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Chemical Kinetics
“The branch of chemistry which deals with the study of the speed or the rate of chemical
reactions, the factors affecting the rate of reactions and the mechanism by which the reaction
proceed is known as chemical kinetics”.
Based upon their rates, the various chemical reactions are classified into three types as
follows:(i)
Very fast reactions i.e. which takes place very quickly. For example ionic
reactions like:
AgNO3 + NaCl
AgCl + NaNO3
Na+Cl- + H2O
NaOH + HCl
(ii)
Very slow reactions i.e. which may take place days or months. For example
rusting of iron.
(iii)
Reactions which neither very slow nor very fast but takes place at moderate
speeds. For example:
C12H22O11 + H2O
C6H12O6 + C6H12O6
(Sucrose)
(Glucose) (Fructose)
“The reason for the difference in rates is that reaction involves the breaking and making of
bonds. Since different bonds require different amounts of energy for breaking and different
amounts of energies are evolved when different kinds of new bonds are formed, the rates of
reactions are different”.
Rate of Reaction- The rate of reaction is the change in the concentration of the reactants or
products per unit time.
i.e. Rate of reaction = Decrease in the concentration of a reactant
Time interval
Or
Increase in the concentration of a product
Time interval
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For Example, PCl5
PCl3 + Cl2
Rate of reaction = - ∆ [PCl5]
= + ∆ [PCl3]
∆t
= + ∆ [Cl2]
∆t
∆t
The minus sign along with the first term is used to show that the concentration of the reactant
(PCl5) is decreasing while plus sign along with the other two terms is used to show that the
concentration of the products (PCl3 and Cl2) is increasing.
2N2O5
4 NO2 + O2
Rate of reaction = - 1 d [N2O5] = + 1 d [NO2] = + d[O2]
2
dT
4
dT
dT
The minus sign along with the first term is used to show that the concentration of the reactant
(N2O5) is decreasing while plus sign along with the other two terms is used to show that the
concentration of the products (NO2 and O2) is increasing.
Units of the Rate of Reaction. Since concentration is usually expressed in moles/litre and
the time is taken in seconds or minutes, the unit of the rate of reactions is moleslitre-1sec-1
(mol L-1 s-1) or moleslitre-1min-1 (mol L-1 min-1).
Factors affecting the Reaction Rate1. Concentration of the reactants. Greater are the concentration of reactants, faster is the
reaction. If the concentration of the reactants decrease, the rate of reaction also
decrease.
2. Temperature. The rate of reaction increase with the increase in the temperature.
3. Presence of catalyst. A catalyst generally increases the rate of reaction without being
consumed in the reaction.
4. Surface area of the reactants. Greater is he surface area, faster is the reaction.
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Rate law, Rate constant and Order of reaction.
For a general reaction
k [A]α [B]β
αA+βB
(Rate law)
where [A] and [B] are the molar concentrations of A and B respectively and k is a constant
called rate constant. The above expression is called Rate law.
If all the concentrations are taken as unity i.e.,
[A] = [B] = 1 mole/litre,
Then Rate = k
Hence “rate constant may be defined as the rate of the reaction when the concentration of
each reactant is taken as unity.”
Rate constant is a measure of the rate of reaction. Greater the value of the rate constant, faster
is the reaction.
Order of reaction. The sum of the concentration terms on which the rate of reaction actually
depends as observed experimentally is called the order of reaction.
Depending upon whether α+ β = 0, 1, 2 or 3, the reactions are said to be of zero order, first
order, 2nd order and 3rd order respectively.
Units of Rate constant for reactions of different orders:
(i)
For zero order reactions, n=0
k= moles L-1 time -1
(ii)
For Ist order reactions, n=1
k = time-1
(iii)
For 2nd order reactions, n= 2
k = L mol-1 time-1
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Example. Identify the order of a reaction order from each of the following rate constant:
(i)
k = 2.3 × 10-5 litre mol-1 sec-1
(ii)
k = 3.1 × 10-4 sec-1
(iii)
k = 9.3 × 10-4 mol litre-1 sec-1
Solution: (i) is a reaction of 2nd order
(ii) is a reaction of 1st order
(iii) is a reaction of zero order.
