SOLUTION
Solution-
A homogenous mixture of two or more substances is called solution. It is of following types-
ON THE BASIS OF NUMBER OF COMPONENTS:
NAME NUMBER OF COMPONENTS
Binary Solution 2
Tertiary Solution 3
Quaternary Solution 4
The binary solution has two phases- solute and solvent. Generally, the substance present in excess
and whose physical state is the same as that of the solution is called solvent and the second
component is known as solute.
ON THE BASIS OF PHYSICAL STATE OF SOLUTE AND SOLVENT:
SOLUTE SOLVENT EXAMPLE
SOLID SOLUTION
Solid Solid Alloy
Liquid Solid Amalgam
Gas Solid Solution of H2 in Pd
LIQUID SOLUTION
Solid Liquid Salt solution
Liquid Liquid Solution of alcohol & water
Gas Liquid Oxygen dissolved in water
GASEOUS SOLUTION
Solid Gas Camphor in air
Liquid Gas Water vapours in air
Gas Gas Air
Concentration of Solution-
It is the amount of solute present in a fixed amount of solvent. It is measured in different units which
are as follow-
1. Mass Percentage-
It is the mass of solute (in g) dissolved in per 100 g of solution.
Mass Percentage = Mass of Solute 100
Mass of Solution
Where; mass of solution = mass of solute + mass of solvent
2. Volume Percentage-
It is the volume of solute dissolved in per 100 units of solution.
Volume Percentage = Volume of Solute 100
Volume of Solution
Where; volume of solution = volume of solute + volume of solvent
3. Gram per liter-
It is the amount of solute (in grams) present in one liter of the solution.
4. Molarity-
The number of moles of solute dissolved in one liter of solution is called molarity. It changes
with temperature. Its unit is mol/L & is indicated by M.
Molarity = Number of moles of Solute
Volume of Solution (in L)
5. Molality-
The number of moles of solute dissolved in one kg of solution is called molality. It does not
change with temperature. Its unit is mol/kg & is indicated by m.
Molality = Number of moles of Solute
Mass of Solution (in kg)
6. Formality-
The number of gram formula mass of an ionic compound dissolved in one liter of solution is
called formality. It changes with temperature.
Formality = Number of gram formula mass of Solute
Volume of Solution (in L)
7. Normality-
The number of gm. equivalent of solute dissolved in one liter of solution is called normality. It
changes with temperature. Its unit is gram. eq. /L & is indicated by N.
Normality = Number of gm. eq. of solute
Volume of Solution (in L)
8. Mole Fraction-
The mole fraction of a particular component in a solution is the ratio of number of moles of that
component to the total number of moles present in the solution. It is independent of
temperature. It is denoted by .
Mole Fraction = Number of moles of given component
Total number of moles in the solution
Thus for a binary mixture of components A and B we have
nA
A
n A nB
nB
B
n A nB
Where n A and n B are the number of moles of A and B respectively.
Note – The sum of the mole fractions of all the components of a solution is always equal to one.
9. ppm-
The mass of solute (in g) dissolved in 106 g of solution is called concentration in ppm.
ppm = Mass of solute (in g) 106
Mass of solution (in g)
Henry Law-
This law was proposed by William Henry in 1803. According to this law-
“The mass of a gas dissolved per unit volume of the solvent at a constant temperature is
directly proportional to the pressure of the gas in equilibrium with the solution.”
m p
m K. p
Where K is proportionality constant whose value depends upon the nature of gas, nature of solvent,
temperature and units of pressure.
The law can also be stated as:
“The partial pressure of the gas in the vapour phase is directly proportional to the mole
fraction of the gas in the solution.”
p
p KH
Where KH is Henry constant whose value depends upon the nature of gas. Its value increases with
increase in temperature which decreases the solubility of the gas.
Applications of Henry Law-
1. In the packing of cold drinks.
2. In the oxygen cylinder of scuba divers to prevent from bends.
3. In anoxia which happens at high altitudes due to low partial pressure of O2.
Limitations of Henry Law-
Henry’s law is valid if,
1. Pressure is low.
2. Temperature is not too low
3. Gas is not highly soluble
4. Gas doesn’t associate or dissociate in the solvent
5. Gas doesn’t react with water when dissolved in it.
Solubility-
The maximum amount of a substance which can be dissolved in a fixed amount of solvent at a
particular temperature to form saturated solution is called the solubility.
