15_chemical-kinetics (chemistry).pptx

CHEMICAL
KINETICS
Chemistry for Industrial Technologist

The branch of chemistry, which deals with the
study of reaction rates and their mechanisms,
called chemical kinetics.
Thermodynamics tells only about the feasibility
of a reaction whereas chemical kinetics tells
about the rate of a reaction.
For example, thermodynamic data indicate that
diamond shall convert to graphite but in reality
the conversion rate is so slow that the change is
not perceptible at all.
Chemical Kinetics

Kinetic studies not only help us to determine
the speed or rate of a chemical reaction but
also describe the conditions by which the
reaction rates can be altered.
The factors such as concentration,
temperature, pressure and catalyst affect the
rate of a reaction.
Chemical Kinetics

The speed of a reaction or the rate of a
reaction can be defined as the change in
concentration of a reactant or product in unit
time. It can be expressed in terms of:
(i) the rate of decrease in concentration of any
one of the reactants, or
(ii) the rate of increase in concentration of any
one of the products.
Rate of a Chemical Reaction

Consider a hypothetical reaction, assuming that the
volume of the system remains constant
R P
→
One mole of the reactant R produces one mole of the
product P. If [R]1 and [P]1 are the concentrations of R
and respectively at time t1and [R]2 and [P]2 are their
concentrations at time t2 then,
Δt = t2 – t1
Δ[R] = [R]2 – [R]1 Δ [P] = [P]2 – [P]1
&
The square brackets in the above expressions are used to express
molar concentration.

• Rate of disappearance of R
= Decrease in concentration of R = − Δ [R]
Time taken Δt
Rate of appearance of P
= Increase in concentration of P = + Δ [P]
Time taken Δ t
Since, [R] is a negative quantity (as concentration of reactants is
Δ
decreasing), it is multiplied with –1 to make the rate of the reaction
a positive quantity.

2 Fe3+
(aq) + Sn2+
→ 2 Fe2+
(aq) +Sn4+
(aq)
t = 38.5 s [Fe2+
] = 0.0010 M
Δt = 38.5 s Δ[Fe2+
] = (0.0010 – 0) M
Rate of formation of Fe2+
= = = 2.6x10-5
M s-
Δ[Fe2+
]
Δt
0.0010 M
38.5 s
Consider the following chemical reaction -

Δ[Sn4+
]
Δt
2 Fe3+
(aq) + Sn2+
2 Fe
→ 2+
(aq) + Sn4+
(aq)
Δ[Fe2+
]
Δt
=
1
2
Δ[Fe3+
]
Δt
= -
1
2

a A + b B → c C + d D
Rate of reaction = rate of disappearance of reactants
=
Δ[C]
Δt
1
c
=
Δ[D]
Δt
1
d
Δ[A]
Δt
1
a
= -
Δ[B]
Δt
1
b
= -
= rate of appearance of products
Δ[A]
Δt
1
a
= -
Δ[B]
Δt
1
b
-
=
Δ[C]
Δt
1
c
=
Δ[D]
Δt
1
d
or
Eqn.1
Eqn.2
Eqn.3
General Rate of Reaction

Average rate depends upon the change in conc. of
reactants or products and the time taken for that change
to occur.
Equations 1-3 represent the average rate of a reaction,
rav.
The rate of reaction at a particular moment of
time is called as the instantaneous rate, rins.
It is obtained when we consider the average rate at the
smallest time interval say dt ( i.e. when Δt approaches zero).
Average rate & Instantaneous rate

Mathematically for an infinitesimally small time
interval, dt, instantaneous rate is given by –
rav = −Δ[R ] = Δ[P ]
Δt Δt
As Δt 0
→ or
rins. = - d[R] = d[P]
dt dt
Unit of rate of reaction:– mol L-1
s-1

H2O2(aq) H
→ 2O(l) + ½ O2(g)
-(-1.7 M / 2600 s) =
6 x 10-4
M s-1
-(-2.32 M / 1360 s) = 1.7 x 10-3
M s-1
Rate =
-Δ[H2O2]
Δt
Initial rate ,Average rate over a time period. Instantaneous rate – slope of
tangent lin.

