empty spaces in voids in struc ture of liquids.

Volume is tempera ture dependent and hence (v/v) c hanges with tempera ture.

(w/v) is mass of solute in gra ms present in 100 ml of solution.
3) Mole fraction (x): The mole fraction of any component of solution is defined as the ra tio of
number of moles of tha t component present in the solution to the total number of moles of all
the components of the solution.
Math ematical expression of x :
For binary solution,
n1  number of moles of solvent
n 2  number of moles of solute
mole fraction of solvent x1 
n1
n1  n 2
mole fraction of solute x 2 
n2
n1  n 2
Note:
x1  x 2 
n1  n 2
1
n1  n 2

Sum of mole fractions of solvent and solute

Sum of mole fraction of all components of any solution is always unity.

Mole fraction is tempera ture independent.
4) Molarity (M) : It is defined a s the number of moles of solute present in 1 d m3 (lit) volume of
the solution.
Molarity(M) 
No. of moles of solute
volume of solution in dm3 or litre
No. of moles of solute 
Mass of solute in gram
Molecular weight in gram
Note :
mol dm3

Molari ty is expressed in

It depends on tempera ture as i t contains the term volume.
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5) Molality (m): It i s defined as the number of moles of solute dissol ved in 1kg of solvent.
Molality (m) 
number of moles of solute
mass of solvent in kg
Note: Best method to express concentra tion as i t i s tempera ture independent.
6) Normality (N): It is defined as the no. of gra m equivalents of solute dissolved in 1 dm3 of
solution.
Normality (N) 
No. of gram equivalents of solute
volume of solution in dm3
Where

No. of gram equivalent 
mass of solute in gram
Equivalent wt. of solute in gram

Equivalent wt. of acid 
Molecular wt of acid
Basicity
(Basicity is the no. of moles of H + ions produced by 1 mole of acid)

Equivalent wt. of Base 
Molecular wt of Base
Acidity
OHions produced by 1 mole of base)
Molecular wt of salt
Equivalent wt of salt 
Total ch arg e present on cations
(Acidity is the no. of moles of

Relation between molarity and Normality.
N  nM
Where n = acidity / basicity
(Note: normality is temperature depend ent)
7) Parts per million (ppm): It is defined as the mass or volume of solute in gram or cm3 per 106
gra m of 106 cm3 of the solution.
ppm 
mass or volume of solute
106
total mass or volume of solution
( Note: It can be expressed as mass to mass, mass to volume or volume to volume. )
Solubility of solute in solvent.
Depending on a mount of solute present in given volume of solution i t is classified into 3
categories.
1)
Satura ted solution
2) Unsatura ted solution
3) Supersa tura ted solution
Concept of Solubility (Saturated solution)

When solute (sugar) i s added to solvent (water) , i t gets dissol ved due to a ttrac tive force
between solute particles and solvent molecules.

Solute particles are constantly in sta te of random motion and constantly collide with each
other and with solvent molecules.

Solute particles are held together due to/ by physical forces of a ttrac tion.
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
If physical forces are not sufficient, dissolved sugar solute crystallizes out.

If solute is added continuously, Dissolution and crystallization takes place si mul taneously.

At low concentra tion of solute, ra te of dissolution is very high and ra te of crystalliza tion is
very low.

Wi th increase in concentra tion of solute ra te of dissolution decreases and rate of
crystallization increases.

At a particular stage, ra te of dissolution and ra te of crystalliza tion becomes equal and
equillibrium is established.

At this stage solution is called as sa tura ted .

sugar(s)  H2O(l )
sugar solution .
Definition:

Saturated solution: It is defined as the solution tha t contains just the a mount of dissolved
solute necessary to establish equilibrium between dissol ved solute and undis solved solute.

Unsaturated solution: A solution which contains less a mount of solute than required for forming
sa tura ted solution.

Note: Equilibrium does not exist between dissolution and crystalliza tion.

Supersaturated solution: A solution which contains excess of solute than required for forma tion
of satura ted solution.

Solubility- It is defined as the maxi mum a mount of solute which dissolves completely in given
amount of solvent a t a constant tempera ture.

It is expressed as mol/lit.

Solubility changes wi th tempera ture.
Effect of temperature on solubility of solid solute in liquid solvent.

Generally solubility of solid in liquid increases with increase in tempera ture.

Solubility of solid solute is al most doubled for every rise of tempera ture by 10 0 C which is always
not true.

The solubility of solid solute in liquid solvent may be exothermi c or endothermic process.

Depending on na ture of process, solubility may increase or decrea se by increasing tempera ture.

For exothermic process, solubility d ecreases by increasing tempera ture while in case of
endothermic process, solubility increases with increase in tempera ture.
Variations of solubility with temperature for some ionic compounds.

Solubility of NaBr, NaCl, KCl change slightly with tempera ture.

Solubility of salts like KNO3 , NaNO3 , KBr increases appreciably with tempera ture.

Solubilities of Na 2 SO4 decrease with increase in tempera ture.

Solubility of NH4 NO3 being endothermic process increa ses with increase in tempera ture.

Exceptional behavior: solubility of CaCl 2 is exothermic process still it is increased when
tempera ture increases.

By knowing solubility, it is easy to separa te individual component fro m mix ture of water soluble
salt from aqueous solutions. This process is called as frac tional crystallization.

