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Kinetic Molecular Theory of Gases
Main Postulates
Following are the main postulates of kinetic molecular theory of gases:
 A gas consists of very small microscopic particles called 'molecules'. Depending
upon the nature of gas each gas molecule may consists of an atom or group of
atoms. Molecules are in a state of continuous motion.
 All the molecules of a gas are in stable state and are considered identical.
 Any finite volume of a gas consists of very large number of molecules at S.T.P.
there are 3 x 1025 molecules in a cubic meter.
 The molecules are wide separated from each other as compared to their own
dimensions.
 The diameter of a molecule is about 3 x 10-10 meter.

Gas molecules move in straight line in all possible directions (random movement)
with various speeds
 Gas molecules collide with each other and with the walls of container. There
collisions are perfectly elastic in nature.
 Gas molecules when collide with the walls of container, they transfer their
momentum which appears as pressure of gas.

Molecules of an ideal gas exert no force of attraction or repulsion on one another
except during collision.
 The average kinetic energy of gas molecules is directly proportional to absolute
temperature.
 At a given temperature, the molecules of all gases have the same kinetic energy.

Newtonian mechanics is applicable to molecular motion.
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Boyle’s law
Introduction
Boyle’s law is a quantitative relationship between volume and pressure of a gas at constant
temperature.
Statement
"The volume of a given mass of a gas is inversely proportional to pressure if
temperature remains constant ".
Mathematical representation of Boyle’s law:
According to Boyle’s law
V

𝟏

𝐏
V
=
(Constant)
PV
=
constant
𝟏
𝐏
At P1 pressure
P1V1
=
constant ------------------ (1)
At P2 pressure
P2V2
=
constant ------------------ (2)
Comparing Eq(1) & Eq(2)
P1V1
=
P2V2
.
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Second statement
"At constant temperature, the product of pressure and volume of a gas remains
constant”
Graphical representation of Boyle’s law
Graph between P & V at constant temperature is a smooth curve known as "parabola"
Graph between 1/P & V at constant temperature is a straight line.
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Charles law
Introduction
It is quantitative relation between volume and absolute temperature of a gas at constant
pressure.
Statement
"The volume of a given mass of a gas at constant pressure is directly proportional
to absolute temperature"
Second statement
"The volume of a given mass of a gas increases or decreases by 1/273 times of it’s
original volume at 0 0C for every degree fall or rise of temperature at given
pressure."
Mathematical representation
Then according to Charles’s law
V
V
 
=
T
(constant) T
𝐕
=
K
𝐓
At Volume 1
𝐕₁
𝐓₁
=
K------------------------------ (1)
At volume 2
𝐕₂
𝐓₂
=
K------------------------------ (2)
Compare Eq (1) & Eq (2)
𝐕₁
𝐓₁
=
𝐕₂
𝐓₂
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Third statement
"The ratio of volume to absolute temperature of a gas at given pressure is always
constant"
Graphical representation
Graph between Volume and absolute temperature of a gas at constant pressure is a
"straight line"
Absolute scale of temperature or absolute zero If the graph between V and T is
extra plotted, it intersects T-axis at -273.16 0C At -273.16 0C volume of any gas
theoretically becomes zero as indicated by the graph.
But practically volume of a gas can never become zero. Actually no gas can achieve the
lowest possible temperature and before -273.16 0C all gases are condensed to liquid. This
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temperature is referred to as
motions are ceased.
absolute scale or absolute zero. At -273.16 0C all molecular
Polymorphism
Existence of substance into more than one crystalline forms is known as
"Polymorphism".
In other words:
Under different conditions of temperature and pressure, a substance can
form more than one type of crystals. This phenomenon is called
Polymorphism and different crystalline forms are known as
‘POLYMORPHICS’
Example:
1) Mercuric iodide (HgI2) forms two types of crystals.
a. Orthorhombic
b. Trigonal
2) Calcium carbonate (CaCO3) exists in two types of crystalline forms.
a. Orthorhombic (Aragonite)
b. Trigonal
Polymorphous substances have similar chemical properties but different physical properties.
Allotropy
"Existence of an element into more than one physical forms is known as
ALLOTROPY
Or
Under different conditions of temperature and pressure an element can exist in
more than one physical forms. This phenomenon is known as Allotropy and
different forms are known as "Allotropes"
Example:
Coal, lamp black, coke, Diamond, graphite etc. are all allotropic forms of carbon.
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Isomorphism
Existence of different substances in one crystalline form is known as
"ISOMORPHISM"
Or
Different substances may exist in identical crystalline forms. This phenomenon is
called as Isomorphism and these substances are known as ‘Isomorphous’.
Examples:
1) Na2SO4 & Ag2SO4 both exist in Hexagonal crystalline form.
2) KBF4 & BaSO4 both exist in Orthorhombic
3) ZnSO4 & NiSO4 both exist in Orthorhombic
4) CaCO3 & NaNO3 both exist in Trigonal
Properties of Isomorphic Substances
1) Isomorphic substances have same atomic ratio
2) Empirical formula of isomorphic substances is same
For example

CaCO3 NaNO3
1:1:3 1:1:3

NaF MgO
1:1 1:1
3) They have different chemical & physical properties.
4) When their solutions are mixed, they form mixed type of crystals.
5) They show property over growth.
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Types of Solids
Solids can be divided in to two distinct classes.
1) Crystalline solids
2) Amorphous solids
1) Crystalline solids:
Crystalline solids have the following fundamentals properties.
1. They have characteristic geometrical shape.
2. They have highly ordered three-dimensional arrangements of particles.
3. They are bounded by PLANES or FACES
4. Planes of a crystal intersect at particular angles.
5. They have sharp melting and boiling points.
Examples:
Copper Sulphate (CuSO4), NiSO4, Diamond, Graphite, NaCl, Sugar etc
2) Amorphous solids:
Solids that don’t have a definite geometrical shape are known as Amorphous Solids.
1. In these solids particles are randomly arranged in three dimension.
2. They don’t have sharp melting points.
3. Amorphous solids are formed due to sudden cooling of liquid.
4. Amorphous solids melt over a wide range of temperature
Examples:
Coal, Coke, Glass, Plastic, rubber etc
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Types of Crystals
Solid crystals can be divided into four categories.
1) Metallic crystals
2) Ionic crystals
3) Covalent crystals
4) Molecular crystals
1) Metallic Crystals
In metallic crystals, atoms are joined together by metallic bond. Metallic crystals are very
hard.





They
They
They
They
have high melting point and boiling point.
have shiny surface.
conduct electricity and heat.
are ductile.
They are malleable
2) Ionic Crystals









Solids that contain ionic bond in their structure consist of ionic crystals.
In ionic crystals, oppositively charged ions are joined together by strong electrostatic
forces.
They are hard substances.
They have high melting and boiling point.
They posses ionic bond.
They conduct electricity in molten state and in the form of solution.
They are brittle.
They are not ductile.
They can not be drawn into sheets.
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3) Covalent Crystals


Solid substances in which atoms are held together by covalent bond are known as
covalent crystals.
These crystals are very stable.
For example:
Diamond
Graphite
4) Molecular Crystals:
In molecular crystals, molecules are joined together by weak Vander Wall forces.
These substances have low melting point and boiling point.
Generally they are volatile (evaporates)
Difference between Amorphous Solids and
Crystalline Solids
Amorphous Solids
Crystalline Solids
1. Solids that don't have definite
geometrical shape.
1. They have characteristic geometrical
shape
2. Amorphous solids don't have
particular melting point. They melt
over a wide range of temperature.
2. They have sharp melting point.
3. Physical properties of amorphous
solids are same in different
direction,i.e. amorphous solids are
isotropic.
4. Amorphous solids are unsymmetrical.
5. Amorphous solids don't break at fixed
cleavage planes.
3. Physical properties of crystalline solids
are different in different directions.
This phenomenon is known as
Anisotropy.
4. When crystalline solids are rotated
about an axis, their appearance does
not change. This shows that they are
symmetrical.
5. Crystalline solids cleavage along
particular direction at fixed cleavage
planes.
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Vapour Pressure
Pressure exerted by the vapour of a liquid at equilibrium is called "Vapour
Pressure" of that liquid.
OR
Pressure exerted by the vapours of a liquid when rate of evaporation is and the
rate of condensation becomes equal is called "Vapour Pressure".
· Different liquids have different vapor pressure under similar conditions.
· Vapour pressure varies with temperature.
· At elevated temperature, vapor pressure also increases
Boiling Point
The temperature at which the vapour pressure of a liquid becomes equal to
atmospheric pressure is called BOING PONT. At this temperature a liquid starts
boiling.
Boiling point of liquid varies with atmospheric pressure. If atmospheric pressure is less then
760 torr then the boiling point of a liquid will decrease from its standard boiling point.Boiling
point of a liquid decreases with the decrease in pressure and vice versa
Normal boiling point
Boiling point of a liquid when atmospheric pressure is 1.00 atmp or 760 torr is
referred to as normal boiling point
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Dalton’s Law of Partial Pressure
Partial Pressure
In a mixture of different gases which do not react chemically each gas behaves
independently of the other gases and exerts its own pressure. This individual pressure that
a gas exerts in a mixture of gases is called its partial pressure.
Dalton’s Law of Partial Pressure
Introduction:
Based on this behaviour of gases, John Dalton formulated a basic law which is known as
"The Dalton's law of partial pressure”.
Statement
"If two or more gases (which do not react with each other) are enclosed in a
vessel,
the total pressure exerted by them is equal to the sum of their partial pressure".
Mathematical Representation
Consider a mixture of three non-reacting gases
are
a , b and c .Partial pressures of these gases
Pa ,Pb and Pc .
According to Dalton's law of partial pressure, their total pressure is given by:
Ptotal = Pa + Pb + Pc
Dalton’s Law in the light of Kinetics Molecular Theory
According to kinetic molecular theory of gases there is no force of attraction or repulsion
among the gas molecules. Thus each gas behaves independently in a mixture and exerts its
own pressure.
In terms of KINETIC MOLECULAR THEORY, Dalton's law of partial pressure can be explained
as:
"In a non-reacting mixture of gases, each gas exerts separate pressure on the
container in which it is confined due to collision of it's molecules with the walls of
container.
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The total pressure exerted by the gaseous mixture is equal to
the sum of collisions of the molecules of individual gas.”
Expression for Partial Pressure
Consider a gaseous mixture of three different gases a , b and c enclosed in a container of
volume Vdm3 at T Kelvin. Let the partial pressures of these gases are Pa ,Pb and Pc
respectively and total pressure of mixture is Pt. Let there are na ,nb and nc moles of each
gas respectively and the total number of
moles are nt.
Three gases confined in a cylinder under similar conditions:
Using equation of state of gas:
PV
=
Or
P
=
For gas a:
nRT
Pa
na RT
=
nRT
V
----------------------------- (1)
V
For gas b:
Pb
=
For gas c:
Pc
=
nb RT
----------------------------- (2)
V
nc RT
V
----------------------------- (3)
For any gas
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Pgas
=
ngas RT
Pgas
=
RT
ngas
V
V
-------------------------- (a)
Adding equation (1), (2) and (3), we get,
na RT nb RT nc RT
+ V + V
V
RT
(na + nb + nc ) V
Ptotal
=
Ptotal
=
ntotal
=
na + nb + nc
Ptotal
=
Ptotal
(nt ) V
=
ntotal
RT
RT
V
-------------------------- (b)
Comparing equation (a) and (b), we get,
Ptotal
ntotal
=
Pgas
ngas
Or
Pgas
ngas
=
Ptotal ntotal
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This expression indicates that the pressure of a gas is proportional to number of moles if
confined under similar conditions.
Diffusion – Graham’s Law of Diffusion
Diffusion of gases
Inter mixing of two or more gases to form a homogeneous mixture without any chemical
change is called "DIFFUSION OF GASES" . Diffusion is purely a physical phenomenon. Gases
diffuse very quickly due to large empty spaces among molecules. Different gases diffuse
with different rates (velocities).
Graham’s Law of Diffusion
Graham's law is a quantitative relation between the density and rate of diffusion of gases.
Statement
The rate of diffusion of a gas is inversely proportional to the square root of its density.
The comparative rates of diffusion of two gases are inversely proportional to the square
root of their densities.
Mathematical Representation of the law
Consider two gases A and B having mass densities d1 and d2 and their rates of diffusions
are r1 and r2 respectively. According to Graham's law of diffusion:
For gas A:
OR
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.................. (i)
For gas B:
OR
.................. (ii)
Dividing equation (i) by equation (ii)
Since density  molecular mass, therefore, we can replace density d by Molecular mass M.
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Viscosity
Viscosity is characteristic property of liquid, viscosity describes the flow of a liquid.
Definition:
Viscosity is defined as the resistance in the flow of a liquid
Or
Internal friction present between two layers of a liquid
or
which resists the flow of liquid is commonly known as Viscosity.
· A liquid with high viscosity is thick and flows slowly.
· A liquid with low viscosity is thin and flows quickly.
· Different liquids have different viscosities.
Factors affecting Viscosity
Size of molecules
Viscosity of a liquid having large molecules is high whereas the viscosity of those liquids
that have small molecules is low.
Shape of molecules
Spherical molecules provide resistance but oval shaped or disc like molecules provide
greater resistance in the flow of liquid. That’s why viscosity of liquids having spherical
molecules is low.
Inter molecular forces
Liquids having large inter molecular forces have greater viscosity.
Temperature
Viscosity of liquid decreases with increase in temperature. Because an increase in
temperature, reduces the forces of attraction between molecules.
Units:
· Most common unit is "POISE"
· Small unit is "CENTI POISE"
· In S.I system unit is N.S/m2
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Conversion factors
1Centipoise = 10-3 NS/m2 or 0.001 NS/m2
Surface Tension
Surface tension is a characteristic property of a liquid.
Definition:
"Perpendicular force acting on the unit length of the surface of a liquid is called
SURFACE TENSION".
Surface tension=
 =
𝐅𝐨𝐫𝐜𝐞
𝐋𝐞𝐧𝐠𝐭𝐡
𝐅
𝐋
2nd definition:
"Energy per unit area on the surface of a liquid is called SURFACE TENSION"
=
𝐄𝐧𝐞𝐫𝐠𝐲
𝐀𝐫𝐞𝐚
Unit of surface tension
· N/m (in S.I system)
· Dyne/cm (in C.G.S system)
· Joule/m2 (in S.I system)
· Erg/cm2 (in C.G.S system)
Factors affecting Surface Tension
Inter molecular forces
If force of attraction between molecules is high then surface tension will also be high.
Hydrogen bonding
Liquids that have H-bond such as water, have high values of surface tension.
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Temperature
Surface tension of a liquid decreases with the increase in temperature because an increase
in temperature, reduces force of attraction between molecules.
Scan70
ATOMIC
STRUCTURE
ATOM:
Smallest particle of an element which shows all properties of element is called atom.
Some characteristics of "atoms" are as follows:

Atom takes part in chemical reactions independently.
 Atom can be divided into a number of sub-atomic particles.
Fundamental particles of atom are electron, proton and neutron.
CHARACTERISTICS OF ELECTRON:
 Charge: It is a negatively charged particle.
 Magnitutide of charge: Charge of electron is 1.6022 x 10-19 coulomb.
 Mass of electron: Mass of electron is 0.000548597 a.m.u. or 1.1 x 10-31 kg.
 Symbol of electron: Electron is represented by "e".
 Location in the atom: Electrons revolve around the nucleus of atom in different
circular orbits.
CHARACTERISTICS OF PROTON
 Charge: Proton is a positively charged particle.
 Magnitude of charge: Charge of proton is 1.6022 x 10-19 coulomb.
 Mass of proton: Mass of proton is 1.0072766 a.m.u. or 1.6726 x 10-27 kg.
 Comparative mass: Proton is 1837 times heavier than an electron.
 Position in atom: Protons are present in the nucleus of atom.
CHARACTERISTICS OF NEUTRON
 Charge: It is a neutral particle because it has no charge.
 Mass of neutron: . Mass of neutron is 1.0086654 a.m.u. or 1.6749 x 10-27 kg.
 Comparative mass: Neutron is 1842 times heavier than an electron.
 Location in the atom: Neutrons are present in the nucleus of an atom.
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ATOMIC NUMBER:
Total number of protons present in the nucleus of an atom is called
"Atomic number" or "Charge number"
Since the total number of protons and the total number of electrons in an atom are equal
therefore atomic number may also be defined as:
"Total number of electron in an atom is called Atomic number"
SYMBOL: It is denoted by "z".
MASS NUMBER:
Total number of protons and neutrons present in the nucleus of an atom is called
"Mass number".
SYMBOL: It is denoted by "A".
A=p+n
SYMBOL OF NUCLEUS
A nucleus is represented by the symbol :
zX
A
Where
X= symbol of element (Cl, Br, H etc.)
A= mass number.
Z= atomic number.
For Examples:
1
23
35
14
27
1H , 11Na , 17Cl , 7N , 13Al
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CATHODE RAYS-DISCOVERY OF ELECTRON-DISCHARGE TUBE EXPERIMENTCROOK’S TUBE EXPERIMENT
INTRODUCTION
Gases are bad conductors of electricity. However under reduced pressure and at high
potential difference gases conduct electric current.
DISCHARGE TUBE
Discharge tube is a glass tube fitted with two electrodes placed opposite to each other. The
tube is sealed and contains a vacuum pump. The function of vacuum pump is to reduced or
change the pressure inside the tube. The two electrodes are connected to a high voltage
battery.
EXPERIMENT
In discharge tube experiment, at low pressure and at very high potential difference, electric
current is passed through the gas.
OBSERVATION
Under different pressure different observations were noted;
At 1cm Hg pressure: When pressure inside the tube is reduced to 1 cm of Hg, at a
potential difference of a few thousand volts causes a spark to pass like a flash of
light.
At 1 mm Hg: At 1 mm Hg, the tube is mostly filled with a glow extending from the
positive electrode. This is known as "positive column".
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At 0.001 mm Hg: At 0.001 m Hg, the glow disappears and the walls of the glass
tube begin to glow with a brilliant green light.
RESULT
These observations indicate that some radiation or rays are emitted from cathode. These
rays are known as "Cathode Rays".
PROPERTIES OF CATHODE RAYS
ORIGIN
These rays originate from cathode.
PATH
Cathode rays travel in straight line.
PRESSURE
Cathode rays exert mechanical pressure.
SHADOW FORMATION
The cathode rays consist of material particles because they produced shadow of objects
placed in
the way.
EFFECT OF ELECTRIC FIELD
Cathode rays deflect in applied electric field towards the positive terminal.
EFFECT OF MAGNETIC FIELD
Cathode rays are deflected by magnetic field.
PENETRATION POWER
Cathode rays penetrate small thickness of matter such as aluminum foil, gold foil, etc.
CHARGE
These rays carry a negative charge.
DEPENDENCE ON MATERIAL
Cathode rays are independent of the material of electrode or the nature of gas in the
tube.
E/m RATIO
Their e/m ratio was equal to that of an electron.
RADIOACTIVITY
All the elements having atomic number greater than 82 emit invisible radiation all the time.
The phenomenon of emission of these powerful rays is called "Natural Radioactivity" and
the element that emits such rays is called "Radio Active Elements".
TYPES OF RADIO ACTIVE RAYS
There are three types of radioactive rays:
-Rays
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-RAYS
-RAYS
PROPERTIES OF -RAYS
NATURE: rays consist of α particle. Each α particle consists of 2He4 nucleus.
CHARGE:  particle carry positive charge.
MASS: Mass of each  - particle is 4 times that of a proton or H-atom.
IONIZATION: Ionization power of rays is very high.
PENETRATION POWER: Penetration power of rays is very small.
FLUORESCENCE: rays produce fluorescence in different substances.
IONIZATION CAPABILITY: They have strong ionizing power because they remove
electrons from the
atoms of gas through which they pass.
VELOCITY: Their velocity range is 3 x 10 7 m/s to 3 x 106 m/s.
PROPERTIES OF -RAYS
NATURE: rays consist of fast moving electrons.
CHARGE: rays have negative charge.
VELOCITY: Velocity of rays is from 9 x 107 m/sec to 27 x 107 m/sec.
EFFECT ON PHOTO GRAPHIC PLATE:rays affect the photo graphic plate.
IONIZTION POWER: Ionization power of rays is very small.
KINETIC ENERGY: Kinetic energy of rays is less than that of  - rays.
FLUORESCENCE: rays produce fluorescence in different substance.
PROPERTIES OF -RAYS
NATURE: rays are electromagnetic radiations.
CHARGE:  - rays are no charge.
VELOCITY:  - rays travel with the velocity of light that is 3 x 108 m/sec.
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PENETRATION POWER: Penetration power of  - rays is very large. It is about hundred
times
larger than that of rays.
FLUORESCENCE:  - rays produce feeble fluorescence When incident on screen coated
with barium platino cyanide.
DALTON ‘S ATOMIC THEORY
Postulates of Dalton atomic theory:
Main postulates of Dalton atomic theory is as follow:
1. Matter is composed of very tiny or microscopic particles called
"Atom".
2. Atom is an indivisible particle.
3. Atom can neither be created nor it is destroyed.
4. Atoms of an element are identical in size, shape, mass and in
other properties.
5. Atoms of different elements are different in their properties.
6. Atoms combine with each other in small whole numbers.
7. All chemical reactions are due to combination or separation of
atoms.
DEFECTS IN DALTON’S THEORY:
Postulate number 2, 3, 4 and 6 are not correct as described below:
DEFECT NO: 1
Atom can be divided into a number of sub-atomic particles such as electron, proton and
neutron etc.
DEFECT NO: 2
Atoms of an element may be different in their masses.
For example:


1H
, 1H2, 1H3
35
37
17Cl , 17Cl
1
DEFECT NO: 3
All compounds do not have small number of atoms.
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For example:


Decane C10H22.
Sugar C12H22O11.
DEFECT NO: 4
Atom can be destroyed by fission process in


Atom bomb.
Nuclear reactor.
On the basis of above defects, Dalton's atomic theory has failed now.
RUTHERFORD’S ATOMIC THEORY-ELECTRONEGATIVITY
RUTHERFORD’S ATOMIC MODEL
Rutherford's atomic model shows the existence of nucleus in the atom, nature of charge on
the nucleus and the magnitude of charge on the nucleus.
Apparatus for Experiment

Alpha particles.

Gold foil. (0.0004 cm thick)

Zinc sulphide screen.

Electron Gun.
Experiment
In his experiments, Rutherford bombarded alpha particles on very thin metallic foils such
as gold foil. In order to record experimental observations, he made use of circular screen
coated with zinc sulphide.
OBSERVATIONS
He observed that most of the alpha particles were pass through the foil undeflected.
Very few particles were deflected when passed through the foil.
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One particle out of 8000 particles was deflected at 90o.
Few particles were deflected at different angles.
Main points of Rutherford’s Theory
Major portion of the atom is empty.
The whole mass of the atom is concentrated in the center of atom called nucleus.
The positively charged particles are present in the nucleus of atom.
The charge on the nucleus of an atom is equal to (+z.e) where Z= charge number, e =
charge of proton.
The electrons revolve around the nucleus in different circular orbits.
Size of nucleus is very small as compare to the size of atom.
Explanation of postulates
1. Since most of the alpha particles were passed through the foil undeflected, therefore, it
was concluded that most of the atom is empty.
2. Small angles of deflection indicate that positively charged alpha particles were attracted
by electrons.
3. Large angles of deflection indicate that there is a massive positively charged body
present in the atom and due to repulsion alpha particles was deflected at large angles.
Defects of Rutherford’s Theory
There were two fundamental defects in Rutherford's atomic model:
According to classical electromagnetic theory, being a charge particle electron when
accelerated must emit energy. We know that the motion of electron around the nucleus is
an accelerated motion; therefore, it must radiate energy. But in actual practice this does
not happen. Suppose if it happens then due to continuous loss of energy orbit of electron
must decrease continuously. Consequently electron will fall into the nucleus. But this is
against the actual situation and this shows that atom is unstable.
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If the electrons emit energy continuously, they should form continuous spectrum .But
actually line spectrum is obtained.
Electronegativity
"Relative tendency or relative power of an atom to attract shared
pair of electrons towards itself is called ELECTRONEGATIVITY."
E.N depends upon the size of atom.
Small atoms have large values of E.N.
Big atoms have small values of E.N.
E.N decreases in a group.
E.N increases in a period.
Most Electronegativity element is "Fluorine". E.N = 4
SPECTROSCOPY
The branch of chemistry which deals with the study of absorption or emission of radiation is
called Spectroscopy.
SPECTRUM
When a ray of light consists of different wave lengths is passed through a spectrometer or a
prism, it is dispersed into component wave lengths and a band of different colors is obtained
which is known as spectrum.
Or
A spectrum is energy of waves or particles spread out according to the increasing or
decreasing of some property. E.g. when a beam of light is allowed to pass through a prism
it splits into seven colours.
SPECTROMETER
Spectrometer is an instrument used for spectroscopic studies. When radiations are passed
through the prism of spectrometer, they are separated in to component wavelengths. In this
way an image of different colors is formed which is known as spectrum.
TYPES OF SPECTRA
Emission Spectra.
Absorption Spectra.
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..........
Spectrum
Emission
Spectrum
..........
.........
Continuous
Spectrum
Absorption
Spectrum
Line
Spectrum
EMISSION SPECTRUM
When an element absorbs sufficient amount of energy from an electric arc or by heating, it
emits radiation. These radiations when passed through spectrometer, spectrum so obtained
is called Emission Spectrum. There are two types of emission spectra.
Continuous Spectrum.
Line Spectrum.
CONTINUOUS SPECTRUM
When white light from sun or any incandescent body or lamp is passed through a prism, it
disperses into its component colors and a spectrum is obtained known as Continuous
Spectrum. A continuous spectrum is one in which colors are diffused in one another without
any line of demorcation.
CHARACTERISTICS