Factors affecting the Rate of a
Chemical Reaction
1-Nature of reactant : Ionic substance react much faster
than covalent substances.
2-Concencentration of Reactants : Rate of reaction is
directly proportional to conc. of reactants (partial
pressure in case of gaseous - phase reactions).
3-Temperature : Rate of reaction increases with increase
in temperature.
4-Presence of Catalyst : A catalyst alters the Rate of a
reaction.
5-Surface Area of the Reactants: Rate of rean. surface
∝
area.
6- Radiations

• The expression which relates of rate of
reaction to concentration of the
reactants is known as rate law. It is also
called as rate equation or rate expression.
• Consider a general reaction
aA + bB cC + dD
→
• where a, b, c and d are the
stoichiometric coefficients of reactants
and products.
Rate Law or Rate Expression and
Rate Constant

• The rate expression for this reaction is -
• where exponents x and y may or may not be
equal to the stoichiometric coefficients (a and
b) of the reactants.
Rate of reaction ∝ [A]x
[B]y
or eqn.4
Rate of reaction = k [A]x
[B]y
eqn.5
Rate Constant

d[R]
dt
= k[A]x
[B]y
Rate Constant
Equation 5 can also be written as-
eqn.6
This form(eq.6) of equation (5) is known as
differential rate equation, where k is a
proportionality constant called rate constant or
velocity constant or specific reaction rate.

Rate Constant
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.
Note:Rate law for any reaction cannot be
predicted by merely looking at the balanced
chemical equation, i.e., theoretically but must be
determined experimentally.

• Rate Constant (k) : For a general reaction
aA + bB cC + dD
→
Where k is known as rate constant
When [A] = [B] = 1 mol/L, than
thus rate constant of a chemical reaction may be defined
as the reaction rate when the
concentration of each reactant is unity.
Rate of reaction = k [A]x
[B]y
Rate of reaction = k
Rate Constant

Rate Constant
The value of rate constant is definite and constant for
a particular reaction at given temperature.
Rate constant is independent of concentration of
reactants it depends only upon temperature and
presence of catalyst.

Order of a Reaction
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 general reaction
aA + bB cC + dD
→
Let Rate of reaction = k [A]x
[B]y
Here ,
x = order of reaction w.r.t.A
y = order of reaction w.r.t. B
Overall order of reaction(n) = x + y

Examples of observed rate laws for some reactions follow.
Order of a Reaction

 Order of a reaction can be 0, 1, 2, 3 and even a
fraction.
 Depending upon order of reaction, reactions are
termed as zero, first or second order reactions.
 A zero order reaction means that the rate of
reaction is independent of the concentration of
reactants.
 Order of reaction cannot be predicted by merely
looking at the balanced chemical equation, i.e.,
theoretically but must be determined
experimentally.
Order of a Reaction

For a nth
order reaction- A Product
→
Rate = k [A]n
a
Rate
k =
[A]n
=
concentration
time
x
(concentration)n
1
= (concentration)1-n
time-1
k
Order of a Reaction & Units
of Rate Constant

1.
2.
3.
Practice Problems
For the reaction
A + B Products
The following initial rates were obtained at various given
intial concentrations
S. No [A] [B] Rate (mol lt–1
sec–1
)
1. 0.1 0.1 0.05
2. 0.2 0.1 0.10
3. 0.1 0.2 0.05
Write rate law and find the rate constant of the above
reaction.
 


Elementary reactions are those which complete is one
step while complex reactions are multistep reactions
where products are obtained after completion of a
sequence of elementary reactions.
e.g. (a) Elementary reaction
(b) Complex reaction
Elementary & complex reactions

Molecularity of a reaction is simply the
number of reacting species (atoms, ions or
molecules) involving is an elementary
reaction which must collide simultaneously.
Let us consider the following reactions,
Molecularity of a Reaction

Ans:- Since the chances of collision and
reaction of more than three molecules at
a time are very less, the molecularity
greater than three is rare.
Q.Why the reactions having molecularity
greater than three is rare ?

Molecularity in case of complex reactions?
Molecularity of a complex reaction has no
meaning. Actually a complex reaction is the
series of two or more elementary reactions and
thus, it completes in several steps. The slowest
step or slowest reaction determines the rate of
the reaction. Hence we find out the
molecularity of the slowest elementary reaction
of a complex reaction which is, in general,
similar to the overall order of the complex
reaction.