This technique can be used if the substance is highly soluble a t higher tempera ture and
solubility is poor a t lower tempera ture. E.g. separa tion of pure NaCl from mix ture of NaCl and
NaBr a t 00 C. Separa tion of 80% dissol ved KNO3 from mix ture of KNO3 and NaNO3 .
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SAPTARSHI
Effect of pressure on solubility of solid solute in liquid solvent.
Solids are incompressible hence change of pressure has no effec t on solubility of solids in
liquids.
How Solubility of gases in liquids depends on their nature?

Gases are soluble in liquids including water.

Being non polar, solubility of gases like oxygen and nitrogen is very low in water.

CO2 reacts with water to form carbonic acid and ammonia reac ts with water to form a mmonium
hydroxide, hence CO2 and NH3 are more soluble in water.

HCl is polar; hence i ts solubility is very high in water.
Effect of change of temperature on solubility of gas in liquid –

According to Charle’s law, volume of given ma ss of gas increases with increase of tempera ture.

Thus volume of given ma ss of dissolved ga s in solution increases with increase of tempera ture.

Due to this, solvent in the solution cannot accommoda te the gaseous solute and hence gas
bubbles out.

Thus solubility of gas in liquid decreases with increase in temperature.
Adverse effect of increase in temperature on solubility of O2 .

Many ti mes, sea water or river water is used as coolant.

Cold water i s taken from sources of water and af ter removing hea t, hot wa ter f rom plant is
released into source of water.

Due to this tempera ture increa ses and solubility of oxygen ga s in water dec reases.

This resul ts in difficulty of survival of marine life
Explain why marine life like fish prefers to stay at lower sea level in summer?

In summer hot day, tempera ture of surface of water is rela tively very high and solubility of
oxygen at upper layer i s mini mum.

While tempera ture of water a t lower level is much less and hence i t contains more a mount of
dissolved oxygen.

Due to this, ma rine life prefers to stay a t lower level for their survival.
Effect of change of pressure on th e solubility of gases.

As ga ses a re highly compressible, ex ternal pressure affec ts their solubility.

Increase in external pressure increases solubility of gas.
Henry’s law –Statement – solubility of gas in a liquid at constant tempera ture is proportional to the
pressure of ga s above the solution.
Ma thema tical expression
S P
S  KP
Where S is solubility of the gas in mol/d m3
P is pressure of the gas in a tmosphere.
K is constant of proportionality. i.e. Henry’s constant.
If P = 1 a tm.
S = K
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Definition of K and its unit.
K is defined as solubility of gas in mol/d m3 at 1 a tm pressure and a t ref erence tempera ture.
Note: for several gases, solubility of ga s is calculated by using P as partial pressure of gas in the
mix ture
Explain Henry’s law with suitable ex ample.

When carbona ted sof t drink beverage bottle is sea ted with cap,it is pressurized by mix ture of
air and CO2

Due to high pa rtial pressure of CO2 , the a mount of CO2 in dissolved sta te i s high in sof t drinks.

When cap is removed ex ternal pressure decreases, solubility of CO 2 decreases and excess of
CO2 and air in the bottle escapes out.
Effect of addition of soluble salt on solubility of gases.
The solubility of dissolved gas i s reduced by addi tion of soluble salt to the solution of gas.
E.g. addi tion of table sal t, to carbona ted sof t d rink decrea ses solubility of CO 2 gas hence i t escapes out
with effervescence.
Solid solutions – A solid solution of two or more metals or of a metal or metals with one or more non
metal is called an Alloy or solid solution.
Name of Alloy
Composition
Duralumin
Aluminium
Properties
.copper,
magnesium
and
It
is
light
Uses
and
strong a s steel
It
is
used
in
construc tion
manganese.
the
of
aircrafts.
Lead ha rdened by
Lead and 10 to 20%
the addi tion of 10-
Sb (Anti mony)
It is acid resistant
Used for
manufac turing lead
20% anti mony
storage ba ttery pla tes
and bearings, bullets,
and shrapnel.
Babbitt metal
Alloy
of
anti mony
it is antifric tion
extensively
with tin and copper
Stainless steel
Contains
chromium
and some nickel.
used
in
mac hine bearings
Hard and strong. It
is
resistant
Used in cutlery.
to
corrosion,
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spiegeleisen
5 to 20% manganese
very hard
to manufac ture rails,
in iron
safes
and
hea vy
mac hinery
Ferromanganeous
Manganin
70
to
80%
very hard
to manufac ture rails,
manganese and 30 to
safes
20% iron
mac hinery
84% Cu, 12% Mn and
almost
zero
4% Ni
tempera ture
Used
used
coefficient
of
electrical
and
in
hea vy
instruments
for
making
electrical
measurements.
resistance
Amalga ms.
Mercury with other
This
property
metals
mercury
amalga ms
of
Silver and gold from
to
from
the ores, dissolve in
is
used
mercury to form liquid
for
ex trac ting
amalga ms.
metals
from
silver are recovered
ores.
the
by
Gold
and
distilling
off
mercury.

In alloys like bronze and lead shot arsenic is used as hardening agent.

Most of the chromium produced all over the world is used to produce steel alloys

Aluminium bronze contains Aluminium, copper and small amount of manganese.
Colligative properti es: The properties of solutions tha t d epend only on the number of solute particles in
solution and not on the na ture of the solute particle are called as Colligative properties.