Molecularity of a reaction- In case of simple reactions (Elementary reactions),
“The number of atoms, ions or molecules that must collide with one another simultaneously
so as to result into a chemical reaction is called the molecularity of the reaction.” Or
“The molecularity is simply the sum of the molecules of the different reactants as represented
by the balanced chemical equation.”
A few examples are given below:
(i) Decomposition of O2F2: O2F2
O2 + F2
Hence the molecularity of the reaction is 1 and the reaction is Unimolecular.
(ii) Dissociation of HI: 2 HI
H2 + I2
Hence the molecularity of the reaction is 2 and the reaction is Bimolecular.
(iii) Reaction between NO and O2: 2NO + O2
2NO2
Hence the molecularity of the reaction is 3 and the reaction is Termolecular.
Molecularity can only be defined for an elementary reaction. It has no meaning for the
complex reactions.
Catalysis
Reaction rates are affected not only by reactant concentrations and temperature but also by
the presence of catalysts.
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“Catalyst is a substance which can change the speed of the chemical reaction without being
consumed in that reaction and the phenomena is known as catalysis.”
For example:
2 KClO3 (s)
MnO2 catalyst
2 KCl (s) + 3 O2 (g)
heat
In the absence of a catalyst, KClO3 decomposes very slowly, even when heated, but when a
small amount of MnO2 is mixed with the KClO3, the reaction become rapid.
Catalysts are very important both in chemical industry and in living organisms. In living
organisms, almost all the hundreds of thousands of chemical reactions are catalyzed by large
molecules called enzymes.
How does a catalyst work? A catalyst lowers the activation energy for the forward reaction
as well as for the backward reaction. As a result, the reaction follows alternate path (short
path) and the rate of reaction increase.
Types of catalysis:
1. Homogeneous catalysis. If the catalyst is present in the same phase as the reactants, it is
called a homogenous catalyst and this type of catalysis is called homogeneous catalysis.
For example: 2SO2 (g) + O2 (g)
NO (g)
2 SO3 (g)
Here all the substances are present in the gaseous phase.
C12H22O11 (aq) + H2O (l)
H+ (aq)
(Sucrose)
C6H12O6 (aq) + C6H12O6 (aq)
(Glucose)
(Fructose)
Here all the substances are present in the liquid phase.
1. Heterogeneous catalysis. If the catalyst is present in the different phase as the reactants, it
is called a heterogeneous catalyst and this type of catalysis is called heterogeneous catalysis.
For example: 2SO2 (g) + O2 (g)
Pt (metal)
2 SO3 (g)
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CH2=CH2 (g) + H2 (g)
(metal)
CH3=CH3 (g)
Zeolites as Catalysis- Zeolites are aluminosilicates, i.e. three dimensional network silicates
in which some silicon atoms are replaced by aluminum atoms. They are found in nature as
well as synthesized in the laboratory or industry.
Zeolites are being very widely used as catalysts in petrochemical industries for cracking of
hydrocarbons and isomerization. An important zeolite catalyst used in petrochemical industry
is ZSM-5 (Zeolite Sieve of Moleular Porosity 5). It converts alcohol directly into petrol.
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ATOMIC STRUCTURE
Electron - Electron is a negatively charged particle having a charge equal to 1.60 × 10 -19
and mass equal to 9.10 × 10 -31 kg.
Proton- Proton is a positively charged particle with charge equal to electron and mass equal
to 1.6727 × 10 -27 kg.
Neutron- Neutron is a neutral particle having mass equal to 1.6748 × 10 -27 kg. Thus neutron
carries no charge.
Rutherford (in 1911) on the basis of his scattering experiments proposed a model called
‘Rutherford’s model of the atom’. According to this model, an atom consists of a small, heavy
positively charged body within the atom, called the nucleus. This nucleus contains all the
protons and neutrons and it surrounded by a suitable number of electrons revolving around it
to balance the positive charge. This model failed because it could not explain the stability of
the atom.