Continuous Spectrum consists of seven colors.
The colors are so mixed that there is no boundary or line of demarcation between
two colors.
Examples:
Spectrum of sunlight, incandescent solids and liquids, bulb light, tube light.
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Diagram
LINE SPECTRUM
When electric current is passed through a gas at low pressure, the atoms of gas are excited
and radiate light. When this light is passed through the prism, a spectrum is obtained
known as Line Spectrum.
CHARACTERISTICS
 In line spectrum, every two colors are separated by a line of demarcation.
 Each spectral line has a definite wavelength.
 Color of spectral line depends upon the nature of gas.
 Each element produces a characteristic set of lines which is used fir the identification
of elements.
Diagram
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Introduction:
Bohr in 1913 was the first to present a simple model of the atom which explained the
appearance of line spectra.
Postulates of Bohr’s theory:
Main postulates of Bohr’s atomic theory are:
1. CONSTANT ENERGY CONCEPT
Energy of an electron is constant in one of its allowed orbits. As long as an electron remains
in its orbit, it neither absorbs nor radiates energy.
2. CONCEPT OF ENERGY LEVELS
Electrons revolve around the nucleus of atom in circular orbits in which energy of electrons
is constant. These circular paths are known as "energy levels" or "stationary states".
3. RADIATION OF ENERGY
If an electron jumps form higher energy level to a lower energy level, it radiates a definite
amount of energy.
4. AMOUNT OF ENERGY
Energy released or absorbed by an electron is equal to the difference of energy of two
energy levels.
Let an electron jumps from a higher energy level E2 to a lower energy level E1.The energy is
emitted in the form of light . Amount of energy released is given by:
∆E
h
=
E2 - E1
=
E2 - E1
Where
h = Planck's constant (6.6256 x 10-34 j.s)
= Frequency of radiant light
ANGULAR MOMENTUM OF ELECTRON
Angular momentum of an electron in an energy level is given by:
m v r = nh /2
Where n =1, 2, 3, ………..
m = mass of electron
V = velocity of electron
r = radius of orbit
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OR
Only those energy levels or orbits are possible for which angular momentum of electron is
an integral
multiple of h /2
.
Calculation of Radius of Orbits
Consider an electron of charge e revolving.
Atomic number and e the charge on a proton.
Let “m” be the mass of the electron, “r
velocity of the revolving electron.
“ the radius of the orbit and v the tangential
The electrostatic force of attraction between the nucleus and the
electron :
According to Coulomb’s law
𝐹=
𝑍𝑒.𝑒
𝑟²
-------------- (1)
The centrifugal force acting on the electron:
F=
mv²
r
--------------- (2)
Bohr assumed that these two opposing forces must be balanced each other exactly to keep
the electron in an orbit.
Therefore Compare equation 1 and equation 2
𝒁𝒆²
𝒓²
𝒛𝒆²
𝒎𝒗²
𝒛𝒆²
𝒎𝒗²
=
𝒎𝒗²
=
𝒓²
=
𝒓
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𝒓
𝒓
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Or
=
𝒓
𝒛𝒆²
𝒎𝒗²
----------- (A)
According to the Bohr’s postulate only those orbits are possible in which
𝒎𝒗𝒓
=
𝒗
=
Above value of
𝒗
𝒏𝒉
𝟐𝝅
𝒏𝒉
𝟐𝝅𝒎𝒓
put in equation (A)
𝒛𝒆²
r
=
r
=
r
=
r
=
𝒁𝒆² ÷
r
=
𝒁𝒆² ×
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𝒏𝒉
)²
𝟐𝝅𝒎𝒓
𝒎(
𝒛𝒆²
𝒎
𝒏²𝒉²
𝟒𝝅²𝒎²𝒓²
𝒛𝒆²
𝒎𝒏²𝒉²
𝟒𝝅²𝒎²𝒓²
𝒎𝒏²𝒉²
𝟒𝝅²𝒎²𝒓²
𝟒𝝅²𝒎²𝒓²
𝒎𝒏²𝒉²
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r
𝒏²𝒉²
𝒛𝒆²𝟒𝝅²𝒎
𝒏²𝒉²
𝒛𝒆²𝟒𝝅²𝒎
r
=
𝒁𝒆² ×
=
𝒓²
=
r
𝟒𝝅²𝒎𝒓²
𝒏²𝒉²
𝒓
𝒏²𝒉²
=
𝟒𝝅²𝒎𝒛𝒆²
---------- (B)
This equation gives the radii of all the possible stationary states. The values of constants
present in this equation are as follows.
H = 6.625 x 10−27 ergs sec
Me = 9.11 x 10−28 gm
E = 4.802 x 10−10 e.s.u
OR
OR
OR
6.625 x10−37 J.s
9.11 x 110−31 kg
1.601 x 10−19 C
By substituting these values in equation (B) we get for first shell of H atom
r = 0.529 x 10−8 m
OR
0.529
The above equation may also be written as
r
=
𝒏²𝒉²
𝟒𝝅²𝒎𝒛𝒆²
r = n2 (h2 / 4π2mZe2) x n2 a0 ……………….. (3)
For the first orbit n = 1 and r = 0.529. This is the value of the terms in the brackets
sometimes written as a0 called Bohr’s Radius. For the second shell n = 2 and for 3rd orbit n
= 3 and so on.
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Hydrogen Atom Spectrum
Balmer Series
The simplest element is hydrogen which contains only one electron in its valence shell.
Balmer in 1885 studied the spectrum of hydrogen. For this purpose he used hydrogen gas in
the discharge tube. Balmer observed that hydrogen atom spectrum consisted of a series of
lines called Balmer Series. Balmer determined the wave number of each of the lines in the
series and found that the series could be derived by a simple formula.
Lyman Series
Lyman series is obtained when the electron returns to the ground state i.e. n = 1 from
higher energy level n (2) = 2, 3, 4, 5, etc. This series of lines belongs to the ultraviolet
region of spectrum.
Paschen Series
Paschen series is obtained when the electron returns to the 3rd shell i.e. n = 3 from the
higher energy levels n2 = 4, 5, 6 etc. This series belongs to infrared region.
Bracket Series
This series is obtained when an electron jumps from higher energy levels to 4th energy
level.
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Heisenberg's Uncertainty Principle
Introduction:
It is found that however refined our instruments there is a fundamental limitation to the
Accuracy with which the position and velocity of microscopic particle can be known
simultaneously. This limitation was expressed by a German physicist Werner Heisenberg in
1927 and known as 'Heisenberg's uncertainty principle'.
Statement:
According to Heisenberg's uncertainty principle:
It is impossible to determine both position and momentum of an electron simultaneously.
If one quantity is known then the determination of the other quantity will become
impossible.
Mathematical Representation:
Let
x = uncertainty in position
P = uncertainty in momentum
According to Heisenberg's uncertainty principle:
The product of the uncertainty in position and the uncertainty in momentum is in
the order of an amount involving h, which is Planck’s constant.
P × x  h/2

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Energy Levels and Sub-Levels
According to Bohr’s atomic theory:
Electrons are revolving around the nucleus in circular orbits which are present at
definite distance from the nucleus. These orbits are associated with definite
energy of the electron increasing outwards from the nucleus, so these orbits are
referred as Energy Levels or Shells.

These shells or energy levels are designated as 1, 2, 3, and 4 etc K, L, M, N etc.
The spectral lines which correspond to the transition of an electron from one energy
level to another consists of several separate close lying lines as doublets, triplets and
so on.

It indicates that some of the electrons of the given energy level have different
energies or the electrons belonging to same energy level may differ in their energy.

So the energy levels are accordingly divided into sub energy levels which are
denoted by letters s, p, d, f (sharp, principle, diffuse & fundamental).