Colligative properti es are used to d etermine molar ma sses of non elec trolyte solutes.

The relations derived by mea suring colligative properti es hold good for dilute solutions, with
concentra tion less than or equal to 0.2M.
Four Colligative Properties
1.
Lowering of vapour pressure of solvent in solution
2. Eleva tion of boiling point of solvent in solution
3. Depression of freezing point of sol vent in solution
4. Osmotic pressure
Lowering of vapour pressure of sol vent in solution


All liquids exhibit tendency for evapora tion. The gaseous sta te of a substance is called vapour
If the intermolecular forces of a ttrac tion are weak the liquids evapora te readily and are
called volatile liquids. E.g Ethyl aceta te is the most vola tile liquid. Ethyl alcohol, acetone are
also volatile liquids

Due to strong intermolecular forces of a ttrac tion, Lubricating oils are slightly volatile..
Concept of Vapor pressure of liquid

Liquid escapes from an open vessel by evapora tion.

If the vessel is closed, the process of evapora tion continues.
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
The molecules of liquid escaping from the surface of liquid remain in the container above the
surface of liquid.

These molecules of vapour are in continuous random motion

They collide with each other, with the walls of the container and with the surface of the liquid
and return to the liquid sta te. This is reverse of evapora tion, called condensation

Af ter some ti me interval, equilibrium is established between two phases of the substance, liquid
and its vapour. At thi s stage the ra te of evapora tion equals the ra te of condensa tion.

The pressure exerted by vapor a t this sta ge is called as Vapor pressure.

Vapour pressure of a liquid, increases with the increa se of tempera ture.

Note: If the boiling is carried out in an open atmosphere then external pressure is the
atmospheric pressure.
Definition of Vapor pressure of Liquid

The vapour pressure of a substance is d efined as the pressure exerted by the gaseous sta te of
tha t substance when i t i s in equilibrium with the solid or liquid phase.
Concept of Lowering of vapor pressure of solvent in solution

The vapour pressure of a liquid solvent is lowered when a non –vola tile solute is dissolved in i t to
form a solution.

In case of pure solvent, i ts surface area is completely occupied by volatile solvent molecules.

In case of solution of nonvolatile solute, i ts surface area is not completely available for volatile
solvent but i t i s partly occupied by non vola tile solute.

Hence, ra te of evapora tion of the solution will be less as compared to tha t of pure solvent

Thus vapour pressure of solution is lower than tha t of the pure solvent.

Definition: The difference between vapour pressures of pure solvent and the vapor pressure of
solvent from solution is called vapour pressure lowering.
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Describe th e experiment for lowering of vapor pressure of solvent due to addition of non-volatile
solute.

Consider three beakers numbered as 1, 2, and 3 containing 100 ml each of pure solvent wa ter,
1M copper sulpha te and 2 M copper sulpha te solution respec ti vely.

The three beakers are placed in airtight dessica tor, so tha t a t constant tempera ture, sol vent
from all the three beakers evapora tes and condense and equillibrium is reached .

Observations at Equillibrium
o
Beaker 1 i s empty i.e solvent evapora tes completely from beaker 1.
o
In beaker 2, conc. Of copper sulpha te does not c hange i.e. volume of solution remains
almost sa me.
o
In beaker 3, condensa tion of solvent ta kes place hence volume of solution becomes
almost 200 ml and conc. Of solution becomes 1M i.e. al most equal to tha t of beaker 2.


Conclusion of experiment
o
Vapor pressure of pure solvent wa ter is maxi mum.
o
Vapor pressure of 1 M copper sulpha te is intermedia te.
o
Vapor pressure of 2 M copper sulpahte i s mini mum.
Thus lowering of vapor pressure of solvent takes place due to addition of non -volatile
solute.
Math ematical Expression for lowering of vapour pressure

If
p10 is the vapour pressure of pure solvent and p is the vapour pressure of the solution of
nonvolatile solute in the sa me solvent, then
p  p10 and the lowering of vapour pressure is,
p  p10  p
The relati ve lowering of vapour pressure: The rela tive lowering of vapour pressure for the given
solution i s the ra tio of vapour pressure lowering of solvent f rom solution to the vapour pressure of pure
solvent. Thus,
Relati ve lowering of vapour pressure

p p10  p

p10
p10
Raoult’s law: The partial vapour pressure of any volatile component of a solution is the produc t of
vapour pressure of tha t pure component and the mole frac tion of the component in the solution.
Deri ve expression of Raoult’s Law for a solution containing both volatile c omponents

Consider a solution containing two vola tile components
A1 and A2 with mole frac tion
x1 and x 2 respectively.
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
Let
p and p be the vapour pressures of the pure components A1 and A2 respec tively.

According to Raoult’s law, the partial pressures,
0
1
0
2
p1 and p2 of the two components in the given
solution are given by,
p1  p10 x1 and p2  p02 x 2

Total vapour pressure,
p T of solution of two vola tile components is the sum of pa rtial vapour
pressures of the two components.
pT  p1  p2  p10 x1  p02 x 2

Hence,

For binary solution,

Hence,
x1  x 2  1 or x 2  1  x1
pT  p10 x1  p02 (1  x1 )
pT  p10 x1  p02  p02 x1


pT  p02  p10  p02 x1
Note: The solution which obeys Raoul t’s law over the entire range of concentra tion is called an ideal
solution. If a solution does not obey Raoul t’s law, the solution is non –ideal.
Deri ve Expression of Raoult’s l aw for a solution of non-volatile solute or Derive Expression for
relative lowering of vapor pressure of solution contaning non -volatile solute.