Solubility of solids in liquid depends upon the following factors-
1. Nature of solute and solvent (polar or nonpolar).
2. Dielectric constant of solvent. Higher the dielectric constant of the solvent, greater is the
solubility of an ionic compound.
3. It increases with increase in temperature for endothermic process.
4. It decreases with increase in temperature for exothermic process.
5. It shows irregular behavior in case of some compounds due to change in one solid form into
another solid form.
Vapour Pressure-
The pressure exerted by the vapours of a liquid at a particular temperature is called vapour
pressure. It depends upon the nature of liquid and temperature. The vapour pressure of a liquid is
directly proportional to temperature.
Raoult’s Law-
1. Raoult’s Law for Solutions Containing Volatile Liquids-
According to this law-
”For a solution of volatile liquids, the partial pressure of each component is directly
proportional to its mole fraction.
P
P = constant ….1
If P = P0 and = 1, then
P0 = constant 1
P0 = constant
Put this value in equation 1, we get
P = P0
Thus the partial vapour pressure of each component in the solution is equal to the product of its
vapour pressure and its mole fraction.
Let the solution is composed of two liquids A and b, then
PA = PA0 A
PB = PB0 B
Now the total pressure is given by
P = PA + PB
P = PA0 A + PB0 B
PA P
Note : Mole fraction of a component in vapour phase y A and y B B
P P
2. Raoult’s Law for Solutions Containing Nonvolatile Solute-
For this type of solution-
Vapour pressure of solution = vapour pressure of solvent
P = Psolv = P0 solv …1
Thus for solution containing nonvolatile solute, vapour pressure of solution is equal to the product of
vapour pressure of the solvent and its mole fraction.
For a binary solution Solute + Solvent = 1
Solvent = 1 - Solute
Put this value in equation (1), we get
P = Psolv = P0 (1 - Solute)
P
1 solute
P0
P
1 0 solute
P
P P
0
solute
P0
Ideal Solution-
A solution is said to be ideal if it obeys Raoult’s law at all concentrations and temperature.
Example – n-Hexane and n-Heptane
Graphical Representation of Ideal Solution-
We know that
P = PA0 A + PB0 B
P = PA0 (1 - B) + PB0 B
P = ( PB0 – PA0 ) B + PA0
This equation of the type y = mx + c. thus on plotting graph between P and we will get a straight
line.
P0B
P0A
Vapour Pressure
A 1 A 0
Mole Fraction
B 0 B 1
Non Ideal Solution-
A solution which does not obey Raoult’s law is called non ideal solution. They are of two types:
1. Solutions Showing Positive Deviation from Raoult’s Law-
These solutions show higher vapour pressure than that given by Raoult’s law.
Example – Water and Ethanol
They are also of two types.
a) Type I Solutions-
P0B
P0A
Vapour Pressure
A 1 A 0
Mole Fraction
B 0 B 1
In these solutions, the vapour pressure of solution does not exceed the vapour pressure of more
volatile component in its pure state.
b) Type II Solutions-
In these solutions, the vapour pressure of solution at a particular composition exceed the vapour
pressure of more volatile component in its pure state.
P0B
P0A
Vapour Pressure
A 1 A 0
Mole Fraction
B 0 B 1
2. Solutions Showing Negative Deviation from Raoult’s Law-
These solutions show lower vapour pressure than that given by Raoult’s law.
Example – Water and Hydrochloric Acid
P0B
P0A
Vapour Pressure
A 1 A 0
Mole Fraction
B 0 B 1
Difference between Ideal and Non-Ideal Solution-
NON-IDEAL SOLUTION
S. NO. IDEAL SOLUTION
NEGATIVE
POSITIVE DEVIATION
DEVIATION
A-B molecular A-B molecular A-B molecular
interaction forces are interaction forces are interaction forces are
1 similar to A-A or B-B weaker than A-A or B-B stronger than A-A or B-B
molecular interaction molecular interaction molecular interaction
forces. forces. forces.
PA = P0A A PA > P0A A PA < P0A A
2
PB = P0B B PB > P0B B PB < P0B B
Dissolution is neither
Dissolution is Dissolution is
3 exothermic nor
endothermic. exothermic.
endothermic.