The number of sub levels in a given energy level or shell is equal to its value of n.
e.g. in third shell where n = 3 three sub levels s, p, d are possible.
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Planck’s Quantum Theory
Introduction:
In 1900, Max Planck studied the spectral lines obtained from hot body radiations at different
temperatures.
Statement:
According to this theory:
When atoms or molecules absorb or emit radiant energy, they do so in separate
units of waves called Quanta or Photons.
Thus a light radiation obtained from excited atoms consists of a stream of
photons and not continuous waves.
Mathematical Expression:
The energy E of a quantum or photon is given by the relation
E=hv
Where v is the frequency of the emitted radiation and
h is the Planck’s constant. The value of h = 6.62 x 10(-27) erg. sec.
The main point of this theory is that the amount of energy gained or lost is quantized which
means that energy change occurs in small packets or multiple of those packets, hv, 2 hv, 3
hv and so on.
QUANTUM NUMBERS
For complete description of an orbital in an atom, few constant numbers are necessary.
These constant numbers are necessary to describe the position, spin, energy and orientation
of an orbital in space. These are the numbers that complete behavior of an electron in an
orbital. These numbers are known as quantum numbers.
There are four quantum numbers:
Principle quantum number (n)
Azimuthal quantum number (l)
Magnetic quantum number (m)
Spin quantum number (s)
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PRINCIPLE QUANTUM NUMBER
Principle quantum number represents the energy level of an electron. It is denoted by 'n'.
The values of principle quantum number are from 1 to n (where n is a positive whole
number i.e. n = 1,2,3,4 ...). Principle quantum number also describes the energy of
electron. It also describes the size of orbit.
AZIMUTHAL OR SUBSIDIARY QUANTUM NUMBER
Azimuthal quantum number describes the shape of orbital. It is denoted by . Values of
are from zero to n-1.
For s-orbital
=0
For p-orbital
=1
For d-orbital
=2
For f-orbital
=3
With the help of the value of Azimuthal quantum number we can determine the total
number of energy sub levels in a given energy level.
MAGNETIC QUANTUM NUMBER
Magnetic quantum number indicates the orientation of an orbital in space in an applied
magnetic field. It is denoted by ‘m’.
Values of ‘m’ are from (- ) to (+ l) through zero.
Orbital
l
m
s
0
0
p
1
-1, 0, +1
d
2
-2, -1, 0, +1, +2
f
3
-3, -2, -1, 0, +1, +2, +3.
SPIN QUANTUM NUMBER
Spin quantum number describes the spin of an electron in an orbital.
It is denoted by‘s’.
It has only two possible values.
s = +1/2, S = -1/2
s = +1/2 for clockwise spin.
s = -1/2 for anti-clockwise spin.
An electron spinning clockwise is indicated by (
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) and anti-clockwise by (
)
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Rules of Electronic Configuration
1. AUFBAU PRINCIPLE
According to Aufbau Principle:
"The electrons are filled to the orbitals of lowest energy in
sequence, two electrons to each orbital."
In other words:
"The electrons are filled in different orbitals in the order of
increasing energy of orbitals starting with the 1s orbital."
With reference to AUFBAU PRINCIPLE electronic arrangement will follow the following order:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d...........
EXAMPLES
Li (z = 3)
:
ELECTRONIC CONFIGURATION = 1s2, 2s1
B (z = 5)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p1
Mg (z = 12) :
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2
Cl (z = 17)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2, 3p5
Ca (z = 20)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2, 3p6, 4s2
Sc (z = 21)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d1
Ti (z = 22)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d2
Fe (z = 26)
:
ELECTRONIC CONFIGURATION = 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d6
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2. (n+l ) Rule:
According to (n+l) rule:
1. Orbital which has the least value of (n+l) will be filled first to the
electrons.
Explanation:
EXAMPLE # 01:
3s-orbital will be filled prior to 3p-orbital.
ORBITAL
3s
3p
n
3
3
l
0
1
(n+l)
3+0 = 3
3+1 = 4
COMMENTS:
Since 3s-orbital has least value of (n+l), therefore, it will occupy electrons before 3p-orbital.
EXAMPLE # 02:
4s-orbital will be filled prior to 3d-orbital.
ORBITAL
4s
3d
n
4
3
l
0
2
(n+l)
4+0 = 4
3+2 = 5
COMMENTS:
Since 4s-orbital has least value of (n+l), therefore ,it will occupy electrons before 3d-orbital.
EXAMPLE # 03:
4d-orbital will be filled prior to 4f-orbital.
ORBITAL
4d
4f
n
4
4
l
2
3
(n+l)
4+2 = 6
4+3 =7
COMMENTS:
Since 4d-orbital has least value of (n+l), therefore, it will occupy electrons before 4f-orbital.
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2. If there are two orbitals that have the same value of (n+l) then the
orbital that has the least value of 'n' will be filled first.
Explanation:
EXAMPLE # 01:
2p-orbital will be filled prior to 3s-orbital.
ORBITAL
2p
3s
n
2
3
l
1
0
(n+l)
2+1 = 3
3+0 = 3
COMMENTS:
Since 2p-orbital has least value of n, therefore, it will occupy electrons before 3s-orbital.
EXAMPLE # 02:
4d-orbital will be filled prior to 5p-orbital.
ORBITAL
5p
4d
n
5
4
l
1
2
(n+l)
5+1 = 6
4+2 = 6
COMMENTS:
Since 4d-orbital has least value of n, therefore, it will occupy electrons before 5p-orbital.
3. Hand’s Rule of Maximum Multiplicity:
According to Hand’s Rule of Maximum Multiplicity:
1. The electrons tend to avoid being in the same orbital. Thus as the electrons are
successively added, a maximum number of electrons will try occupy orbitals singly.
2. When all the orbitals are singly occupied only then the pairing of electrons
commences.
3. In the ground state, the electrons occupying the orbitals singly will have their spin
parallel. This rule indicates that the electronic Arrangement
is more stable
than
Explanation:
N (Z = 7):
CORRECT AND STABLE ELECTRONIC CONFIGURATION = 1s2, 2s2, 2px1, 2py1,
2pz1
WRONG AND UNSTABLE ELECTRONIC CONFIGURATION = 1s2, 2s2, 2px2, 2py1,
2pz0
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4. Pauli’s Exclusion Principle:
According to Pauli's exclusion principle:
"In an atom no two electrons can have the same set of four quantum numbers."
Pauli's exclusion principle indicates that two electrons may have three same quantum
numbers but the fourth quantum number must be different.
In other words Pauli's exclusion principle can also be stated as:
"An orbital can not accomodate more than two electrons i.e. maximum
number of electrons that an orbital can accomodate is two."
Explanation:
Example:
We know that 1s-orbital contains two electrons. Their set of quantum numbers is
electron n
e1
1
e2
1
l
0
0
m
0
0
s
+1/2
-1/2
Notice that the fourth quantum number i.e. spin quantum number is different for both
electrons. Let us suppose that 1s-orbital contains three electrons i.e. 1s3, in this situation:
electron n
e1
1
e2
1
e3
1
l
0
0
0
m
0
0
0
s
+1/2
-1/2
???
Since there are only two possible values of spin quantum number, therefore, third electron
can not be accomodated in 1s-orbital.This clearly points out that an orbital can not contain
more than two electrons. Hence by Pauli's exclusion principle, 1s2 is correct but 1s3 is not
possible.
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Discovery of Neutron
Chadwick Experiment
Chadwick in an experiment bombarded Be with a-particles. In his experiment he observe
that some very penetrating radiations coming out from Be. These radiations consist of
material particles. Mass of these particles was nearly equal to the mass of one hydrogen
atom. Since these particles were not deflected by magnetic or electric field ,therefore they
are named as Neutrons.
9
4Be
+ 2H4  6C12 + 0n1
Discovery of Proton
Passage of electricity through the gases at low pressure also resulted in the discovery of
proton. During the discharge tube experiments, a famous scientist Gold Stein observed that
if a perforated cathode is used, some radiations appear behind the cathode. Since radiations
are coming from anode, therefore, it was assumed that they must carry a positive charge.
These rays are known as Anode Rays.
Properties of Anode Rays:
Anode rays travel in straight line.
They consist of material particles.
These rays contain positive charge.
These rays actually consist of positive ions of various gases used in the experiment.
Their positive charge is either equal to electronic charge (e) or some multiple of it.
These particles which have a mass 1836 times that of the electron are known as protons.
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Ionization Potential
Ion
If an electron or more than one electron are added to or removed from an atom then it
becomes negative or positive charged particles which are known as "Ion".
Cation
If an electron or more than one electrons are removed from an atom,
it becomes a positive ion which is also known as "cation".
For example: Na+1, K+1, Ca+2, Mg+2, Al+3.
Anion
If an electron or more than one electron is added to an atom
it becomes a negative ion which is also known as "anion".
For example: Cl-1, Br-1, O-2, N-3, F-1
Ionization Potential
"Amount of energy required to remove an electron from
an isolated gaseous atom is called ionization potential."
ATOM + ENERGY  CATION + ELECTRON
Unit: kJ / mole
A + Energy  A+ + e-
Factors affecting Ionization Potential:
1. Size of the Atom
If the size of an atom is bigger the I.P of the atom is low, but if the size of the atom is small
then the I.P will be high, due to fact if we move down the group in the periodic table. The
I.P value decreases down the group.
2. Magnitude of Nuclear Charge
If the nuclear charge of atom is greater than the force of attraction on the valence electron
is also greater so the I.P value for the atom is high therefore as we move from left to right
in the periodic table the I.P is increased.
3. Screening Effect
The shell present between the nucleus and valence electrons also decreases the force of
attraction due to which I.P will be low for such elements.
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Electron Affinity
The amount of energy liberated by an atom when an electron is added in it is
called electron affinity.
It shows that this process is an exothermic change which is represented as
Cl
+
e-
𝐂𝐥− --------- ΔH = -348 kJ / mole
Factors on which Electron Affinity Depends
1. Size of the Atom
If the size of atom is small, the force of attraction from the nucleus on the valence electron
will be high and hence the E.A for the element will also be high but if the size of the atoms
is larger the E.A for these atoms will be low.
2. Magnitude of the Nuclear Charge
Due to greater nuclear charge the force of attraction on the added electron is greater so the
E.A of the atom is also high.
3. Electronic Configuration
The atoms with the stable configuration have no tendency to gain an electron so the E.A of
such elements is zero. The stable configuration may exist in the following cases.
1. Inert gas configuration
2. Fully filled orbital
3. Half filled orbital
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Electronegativity
The force of attraction by which an atom attracts a shared pair of electrons is
called Electronegativity.
Application of Electronegativity
1. Nature of Chemical Bond
If the difference of electronegativity between the two combining atoms is more than 1.7 eV,
the nature of the bond between these atoms is ionic but if the difference of electronegativity
is less than 1.7 eV then the bond will be covalent.
2. Metallic Character
If an element possesses high electronegativity value then this element is a non-metal but if
an element exists with less electronegativity, it will be a metal.
Factors for Electronegativity
1. Size of the Atom
If the size of the atom is greater the electronegativity of the atom is low due to the large
distance between the nucleus and valence electron.
2. Number of Valence Electrons
If the electrons present in the valence shell are greater in number, the electronegativity of
the element is high.
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Chemical Bonding
CHEMICAL BOND
Chemical bond can be defined as:
”the force of attraction between two atoms or ions that hold them
together in a unit is called Chemical Bond".
Actually chemical bond is the main factor that makes molecules and compounds. By the
interaction of outer electrons, great forces of attraction are developed between two atoms.
This force of attraction is called chemical bond.
TYPES OF CHEMICAL BOND
There are three types of chemical bonds:
1) Ionic bond or Electrovalent bond
2) Covalent bond
3) Coordinate Covalent bond
1. Ionic bond or Electrovalent bond
In 1916, W Kossel described the ionic bond which is formed by the transfer of electron from
one atom to another it is defined as:
“Chemical bond formed between two atoms due to transfer of electron(s) from
one atom to the other atom is called "Ionic bond" or "electrovalent bond”.
Or
“The electrostatic attraction between positive and negative ions is called ionic
bond.”
Explanation
In ionic bond formation one atom looses electron(s) and the other picks it up. The atom that
looses the electron acquires positive charge and the other atom which gains the electron
becomes a negatively charged particle. Due to opposite charge an electrostatic force of
attraction is setup between them.
This force holds these atoms together in a unit. This force of attraction is referred to as
"IONIC BOND".
Formation of Ionic Bond Between Na & Cl
Step # 1:
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



Electronic arrangement of Na (Z=11) is K = 2, L = 8, M = 1
Electronic configuration of Na is 1s2, 2s2, 2p6, 3s1
It has one valence electron.
The loss of the valence electron from Na-atom 495 KJ/mole energy is needed.

Due to loss of one electron Na becomes Na+ -ion.
Step # 2:
 Electronic arrangement of Cl (Z=17) is K = 2, L = 8, M = 7
 Electronic configuration of Cl is 1s2, 2s2, 2p6, 3s2 3p5.
 Cl-atom needs one electron to complete its octet.
 The gain of one electron by chlorine atom releases 348 KJ/mole energy.
 Electron lost by Na atom picks up by Cl atom.
 Electronic arrangement after acquiring an electron: K = 2, L = 8, M = 8
Electronic configuration of Cl is 1s2, 2s2, 2p6, 3s2, 3p6 . This shows that its octet is
also complete.
Cl + e-  Cl- : H = -348 KJ/mole
 Chlorine atom is now converted into Cl-_ion.
We know that positive and negative ions attract each other, therefore an electrostatic
force of attraction is set up between Na+ & Cl- ions. This force unites these ions in a
unit. In this way ionic bond is formed between Na and Cl atoms which results in the
formation of sodium chloride.
Step # 3:
 In the above two steps we clearly observe that there is a difference of energy i.e.
This shows formation of one mole of NaCl increases the energy of system by 147 KJ /mole.
Properties / Characteristics of Ionic Bond:
NON-MOLECULAR FORM
Ionic compounds are not in molecular form. Their formula only indicates the number of
atoms. In ionic compounds each ion is surrounded by a number of oppositely charged ions.
STATE
Due to strong binding forces ionic compounds exist in solid form.
MELTING AND BOILING POINT
Ionic compounds have high M.P. and B.P.
HARDNESS
Due to strong attraction forces between ions, ionic compounds are very hard.
SOLUBILITY IN WATER
Ionic compounds are soluble in water except few compounds.
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SOLUBILITY IN THE ORGANIC COMPOUNDS
They are insoluble in non-polar organic compounds.
ELECTRICAL CONDUCTIVITY
Ionic compounds are electrolytes because they conduct electricity in molten state and in the
form of solution.
Covalent Bond:
“Chemical bond formed between two atoms by the mutual sharing of electrons is
known as Covalent bond.”
In covalent bond formation each atom provides equal number of electrons for sharing but
no transfer of electrons takes place. Each electron pair is attracted by both the nucleus.
Chemical bond formed between two similar atoms is always a covalent bond.
Shared electrons spend much of the time between the nuclei, resulting in the attractive
forces between negative charge of electron and positive charge of nuclei.
Representation:
Covalent bond between two atoms is represented by a short line (_____)
Covalent Bond between H-Atom & Cl-Atom
Consider the example of HCl molecule.
 H atom has only one electron in its valance shell.
 It requires one electron to complete its doublet or achieve inert gas configuration.


Electronic configuration of Cl is K = 2, L = 8 and M = 7.
Cl atom requires 1 electron to complete its octet shell.

Due to small difference b/w the values of E.N., electron transfer from H or Cl is not
possible.
H and Cl share one electron.
In this way without any transfer of electron both H & Cl complete their outer shell
and a stable HCl molecule is formed.