Consider a solution of two components
A1 and A2 with the mole frac tion x1 and x 2
respectively.

In this solution the component A2 (i.e. solute) is non -vola tile, hence i t does not evapora te
and does not contribute to the total vapour pressure of solution.

The vapour pressure of pure component

A1 is p10 and tha t of component A2 is p02  0 .

pT  p02  p10  p02 x1
As
p02  0
pT  p10 x1

Thus Vapor pressure of a solution of non-vola tile solute is the produc t of vapour pressure of
pure solvent

p10 and mole fraction of the sol vent, x1 which is Raoult’s law.
For two component solution,
x1  x 2  1 .
volatile solute, not equal to zero. Hence,

Hence Product
 x1  1  x 2  , where x 2 is mole frac tion of non-
x1  1
p10 x1 is always less than p10 . Therefore vapour pressure of solution, pT  p10
which proves tha t lowering of vapour pressure of solution contaning non -vala tile solute.
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
The lowering of vapour pressure
p is given by,
p  p10  pT
 p10 1  x1 
 p10  p10 x1
Hence,

But
1  x1
 x2
p  p10 x 2
Lowering of vapour pressure is the produc t of vapour pressure of pure solvent and mole frac tion
of non-vola tile solute dissolved in vola tile solvent to form a solution.

The lowering of vapour pressure depends on na ture of pure sol vent and concentra tion of solute
in mole fraction.
The rela tive lowering of vapour pressure i s given by,
p p10  p p10 x 2


 x2
p10
p10
p10
Hence, relative lowering of vapour pressure =
x 2 (Mole fraction of non-volatile solute)
The above expression proves tha t the lowering of vapour pressure i s a colligative property because i t
depends on the concentra tion of non-vola tile solute.
Determination of Molar mass of non –volatile solute and relati ve lowering of vapour pressure:

Let W2 g of solute of molar mass M2 be dissolved in W1 g of solvent of molar mass M1 .

Hence number of moles of sol vent, n 1 and number of moles of solute n 2, in solution are gi ven
as,
n1 

W1
W
and n 2  2
M1
M2
The mole f raction of solute
x2 
x 2 is given by,
n2
W2 / M 2

n1  n 2 W1 / M1  W2 / M 2
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
Combine equa tions
W2 / M 2
 p p10  pT

 x2 
0
0
p1
p1
W1 / M1  W2 / M 2

For dilute solutions,
n1  n 2 . Hence n2 may be neglec ted in compa rison wi th n 1 in equa tions
takes the form.
 p n 2 W2 / M 2 W2 M1



p10
n1 W1 / M1 W1M 2

Knowing the masses of non-vola tile solute and the sol vent in dilute solutions and by determining
experi mentally vapour pressure of pure solvent and the solution i t is possible to determine molar
ma ss of a non –vola tile solute.
Boiling point:
Boiling point i s defined a s the tempera ture a t which the vapour pressure of liquid
becomes equal to the a tmospheric pressure.
It increases with increase in ex ternal pressure. Liquids having grea ter intermolecular forces ha ve high
boiling points.
Concept of Elevation of boiling point

The vapour pressure of a solution of non-vola tile solute is always less than the vapour pressure
of pure solvent.

At the tempera ture of boiling point of pure solvent, solution will not boil as its vapour pressure
is less than tha t of the vapour pressure of pure solvent which is also equal the ex ternal
pressure.

Thus
solution
will
only
boil
if
its
vapour
pressure
is
increased
upto
ex ternal
atmosphericpressure.

The tempera ture must be increased by Tb
 T  T0 . Where T is boiling point of solution and
T 0 tha t of pure solvent and T  T0 . Tb is eleva tion of boiling point

Definition - Eleva tion of boiling point is the differenc e between boiling points of solution and
tha t of pure solvent.
Show graphical representation of elevation of boiling point of solvent in solution or Show
Variation of the vapour pressure of pure solvent and solution with temperature.

The vapour pressure tempera ture curve of solution i s always below the vapour pressure –
tempera ture curve of pure solvent.

The boiling point of pure sol vent is
T 0 and tha t of solution is T.

The eleva tion of boiling point

The lowering of vapour pressure

The eleva tion of boiling point is proportional to the lowering of vapour pressure i .e.
Tb is represented by the distance AB. ( Tb  T  T0 )
p
0
1

 p a t the tempera ture T 0 is equivalent to AC.
Tb  p
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SAPTARSHI
Deri ve the expression to calculate the molecular weight of unknown solute by measuring elevation
in boiling point.

For a dilute solution the eleva tion of boiling point ( Tb ) is direc tly proportional to the molality, m
of the solution.
Tb  m

Thus,

Tb  K b m...............eqn(1)
Where m is the molality of the solution,
K b is called molal elevation of boiling point constant or
ebullioscopic constant.

