Chemical Kinetics
For a chemical reactions
(a) the feasibility of a chemical reaction which can be predicted by thermodynamics ( as you
know that a reaction with ΔG < 0, at constant temperature and pressure is feasible);
(b) extent to which a reaction will proceed can be determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to reach equilibrium
The word kinetics is derived from the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a reaction whereas chemical kinetics tells
about the rate of a reaction.
Branch of physical chemistry which deals with the study of rate of reactions, the mechanism
by which the reactions proceed and factors affecting rate of reaction
Q) When 0.3 mole of A are heated in a 5litre vessel for 10 minutes, then 0.18 mole of A changes
into B according to the reaction A→ B . Find out rate of reaction in mol/Ls
Q) Reaction 2A → 3C+ B . Initial concentration of A is 10mol/L and after 10 minute its
concentration is 4 mol/L . Find out a) Rate of reaction
b) Rate of formation of C
Q) 2A+ 3B → 4C + D . If rate of disappearance of B is 0.006 mol/Ls . Find out a) Rate of reaction
b) Rate of disappearance of A
c) Rate of formation of C
Example 4.2
Intext 4.1
Intext 4.2
Q) Rate of formation of SO3 according to the reaction is 1.6*10-3 kg/min . Find out rate of
disappearance of SO2 in kg/min
Q) The rate of a reaction is expressed as
The reaction is
Rate Law and Order Of Reaction
The rate of a chemical reaction at a given temperature may depend on the
concentration of one or more reactants and products. The representation of rate of
reaction in terms of concentration of the reactants is known as rate law. It is also called
as rate equation or rate expression.
The sum of powers of the concentration of the reactants in the rate law expression is
called the order of that chemical reaction.
For a reaction,
x and y are called order of the reaction with respect to A and B respectively. These are
experimentally determined terms.
Thus, rate law is the expression in which reaction rate is given in terms of molar
concentration of reactants with each term raised to some power, which may or may not
be same as the stoichiometric coefficient of the reacting species in a balanced chemical
equation.
If [A] = [B] =1 mol/L, then Rate = K
Rate of reaction at unit concentration of reactants is called rate constant of the reaction or
specific reaction rate
The unit of this constant depends on the overall order of the reaction which is defined as the
sum of all individual orders
Order may or may not be equal to the stoichiometric coefficients
Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero order reaction means that the
rate of reaction is independent of the concentration of reactants
Rate constant does not depend on concentration of reactant but it depends on temperature
and catalyst
Unit of Rate Constant
Order Unit Of K
Zero order Reaction
First order Reaction
Second order reaction
Example 4.3) Calculate the overall order of a reaction which has the rate expression
(a) Rate = k [A]1/2 [B]3/2 (b) Rate = k [A]3/2 [B]–1
Example 4.4) Identify the reaction order from each of the following rate constants.
(i) k = 2.3 × 10–5 Lmol–1s–1
(ii) k = 3 × 10–4 s–1
I
N
T
E
X
T
Q)
Order of reaction wrt A is 2 and wrt B is -1. Write rate law expression and calculate order of
reaction. What is the effect when (i) Concentration of A is doubled
(ii) Concentration of Bis halved
(iii) Concentration of A and B is doubled
(iv) Volume of container increases 4 times
Q)
When concentration of A is doubled, ROR increases 2 times , When concentration of A and B
both doubled, ROR increases 8 times. Write rate law expression and find order of reaction
Q) A+2B + 4C → P
Volume of container is doubled , ROR decreases 8 times
When [A] is doubled, [B] is halved, ROR increases 4 times
When [C] increases 4 times alone , ROR increases 64 times
Find out rate law expression and rate of reaction
Molecularity Of a Reaction
The number of reacting species (atoms, ions or molecules) taking part in an elementary
reaction, which must collide simultaneously in order to bring about a chemical reaction is called
molecularity of a reaction.