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Types of Covalent bond:
There are three types of covalent bond depending upon the number of shared electron
pairs.
1. SINGLE COVALENT BOND
2. DOUBLE COVALENT BOND
3. TRIPLE COVALENT BOND
Single Covalent bond:
A covalent bond formed by the mutual sharing of one electron pair between two atoms is
called a "Single Covalent bond." It is denoted by single short line(____) Examples:
In single bond formation each atom provides one electron.
Double Covalent bond:
A covalent bond formed between two atoms by the mutual sharing of two electron pairs is
called a "double covalent bond". It is denoted by double short line (____)
Examples:
Triple Covalent bond:
A covalent bond formed by the mutual sharing of three electron pairs is called a "Triple
covalent bond". It is denoted by triple short line (
). Examples:
Polar Covalent Bond:
A covalent bond formed between two different atoms is known as Polar covalent bond.
For example when a Covalent bond is formed between H and Cl , it is polar in nature
because Cl is more electro negative than H atom . Therefore, electron cloud is shifted
towards Cl atom. Due to this reason a partial -ve charge appeared on Cl atom and an equal
+ve charge on H atom
Examples:
Non-Polar Covalent Bond:
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A covalent bond formed between two like atoms is known as Non-polar bond. Since
difference of electro negativity is zero therefore, both atoms attract electron pair equally
and no charge appears on any atom and the whole molecule becomes neutral.
Examples:
H-H
Cl - Cl
F-F
Properties of Covalent Bond:
MOLECULAR FORM
Covalent compound exists as a separate molecules because they are formed by neutral
atoms (they are electrically neutral) and the forces of attraction between these molecules is
small.
STATE
Due to weak intermolecular forces, generally covalent molecules or covalent compounds are
liquids and gases. However, some covalent substances are solids like iodine.
Liquid (H2O, HCl, Br2)
Gas (CO2, H2, Cl2,NH3)
VOLATILITY
They are volatile.
MELTING POINT, BOILING POINT (THERMAL STABILITY)
Generally they have low M.P and B.P.
SOLUBILITY IN WATER
Covalent compounds are generally insoluble in water.
SOLUBILITY IN THE ORGANIC COMPOUNDS
Covalent compounds are non-electrolyte because they do not conduct electricity.
ELECTRICAL CONDUCTIVITY
 Non-polar covalent compounds do not conduct electricity.
 Polar covalent compounds conduct small amount of electricity.
Coordinate Covalent Bond:
“The type of chemical bond in which one atom provides shared pair of electron for
bond formation is called "Coordinate Covalent Bond”.
OR
“Chemical bond formed between two atoms due to sharing of electron pair in
which only one atom provides shared pair of electron for the formation of bond, is
known as coordinate covalent bond or dative bond.”
Formation of Coordinate Covalent Bond:
In the formation of coordinate bond other atom does not provide electron for sharing. It is
one sided sharing.
Formation of coordinate covalent bond is the property of atoms that have lone pair of
electrons.
 The atom that provides electron pair is called "Donor”.
 The other which takes it is called "Acceptor".
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Symbol:
Dative bond is represented by an arrow (), pointing from donor atom to the acceptor.
Examples:
Ammonium ion
Hydronium ion
Theories of Chemical Bonding:
Valence bond theory
According to Valence bond theory:
 A covalent bond is formed by the overlapping of partially filled orbitals of two atoms.
 Overlapping orbitals must have electrons with opposite spin.
 Atoms involved in bond formation should have unpaired electrons.
 The number of covalent bonds formed by an atom would be equal to the number of
half filled orbital.
 Resulting molecular orbital is obtained by the combination of the two wave functions
(AOs) of two unpaired electrons.
 Atoms which are involved in bond formation maintain their identity.
Molecular orbital theory
According to Molecular orbital theory:
 A covalent bond is formed by the overlapping of atomic orbitals which form
molecular orbital.
 Bonding electrons occupy molecular orbital not atomic orbital.
 An electron in a molecular orbital is polycentric because it is influenced by more than
one nuclei.
 Formation of molecular orbital is based on the linear combination of atomic orbitals
(LCAO).
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 There are two kinds of molecular orbitals:
1. BONDING MOLECULAR ORBITAL
2. ANTI-BONDING MOLECULAR ORBITAL
Bond Energy
Definition
“The amount of energy required to break a bond between two atoms in a diatomic
molecule is known as Bond Energy.”
Or
“The energy released in forming a bond from the free atoms is also known as Bond
Energy.”
Or
“Amount of energy required to break a bond between two atoms in a di-atomic
molecule is called bond energy.”
Or
“The amount of energy released when two atoms unite together with a covalent
bond.”
Example:
Cl-Cl; B.E. = 2.44 KJ/mole.
H-H; B.E. = 4.35 KJ/mole.
Unit:
Its unit is KJ/mole and Kcal/mole.
Bond breaking is an endothermic reaction. Bond formation is an exothermic reaction,
FACTORS ON WHICH BOND ENERGY DEPENDS:
BOND LENGTH:
Shorter the bond length, greater is the bond energy.
IONIC CHARACTER:
Greater the ionic character, greater is the bond energy.
MULTIPLE BOND:
Multiple bonds have short length, therefore, they have high bond energy.
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Example
i. The bond energy for hydrogen molecule is
H – H (g)
2 H(g) …………………….. ΔH = 435 kJ/mole
OR
H (g) + H (g)
H – H ………………….. ΔH = 435 kJ/mole
It can be observed from this example that the breaking of bond is endothermic whereas the
formation of the bond is exothermic.
Sigma & PI Bond
Sigma Bond Definition
When the two orbitals which are involved in a covalent bond are symmetric about
an axis, then the bond formed between these orbitals is called Sigma Bond.
OR
A bond which is formed by head to head overlap of atomic orbitals is called Sigma
Bond.
Explanation
In the formation of a sigma bond the atomic orbital lies on the same axis and the
overlapping of these orbital is maximum therefore, all such bonds, in which regions of
highest density around the bond axis are termed as sigma bond.
Types of Overlapping in Sigma Bond
There are three types of overlapping in the formation of sigma bond.
1. s-s orbitals overlapping
2. s-p orbitals overlapping
3. p-p orbitals overlapping
1. S-S overlap in H2 molecule
Hydrogen molecule consists of two H-atoms. Each atom contains one electron in 1s-orbital.
E.C = 1s1
According to molecular orbital theory
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“Two 1s1 orbitals of two H-atoms overlap linearly to produce two types of
molecular orbitals.”
1. Bonding molecular orbital (-orbital)
2. Anti-bonding molecular orbital (*-orbital)
Bonding molecular orbital (-orbital) has lower energy and results in the covalent bond
formation which is a sigma bond between two H-atoms while the anti-bonding molecular
orbital (*-orbital) possess high energy remains unoccupied.
2. S-P overlap in HF molecule
S-P type overlap occurs in HF molecule when one 1s-orbital of hydrogen atom overlaps
2p-orbital of fluorine to form two types of molecular orbitals.
1. Bonding molecular orbital (-orbital)
2. Anti-bonding molecular orbital (*-orbital)
Bonding molecular orbital (-orbital) has lower energy and results in the covalent bond
formation (sigma bond) between H-atom and F-atom while the anti-bonding molecular
orbital (*-orbital) possess high energy remains unoccupied.
3. P-P overlap in HF molecule
P-P type overlap occurs in F2 molecule when one 2pz-orbital of one fluorine atom overlaps
2pz-orbital of other fluorine atom form two types of molecular orbitals.
1. Bonding molecular orbital (-orbital)
2. Anti-bonding molecular orbital (*-orbital)
Bonding molecular orbital (-orbital) has lower energy and results in the covalent bond
formation (sigma bond) between two F-atoms while the anti-bonding molecular orbital (*orbital) possess high energy remains unoccupied.
Strength of sigma bond
The relative strength of a sigma bond is related to the extent of overlap of the atomic
orbitals. This is known as the 'principle of maximum overlap'.
Due to spherical charge distribution in s-orbital, generally s-s overlapping is not so effective
as s-p and p-p overlapping.
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Where p-orbitals have directional charge distribution and longer lobes which cause more
effective overlapping. Thus s-s sigma bond is relatively weak.
Order of the strength of sigma bonds is as follows:
nature of sigma bond
s-s
s-p
p-p
bond strength
1.0
1.73
3.0
Pi bond
A Pi bond is formed by the lateral or side ways or parallel overlapping of P-orbital of the
atoms which are already bonded by a sigma bond and their axes are coplanar.
This type of overlap generates two types of molecular orbitals:
(a) Pi-bonding molecular orbital (-orbital)
(b) Pi-antibonding molecular orbital (*-orbital)





A pi-bonding orbital has two regions of electron density below and above the nodal
plane. The electron contained in it is called pi-bonding electrons which form the pi
bond. It is not linearly symmetrical with respect to the bond axis, rather it has a
nodal plane.
Pi-bonds are weaker than sigma bonds.
In Pi-bonds, electron density lies in the regions above and below the nuclei.
Compounds having pi bonds are more reactive.
Pi bond is formed when two atoms already bonded by a sigma bond.
Hybridization
“The process in which atomic orbitals of different energy and shape are mixed
together to form new set of equivalent orbitals of the same energy and same
shape.”
Or
“There are many different types of orbital hybridization but we will discuss here
only three main types.”
Or
“The phenomenon of mixing up of different orbitals of same energy level of an
atom to produce equal number of hybrid-orbitals of same energy and identical
properties is known as hybridization.”
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A hybrid orbital contains maximum two electrons with opposite spin. In hybridization, only
that orbital take part that has very little difference of energy. Hybridization takes place in
the orbitals of a single atom. Two different atoms cannot produce hybrid orbitals by
overlapping their orbitals.
Types of Hybridization
There are three categories of hybridization:
1. Sp3-hybridization.
2. Sp2- hybridization.
3. Sp- hybridization.
1. Sp3- Hybridization
“The process of hybridization in which one s-orbital and three p-orbitals overlap to
produce four hybrid-orbital is known as Sp3-hybridization.”
Or
“The mixing of one
s and three p orbitals to form four equivalent sp3 hybrid orbitals is
called sp3 hybridization.”
These hybrid-orbital are identical in shape and energy. These orbital are known as Sp 3hybrid orbitals. Sp3-orbitals are at an angle of 109.5o from each other. Sp3-orbital is
arranged in tetrahedral fashion.
Sp3- Hybridization & Methane
o Methane molecule composed of one carbon atom and four hydrogen atom i.e. CH 4.
o In methane molecule central atom is carbon. Here carbon atom is Sp 3-hybridized.
o
o
o
One s-orbital (2s) and three p-orbital (2px, 2py, 2pz) overlap to produce four Sp3hybrid orbitals.
These Sp3- hybrid orbital are at a angle of 109.5o from each other. These Sp3orbitals are attached at the corner of a tetrahedron.
Each Sp3-orbital of carbon atom overlaps 1s-orbital of hydrogen atom. In this way
four sigma bonds (Sp3-S bonds) are generated.
The final geometry of methane molecule is tetrahedral as shown.
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2. Sp2- Hybridization
“The mixing of one s and two p orbitals to form three orbitals of equal energy is
called sp2 or 3sp2 hybridization.”
Each sp2 orbital consists of s and p in the ratio of 1:2. These three orbitals are co-planar
and at 120º angle as shown
Sp2- Hybridization & Ethane
A typical example of this type of hybridization is of ethane molecule.
In ethylene, two sp2 hybrid orbitals of each carbon atom share and overlap with 1s orbitals
of two hydrogen atoms to form two σ bonds. While the remaining sp2 orbital on each
carbon atom overlaps to form a σ bond. The remaining two unhybridized p orbitals (one of
each) are parallel and perpendicular to the axis joining the two carbon nuclei. These
generates a parallel overlap and results in the formation of 2 π orbitals. Thus molecules of
ethylene contain five σ bonds and one π bond.
3. Sp Hybridization
“When one s and one p orbitals combine to give two hybrid orbitals the process is
called sp hybridization.”
The sp hybrid orbital has two lobes, one with greater extension in shape than the other and
the lobes are at an angle of 180º from each other. It means that the axis of the two orbitals
form a single straight line.
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Sp- Hybridization & Acetylene
Now consider the formation of acetylene molecule HC ≡ CH. The two C-H σ bonds are
formed due to sp-s overlap and a triple bond between two carbon atoms consist of a σ bond
and two π bond. The sigma bond is due to sp-sp overlap whereas π bonds are formed as a
result of parallel overlap between the unhybridized four 2p orbitals of the two carbon.
Electron Pair Repulsion Theory:
Following are the main points of electron pair repulsion theory:







There are two types of electron pairs surrounding the central atom.
1) Bond pair
and
2)
Lone pair.
These bond pairs are known as active set of electrons.
These electron pairs (bond pairs or lone pairs) repel each other.
Due to repulsion, electron pairs of central atom try to be as far as possible. Hence,
they arrange themselves in space in such a manner that the force of repulsion
between them is minimized.
The force of repulsion between lone pairs and bond pairs is not the same. The order
of repulsion is as follows:
lone pair-lone pair>lone pair-bond pair>bond pair-bond pair.
Pi-electron pairs are not considered as an active set of electrons.
The shape of molecule depends upon total number of electron pairs surrounding the
central atom.
For Examples
a) If central atom has two electron pairs, geometry of molecule will be linear
with bond angles of 180o.
b) If central atom has three electron pairs, geometry of molecule will be trigonal
with bond angles of 120o.
c) If central atom has four electron pairs, geometry of molecule will be
tetrahedral with bond angles of 109.5o
Hybrid Orbital Model
According to hybrid orbital model the shape of a molecule is determined by the nature of
hybridization in central atom.
According to hybrid orbital model:
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
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Sp-hybridization in central atom gives linear molecule with an angle of 180 o.
For example: C2H2, CO2, CS2, BeCl2.
Sp2-hybridization in the central atom gives planar trigonal structure with bond angles
of 120o.
Sp3-hybridization with no lone pair or non-bonding orbital on the central atom gives
tetrahedral geometry with bond angles of 109.5 o.
Sp3-hybridization with one non-bonding orbital (lone pair) gives pyramidal structure
with an angle of 107o.
Sp3-hybridization with two non-bonding orbital on central atom gives bent or angular
structure with bond angle of 104.5o.
The larger atoms of group VA and VIA such as phosphorus and sulphur do not use
Sp3-hybrid orbital in bond making, instead they utilize their p-orbital which are
mutually at right angles. Such elements form compounds with bond angles of about
90o.
Dipole Moment
Introduction:
The degree of polarity of a molecule is expressed in terms of dipole moment.
Definition:
The product of magnitude of charge on a molecule and the distance between two charges of
equal magnitude with opposite sign is equal to dipole moment.
Mathematical representation:
Dipole moment
=
charge x distance
µ
=
exd
Symbol:
It is represented by an arrow
Unit:
(
µ)
Its unit is Debye. (D)
Dependence of dipole moment:
Dipole moment depends on three factors:
1. Polarity of molecule
2. Magnitude of charge
3. Geometry of molecule
1. Homo-nuclear diatomic molecules have zero dipole moment due to absence of charge.
For example:
H-----H
,
O===O
,
Cl----Cl
Have zero dipole moment.
2. Diatomic molecules of two different atoms have specific values of dipole moment.
For example:
H----F =1.9 Debye
H----Cl =1.03 Debye
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3. Polyatomic molecules of linear structure have zero dipole moment.
For example:
CO2=0 Debye
CS2=0 Debye
4. Molecules having angular or bent structure have certain values of dipole moment.
For example:
H2O = 1.84 Debye,
NH3 = 1.46 Debye
5. If molecular structure of a poly atomic molecule is symmetrical than the dipole moment
of molecule will be zero.
For example:
CH4 = 0 Debye,
C6H6 = 0 Debye,
CCl4 = 0 Debye
Thermodynamics:
"The branch of science which deals with the interconversion of heat energy
and other forms of energies is called thermodynamics."
OR
"It is the study of the flow of heat or any other form of energy into or out
of a system, as it under goes a physical or chemical change."
In thermodynamics we discuss all those problems which are related to the conversion of any
other form of energy into heat energy. Heat engines or I.C. engines or E.C. engines are
discussed under the field of thermodynamics.
Thermochemical Reactions:
All those chemical reactions which accompanied with mass change as well as energy change
are known as thermo-chemical reactions.
Types of thermochemical Reactions:
There are two types of thermo chemical reactions:
1. ENDOTHERMIC REACTIONS
2. EXOTHERMIC REACTIONS
1. Endothermic Reaction:
"All those chemical reaction in which heat is absorbed in going
from reactants to product are known as "Endothermic reactions."
These reactions can not proceed without addition of heat.
For example:
2KClO3 + Heat  2KCl + 3O2
CaCO3 + Heat  CaO + CO2
Graphical Representation:
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Exothermic Reaction:
“All those chemical in which heat is released in going from reactant to
product are known as exothermic reactions.”
For example:
3H2 + N2  2NH3 + Heat
2SO2+O2 2SO3 + Heat
Graphical Representation:
Internal Energy:
“Internal energy of a thermodynamic system is defined as the total energy
possess by a system.”
It is numerically equal to the sum of all microscopic kinetic energies and potential energies
of all the atoms or molecules or ions present within a system.
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


Internal energy of a thermodynamic system is a state function which strictly depends
upon the initial and final states of the system.
The change in internal energy of a system is the amount of energy exchanged by a
system with its surroundings during a thermodynamic process, chemical or physical.
Change in internal energy of a system is equal to the difference between final
internal energy and initial internal energy.

E = E2 - E1
In the light of the first law of thermodynamics, change in internal energy of a system is
equal to the difference between the heat absorbed or released by the system and the work
done.
E =Q - W
Internal energy of a system depends upon the temperature of system. If temperature of a
system is constant, then its internal energy will also be constant.
System:
A thermodynamic system is a collection of matter which has distinct boundaries.
OR
A real or imaginary portion of universe which has distinct boundaries is called
system.
OR
A thermodynamic system is that part of universe which is under thermodynamic
study.
FOR EXAMPLE:
A BALLOON FILLED WITH AIR
A BEAKER FILLED WITH WATER
Thermodynamic Terms
1. System
Any real or imaginary portion of the universe which is under consideration is called system.
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2. Surroundings
All the remaining portion of the universe which is present around a system is called
surroundings.
3. State
The state of a system is described by the properties such as temperature, pressure and
volume when a system undergoes a change of state, it means that the final description of
the system is different from the initial description of temperature, pressure or volume.
Types of System
There are three types of thermodynamic systems.
1. Open system
2. Closed system
3. Isolated system.
1. OPEN SYSTEM
An open system is one in which both mass & energy transfer takes place across the
boundaries.
Example: An open tank of water.
2. CLOSED SYSTEM
A closed system in which there is no transfer of mass takes place across the boundaries
of system but energy transfer is possible.
Example: A gas in a balloon
3. ISOLATED SYSTEM
An isolated system is that in which there is no transfer of mass & energy takes place
across the boundaries of system.
Example: A thermo flask containing hot or cold liquid.
Macroscopic Properties:
All the properties of a system in bulk which are easily measurable are known as
macroscopic properties.
Types of Macroscopic Properties:
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Macroscopic properties can be divided in to two main classes.
1. Intensive properties
2. Extensive properties
1. INTENSIVE PROPERTIES
Macroscopic properties of a system which are independent of mass are known as intensive
properties. Whatever is the mass but properties remain unchanged.
Example:
MELTING POINT, BOILING POINT, DENSITY, TEMPERATURE, PRESSURE,
VISCOSITY.
2. EXTENSIVE PROPERTIES
Macroscopic properties of a system which are strictly dependent on there mass or quantity
of matter are known as extensive properties.
If mass is halved the property will also be half.
Example:
volume, mole, mass, enthalpy, internal energy, kinetic energy.
Thermodynamic terms
Surroundings
“The environments that contained the system are known surroundings.”
Or
“Any thing which is not a part of system is called surroundings.”
System and surroundings are separated from each other by a real or imaginary boundary.
Example:
When a reaction is carried out in a flask placed in a thermostat, the content of flask is the
system, flask itself is the real boundary and thermostat is surroundings.
Enthalpy
“The total heat content of a system is called enthalpy.”
Or
“The total heat content of a system at constant pressure is equivalent to the sum
of its internal energy and PV which is called enthalpy.”
Enthalpy = E + PV

It is denoted by H
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Heat of Formation
“Heat of formation of a compound is defined as the amount of enthalpy change
when one gram mole of a compound is formed from its elements.”


It is represented by H
Unit of heat of formation:
joule / mole
OR
Kilo joule / mole
OR
calorie / mole
OR
Kilo calorie / mole
Standard Heat of Formation
“Standard heat of formation is the heat of formation when all the substances
involved in the reaction are at unit activity i.e. at 25oC and one atmospheric
pressure.”

It is represented by Hf
State
“A thermodynamic system is said to be in a certain state when all its properties
are specified or fixed.”
The fundamental properties, which determine the state of a system, are:
 Temperature
 Pressure
 Volume
 Mass
 Composition
Any change in the above properties changes the state of system. Due to this reason
they are called 'State Functions'.
There are two states of a system
1. Initial state
2. Final state
1. Initial State
The description of the system before it suffers any physical or chemical change is called
'Initial State' of the system.
2. Final State
The description of the system after it undergoes a physical or chemical change is called
'Final State' of the system.
Change in State
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Comparison between the final state and initial state of the system is referred to as 'change
in state'.
The change in state of a system is completely defined when its initial and final states are
specified.
Change in state = Value of property in the final state - Value of property in the
initial state
First Law of thermodynamics
Introduction:
First law of thermodynamics is a statement of conversion of energy. It was enunciated by
Helmholtz in 1847.
Statement:
"Energy can neither be created nor destroyed but it can be changed
from one form of energy to another form of energy."
Or
"During any process total energy of system remains constant."
Or
"During any change the total energy of system and its surrounding remains
constant."
Mathematical Representation
Consider a thermodynamic system initially has internal energy E1 absorbs Q amount of
heat from its surroundings and performs W amount of work and at the same time its
internal energy increases to 
hen according to the first law of thermodynamics:
Heat supplied = increase in internal energy +work done

Q =  + W
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OR
QE2 - E1W
OR
QE2 - E1P V
Where
 = E2 - E1
W = P V
Pressure Volume Work:
Consider a cylinder fitted with a frictionless and weightless non-conducting piston of area of
cross section "A”. An ideal gas is enclosed in the cylinder. Let the volume of gas at initial
state is "V1". An external pressure "P" is exerted on the piston.
If we supply "q" amount of heat to the system then it will increase its internal energy by .
"After a certain limit gas exerts pressure on the piston. If piston is free to move, it will be
displaced by "d" and the volume of system increases from V to V.
We know that pressure is the force per unit area i.e.
P = F/A
OR
F = PA........ (i)
We also know that the work done by the gas on the piston is given by:
W = F d
Where d = displacement of piston
Putting the value of F and d, we get
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W = (PA) d
W = P (Ad)
But Ad = change or increase in volume = V
Hence
W = PV
According to the first law of thermodynamics:
Q =  + W
Q =  + PV
Applications of First law of thermodynamics
Heat can be supplied to a gas under two conditions:
 At constant volume
 At constant pressure
At constant volume
Heat supplied at constant volume is also known as "ISOCHORIC SYSTEM". An isochoric
process is one in which the volume of system during the supply of heat does not change.
This is achieved only when the piston of cylinder is fixed.
In order to supply heat at constant volume piston of cylinder is fixed at a certain position
so that during heat supply volume of system remains constant.
In this condition no change in volume will take place i.e.
V = 0 Since
W = PV
Putting the value of V
W = P (0)
W = 0
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Hence under constant volume no work is done.
APPLYING FIRST LAW OF THERMODYNAMICS
qv =  E +  W
qv =  E
E
= E2 – E1
OR
qv= E2 – E1
CONCLUSION
This expression shows that heat supplied at constant volume is used in increasing the
internal energy of system, but no work is done by the system.
Isobaric Process:
At constant pressure
Heat supplied at constant pressure is also known as "ISOBARIC PROCESS". An isobaric
process is one in which no pressure change takes place during the supply of heat to system.
In order to understand an isobaric process considers a cylinder fitted with a frictionless
piston, the piston is free to move. An ideal gas is enclosed in the cylinder.
Let the internal energy of the system at initial state is E1, the temperature of system is T1,
volume of gas is V1 and pressure is P. If qp amount of heat is supplied to the system, its
internal energy will increase from E1 to E2 and the temperature of system also rises from T1
to T2, At the same time gas exerts some pressure on the piston, since the piston is free to
move, it displaces by "h" the volume of gas increases from V1 to V2 . Due to increase in
volume, pressure again decreases to its original value i.e. P1.
ACCORDING TO THE FIRST LAWOFTHERMODYNAMICS
Qp = E + work
Qp = E + P V
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Qp = E + P V
but (E = E2- E1)
Qp = E2-E1 + P (V2 – V1)
Qp = E2-E1 + PV2- PV1
Qp = E2+ PV2 – E1 – PV1
Qp = (E2+ PV2) – (E1+ PV1)
But
(E + PV =H)
(H= enthalpy)
Therefore,
q
p
qP =  H
OR
E + P V = H
q
p
= H
CONCLUSION
This expression indicates that heat supplied at constant pressure is equal to increase in
enthalpy of system.
HESS'S LAW OF CONSTANT HEAT SUMMATION
Introduction:
Heat absorbed or evolved in a certain reaction is equal to the difference of intrinsic energies
of reactants and products, no matter in what manner the reaction is carried out.
In the light of this fact, the Hess's law stated as:
Statement:
"The amount of heat evolved or absorbed in any chemical reaction is
constant and is independent of the method followed"
In other words:
"The change in enthalpy in any chemical reaction is constant and is
independent whether the reaction takes place in one step or in many steps"
Explanation:
Consider a system chemical whose initial and final states are represented by "A" and "E"
respectively. The change from A to E may take place in single step.
In single step change in enthalpy is H. This change of reactant (A) to product (E) may take
place in more than one steps:
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.
According to Hess's law of constant summation:

H = H1 H2+ H3 +H4
Example:
Consider the reaction between sulphur and oxygen which is exothermic in nature. In this
example formation of sulphur trioxide takes place in two steps: In the first step sulphur
reacts with oxygen to produce sulphur dioxide
S + O2

SO2
Kcal/mol
In the second step SO2 reacts with more oxygen to produce SO3
SO2 +1/2 O2

SO3
Kcal/mol
Total change in enthalpy =  + 
Total change in enthalpy = 
Total change in enthalpy =  94.45 Kcal/mol
We can also prepare sulphur trioxide in one step as shown by the equation:
S+
3/2
O2

SO3
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In the direct one step preparation, change in enthalpy is 94.45 Kcal/mol.
Chemical Equilibrium
Irreversible Reactions and Reversible
Reactions
Irreversible reactions
Chemical reactions which proceed to completion in one direction only are known
as irreversible reactions.
In irreversible reactions reactants are completely converted into products in a certain
interval of time. In these reactions products do not form reactants again.
Examples
CaCO3 CaO + CO2
CaO + H2O  Ca (OH)2
NH4HCO3 + NaCl NaHCO3 + NH4Cl
Reversible reactions
Chemical reactions which proceed in both directions forward and backward
simultaneously are known as reversible reactions.
These reactions never go to completion but always continue in both directions.
Examples
N2 +3H2
H2 + I 2
NH3
2HI
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2SO2+ O2
2SO3
Chemical Equilibrium:
Reversible reactions proceed in both directions simultaneously. In a reversible reaction a
state is achieved at which the rate of forward reaction becomes equal to the rate of
backward reaction. This state is referred to as 'chemical equilibrium'.
Explanation:
Consider a reversible reaction A + B
allowed to react together.