If W2 gra m of solute with molar mass M2 is dissol ved in W1 Kg of solvent then,

Molality 
No. of moles of solute
Mass of solvent in Kg
W2



m
M2
W1
Thus substi tuting value of m in eqn (1), we get,
Tb 
K b W2
K W
 M2  b 2
M 2 W1
Tb W1
Define

K b State its unit. K b
.
.
1
According to equa tion K b  Tb / m Tb is expressed in Kelvin and m in mol kg .

Hence uni t of

For m = 1 molal, K b

Definition of
K b is K kg mol -1 .
 Tb .
K b - It is the eleva tion of boiling point produced, when one mole of solute is
dissolved in 1 kg of solvent.

Value of
K b depends on nature of solvent.
Freezing point: Freezing point of a liquid is a tempera ture a t which the vapour pressure of solid is equal
to the vapour pressure of liquid.
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SAPTARSHI
Depression of freezing point: Solution ha s lower vapour pressure than pure sol vent and hence freezes
at lower tempera ture than pure sol vent. Thus depression of freezing point is the difference between
the freezing point of pure solvent and freezing point of solution contaning non -vola tile solute.
Show graphical representation of freezing point depression of pure solvent by addition of non volatile solute.
AB i s the solid –vapour subli ma tion curve of the solid solvent, CD is the liquid-vapour pressure curve

of pure liquid solvent.

At the f reezing point, solid and liquid phases have identical vapour pressures.

At point B, the two forms ha ve sa me vapour pressure and therefore T 0 , the tempera ture
corresponding to B, must be the freeing point of pure solvent.
When solute i s dissolved in the solvent, the vapour pressure of solvent lowered and can no longer

freeze a t tempera ture T 0 .
A new equilibrium is established at point E, where vapour pressure of solvent of the solution and

solid solvent becomes identical. It i s assumed tha t solute does not dissolve in solid solvent
The tempera ture T, corresponding to the point E, where the vapour pressure curve of the solution

intersects the subli ma tion curve, is the freezing point of the solution.
The vapour pressure curve of the solution EF always lies below the vapour pressure curve of pure

solvent. Hence intersection of vapour pressure curves of solution and solid sol vent can occur only a t
a point lower than T 0 .

Therefore any solution of the solute must ha ve freezing point T, lower than tha t of the pure
solvent.
Thus

T f  T 0  T
For dilute solutions, of different solutes for a given solvent,
Tf varies linearly with concentra tion
irrespective of the na ture of the nonvola tile, non electrolyte solute.

The depression of freezing point is proportional to the lowering of the vapour pressure and hence
to the mole fraction of the solute. Thus, for dilute solutions,

Grea ter the lowering of vapour pressure
p
0
1
Tf  p10  p

 p , grea ter will be the depression of freezing point.
15
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SAPTARSHI
Deri ve the expression to calculate the molecular weight of unknown solute by measuring
depression in freezing point of pure solvent by addition of non -volatile solute.

Freezing point depression of any solution is direc tly proportional to the molality of solution.
Thus,
Tf  m m is molality of solution
Tf  Kf m............eqn(1)
K f , the proportionality constant called molal depression in freezing point constant or
cryoscopic constant or f reezing point depression constant.

If W2 gra m of solute with molar mass M2 is dissol ved in W1 Kg of solvent then,
Molality 

No. of moles of solute
Mass of solvent in Kg
W2
m

M2
W1
Thus substi tuting value of m in equa tion (1), we get ,
Tf 
K f W2
KW
 M2  f 2
M 2 W1
Tf W1
Definition of Kf and its unit

Tf  m m is molality of solution

If m = 1 then Tf

 Kf .
Cryoscopic constant is defined as, the depression of freezing point produced by dissolving
1
mole of solute in 1 kg of solvent (i.e.1 molal solution)

According to equa tion,

Unit of
Tf  Kf m, hence, Kf  Tf / m
K f is K kg mol -1 .
Semi permeable membrane:

It is a membrane which allows the solvent molecules, but not the solute molecules, to pa ss
through i t.

The thin fil ms of the copper ferrocyanide Cu 2
 Fe(CN)6  , deposi ted in pores of porous porcelain
pot i s the best semi permeable membrane.

Cellulose, cellulose nitra te, ani mal bladder, etc. are used as semi permeable membranes.
Osmosis

When a solution is sepa ra ted from pure solvent by a semipermeable membrane a s shown in figure,
the solvent molecules pa ss through the membrane into the solution and dilute i t.
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SAPTARSHI

Similarly, when two solutions of different concentra tions are sepera ted by semipermeable
membrane then the direction of flow of solvent molecules is f rom the solution of lower
concentra tion to the solution of higher concentra tion.

Due to flow of solvent into the high concentra ted solution, the solution gets diluted.

The flow continues till the concentra tions of the two solutions become equal.
Definition of OsmosisThe spontaneous and unidirectional flow of solvent molecules through a semi permeable membrane, into
the solution or flow of solvent f rom a solution of lower concentra tion to the solution of higher
concentra tion through a semi permeable membrane is called osmosis.
Describe the Abbe Nollet Experiment for osmosis

The appara tus consists of a long stem thistle funnel.

The mouth of the thi stle funnel is closed by semipermeable membrane like pig’s bladder.

Sucrose solution of some concentra tion is then filled in the thistl e funnel.