Molecularity only defined for elementary reactions
The reactions taking place in one step are called simple/elementary reactions. When a
sequence of elementary reactions (called mechanism) gives us the products, the reactions are
called complex reactions
The reaction can be unimolecular, bimolecular reactions, trimolecular or termolecular based on
reacting species involved
Unimolecular, decomposition of ammonium nitrite
Bimolecular, dissociation of hydrogen iodide
Termolecular,
Molecularity is always in positive whole number
Reactions with the molecularity three are very rare and slow to proceed. The probability
that more than three molecules can collide and react simultaneously is very small
Ex→
This reaction is a second order reaction not a tenth order reaction. This reaction takes
place in several steps
The overall rate of the reaction is controlled by the slowest step in a reaction called the
rate determining step
Ex → Decomposition of hydrogen peroxide catalysed by iodide ion in an alkaline medium.
First order reaction with respect to both H2O2 and I– . Reaction takes place in two steps
Both the steps are bimolecular elementary reactions. IO- is an intermediate formed during the
reaction but not in the overall balanced equation. ( I- is a catalyst)
The first step is the rate determining step. Rate of formation of intermediate will determine the
rate of this reaction.
(i) Order of a reaction is an experimental quantity. It can be zero and even a fraction and
negative but molecularity is a theoretical quantity cannot be zero or a non integer.
(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is
applicable only for elementary reactions. For complex reaction molecularity has no meaning.
(iii) For complex reaction, order is given by the slowest step and molecularity of the slowest step
is same as the order of the overall reaction. Molecularity is defined for each step in complex
reaction
• Stoichiometric coefficients may or may not relate with order of reaction
• In rate law concentration of products can be present
• In rate law concentration of reactant may be absent
• In rate law, concentration of catalyst may be present
For zero order reaction, unitary method is applied for time calculation
Q) For reaction A→ P , zero order. If time taken for 50% completion is 2minute .
a) Find time required for 75% completion of reaction
b) Find out time required for 33.3% completion of the reaction
Q) For 10% completion of a reaction time required is t . Find out time required for 80%
completion of a reaction.
Q) The rate constant for a zero order reaction is 3*10-2 molL-1 s-1 . If the concentration of
reactant after 25 second is 0.5M, then find out initial concentration of reactant
Q) The volume of a drop of a solution is 0.05ml and in it 3*10-6 moles H+ ions are present . If
rate constant for disappearance reaction of H+ is 10-7 mol/Ls . Then how much time is required
for complete disappearance of H+
Q) 3.4g NH3 is heated in 100mL vessel in presence of Molybdenum. The value of rate constant
is 10-2 mol/Ls. Then find out time period for 40% dissociation of NH3
Special Zero Order Kinetics
Ex→ Initial concentration of reactant is A0. Find concentration of A after time t
and half life time. Rate = K[A]0
Q)
2) First order Reaction
b) Integrated Rate equation
c) Graphs
Half life time
Examples
1) All natural and artificial radioactive decay of unstable nuclei
2)
3) Acidic hydrolysis of ester
4) Inversion of Cane Sugar
5) Dissociation
Pseudo First Order Reaction
Q) A first order reaction ,the concentration of reactant decreases from 800mol/dm3 to
50mol/dm3in 2*10-4 s. Find rate constant ,K
Q) A first order reaction is 20% complete in 5 minute . Find the time period in which 60% of
reaction will complete
a) 10 minutes b) 20 minutes c) 30 minutes d) 40 minutes
Q) A→ P follows first order kinetics.
