B.Sc. I Year Physical Chemistry_Unit-IV_A. Chemical Kinetics

1. TEJASVI NAVADHITAMASTU
“Let our (the teacher and the taught) learning be radiant”
Let our efforts at learning be luminous and filled with joy, and endowed with the force of purpose
Paper III: PHYSICAL CHEMISTRY
Dr. Prabhakar Singh. D.Phil. Biochemistry
Department of Biochemistry, VBSPU, Jaunpur
Unit-III: A. Chemical Kinetics and Catalysis Chemical kinetics and its scope, rate of a reaction,
factors influencing the rate of a reaction - concentration, temperature, pressure, solvent, light,
catalyst, concentration dependence of rates, mathematical characteristics of simple chemical
reactions - zero order, first order, second order, pseudo order, half life and mean life,
Determination of the order of reaction - differential method, method of integration, method of
half life period and isolation method. Radioactive decay as a first order phenomenon

2. CHEMICAL KINETICS
The branch of Physical chemistry which deals with the rate of reactions is called
Chemical Kinetics. The study of Chemical Kinetics includes :
1. The rate of the reactions and rate laws.
2. The factors as temperature, pressure, concentration and catalyst, that influence
the rate of a reaction.
3. The mechanism or the sequence of steps by which a reaction occurs.
The knowledge of the rate of reactions is very valuable to understand the chemical
of reactions. It is also of great importance in selecting optimum conditions for an
industrial process so that it proceeds at a rate to give maximum yield.
In various reactions, the rates of the two opposing reactions are equal
and the concentrations of reactants or products do not change with lapse of time.
But most chemical reactions are spontaneous reactions. These reactions occur
from left to right till all the reactants are converted to products.
A spontaneous reaction may be slow or it may be fast. For example, the reactions
between aqueous sodium chloride and silver nitrate is a fast reaction.

3. What is Chemical Kinetics?
Chemical kinetics also called reaction kinetics helps us understand the rates of reactions
and how it is influenced by certain conditions. It further helps to gather and analyze the
information about the mechanism of the reaction and define the characteristics of a
chemical reaction.
Rate of Formations and Disappearances
In any chemical reaction, as the reaction proceeds, the amount of reactants decreases,
whereas the amount of products increases. One has to understand that the rate of the
overall reaction depends on the rate at which reactants are consumed or the rate at which
the products are formed.
If a graph is plotted between the
concentration of reactants and
products and time, rate of formation
of products and rate of
disappearance of reactants can be
easily calculated from the slope of
curves for products and reactants.
The overall rate of the reaction may
or may not be equal to the rate of
formations and disappearances.

4. What is Reaction Rate?
The rate of reaction or reaction rate is the speed at which reactants are
converted into products. When we talk about chemical reactions, it is a given fact
that rate at which they occur varies by a great deal. Some chemical reactions
are nearly instantaneous, while others usually take some time to reach the final
equilibrium.
As per the general
definition, the speed with
which a reaction takes
place is referred to as the
rate of a reaction.
For example, wood
combustion has a high
reaction rate since the
process is fast and rusting
of iron has a low reaction
rate as the process is slow.

7. Factors Affecting the Rate of Reaction
The various factions that can affect the rate of a chemical reaction are
listed in this subsection.
Nature of the reaction
1. The rate of reaction highly depends on the type and nature of the reaction.
As mentioned earlier, few reactions are naturally faster than others while
some reactions are very slow.
2. The physical state of reactants, number of reactants, complexity of reaction
and other factors highly influence the reaction rate as well.
3. The rate of reaction is generally slower in liquids when compared to gases
and slower in solids when compared to liquids. Size of the reactant also
matters a lot. The smaller the size of reactant, the faster the reaction.