C + D in which two reactants A and B are
At initial stage the reaction proceeds in the forward direction only because no
product is formed.
As the reaction starts A and B reacts to form C and D. Now C and D react each other
to reproduce A and B and the reaction now proceeds in both forward and backward
directions but the rate of forward reaction and the rate of backward reaction are
different.
Finally a state is established at which the rate of backward reaction becomes equal to the
rate of forward reaction. This state is called 'chemical equilibrium'. At equilibrium state,
the reaction does not stop. Reactants form products and products again converted into
reactants. This process is always continue but with the passage of time, there is no change
in the concentration of reactants and products due to same rate of reaction. At this point, it
apparently appears as the reaction has stopped because we don't see any change in the
Concentration of reactants and products with time.
Since chemical equilibrium continues and never go to stop, therefore, chemical equilibrium
is a dynamic equilibrium.
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Law of Mass Action
ACTIVE MASS
Concentration of a substance expressed in mole/dm3 or in molar unit is called ACTIVE
MASS. Active mass in mole/dm3 is represented by a square bracket [ ].
Statement:
According to the law of mass action:
"The rate at which a substance reacts is directly proportional to its active mass "
Rate  [Reactant]
The rate of reaction is directly proportional to the product of the active masses of
reactants.
Consider a general reversible reaction
A+B
C+D
According to the law of mass action:
Rate of reaction [A][B]
Determination of equilibrium constant by using equilibrium law Consider a general
reaction
aA + bB
cC + dD
According to the law of mass action
Rate of forward reaction  [A]a[B]b
Rate of forward reaction = Kf [A]a[B]b
Similarly,
Rate of backward reaction  [C]c[D]d
Rate of backward reaction = Kb [C]c [D]d
Where
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Kf = rate constant for forward reaction
Kb = rate constant for backward reaction
a, b, c, d = number of moles At equilibrium rate of forward reaction becomes equal to the
rate of backward reaction, thus,
Rate of forward reaction =
Rate of backward reaction
Kf [A]a [B]b
=
Kb [C]c [D]d
Kf / K b
=
[C]c [D]d/ [A]a [B]b
=
[C]c [D]d/ [A]a [B]b
Let
Kf/Kb = Kc
Kc
This is the expression of equilibrium constant where c represents concentration.
Define KP
KP
For gaseous equilibrium systems we can use partial pressure of gases instead of
concentration. Therefore,
"Equilibrium constant determined by using partial pressure
of gases in a gaseous chemical equilibrium is denoted by Kp"
Consider a general reversible reaction :
aA(g) + b B(g)
c C(g) + d D(g)
For the reaction Kp is
Kp = [PC]c[PD]d/[PA]a[PB]b
Where [P] = partial pressure of gas
RELATION BETWEEN Kp AND Kc
We know that Kp and Kc are related to each other as:
Kp = Kc[RT]n
From above relation we conclude three results as follows. 1. If Kp=Kc In this case there is
no change in volume For example:
H2 + I 2
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In this example volumes of products are equal to the volumes reactants. 2. If Kp>Kc In
this case reaction occur with the increase in volume. For example:
2NH3
N2 + 3H2
In this example volumes of products are greater than the volumes reactants. 3.If Kp<Kc In
this case reaction occur with the decrease in volume. For example:
2SO2(g) + O2(g)
2SO3(g)
In this example volumes of products are less than the volumes reactants.
Determination of Equilibrium Constant
The value of equilibrium constant K(C) does not depend upon the initial concentration of
reactants. In order to find out the value of K(C) we have to find out the equilibrium
concentration of reactant and product.
1. Ethyl Acetate Equilibrium
Acetic acid reacts with ethyl alcohol to form ethyl acetate and water as shown
CH3COOH + C2H5OH
CH3COOC2H5 + H2O
Suppose ‘a’ moles of acetic acid and ‘b’ moles of alcohol are mixed in this reaction. After
some time when the state of equilibrium is established suppose ‘x’ moles of H2O and ‘x’
moles of ethyl acetate are formed while the number of moles of acetic acid and alcohol are
a-x and b-x respectively at equilibrium.
According to law of mass action
K(C) =
[CH₃COOC₂H₅] [H₂O]
[CH₃COOH] [C₂H₅OH]
K(C) =
𝑥 𝑥
×
𝑣 𝑣
𝑎−𝑥 𝑏−𝑥
×
𝑣
𝑣
K(C) =
(𝑥 )(𝑥)
(𝑎−𝑥 )(𝑏−𝑥)
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𝑥²
(𝑎−𝑥 )(𝑏−𝑥)
K(C) =
2. Hydrogen Iodide Equilibrium
For the reaction between hydrogen and iodine suppose a mole of hydrogen and ‘b’ moles of
iodine are mixed in a scaled bulb at 444ºC in the boiling sulphur for some time. The
equilibrium mixture is then cooled and the bulbs are opened in the solution of NaOH. Let the
amount of hydrogen consumed at equilibrium be ‘x’ moles which means that the amount of
hydrogen left at equilibrium is a-x moles. Since 1 mole of hydrogen reacts with 1 mole of
iodine ‘o’ form two moles of hydrogen iodide hence the amount of iodine used is also x
moles so its moles at equilibrium are b-x and the moles of hydrogen iodide at equilibrium
are 2x.
According to law of mass action
K(C) =
K(C) =
[Hl]²
[H]² [l]²
2𝑥
]²
𝑣
𝑎−𝑥 𝑏−𝑥
×
𝑣
𝑣
[
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Le- Chatelier’s Principle
Introduction:
The equilibrium state of a chemical equilibrium system is changed by change in
concentration, pressure temperature etc. The effect of change in any one of the above
factors changes the equilibrium system. The effect of change of these factors is explained
by Le-Chatelier’s principle.
Statement:
“If a stress or constraint is applied to an equilibrium system, the equilibrium will
shift in such a direction so that the effect of stress is cancelled or minimized.”
In other words:
“If a system at equilibrium is disturbed by some change, the system will shift in a
direction to minimize or undo the effect change.”
MEANING OF STRESS:
Stress on equilibrium is the change in concentration or pressure or temperature. If any one
of these is changed at equilibrium, the equilibrium system will disturb.
Important Industrial Application of Le Chatelier’s Principle
Haber’s Process
This process is used for the production of NH3 by the reaction of nitrogen and hydrogen. In
this process 1 volume of nitrogen is mixed with three volumes of hydrogen at 500ºC and
200 to 1000 atm pressure in presence of a catalyst
N2 + 3 H2
2 NH3 …………… ΔH = -46.2 kJ/mole
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The effect of change in the following factors on equilibrium:
a) The effect of change in concentration
b) The effect of change in pressure
c) The effect of change in temperature
d) The effect of catalyst
a) Effect of Concentration
By changing the concentration of any substance present in the equilibrium mixture, the
balance of chemical equilibrium is disturbed. For the reaction,
A+B
C+D
K(C) = [C][D] / [A][B]
If the concentration of a reactant A or B is increased the equilibrium state shifts tc right and
yield of products increases.
But if the concentration of C or D is increased then the reaction proceed in the backward
direction with a greater rate and more A & B are formed.
b) Effect of Temperature
The effect of temperature is different for different type of reaction.
For an exothermic reaction the value of K(C) decreased with the increase of temperature so
the concentration of products decreases.
For an endothermic reaction heat is absorbed for the conversion of reactant into product so
if temperature during the reaction is increased then the reaction will proceed with a greater
rate in forward direction.
Endothermic Reaction
Temperature increase
More products are formed
Temperature decrease
More reactants are formed
Exothermic Reaction
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Temperature increase
More reactants are formed
Temperature decrease
More products are formed
c) Effect of Pressure
The state of equilibrium of gaseous reaction is distributed by the change of pressure. There
are three types of reactions which show the effect of pressure change.
1. When the Number of Moles of Product are Greater
In a reaction such as
PCl5
PCl3 + Cl2
The increase of pressure shifts the equilibrium towards reactant side.
2. When the Number of Moles of Reactant are Greater
In a reaction such as
N2 + 3H2
2NH3
The increase of pressure shifts the equilibrium towards product side because the no. of
moles of product is less than the no. of moles of reactant.
3. When Number of Moles of Reactants and Products are Equal
In these reactions where the number of moles of reactant are equal to the number of moles
of product the change of pressure does not change the equilibrium state e.g.,
H2 + l2
2 Hl
Since the number of moles of reactants and products are equal in this reaction so the
increase of pressure does not affect the yield of Hl.
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Common Ion Effect
Statement
The process in which precipitation of an electrolyte is caused by lowering the degree of
ionization of a weak electrolyte when a common ion is added is known as common ion
effect.
Explanation
In the solution of an electrolyte in water, there exist an equilibrium between the ions and
the undissociated molecules to which the law of mass action can be applied.
Considering the dissociation of an electrolyte AB we have
AB
K=
𝐴+ + 𝐵 −
[𝐴+ ][ 𝐵− ]
[AB]
(dissociation constant)
If now another electrolyte yielding 𝐴+ or 𝐵 − ions be added to the above solution, it will
result in the increase of concentration of the ions 𝐴+ or 𝐵 − and in order that K may remain
the same, the concentration AB must evidently increase. In other words the degree of
dissociation of an electrolyte is suppressed by the addition of another electrolyte containing
a common ion. This phenomenon is known as common ion effect.
Solubility:
Solubility of a solute in a solvent is the number of grams of solute necessary to
saturate 100 grams of solvent at a particular temperature.
Solubility product:
Solubility product is defined as the product of ionic concentration when dissolved
ions and undissolved ions are in equilibrium.
Or
When a saturated solution of sparingly or slightly soluble salt is in contact with
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undissolved salt, equilibrium is established between the dissolved ions and the
ions in the solid phase of the undissolved salt. Ionic product at this stage is called
solubility product.
Symbol:
It is denoted by Ksp
Determination of solubility product:
Consider a slightly soluble salt such as silver chloride (AgCl).
AgCl(aq)
Ag+(aq) + Cl-(aq)
Applying equilibrium law:
K(C)
=
K(C) [𝐀𝐠𝐂𝐥]
=
[𝐀𝐠]+ [𝐂𝐥]−
[𝐀𝐠𝐂𝐥]
[𝐀𝐠]+ [𝐂𝐥]−
since there is no change in the concentration of salt (AgCl) at equilibrium.
Therefore,
[AgCl] = constant (𝑲′)
K(C) 𝐊 ′
=
[𝐀𝐠]+ [𝐂𝐥]−
Let Kc x 𝐊 ′ = solubility product or Ksp, Therefore,
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Ksp
=
[Ag+] [Cl-]
Ionic product:
Product of ionic concentration other than equilibrium is called ionic product.
Applications of solubility product:
Knowledge of solubility product is very useful to determine whether precipitates will be
obtained or not by the addition of more amount of solute to the solution. There are three
conditions:
When Ksp > ionic product:
If solubility product is greater than the ionic product then, the solution is unsaturated and
no precipitate will form by the addition of more solute.
When Ksp< ionic product:
If solubility product is less than the ionic product then the solution is super saturated and
the excess of solute will precipitate immediately.
When Ksp= ionic product:
In this condition solution is saturated and further addition of solute will cause precipitates.
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Molarity:
It is a unit of concentration of solution.
Definition:
"Molarity is defined as the number of moles of solute dissolves in 1dm3 of solution"
Formula:
𝐌𝐨𝐥𝐚𝐫𝐢𝐭𝐲 =
𝐌𝐨𝐥𝐚𝐫𝐢𝐭𝐲
=
#.𝐨𝐟 𝐦𝐨𝐥𝐞𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞
𝐯𝐨𝐥𝐮𝐦𝐞 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐢𝐧 𝐝𝐦𝟑
𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞 𝐢𝐧 𝐠𝐦𝐬
𝐦𝐨𝐥𝐞𝐜𝐮𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞×𝐯𝐨𝐥𝐮𝐦𝐞 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐢𝐧 𝐝𝐦³
Molality:
It is a unit of concentration of solution
Definition:
"Molality is defined as the number of moles of solute dissolved in 1kg of solvent"
Formula:
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𝐌𝐨𝐥𝐚𝐥𝐢𝐭𝐲
=
𝐌𝐨𝐥𝐚𝐫𝐢𝐭𝐲
=
# 𝐨𝐟 𝐦𝐨𝐥𝐞𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞
𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐯𝐞𝐧𝐭 𝐢𝐧 𝐤𝐠
𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞 𝐢𝐧 𝐠𝐦𝐬
𝐦𝐨𝐥𝐞𝐜𝐮𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞×𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐯𝐞𝐧𝐭 𝐢𝐧 𝐤𝐠³
Hydrolysis
DEFINITION
The reaction of cations or anion or both with water in which pH of water is
changed, is known as hydrolysis
OR
Reaction of a substance with water in which pH of water is changed, is known as
hydrolysis
EXPLANATION
Example #1 when ammonium chloride is treated with water following reaction takes place
NH4+Cl- + H+OH-  HCl + NH4OH
In this example products are HCl which is strong acid and NH4OH which is a weak base.
Due to this reason, pH of solution will change towards acidic nature.
Example #2 When sodium carbonate is treated with water following reaction takes place
Na2CO3 + 2H2O 2NaOH + H2CO3
In this example products are NaOH which is strong base and H2CO3 (Carbonic acid) which is
a weak acid. Due to this reason pH of solution will change towards basic nature.
Example #3 When NaCl is dissolved in water hydrolysis does not take place because by the
addition of NaCl in water, pH of water does not affected.
Hydration
When an ionic compound is dissolved in water it splits into positive and negative ions. These
ions are surrounded by water molecules. The phenomenon in which water molecules
surround a positive or negative ion is called 'HYDRATION'. Hydration occurs either by the
interaction of lone pairs of electrons in water with a cation or by hydrogen bonding with
anions.
Hydrates
Many compounds have crystallized water molecules additional to that required for a simple
stoichiometry. Water can be bonded to cations by coordinate bonds from oxygen or to
anions by hydrogen bonds. These compounds are generally termed as 'HYDRATES'.
EXAMPLES
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CuSO4.5H2O
Na2CO3.10H2O
ZnSO4.7H2O
BaCl2.2H2O
FeSO4.7H2O
MgCl2.6H2O
K2SO4.Al2(SO4)3.24H2O (potash alum)
FeSO4. (NH4)2SO4.6H2O (Mohr's salt)
CHARACTERISTICS OF HYDRATION
In the process of hydration:
Water molecules as a whole are linked with crystal lattice.
No H--O bond of water is broken.
New bonds are formed between water molecules and cation and anions.
It is an exothermic process.
In this process no new compounds are formed.
FACTORS ON WHICH HYDRATION DEPENDS
The ability of an ion to hydrate depends upon two factors:
1. Magnitude of charge on the ion.
2. The size of ion.
Greater is the ionic charge greater is the ability of ion to make hydrate.
Smaller is the ionic size greater is the ability of ion to make hydrate.
EFFECT OF HEAT ON HYDRATES
Many hydrates decompose on heating and loose their water of crystallization and become
anhydrous.
CuSO4.5H2O  CuSO4 + 5H2O
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Arrhenius theory of ionization
Arrhenius theory of ionization consists of the following postulates.
The substance called electrolytes is believed to contain electrically charged particles
called ions. These charges are positive for H+ ion or ions derived from metals and negative
for the ions derived from non-metals. Number of electrical charges carried by an ion is equal
to the valency of corresponding atom.
Molecules of electrolytes (acids, bases and salts) dissociate into oppositely charged ions
on dissolution in water, e.g.
Na+ +ClH+ +ClNa+ + OH-
NaCl
HCl
NaOH
The number of positive and negative charges on the ions must be equal so that the
solution as a whole remains neutral.
In solution, the ions are in a state of disorderly or random motion. Upon colliding they
may combine to give unionized molecules. Thus ionization is a reversible process in which
the solution contains ions of electrolyte together with unionized molecules.
H2SO4(aq)
2H+(aq) + SO4-2(aq)
The extent of ionization or the degree of ionization depends upon the nature of
electrolyte. Strong electrolytes such as HCl etc. ionize completely in water. Weak
electrolytes such as acetic acid (CH3COOH) ionize only slightly.
Ionization is not affected by electric current.
When electric current is passed through an electrolytic solution, charges move towards
their respective electrodes, i.e. cations towards anode and anions towards cathode. When
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these ions reached their respective electrodes, they change into neutral species by the gain
or loss of electron.
The dissociation of electrolyte depend upon
Nature of electrolyte
Degree of dilution
Temperature
The electrical conductivity depends upon:
The number of ions present in the solution Speed of ions.
Electrode Potential
Definition
.
When a metal (electrode) is immersed in a solution containing the ions of that metal, a
potential difference is set up between the metal and its ions in the solution. This potential
difference is referred to as "Electrode Potential ".
Explanation
.
If a copper plate is dipped in a solution of copper sulphate (CuSO4) a potential difference is
set up between copper and Cu+ -ions which is known as electrode potential.
Characteristics of Electrode Potential
Electrode potential is the measure of the tendency of an electrode to loose or gain
electron (s).
In other words electrode potential describes the tendency of an element to oxidize or
reduce.
Electrode potential also determines the chemical activity of an element.
OXIDATION POTENTIAL
It is the measure of tendency of an element to oxidize.
REDUCTION POTENTIAL
It is the measure of tendency of an element to reduce.
UNIT OF ELECTRODE POTENTIAL
Unit of electrode potential is "VOLT".
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HYDROGEN ELECTRODE
Hydrogen electrode is the reference electrode used to compare electrode potential of
different electrode because absolute electrode potential can not be measured.
"A hydrogen electrode consists of a platinum bar immersed in 1.00M solution of
H2SO4. A current of pure hydrogen gas is passed through the solution under 1.00
atmosphere. The platinum plate adsorbs hydrogen at its surface and platinum
plate is coated with hydrogen. The plate now behaves as if it were made of
hydrogen. The electrode potential of hydrogen electrode is assumed to be 0.00V at
all temperatures.”
POTENTIAL OF ZINC
ELECTRODE POTENTIAL OF ZINC
In order to determine the electrode potential of zinc a voltaic cell is constructed by a zinc
electrode( a zinc strip dipped in 1.00 molar solution of ZnSO4) and hydrogen electrode. Salt
bridge is made of potassium chloride (KCl) jelly which completes the circuit between half
cells and prevents mixing of solutions.
The potentiometer reading gives the E.M.F. of the cell which is 0.76 Volt. Since hydrogen
electrode has the potential of 0.00 Volt, hence potential of Zn electrode is 0.76 Volt.
0.76 - 0.00 = 0.76 Volt
In external circuit it is observed that the flow of electrons takes place from Zn to H.
Thus it concludes that the electrons must have originated from Zn i.e. it is oxidized and it is
anode and it is negative with respect to hydrogen electrode. Thus standard reduction
potential of zinc is - 0.76V.
The standard oxidation potential of zinc is therefore + 0.76V.
Ered = Eox
- 0.76 Volt = +0.76 Volt
The negative sign shows that the reaction at Zn electrode occurs in the opposite direction
and at Zn electrode oxidation takes place not reduction:
Reduction takes place on hydrogen electrode:
CELL REACTION
Adding two equations:
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CHEMICAL KINETICS
Chemical Kinetics
Chemical Kinetics
The branch of chemistry, which deals with the "RATE" and the SPEED at which a chemical
reaction occurs, is called "CHEMICAL KINETICS". The study of chemical kinetics, therefore,
includes the rate of a chemical reaction and also the factors that influence or alter or control
the rate of chemical reactions. In chemical kinetics we study how molecules react, bond
breaking and new bond formation.
RATE OF A CHEMICAL REACTION
"It is defined as the quantity of a reactant consumed or the
quantity of a product formed in unit time."
In other words:
The conversion of the number of moles of reactants into products in unit time. The rate of
reaction is not constant through out the activity but decreases with time due to decrease in
the concentration of reactants.
MATHEMATICALLY:
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Velocity of Reaction:
Since the rate of reaction is not constant through out the reaction, therefore, we can not
determine the uniform rate of reaction precisely.
Thus velocity of reaction may be defined as the rate of reaction at a particular given
moment i.e. at a specific time.
If we consider a very small interval of time dt in which the change in concentration
taken to be nearly constant, then velocity of reaction is given by:
dx is
Velocity of reaction is actually the instantaneous rate of reaction.
RATE EXPRESSION & RATE CONSTANT
Consider a general reaction:
According to the law of mass action, rate of reaction is directly proportional to active mass,
hence for the above reaction:
This expression is called rate expression and
K is called rate constant or velocity constant.
CHARACTERISTICS OF RATE CONSTANT
(i) It has a fixed value at a particular temperature.
(ii) Value of K varies with temperature.
(iii) Value of K remains unaltered with the change in concentration of reactants.
Order of Reaction:
"The order of reaction is defined as the sum of all the exponents
of the reactants involved in the rate equation."
It should be noted down that all the molecules shown in a chemical equation do not
determine the value of order of reaction but only those molecules whose concentrations are
changed are included in the determination the order of a reaction.
"The number of reacting molecules whose concentration alters as a
result of chemical reaction is termed as the order of reaction."
For example:
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2NO + O2 2NO2
𝐝𝐱
𝐝𝐭
= K [NO] 2[𝐎𝟐 ]
The reaction is of third order as 2 + 1 = 3
For a reaction maximum order is three and the minimum is zero.
FIRST ORDER REACTIONS
The reaction in which only one molecule undergoes a chemical change is called first order
reactions. Example:
N2O5  2NO2 + ½ O2
SECOND ORDER REACTIONS
The reaction in which two molecules undergo a chemical change is called second order
reactions. Example:
2CH3CHO 2CH4 + 2 CO
THIRD ORDER REACTIONS
The reaction in which only three molecules undergo a chemical change is called third order
reactions. Example:
2NO + O2 2NO2
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