The concentration of A changes from 0.1M to 0.025M in 40 minutes. Find the rate of reaction
when concentration of A is 0.01 M
Q) Calculate the two-third life period of a first order reaction having rate constant
6* 10-12 sec-1
Q) If a graph is plotted between log (a-x) v/s t , Then slope of straight line is equal
to -0.03 . Find out specific rate of reaction
Q) For a first order reaction, c
1) t1/2
2) t1/3
3) t2/3
4) t3/4
Q) In a first order reaction, the A0/At = 8 after 60 minutes . Calculate rate of
reaction in molL-1min-1 when concentration of reactant is 0.1M
Q) 99% of a first order reaction completes in 32 minutes , find out time for
completion of 99.99% of the reaction
Q) Decomposition of SO2Cl2 follows first order kinetics
Value of K is 2.303*10-2 sec-1 .Find out % of SO2Cl2 decomposition on heating for
100 second
Q) Ethylene is produced according to the reaction
Value of K is 2.303*10-4sec-1 . In what time molar ratio of ethylene: cyclobutene in
the reaction will attain value 1
Q) A radioactive substance decay 20% in 10 minutes . If initial 5*1020 atoms are
present, then after what time number of atoms will be reduced to 1018
Q) Two first order reaction have half life in the ratio of 3:2 . Then calculate the
ratio of time interval t1/t2 where t1 is time period for 50% completion of first
reaction and t2 is the time period for 75% completion of second reaction
Q) Reaction 2N2O5 → 4NO2 + O2 . Value of rate constant is 2.303*10-3 s-1 . If initial pressure of
N2O5 is 0.1 atm and total pressure of mixture after time t is 0.16 atm . Find out time t
Q) A substance reacts according to first order kinetics and value of rate constant is 10-2s-1 . If
initial concentration of reactant is 1M . Find out rate of reaction after 1 minute
Q) AsH3 dissociate according to the reaction
The value of rate constant is 1.15* 10-2 s-1 and initial pressure of AsH3 is 2atm . Then after what
time total pressure of mixture will become 2.5 atm
3) Second Order Reaction
Half Life Time
Q) In a second order reaction, initial concentration of both reactant is same. If
time for 20% completion of reaction is 500 seconds, then find out time for 60%
completion of reaction
Q) In a second order reaction, initial concentration of both reactant is same. If
time period for one fourth completion of reaction is 100 second. Find out time for
two third reaction completion
Q) Reactant A → B by first order reaction having rate constant 0.692*10-2min-1.
Reactant A→ Y by second order reaction in presence of catalyst having rate
constant 0.2 mol-1Ls-1 . If half life of both reaction is same, find out initial
concentration of reactant
4) Third Order Reaction
Half life time
nth Order Reaction
Methods To determine Rate of Reaction
1) Initial Rate Data Method
2) Half Life Method
Q) Half Life of decomposition of a compound is 20 minutes, when its initial concentration is
double half life reduces to 10 minute . Find order of reaction
Q) For a gaseous reaction, the initial pressure and half life data is shown . Find order of reaction
Pressure (mm of Hg) Half Life Time(minutes)
100 105
66 235
33 950
Q) Inversion of cane sugar proceeds with constant half life of 500 minutes at pH =5 for any
concentration of cane sugar. If pH =6, then half life changes to 50 minute. Find out value of m and
n in the following rate expression Rate = K [ Canesugar]m[H+]n
Q) Half Life period of a half order reaction is t1/2 . Find x
Q)For a given reaction, concentration of reactant and half life time data is given. Find out order of
reaction [A](mol/L) t1/2 (MIN)
600 80
400 80.5
100 80
3) Graphical Method
4) Integrated Rate Law Method
Hit and Trial Method
First use first order integrated rate equation and calculate value of K , then zero order, second
order,…..we can find value of K based on that order can be predicted
Q) The decomposition of azomethane shows following data
Pressure(mm of Hg) 280 250 220 180
Time(minute) 0 50 100 150
Factors affecting Rate of Reaction
1) Nature of Reactants
a) Physical State → Solid < Liquid < Gas
b) For ionic reactants , high ROR
For molecular reactants , moderate ROR
c) Homogenous reactant > Heterogenous Reactant
d) Surface area of Reactant → More surface area → more rate
e) ROR Stability of product 1/ Stability of reactant
2) Catalyst
• Substance which increases the rate of a reaction without itself
undergoing any permanent chemical change.
• A catalyst participates in a chemical reaction by forming temporary
bonds with the reactants resulting in an intermediate complex.
This has a transitory existence and decomposes to yield products and the catalyst.
• Increase the ROR by providing an alternate path by reducing the activation energy between
reactants and products and hence lowering the potential energy barrier
• If the added substance reduces the rate of reaction, then substance is called inhibitor.
A catalyst does not alter Gibbs energy, ∆G of a reaction.
It catalyses the spontaneous reactions but does not catalyse non-spontaneous reactions.