To explain the stability, Bohr in 1913 put forward a model of the atom called Bohr’s model of
the atom. This method said that the electrons in an atom revolve around the nucleus only in
selected orbits. The energy of an electron remains constant in a particular orbit. The orbits are
also known as energy shells or energy levels. But this theory is objectionable because of
following new concepts:
The de Broglie Relation. Louis de Broglie advanced the idea that like light, all material
particles such as electron, proton, atom, molecule etc. also possessed dual character : as wave
and as particle.
The wave associated with a particle is called a matter wave or de Broglie wave.
λ=
h
mv
or
λ=
h
p
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The above formulation is called de Broglie equation and λ is called de Broglie wavelength.
Example. Calculate the wavelength associated with an electron (mass 9.1 × 10-31 kg) moving
with a velocity of 103 m sec-1 (h= 6.6 × 10-34 kg m2sec-1).
Solution.
m = 9.1 × 10-31 kg, v = 103 m sec-1, h = 6.6 × 10-34 kg m2sec-1.
λ=
h
mv
6.6 × 10-34
=
=
7.25 × 10-7 m.
(9.1 × 10-31) × 103
Heisenberg’s Uncertainty principle
It is impossible to measure simultaneously the position and momentum of a small particle
with absolute accuracy. The product of uncertainty in the position (∆x) and the uncertainty in
the momentum (∆ p = m. ∆v, where m is the mass of the particle and ∆v is the uncertainty in
velocity) is always constant and is equal to or greater than h / 4π.
∆x.∆p= h
(i)
4π
∆ x .( m.∆v) = h
(ii)
4π
∆x =
h
(iii)
4π×m×∆v
∆v =
h
4π×m×∆x
(iv)
or
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Example 1. Calculate the uncertainty in the velocity of an electron if the uncertainty in its
position is 1A0 (10-10 m) (h= 6.6 × 10-34 kg m2sec-1, m = 9.1× 10-31 kg).
Solution.
∆ x = 10-10 m,
h = 6.6 × 10-34 kg m2sec-1,
m = 9.1× 10-31 kg
Applying uncertainty principle:
∆ x .( m.∆v) = h
4π
Or
∆v =
h
4π×m×∆x
=
6.6 × 10-34
= 5.77 × 105 ms-1
4 × 22/7 × 9.1× 10-31
Example 2. Calculate the uncertainty in the position of an electron if the uncertainty in its
velocity is 5.7 × 105 m/sec (h= 6.6 × 10-34 kg m2sec-1, m = 9.1× 10-31 kg).
Solution.
∆ v = 5.7 × 105 m/sec,
h = 6.6 × 10-34 kg m2sec-1,
m = 9.1× 10-31 kg
Putting these values in the equation for uncertainty principle
∆x =
h
4π×m×∆v
=
6.6 × 10-34
4 × 22/7 × 9.1× 10-31 × 5.7 × 105
=
1.0 × 10-10 m.
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“Quantum numbers”
Quantum numbers may be defined as a set of numbers with the help of which we can get
complete information about all the electrons in an atom.
The various quantum number give complete information about an electron i.e. about its
energy, shape, location, orientation and magnetism due to orbital motion.
The various quantum numbers are briefly discussed below:
1. Principal Quantum Number (n).
It is the most important quantum number as it tells
the principal energy level or shell to which the electron belongs. It is denoted by the letter ‘n’
and has positive integer value i.e. n = 1,2,3,4..... etc. and can be designated by the letters, K,
L, M, N, O, P..... etc.
It completely determines the energy of the electron in hydrogen and hydrogen like particles
(which contain only one electron).
2. Azimuthal or Angular Momentum or Secondary Quantum Numbers (l).
The azimuthal or angular momentum quantum numbers gives the following information:
(i) The number of subshells present in the main shell.
(ii) The angular momentum of the electron present in the subshell.
(iii) The relative energies of the various subshells.
This quantum numbers is denoted by the letter ‘l’. For any given value of n, it can have value
ranging from 0 to n-1.
For the 1st shell (K), n = 1,
l can have only one value, i.e. l = 0
For the 2nd shell (L), n = 2,
l can have two values, i.e. l = 0 and 1.
For the 3rd shell (M), n = 3,
l can have three values, i.e. l = 0, 1 and 2.
For the 4th shell (N), n = 4,
l can have four values, i.e. l = 0, 1, 2 and 3.