8. Effect of Substrate/ Reactant concentration
1. According to the collision theory, the rate of reaction increases with the increase in
the concentration of the reactants.
2. As per the law of mass action, the chemical reaction rate is directly proportional to
the concentration of reactants.
3. This implies that the chemical reaction rate increases with the increase in
concentration and decreases with the decrease in the concentration of reactants.
4. Time plays a major role in changing the concentration of reactants and products.
Therefore, even time is a vital factor affecting the reaction rate.
Phase And Surface Area of Reactants
When two or more reactants are in the same phase of fluid, their particles collide more
often than when either or both are in solids phase or when they are in a
heterogeneous mixture.
In a heterogeneous medium, the collision between the particles occurs at an interface
between phase
Compared to the homogeneous case, the number of collisions between reactants per
unit time is significantly reduced, and so is the reaction rate.

9. Temperature
If the temperature is increased, the number of collisions between reactant molecules per
second (frequency of collision). Increases, thereby increasing the rate of the reaction. But
depending on whether the reaction is an endothermic or exothermic increase in temperature
increases the rate of forward or backward reactions respectively.
In a system where more than one reaction is possible, the same reactants can produce
different products under different temperature condition.
At 100 0C in the presence of dilute sulphuric acid, diethyl ether is formed from ethanol.
2CH3CH2OH → CH3CH2OCH2CH3+H2O
At 180 0C in the presence of dilute sulphuric acid, ethylene is the major product.
CH3CH2OH → C2H4+H2O

10. How does temperature affect the reaction rate?
1. According to collision theory, a chemical reaction that takes place at a
higher temperature generates more energy than a reaction at a lower
temperature.
2. This is because colliding particles will have the required activation energy
at high temperature and more successful collisions will take place.
3. There are some reactions that are independent of temperature. Reactions
without an activation barrier are examples of chemical reactions that are
independent of temperature.
It has been observed experimentally that a rise of 10 °C in temperature usually
doubles or triples the speed of a reaction between molecules. The minimum
energy needed for a reaction to proceed, known as the activation energy, stays the
same with increasing temperature. However, the average increase in particle
kinetic energy caused by the absorbed heat means that a greater proportion of the
reactant molecules now have the minimum energy necessary to collide and react.
An increase in temperature causes a rise in the energy levels of the molecules
involved in the reaction, so the rate of the reaction increases. Similarly, the rate of
reaction will decrease with a decrease in temperature.

12. Pressure Effects
1. Pressure increases the concentration of gases which in turn results in the
increase of the rate of reaction. The reaction rate increases in the direction
of less gaseous molecules and decreases in the reverse direction.
2. Thus, it can be understood that pressure and concentration are interlinked
and that they both affect the rate of reaction.
Increasing the pressure for a reaction involving gases will increase the rate
of reaction. As you increase the pressure of a gas, you decrease its volume
(PV=nRT; P and V are inversely related), while the number of particles (n)
remains unchanged. Therefore, increasing pressure increases the
concentration of the gas (n/V), and ensures that the gas molecules collide
more frequently. Keep in mind this logic only works for gases, which are
highly compressible; changing the pressure for a reaction that involves only
solids or liquids has no effect on the reaction rate.

13. Catalysts are substances that increase reaction rate by lowering the
activation energy needed for the reaction to occur. A catalyst is not destroyed
or changed during a reaction, so it can be used again. For example, at
ordinary conditions, H2 and O2 do not combine. However, they do combine in
the presence of a small quantity of platinum, which acts as a catalyst, and the
reaction then occurs rapidly.
Presence of Catalyst
1. A catalyst can be defined as a substance that increases the rate of the
reaction without actually participating in the reaction. The definition itself
describes its effect on chemical reactions.
2. The presence of a catalyst increases the speed of reaction in both forward
and reverse reaction by providing an alternate pathway which has lower
activation energy.

15. Solvent
The rate of reaction also depends on the type of solvent. Properties of
solvent and ionic strength highly affect the reaction rate.
Electromagnetic Radiation
Electromagnetic radiation is a form of energy and its presence at the chemical
reaction may increase the rate of reaction as it gives the particles of reactants
more energy.
Intensity of Light
Even the intensity of light affects the rate of reaction. Particles absorb more
energy with the increase in the intensity of light thereby increasing the rate of
reaction.