Order of reaction is for overall
reaction.
The overall molecularity of complex
reaction has no significance. Individual
step has its own molecularity.
It can even have fractional values.
It is always a whole number.
It is determined experimentally.
It is a theoretical concept.
Order of reaction can be zero.
Molecularity of reaction
Cannot be zero.
It is the sum of the power of
concentration terms on which the rate
of reaction actually depends or it is the
sum of powers of the concentration
terms in the rate law equation.
It is the number of atoms, ions or
molecules that must collide with one
another simultaneously so as to result
into a chemical
reaction.
Order of Reaction
Molecularity of Reaction
Molecularity vs. Order

Integrated Rate Equations
Zero Order Reactions
Zero order reaction means that the rate of the
reaction is proportional to zero power of the
concentration of reactants. Consider the reaction,
R P
→

First Order Reactions
First order reaction means that the rate of the
reaction is proportional to first power of the
concentration of reactants. Consider the reaction,
R P
→

1.The thermal decomposition of HCOOH is a first order
reaction with a rate constant of 2.4 x 10 3
─
s 1
─
at a certain
temperature. Calculate how long will it take for three-
fourth (3/4) of initial quantity of HCOOH to decompose ?
(log 0.25 = 0.6021 )
− [2011]
2.A first order reaction has a rate constant of 0.0051 min 1
─
. If we begin with 0.10 M conc. of the reactant, how much
conc. of the reactant will remain is solution after 3 hrs?
[2011,09]
3.The rate constant for a reaction of Zero order in A is
0.0030 mol L 1
─
s 1
─
. How long will it take for the initial
conc. of A to fall from 0.10 M to .075 M ?
[2010]

The half-life of a reaction is the time in which the
concentration of a reactant is reduced to one half of its
initial concentration. It is represented as t1/2
Half-Life of a Reaction
t1/2 for a Zero Order Reactions

t1/2 for a First Order Reactions
Thus for a first
order reaction, half-
life period is
constant, i.e., it is
independent of
initial concentration
of the reacting
species.

Practice Problems
1.A first order reaction takes 40 minutes for 30 %
completion . calculate its t1/2 value. (2008,13)
2.The decomposition of phosphine PH3 . Proceeds acc. to
following eqn:
4 PH3 (g) ---> P4(g) + 6H2 (g) ;
It is found that he reaction follows the following rate
equation:
Rate = K [PH3] ;
The half lite of PH3 is 37.9 S at 1200
C
(a) How much time is required of 3/4th
of PH3 to
decompose ?
(2) What fraction of original sample of PH3 remains behind
after 1 minute ?
(2010,09)

Pseudo - first order reaction
Reactions which are not truly of the first order but under
certain conditions reactions become that of first order are
called pseudo unimolecular reaction.
For example: Hydrolysis of ester in presence of acid
CH3COOC2H5 + H2O  CH3COOH + C2H5OH
From this reaction, the rate expression should be
r = k [ester] [H2O]
Since, hydrolysis takes place in the excess of H2O and
concentration change of H2O is negligible practically.
therefore, r = k’ [ester]
Where k’ = k[H2O].

Methods of determining the order of a reaction
Integrated method
The equation which gives a constant value of k decides
the order of reaction
Graphical method
The data are plotted acc to different integrated rate
equations so as to yield a straight line .Slope gives the
value of rate constant
Initial rate method
Concentration of one of the reactant is varied
Half life method
In this method we plot half life of the reactant versus
conc. of the reactant.