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Each value of l represents a different subshell. Depending upon the value of l i.e. l = 0, 1, 2
and 3, the different subshells are designated as s, p, d and f respectively.
Thus from above discussion it follows that first principal shell (K- shell, n=1) has only one
subshell (l = 0) called s- subshell.
The second principal shell (L- shell, n=2) has two subshells i.e. s- subshell (l = 0) and psubshell (l = 1).
The third principal shell (M- shell, n=3) has three subshells i.e. s- subshell (l = 0) and psubshell (l = 1), d- subshell (l = 2).
The fourth principal shell (N- shell, n=4) has four subshells i.e. s- subshell (l = 0) and psubshell (l = 1), d- subshell (l = 2), f- subshell (l = 3).
3. Magnetic Quantum Numbers (m). Magnetic quantum number determines the orientation
of the electrons or it determines the number of orbitals present in any subshells.
Magnetic quantum number (m) has the value ranging from –l to +l.
Thus, for example if l = 0 (s- subshell), m can have only one value i.e. m = 0. In other words,
s- subshell has only one orbital called s- orbital.
When l = 1 (p- subshell), m can have three values i.e. m = -1, 0 and +1. In other words, psubshell has three orbitals called p- orbitals.
For l = 2 (d- subshell), m can have five values i.e. m = -2, -1, 0, +1 and +2. In other words, dsubshell has five orbitals called d- orbitals.
Similarly when l = 3 (f- subshell), m can have seven values i.e. m = -3, -2, -1, 0, +1, +2 and
+3. In other words, d- subshell has seven orbitals called f- orbitals.
Example 1. An electron is in a 4f orbital. What are the values of the quantum numbers n, l,
and m?
Solution: Since the electron is in a 4f orbital, the value of quantum number, n = 4.
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For the f orbital, the secondary quantum number, l = 0, 1, 2 and 3.
The values of m are -3, -2, -1, 0, +1, +2 and +3.
Example 2. List the values of l and m for n =2.
Solution. For n =2,
l = 0, 1,
m = -1, 0, +1.
Example 3. What designation is given to an orbital having n =3, l =1.
Solution. 3 p.
Example 4. If the principal quantum number (n) is 2. What will be the magnetic quantum
number (m) ?
Solution. -2, -1, 0, +1, +2
“Aufbau Principle”
The word aufbau means building up. According to this principle in the atom, the electrons
are added one by one to the various orbitals in order of their increasing energy starting with
the orbital of lowest energy.
The order in which the orbitals are filled as follows:
1s, 2s, 2p, 2s, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d,7p.
“Pauli Exclusion Principle”
An orbital can have maximum two electrons and these must have opposite spins.
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Hund’s Rule
Electronic configuration of some elements Atomic number
Element
Electronic configuration
1
H
1 s1
2
He
1 s2
3
Li
1 s2 , 2 s1
4
Be
1 s2 , 2 s2
5
B
1 s2, 2 s2, 2 p1
6
C
1 s2, 2 s2, 2 p2
7
N
1 s2, 2 s2, 2 p3
8
O
1 s2, 2 s2, 2 p4
9
F
1 s2, 2 s2, 2 p5
10
Ne
1 s2, 2 s2, 2 p6
11
Na
1 s2, 2 s2, 2 p6, 3 s1
12
Mg
1 s2, 2 s2, 2 p6, 3 s2
14
13
Al
1 s2, 2 s2, 2 p6, 3 s2, 3 p1
14
Si
1 s2, 2 s2, 2 p6, 3 s2, 3 p2
15
P
1 s2, 2 s2, 2 p6, 3 s2, 3 p3
16
S
1 s2, 2 s2, 2 p6, 3 s2, 3 p4
17
Cl
1 s2, 2 s2, 2 p6, 3 s2, 3 p5
18
Ar
1 s2, 2 s2, 2 p6, 3 s2, 3 p6
19
K
1 s2, 2 s2, 2 p6, 3 s2, 3 p6, 4 s1
20
Ca
1 s2, 2 s2, 2 p6, 3 s2, 3 p6, 4 s2
21
Sc
1 s2, 2 s2, 2 p6, 3 s2, 3 p6, 3 d10, 4 s2