4 H mixing 0 H mixing 0 H mixing 0
5 Vmixing 0 Vmixing 0 Vmixing 0
Forms minimum boiling Forms maximum boiling
6 Don’t form azeotropes.
azeotropes. azeotropes.
Azeotropic Mixture-
A liquid mixture on distillation gives the distillate of the same composition as that of the liquid
mixture itself is known as azeotropic mixture or constant boiling mixture.
It is of two types:
1. Minimum Boiling Azeotropic Mixture-
It is formed by Type II of non-ideal solution which shows positive deviation from Raoult’s law.
TA
TB
Temperature
A 1 A 0
Mole Fraction
B 0 B 1
2. Maximum Boiling Azeotropic Mixture-
It is formed by those non-ideal solutions which shows negative deviation from Raoult’s law.
TA TB
Temperature
A 1 A 0
Mole Fraction
B 0 B 1
Colligative Properties / Democrative Properties-
The properties which depend upon the number of solute particles in solution are called colligative
properties. Some important colligative properties are as follow:
1. Relative Lowering of Vapour Pressure-
The relative lowering of vapour pressure of a solution is equal to the mole fraction of solute.
Thus,
P0 P
Solute
P0
P0 P n
P 0
n N
For dilute solutions,
n+N=N
Then,
P0 P n
P0 N
w
P0 P m'
0
P W
M'
P P wM '
0
P0 Wm'
2. Elevation of Boiling Point-
The increase in boiling point of a solvent on adding a non-volatile solute is called elevation of
boiling point or ebullioscopy.
Tb Tb Tb0
Experimentally,
Tb m
Tb K b m
Or
K b w 1000
m'
Tb W
Where Kb is known as molal elevation constant or ebullioscopy constant which is equal to the
elevation of boiling point when the molality of solution is unity.
Note-
MRTb2 RTb2
a) Kb
1000 H v 1000 Lv
Where M = Molecular mass of solvent
R = Universal gas constant
Tb = Boiling point of solution
H v = Molar enthalpy of vaporization of solvent (latent heat of vaporization for one mole of the
solvent.
Lv = latent heat of vaporization per gram of the solvent
b) Equimolal solutions of different non-volatile and non-electrolytic substances dissolved in same
solvent exhibit the same elevation of boiling point.
3. Depression of Freezing Point-
The decrease in freezing point of a solvent on adding a non-volatile solute is called depression
of freezing point or cryoscopy.
T f T f0 T f
Experimentally,
T f m
T f K f m
Or
K f w 1000
m'
T f W
Where Kf is known as molal depression constant or cryoscopic constant which is equal to the
depression of freezing point when the molality of solution is unity.
Note-
MRT f2 RT f2
a) Kf
1000 H f 1000 L f
Where M = Molecular mass of solvent
R = Universal gas constant
Tf = Freezing point of solvent
H f = Molar enthalpy of fusion of frozen solvent (latent heat of fusion for one mole of frozen
solvent.)
Lf = Latent heat of fusion per gram of the solvent
b) Equimolal solutions of different non-volatile and non-electrolytic substances dissolved in same
solvent exhibit the same depression of freezing point.
Osmosis-
The spontaneous flow of solvent through a semi-permeable membrane from a pure solvent to a
solution or from a dilute solution to a concentrated solution is called osmosis.
Semi-permeable Membrane
Net flow of solvent
Dilute Solution Concentrated Solution
Osmosis can be broadly classified in following two categories:
1. Endosmosis-
It is the movement of water molecules into a cell through a semi-permeable membrane, when the
cell is placed in a hypotonic solution (a solution with a lower solute concentration than the cell's
cytoplasm), causing the cell to swell or to become turbid.
Example – RBC’s placed in NaCl solution (concentration less than 0.9%) causes them to swell.
2. Exosmosis-
It is the movement of water molecules out of a cell through a semi-permeable membrane, when
the cell is placed in a hypertonic solution (a solution with a higher solute concentration than the
cell's cytoplasm), causing the cell to shrink or to become flaccid.
Example – RBC’s placed in NaCl solution (concentration more than 0.9%) causes them to shrink.
Semi-Permeable Membrane-
A membrane which allows the passage of solvent molecules only not of solute particles is called semi-
permeable membrane (SPM).