Methods of determining the order of a reaction
L mole-1
sec-1
k
1/[A] vs t
Second
sec-1
-k
In[A] vs t
[A]=[Ao]e-kt
First
Mole l-1
sec-1
-k
[A] vs t
[A]=[Ao]-kt
Zero
Units of rate
constant
Slope
of
kinetic
s plot
Characteristic
kinetics Plot
Integrated rate
law
Differential
rate law
Reaction
Order
d[A]
k
dt


d[A]
k[A]
dt


2
d[A]
k[A]
dt


[Ao]
A
1 k [A]

 

Conc.
zero order
dx
dt
Conc.
first order
dx
dt
(Conc.)
second order
2
dx
dt
Graphical representation of rate versus concentrations
Graphical Representation

Conc. [A]
t
log [A]
t t
1/ [A]
Graphical representation for concentration of integrated rate equation versus time
zero order first order second order
Graphical Representation

Initial rate method
• This method involves the determination of the order
of each reactant separately.
• To determine the order of a particular reactant, its
concentration is varied keeping the concentrations of
other reactants constant.
• In every experiment, we determine the initial rate of
the reaction and observe the dependence of rate on
that particular reactant.
 m n
r [A] [B]
 
 
 
m
m n
1 1 1 1
m n
2 2 2 2
r [A ] [B] r [A ]
= ; =
r [A ] [B] r [A ]
Keeping [B] constant

Illustrative Example
Rate of the reaction;A + B = products; is given below as a
function of the initial concentration of ‘A’ and ‘B’.
[A](mol L-1
) [B](mol L-1
) rate(mol L-1
min-1
)
0.01 0.01 0.005
0.02 0.01 0.010
0.01 0.02 0.005
Determine the order of the reaction with respect to ‘A’ and ‘B’.
Solution:
For first two experiments, the concentration of the reactant ‘B’ is
constant.
Rate of the reaction depend linearly on reactant ‘A’.
Now, taking experiments first and third, the concentration of the
reactant ‘A’ is constant.
Therefore, rate of the reaction is independent of ‘B’.
Thus, order of the reaction with respect to ‘A’ = one.
Order of the reaction with respect to ‘B’ = zero.

Half life method
1/2 n 1
0
1
t
[A] 

Graphical representation for half lives versus concentration
t1/2
a
z e r o o r d e r
1 / a
s e c o n d o r d e r
t1/2 t1/2
a
f ir s t o r d e r

The half-life of a particular chemical reaction at two
different initial concentrations 5 x 10-4
and 25 x10-5
M are
2 and 16 hours. Calculate the order of reaction.
 
 
n 1
0
1 /2 2 1
1 /2 1
0 2
A
(t )
(t ) A

 
 
 
 
  
 
 
 
 
n 1
4
n 1
5
16 5 10
(2)
2 25 10




 

  
 
 

 
Solution:
n-1
8 = (2)
n - 1 =3
n = 4




Integrated method
In this method, we put the data into the integrated form
of the rate laws and calculate the values of the rate
constants for different kinetics of the reaction.
The order of the reaction is that one for which the value
of rate constant is constant.

Some first order reactions
Decomposition of H2O2
2 2 2 2
1
H O H O O
2
 
Let Vo & Vt be volume of KMnO4 used during zero
& time t respectively
t
o
t
V a
V a x
V
2.303
k log
t V

 


Some first order reactions
Hydrolysis of ester
H
3 2 5 2 3 2 5
CH COOC H H O CH COOH C H OH
a 0 0
a x x x
0 a a

  



 
 
O
t
V HCl
V HCl x
V HCl a


  

t
V V a x
V a
o
t
V V
2.303
k log
t V V





LetV0 , Vt be the volume of alkali required for titration
during 0 ,t & infinite time
V

Theories of chemical kinetics
1. Collision theory
2.Transition state theory

Collision theory
Reaction occurs when reacting species have sufficient
energy to collide and proper orientation in space.
Energy barrier:
The minimum energy which the colliding particles
possess in order to bring about the chemical reaction is
called threshold energy
The energy difference between threshold energy &
average energy of reacting molecules is called activation
energy
Orientation barrier:
Colliding molecules should be in their proper orientation
at the time of collision.

Transition State Theory
In the activated complex theory, we consider two
reactants approaching and their potential energy rising
and reaching a maximum.
a a
H E E `
  
Activation energy - the energy needed to form activated
complex is called energy of activation. It is very low for
some reactions and very high for others.

Some Points about Ea
1. Ea is always positive.
2. The larger the value of Ea, the slower the rate of a
reaction at a given temperature.
3. The larger the value of Ea, the steeper the slope of (ln
k) vs (1/T). A high activation energy corresponds to a
reaction rate that is very sensitive to temperature.