34. Mean life
Radioactive atoms disintegrate spontaneously and it is not possible to predict
which atom is going to disintegrate next. So, in order to deal this type of
difficulty calculation mean life or average life of radioactive substance is
introduced.
The atom which disintegrates at first is said to have zero (0) life and the atom
which disintegrate last is said to have infinite life.
SO the life of radioactive atoms ranges from 0-infinity mean life gives the sum
of the life of all the atoms to the total no. of atoms present initially.
Mathematically, it can be expressed as:
Mean life (τ) = sum of life of all atom / total no of atoms present
Mathematical calculation shows that mean life of radioactive substance is
reciprocal of decay constant,
Mean life = 1/ decay constant

35. Derivation of mean life:
Let us consider, N0 be the total number of
radioactive atoms present initially. After
time t , total no. of atoms present
(undecayed) be N . IN further dt time dN
be the no. of atoms disintegrated. So, the
life of dN atoms ranges lies between t + dt
and dt. Since, dt is very small time, the
most appropriate life of dN atom is t . So
the total life of N atom = t. dN
Now substituting the value of dN
and changing the limit in equation i
from ii we get

36. DIFFERENTIAL METHOD

37. METHOD OF INTEGRATION

39. METHOD OF HALF LIFE PERIOD

40. ISOLATION METHOD/ Ostwald’s Isolation method

41. Radioactive Decay Kinetics
Radioactivity, or radioactive decay, is the emission of a particle or a photon that results
from the spontaneous decomposition of the unstable nucleus of an atom. The rate of
radioactive decay is an intrinsic property of each radioactive isotope that is independent
of the chemical and physical form of the radioactive isotope. The rate is also
independent of temperature.
In any sample of a given radioactive substance, the number of atoms of the radioactive
isotope must decrease with time as their nuclei decay to nuclei of a more stable isotope.
Using N to represent the number of atoms of the radioactive isotope, we can define
the rate of decay of the sample, which is also called its activity (A) as the decrease in the
number of the radioisotope’s nuclei per unit time:
A=−ΔN/Δt……………………(14.5.4)
Activity is usually measured in disintegrations per second (dps) or disintegrations per
minute (dpm).
Radioactive decay reactions are first-order reactions. The rate of decay, or activity,
of a sample of a radioactive substance is the decrease in the number of radioactive
nuclei per unit time. In radioactive decay the number of radioactive atoms decaying
per unit time is proportional to the total number of radioactive atoms present at that
time, i.e. Since the decay rate is proportional to first power of radioactive atoms
present, therefore, radioactive decay is a first order kinetics

42. The activity of a sample is directly proportional to the number of atoms of the radioactive
isotope in the sample:
A=kN………………………………….(14.5.5)
Here, the symbol k is the radioactive decay constant, which has units of inverse time (e.g.,
s−1, yr−1) and a characteristic value for each radioactive isotope. If we combine Equation
14.5.4 and Equation 14.5.6 we obtain the relationship between the number of decays per
unit time and the number of atoms of the isotope in a sample:
−ΔN/Δt=kN…………………………………(14.5.6)
Equation 14.5.6 is the same as the equation for the reaction rate of a first-order reaction
(Equation 14.3.5), except that it uses numbers of atoms instead of concentrations. In fact,
radioactive decay is a first-order process and can be described in terms of either the
differential rate law (Equation 14.4.7) or the integrated rate law:
N=N0e−kt………………………………….(14.5.7)
In N/ N0= −kt………………………………….(14.5.8)
Because radioactive decay is a first-order process, the time required for half of the nuclei in
any sample of a radioactive isotope to decay is a constant, called the half-life of the
isotope. The half-life tells us how radioactive an isotope is (the number of decays per unit
time); thus it is the most commonly cited property of any radioisotope. For a given number
of atoms, isotopes with shorter half-lives decay more rapidly, undergoing a greater number
of radioactive decays per unit time than do isotopes with longer half-lives.

44. Summery : Radioactive decay as a first order phenomenon