Example- Vegetable and animal membrane are natural SPM while cellophane, copper ferrocyanide,
silicates of iron, cobalt and nickel are artificial or chemical SPM.
4. Osmotic Pressure-
The external pressure which should be applied to the solution to stop osmosis is called osmotic
pressure. It is measured by Berkley and Hartley method.
Berkley and Hartley method-
Structure-
The apparatus consists of a porcelain tube with SPM of copper ferrocyanide precipitate deposited in
its walls which is enclosed in a metallic jacket. The porcelain tube is filled with solvent and the
metallic jacket is filled with the solution whose osmotic pressure is to be measured and is fitted with a
piston connected with a pressure gauge to measure the applied pressure.
Working-
As the osmosis proceed, the liquid level in the capillary tube rises which can be stopped by applying
an external pressure which will be the osmotic pressure of the solution and can be read easily on the
pressure gauge.
Reverse Osmosis-
The phenomenon in which the natural process of osmosis is reversed by applying pressure more than
osmotic pressure on the concentrated solution is called reverse osmosis. It is commonly used in the
desalination of water & concentration of fruit juices.
Semi-permeable Membrane External Pressure
Net flow of solvent
Dilute Solution Concentrated Solution
Applications of Reverse Osmosis:
1) Desalination of sea water.
2) Concentration of fruit juices.
3) Purification of drinking water.
4) In the treatment of waste water.
Note – SPM used for RO is cellulose acetate.
Isotonic Solutions-
Tow solutions are called isotonic when they are separated by SPM and no osmosis occur. Thus
isotonic solutions have the same osmotic pressure.
For Solution I
V1 n1 RT
For Solution II
V2 n2 RT
For isotonic solutions
1 2
n1 n
RT 2 RT
V1 V2
n1 n 2
V1 V2
C1 C 2
Thus isotonic solutions have the same molar concentration.
Hypertonic & Hypotonic Solution-
A solution having higher osmotic pressure than the other is termed as hypertonic solution and the
second one is known as hypotonic solution.
Difference between Osmosis & Diffusion-
OSMOSIS DIFFUSION
It involves the movement of solvent molecules
Both solute and solvent molecules can move.
only.
It takes place through a semi-permeable
No semi-permeable membrane is required.
membrane.
It can be stopped or reversed. It cannot be stopped or reversed.
It is limited to solutions only. It is common in gases as well as in liquids.
Abnormal Molecular Mass-
When the experimentally observed molecular mass of a substance determined on the basis of
colligative property is found to be different from the normal value, the observed molecular mass is
known as abnormal molecular mass.
Molecular Mass of Solute = 1
Number of particles of solute in solution
Association of solute particles always leads to a higher value of observed molecular mass of solute
while dissociation of solute particles always leads to a lower value of observed molecular mass of
solute
Van’t Hoff Factor-
It is the ratio of normal molecular mass of solute to its observed molecular mass. It is denoted by i.
i = Normal Molecular Mass = Observed value of colligative property
Observed Molecular Mass Normal value of colligative property
Note:
1. If solute undergoes neither association nor dissociation in solution, i = 1.
2. If solute undergoes association in the solution, i < 1.
3. If solute undergoes dissociation in the solution, i > 1.
4. On including the Van’t Hoff factor, the equations for colligative properties will be
P0 P
i solute
P0
Tb iK b m
T f iK f m
iCRT
Degree of Association-
It is the fraction of total number of moles of solute which undergoes association in the solution.
= Number of moles of solute undergoing association
Total number of moles
Let n moles of solute A undergoes association then,
nA An
Initially 1 0
At equilibrium 1-
n
Now Van’t Hoff factor is given by
1
i n
1
i 1
n
i 1
n
1
i 1 1
n
i 1
1
1
n
n(i 1)
(1 n)
n(1 i )
(n 1)
Degree of Dissociation-
It is the fraction of total number of moles of solute which undergoes dissociation in the solution.
= Number of moles of solute undergoing dissociation
Total number of moles
Let a solute A dissociates as follow
A n1B + n2C + …….
Initially 1 0 0 …….
At equilibrium 1- n1 n2 ……..
Now the Van’t Hoff factor is given by
1 n
i
1
i 1 n
i 1 n 1
i 1
n 1