Effect of temperature on rate of chemical
reaction
For a chemical reaction with rise in temperature
by 10°, the rate constant is nearly doubled
The ratio is called the
temperature coefficient and its value is 2 or 3
k(T+10)
kT

A is frequency factor or Arhenius constant, Ea is
activation energy
-Ea/RT
k = A.e
Plot of log k vs 1/T is a straight line & slope = E
̶ a/2.303R
The temperature dependence of the rate of a chemical
reaction can be accurately explained by Arrhenius equation
or
Arrhenius equation
reaction

Plot of ln k vs 1/T is a straight line & slope =-Ea/R
reaction

At temperature T1 Eqn.1
At temperature T2
Eqn.2
k1 and k2 are the values of rate constants at temperatures T1 and
T2 respectively. Subtracting equation (2) from (1), we obtain
reaction

-Ea/RT
k = A.e
a
2
1 1 2
E
k 1 1
or log = -
k 2.303 R T T
 
 
 
reaction

   
   
   
a
2 2 1
10
1 1 2
E
K T - T
log =
K 2.303 R T T
 
 
 
a
E 320-300
log4=
2.303×1.987 300×320
a
0.60205×2.303×1.987×300×320
E =
20
= 13222.98 cals
Ea = 13.311 K cals
The specific reaction rate for a reaction increases by a
factor 4 if the temperature is changed from 27o
C to 47o
C.
Find the activation energy for the reaction.
Solution:

The activation energy of one of the reactions in the Krebs
citric acid cycle is 87 kJ/mol. What is the change in the
rate constant when the temperature falls from 37o
C to
15o
C?
Solution:

Catalysis
Catalyst: A substance that changes the rate of a
reaction without being consumed in the reaction.
• Provides an easier way to react.
• Lower activation energy.
• Still make the same products.
• Enzymes are biological catalysts.
Inhibitor:A substance that decreases the rate of
reaction (a negative catalyst).

How catalyst change reaction rate
• Catalysts are the
one way to lower
the energy of
activation
for a particular
reaction by
altering the path
of the reaction.
• The lower
activation energy
allows the
reaction to
proceed faster.

Rate Law and Mechanism
A mechanism is a collection of elementary steps devised
to explain the reaction in view of the observed rate law.
For the reaction, 2 NO2 (g) + F2 (g)  2 NO2F (g), the rate
law is,
rate = k [NO2] [F2] .
Can the elementary reaction be the same as the overall
reaction?
If they were the same the rate law would have been
rate = k [NO2]2
[F2],
Therefore, the overall reaction is not an elementary
reaction.

Rate-determining Step in a Mechanism
Slowest step:
The rate determining step is the slowest
elementary step in a mechanism, and the rate law
for this step is the rate law for the overall reaction.
Steady-state approximation:
The steady-state approximation is a general method
for deriving rate laws when the relative speed cannot
be identified. It is based on the assumption that the
concentration of the intermediate is constant.

Illustrative Problem
The hypothetical reaction A2+ B2  2AB
follows the following mechanism
2
A A + A (fast)

2
A + B AB + B (slow)

A B AB (fast)
 
The order of the overall reaction is
(a) 0 (b) 1
(c) 2 (d) 3/2

Solution
The order depends on slowest step
 2
1/2
2 2
1/2
2 2
Rate(slow step) = k[A][B ]
= k[B ].k`[A ]
= k"[A ] [B ]
1 3
Overall order 1
2 2
  
Hence, the answer is (d).

Illustrative Problem
At 380° C, the half-life period for the first order
decomposition of H2O2 is 360 min.The energy of
activation of the reaction is 200 kJ mole-1
.
Calculate the time required for 75%
decomposition at 450° C.

Solution
-3 -1
380
0.693
k = =1.925×10 min
360
 
  
 
450
380
k 200×103 1 1
log = -
k 2.303×8.314 653 723
 -2
450
450
-3
k
log =1.55 k = 6.83×10
1.925×10
 1 -2
2
0.693
t at 450°C = =10.15 min
6.83×10
 75% 1
2
t =2t =20.29 min.

15_chemical-kinetics (chemistry).pptx

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