It is also found that a catalyst does not change the equilibrium constant of a reaction rather, it
helps in attaining the equilibrium faster, that is, it catalyses the forward as well as the backward
reactions to the same extent so that the equilibrium state remains same but is reached earlier.
3) Intensity of Light→ For photochemical reaction, Rate of reaction increase on increasing
intensity of light
4) Concentration of reactant → May increase or same or decrease based on the order of
reaction
5) Pressure→ For gaseous reactants , rate of reaction increases on increasing Pressure because
number of effective collision increases.
6) Temperature
Most of the chemical reactions are accelerated by increase in temperature whether the reaction
is endothermic or exothermic.
Temperature Coefficient
Ratio of rate constant of a reaction at different temperature (differ by 100 C)
For a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.
(Range =2-3)
Q) At 250 C rate of two reaction is same , if temperature coefficient of first reaction is 2 and second
reaction is 3, find out ratio of rate of the first reaction and second reaction at 750 C
Q) For a rection A→ P, temperature coefficient is 2, if rate of reaction at 200 C is r, Then find out rate
at 600 C
Collision Theory
According to this theory, the reactant molecules are assumed to be hard spheres and for a
reaction to occur there must be collisions in between reacting molecules. It is based on kinetic
theory of gases.
The number of collisions per second per unit volume of the reaction mixture is known as
collision frequency (Z).
All collisions do not lead to the formation of products. The collisions in which molecules collide
with (a)sufficient kinetic energy (activation energy) and (b)proper orientation(steric factor), to
form products are called as effective collisions
To account for effective collisions, another factor P, called the probability or steric factor is
introduced.
b) Orientation
Maxwell and Boltzman Energy Distribution Curve
All the molecules in the reacting species do not have the same kinetic energy. It is difficult to predict
the behaviour of any one molecule with precision, therefore distribution of kinetic energy may be
described by plotting the fraction of molecules (NE/NT) with a given kinetic energy (E) vs kinetic
energy
NE is the number of molecules with energy E and NT is total number of molecules.
The peak of the curve corresponds to the most probable kinetic energy, i.e., kinetic energy of
maximum fraction of molecules. There are decreasing number of molecules with energies higher
or lower than this value.
Distribution curve showing energies among gaseous molecules Distribution curve showing temperature dependence of rate of a reaction
Fraction of molecules which cross energy barrier = e –Ea/RT Rate e –Ea/RT
Arrhenious Equation
A is the Arrhenius factor or the frequency factor, pre-exponential factor( specific to a particular reaction)
R is gas constant , Ea is activation energy, T is temperature in Kelvin
→At temp T1 , rate constant is K1 and
at temp T2, rate constant is K2
Q) A first order reaction completes 50% in 30 minute at 27C and in 10 minutes at 47C.
Calculate activation energy in KJ/mol
Differential Form Of Arrhenious equation
Q) A hydrogenation reaction is carried out at 500K . If same reaction is carried out in presence of
catalyst at the same rate temperature required is 400K. Calculate Ea if catalyst lowers the
activation energy by 20 KJ/mol
I
N
T
E
X
T
Q) For nth order reaction , frequency factor is 100 and Ea = 19KJ/mol. Find rate constant at
1000 K
Q) For a first order reaction, the rate constant is given as
Find out temperature at which half life of reaction is 70 minutes
Q) A reaction takes place in 3 steps with rate constant K1, K2, K3 and overall rate constant is
(K3K1)/K2. If Ea1 , Ea2, Ea3 are 60, 30, 10 KJ/mol. Find out overall Ea
Reactions for which rate decrease on increase in T
1) Bacterial decomposition→ First increase and then decrease on increasing temperature
(not work at very high and very low temp)
2) Oxidation of NO
Elementary and Complex Reactions
Mechanism with initial slow step
Q)
A)What is the overall reaction?
B) Identify the intermediates in the mechanism.
C) What is the predicted rate law
Mechanism with initial fast step
A)What is the overall reaction?
B) Identify the intermediates in the mechanism.
C) What is the predicted rate law
Parallel Reaction/Side Reaction
2) Consecutive Reaction
3) Reversible Reaction