The thistl e funnel is then placed in beaker containing water in inverted posi tion.

The net flow of solvent molecules occurs into the solution through the semipermeable membrane.

Due to this, the original volume of the solution increases and the liquid level of solution rise.

Hydrosta tic pressure i s developed due to the liquid column in thi stle funnel.

Due to osmosis, solvent molecules f rom beaker enter into thistl e funnel through semipermeable
membrane. The liquid level in the thi stle funnel tube rises until the excess pressure so produced
is sufficient to stop the flow of solvent molecules. The equilibrium is reached when the
hydrosta tic pressure of the column ma tc hes the osmotic pressure.

Osmotic Pressure: The excess of pressure on the side of solution tha t stops the net flow of
solvent into solution through semipermeable membrane is called osmotic pressure.
Note: The osmotic pressure is not th e pressure produced by solution. It exists only when
the solution is separated from the solvent by the semipermeable membrane. The resulting osmosis
produces an excess pressure (osmotic pressure) in the solution.
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SAPTARSHI
Drawbacks of Abbe Nollet Experiment:

The entry of the solvent into the solution causes i ts dilution and concentra tion changes.
Remedy for Abbe Nollet Experiment:

The experi mental set up must ha ve the a rrangement for applying an external mec hanical pressure
on the solution so tha t there is no flow of solvent and concentra tion remains unchanged.

The ex ternal pressure applied to stop osmosi s is a mea sure of osmotic pressure.
Alternative Definition of Osmotic Pressure (π)

Osmotic pressure of a solution can also be defined as the excess mechanical pressure which must
be applied on the side of solution to stop the flow of solvent molecules through semipermeable
membrane into the solution.
Types of solution on the basis of osmotic pressure
1. Isotonic solution:

Two or more solutions exerting the sa me osmotic pressure are called isotonic solutions.

For exa mple,




0.05M 3.0 gL1 urea solution and 0.05M 17.19 gL1 sucrose solution are
isotonic because their osmotic pressures are the sa me.

If these solutions are separa ted by a semipermeable membrane, there is no flow of solvent in
either direction.
2. Hypertonic solution:

A solution having osmotic pressure higher than tha t of another solution is said to be
hypertonic with tha t solution.

E.g. 0.1 M urea solution exerts higher osmotic pressure than 0.05 M sucrose solution. Hence,
0.1M urea solution is hypertonic to 0.05 M sucrose solution.

If these solutions a re sepera ted by a semi permeable membrane, the solvent flows from
sucrose to urea a s sucrose is having low concentra tion.
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SAPTARSHI
3. Hypotonic solution:

A solution having osmotic pressure lower than tha t of another is sai d to be hypotonic
solution with tha t solution.

For exa mple, 0.05 M sucrose solution has osmotic pressure lower than tha t of 0.1 M urea
solution. Therefore 0.05 M sucrose solution is hypotonic with 0.1 M urea solution.
Osmosis in day today life:


A raw mango kep t in a concentra ted salt solution loses water due to osmosis and shrivel into
pickle.
A li mp carrot and celery due to water loss into a tmosphere can be placed into water making i t
firm once again. Wa ter moves in carrot due to osmosis.

People ea ting lot of sal t experience edema i.e. swelling of tissue cells due to water retention in
cells.

The preserva tion of fruits by adding sugar protec ts against bac terial action. Due to osmosi s, a
bacterium on candid fruit loses water, shrivels and d ies.

0.91 % solution of sodium chloride (called saline water) i s isotonic with Human Blood. Thus
medicines are mixed with saline water during intravenous injec tions which prevents blood cells
from shrinking or bursting.

When blood cells are kept in hypertonic solution (5% NaCl), water comes out of the cells and
they shrink in size. While when blood cells are kept in hypotonic solution (Distilled water) water
flows into the cell and they swell or burst..

Osmotic pressure is responsible for transporting water upward from soil to top of trees. In
plants the leaves of the tree loose water to the a tmosphere constantly by transpira tion. The
solute concentra tion in leaf fluid increases and water is pulled up by osmotic pressure. In case
of some of the tall trees, water reaches to the height of almost 120 meters by osmosi s and
capillary action.
Laws of osmotic pressure:
According to the theory, solute molecules in dilute solutions possess kinetic energy and move in
random directions in the solution and behave like ga s molecules.
On collision against semipermeable membrane, the solute molecules exert osmotic pressure equal to


the pressure, which the solute molecules would exert if i t were gas molecules a t the sa me
tempera ture and occupying the sa me volume as the solution.
Thus the osmotic pressure could be considered to be due to bombard ment of solute particles on

semipermeable membrane.
The osmotic pressure i s thus directly proportional to the number of solute particles or the
concentra tion of solute a t constant tempera ture.

State Van’t Hoff – Boyle’s Law and its math ematical expression.

At constant tempera ture the osmotic pressure
() of a dilute solution is direc tly proportional
to i ts
molar concentra tion or inversely proportional to the volume of the solution.
  C (C is concentra tion in
C
mol L-1 ) ……..(constant T)
n
V
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SAPTARSHI
Hence,

n
1
or   for constant n
V
V
V  constant or
hence,

 constsnt
C
State Van’t Hoff – Charle’s Law and its math ematical expression.

The concentra tion remaining constant; the osmotic pressure of a dilute solution is direc tly
proportional to the absolute tempera ture.
  T (constant C) i.e.

 constant
T
Van’t Hoff general solution equation:
Combining van’ t Hoff Boyle’s and Charle’s laws,.

T
 constant
V
V=kT (k is constant
of proportionality)
K is called general solution constant. The equa tion is called van’t Hoff general solution equa tion.
It is
si milar to general gas equa tion (PV = RT).
Value of k is sa me as R, the ga s constant hence,
where   osmotic pressure
V  RT
V  volume of solution containing 1 mole of solute
R  gas constant equal to 8.314 J mol1 K 1 or 0.082 L atm mol1 K 1
T  absolute temperature
If V is the volume of solution containing n moles of solute, equa tion becomes,
V  nRT
or  
n
RT
V
Where concentra tion, C 
Important Note:
or   CRT
n
, is the number of
V
If  is expressed in
Nm2 and
moles of solute per liter of solution.
volume in m3 then
when  is expressed in atmosph ere and volume in dm 3 then
R  8.314 J mol1 K 1 and
R  0.082 L atm K 1 mol1
Van’t Hoff – Avogadro’s law –
It sta tes tha t two solutions of equal concentra tions of different solutes exert sa me
osmotic pressure a t the sa me tempera ture.
OR
It can also be, sta ted as; equal volumes of i sotonic solutions contain an equal number of solute particles
at the gi ven tempera ture.
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For a given solution,
1 V1  n1RT1.......for solution 1

Where,
2 V2  n 2 RT2 .......for solution 2
n1 and n 2 are the numbers of moles of the solutes in V1 and V2 liters of the solutions
respectively. If

SAPTARSHI
V  n RT
1  2 , T1  T2 and V1  V2 then from equa tions,
n1  n 2
Since, numbers of moles are equal; numbers of molecules are also equal.
Abnormal molecular masses:

Dilute solution of non -electrolytes like urea, glucose, etc . ex hibit colligative properties like
lowering of vapour pressure, eleva tion of boiling point, depression of freezing point and osmotic
pressure.

In dilute solutions of non electrolytes in aqueous or nonaqueous solvents, the solute remains in
normal molecular condition and DOES NOT undergo ei ther dissociation or a ssocia tion.

The solution of nonelectrolytes does not conduc t elec tricity. The colligative properties of
solutions of nonvola tile, nonelectrolyte solutes depend on ac tual number of solute particles
present in the solution.
 Actual number of solute particles present in solution.

Hence, Colligative properties

Molecular masses of nonvola tile, nonelectrolyte solutes from dilute solutions can be determined
by using the value of colligative property. From these equa tions, i t isobserved tha t colliga tive
property is inversely proportional to molecular mass of solute. This molecular ma ss i s theoretical
molecular ma ss of solute.

In case of solutions of electrolytes, value of observed colligative properti es is ei ther
exceptionally higher or lower than the theoretically expected value of colligative property
exhibi ted by solution of non-electrolyte solute of sa me concentra tion.

This is because the electrolyte solute i.e. the solute of acid, base or salt when dissolved in
solvent can undergo dissocia tion or association.

In case of dissociation of solute, the number of particles in the form of ions is more than
actually dissolved. As the no. of pa rticles increa ses the value of col ligative properties also
increases.

In general if solute molecules undergoes dissocia tion producing 2, 3, 4 ions, the observed
molecular ma ss becomes 1/2, 1/3, 1/4 etc . of the theoretical molecular mass of electrolyte
solute.

In case of some solutes, two or more molecules associa te together to produce large aggrega te
molecules. Because of this, effective number of pa rticles of solute in the solution decrea ses

Due to association, observed molecular mass becomes double, triple of the theoretical molecular
ma ss and so on.

In general, observed, lower molecular masses of electrolyte solutes are due to dissocia tion of
solute molecules or observed higher molecular masses of solutes in nonaqueous solvents a re due
to a ssocia tion/polymeriza tion and are called abnormal molecular masses.
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SAPTARSHI
Explain that how the value of colligative property d epend s on d issociation of electrol yte solutes by
taking suitable exampl e.

Consider the colligative property, depression of freezing point. (Applicable for other colligative
property also)



Depression in freezing point of sol vent by addition of solute is calculated by
Tf  Kf m
1
K f For water i s 1.86 K kg mol and Kf  Tf / m . Thus theori tical vlue of Kf is 1.86.
The ra tio of Tf / m for 0.05 molal aqueous solutions of non electrolytes and electrolytes are
experi mentally determined and are listed in table.
Experi mental or observed values of
Tf / m for different solutes in aqueous solutions a re
Solute
Glucose
HCl
NH4 Cl
CoCl 2
Tf / m
1.862
3.635
3.617
5.204
 1.86 1
 1.86  2
 1.86  2
 1.86  3
The observations from th e table are as follows

The non electrolyte solute glucose nei ther associates nor dissociates in solution. As the
number of solute particles are not c hanged, the value of
value of

Tf / m which is the theoretical
K f is equal to 1.86 K kg mol1 of solvent water.
Electrolytic solutes when dissolved in solvent dissociate to produce mul tiple numbers of
ions/particles.

Due to di ssocia tion of solute, number of particles of solute increases and hence the value
of colligative property also increa ses and thus observed tha t
to integral mul tiple of
Tf / m is approxima tely equal
K f value.
The value of integral is equal to total number of ions produced o n dissociation as follows.

1.
HCl  H  Cl ; 2particles; Tf / m  2 1.86Kmol1 kg 1
2.
NH4Cl  NH4 Cl ; 2 particles; 2 1.86 K mol 1 kg 1
3.
CoCl2  Co2  2Cl ; 3 particles; 3 1.86 Kmol1 kg 1
Tf / m  K f Value observed in case of solutions of electrolytes may not be exactly double or
triple to tha t of theoretical

K f value observed in case of solutions of nonelec trolyte solute.
The value fluctua tes with d egree of dissocia tion of solute in solution.
Explain that how the value of colligative property depend s on association of solutes by taking
suitable example.

In some non -polar sol vents, two or more molecules of solute a ssocia tes to form bigger molecules.

For exa mple, in benzene solutes like acetic acid, benzoic acid etc. associa te to form di mmers.

This associa tion is due to the hydrogen bonding between these molecules.
2CH3COOH   CH3COOH 2
2C6 H5COOH   C6 H5COOH 2
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SAPTARSHI

Hence numbers of solute particles a re reduced to half. And thus value of colligative propety also
decreases.

Observed molecular masses of these species in above cases are al most twice the ex pec ted
values in dilute solution.
Van’t Hoff factor

Van’t Hoff factor i s defined as the ra tio of observed colligative property to the theorotical
colligative property
i

observed Colligative Pr operty
theoretical Colligative property
The theorotical colligative property can be considered as the observed colligative property of a
solution assuming the solute as nonelec trolyte of sa me concentra tion

Thus Van’t Hoff factor can also be defined as the ra tio of observed colligative property
produced by a given concentra tion of elec trolyte solution to the property observed for the sa me
concentra tion of non electrolyte solution. Therefore,
i
observed colligative property of electrolyte solution
observed colligative property of non electrolyte solution of same concentration
In short,
i
 p observed    Tb observed    Tf observed     observed 
 p theoretical   Tb theoretical   Tf theoretical    theoretical 
But colligative property
Hence,
i
 number of solute pa rticles present in solution
number of solute particles present in solution  N observed 
theoretical number of solute particles due to solution of non electrolyte  N theoretical 
i.e.
i
n  observed 
n  theoretical 
Similarly,
colligative property 
Hence,
i
1
molecular mass(M)
M  theoretical
M  observed
Express the mathematical relation between Van’t Hoff factor (i) and degree of dissociation

Consider an electrolyte
A y and of Bx  as A x By
( )
A x By dissolved in the solvent and it undergoes dissocia tion into x ions of
xA y  yBx 
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SAPTARSHI

Assume tha t the molality of electrolyte i s m when i t is dissolved in the solvent i.e m moles of the
electrolyte,

A x By is dissolved in 1 Kg of solvent.
On dissolution solute di ssocia tes. Let
 be the degree of dissocia tion of the solute.
A x By
Initial moles
No. of moles
dissociated /
formed
No.of moles
at equillibrium

The total number of moles,
moles of
m
m
m  m
xA y   yB x 
0
xm
xm
0
ym
ym
m t in the solution a t equilibrium will be, m 1   of Ax By and x(m)
A y ions and y  m  moles of Bx ions .
mt  m 1     x  m   y  m 
Hence,
 m 1     x  y 
 m 1   x  y  1  
It is convenient to represent the total number of ions produced by dissociation of one molecule
of solute
Ax By i.e. x  y by n '. Hence, x  y  n '
mt  m 1   n ' 1  
Therefore,
i
Now, Vant Hoff factor,
observed number of moles
theoretical number of moles
m t m 1  (n ' 1) 

m
m
i 1
The degree of dissociation,  
n ' 1

since
i
M  theoretical 
M  observed 
Hence,
i  1  (n ' 1)
 1   n ' 1  
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Hence, degree of dissocia tion

SAPTARSHI
M  theoretical   M  observed 
M  observed  n ' 1
Hence, i t is possible to determine degree of dissocia tion of elec trolyte by determining
experi mentally
M  observed  and by measuring experi mentally any one of the colligati ve properti es.
Desalination:

Probably due the greenhouse effect, every body is facing a problem of shortage of water.

Hence a ttempts are mad e to procure drinking water by removing sal ts from sea water by a
process called as Desalination by reverse osmosis.

Ocean is a large stock of sea -water contaning almost 1.5 X 10 21 L of water. It contains 3.5 %
(w/w) of dissolved sal ts, mainly sodium chloride.

Drinking water is produced by using thi s process.
Concept of Reverse Osmosi s:
 Reverse osmosis i s the flow of solvent f rom high concentra ted solution to low concentra ted
solution.
 In this process, high pressure is applied to force water from concentra ted aqueous solution like
sea water to pure water side through semi -permeable membrane.
 The osmotic pressure of sea-wa ter is 30 a tm. Hence if the pressure on the solution side is
grea ter than 30 a tm. Osmosi s stops and reverse osmosis starts.
 Due to this solvent from sea water enters the other side of pure wa ter.
 Note: The method can be used by using semipermeable membrane which withstands high
pressure over prolonged period. By using thi s method, about 10 million litres of fresh wa ter i s
produced every day from sea water.
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