The document discusses various topics related to chemical kinetics including reaction rates, rate laws, order of reactions, integrated rate equations, and more. Specifically, it provides examples of zero order, first order, and second order reactions. It also discusses factors that affect reaction rates such as concentration, temperature, and catalysts. Molecularity and elementary vs. complex reactions are defined. The document seeks to explain concepts of chemical kinetics through examples of chemical reactions and equations.
15. Chemical Kinetics
• 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 (∆G = -VE VALUE)
• Chemical equilibrium tells only about
extent to which a reaction will proceed ?
• chemical kinetics tells about the rate of a
reaction, that means how fast or how slow
the reaction reaction takesplace?
16. 12/05/20
•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.
(Themodyanamically possible but kinetically
not).
17. Chemical Kinetics WHY?
• 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.
18. Rate of a Chemical Reaction
DEFINITION
• 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.
19. 12/05/20
FAST REACTION
Some reactions such as ionic reactions occur very fast,
for example, precipitation of silver chloride occurs
instantaneously by mixing of aqueous solutions of silver
nitrate and sodium chloride.
23. Consider a hypothetical reaction
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 P
respectively at time t1 . [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.
The Rate of a Chemical Reaction EXPRESSION
24. RATE EXPRESSION
• 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, Δ[R] is a negative quantity (as concentration of reactants is
decreasing), it is multiplied with –1 to make the rate of the reaction a
positive quantity.
25. 12/05/20
Average rate and Instantaneous rate
Average rate cannot be used to predict the rate of a reaction at a
particular instant as it would be constant for the time interval for
which it is calculated. So, to express the rate at a particular
moment of time we determine the instantaneous rate.
It is obtained when we consider the average rate at the smallest
time interval say dt ( i.e. when ∆t approaches zero). Hence,
mathematically for an infinitesimally small dt instantaneous rate is
given by
28. 12/05/20
Units of rate of a reaction
units of rate are
concentration = concentration time –1
time
For example, if concentration is in mol L–1
and time is in seconds then the units will be
mol L–1 = mol L-1s–1.
S
However, in gaseous reactions, when the
concentration of gases is expressed in terms of
their partial pressures, then the units of the rate
equation will be atm s–1
29. What is the rate of formation of Fe2+
2 Fe3+(aq) + Sn2+ → 2 Fe2+(aq) +Sn4+(aq)
Initial time t1 = 0 Final time t 2= 38.5 s
Initial [Fe2+] = 0 Final [Fe2+] = 0.0010 M
Δt = t2-t1 = 38.5 s
Δ[Fe2+] = Final [Fe2+] - Initial [Fe2+]
= (0.0010 – 0) M = 0.0010 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 -
30. General Rate of Reaction
EXPRESSION
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
47. Average rate & Instantaneous rate
Average rate depends upon the change in conc. of
reactants or products and the time taken for that
change to occur.
The average rate of a reaction is represented by, 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).
48. 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
50. 12/05/20
RATE LAW OR RATE EQUATION OR
RATE EXPRESSION
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.
52. 12/05/20
RATE LAW
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. For example
2NO(g) + O2(g) →2NO2 (g
It is obvious, after looking at the results, that when the concentration
of NO is doubled and that of O2 is kept constant then the initial rate
increases by a factor of four from 0.096 to 0.384 mol L–1s–1. This
indicates that the rate depends upon the square of the concentration of
NO.
53. 12/05/20
When concentration of NO is kept constant and concentration of
O2 is doubled the rate also gets doubled indicating that rate depends
on concentration of O2 to the first power. Hence, the rate equation for
this reaction will be
Rate = k [NO]2 [O2]
Some other examples are given below:
54. • The sum of powers of the concentration of the
reactants in the rate law expression OR rate law
equation 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
Order of a Reaction
DEFINITION
55. 12/05/20
•Reaction order represents the number
of species whose concentration directly
affects the rate of reaction.
•It can be obtained by adding all the
exponents of the concentration terms in
the rate expression.
•The order of reaction does not depend
on the stoichiometric coefficients
corresponding to each species in the
balanced reaction.
56. Order of a Reaction
Examples of observed rate laws for some reactions follow.
57. 12/05/20
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.
60. 12/05/20
Under which condition are the enzyme kinetics zero order?
When the concentration of substrate is
high enough to saturate the catalytic site
of the enzyme.
In that case, the rate of the reaction
depends only on the amount of enzyme,
and further increases in the
concentration of substrate does not
increase the rate of the reaction.
61. 12/05/20
What is the decomposition of gaseous
ammonia on a hot platinum surface?
70. 12/05/20
What is the Order of Radioactive Decay?
All natural and artificial radioactive decay of unstable
nuclei take place by first order kinetics.
76. 12/05/20
ELEMENTARY REACTION AND COMPLEX REACTION
The reactions taking place in one step are called elementary
reactions. When a sequence of elementary reactions (called
mechanism) gives us the products, the reactions are called complex
reactions.
Different type of complex reactions:
These may be consecutive reactions (e.g., oxidation of
ethane to CO2 and H2O passes through a series of
intermediate steps in which alcohol, aldehyde and acid
are formed), reverse reactions and side reactions
(e.g., nitration of phenol yields o-nitrophenol and p-
nitrophenol).
80. 12/05/20
An elementary reaction is a chemical reaction in
which one or more chemical species react directly
to form products in a single reaction step and with
a single transition state.
An example of this type of reaction is a
cycloaddition reaction. ...
82. 12/05/20
The overall rate of the reaction is controlled by the
slowest step in a reaction called the rate determining
step. Consider the decomposition of hydrogen
peroxide which is catalysed by iodide ion in an alkaline
medium.
85. Molecularity of a Reaction
Molecularity of a reaction is simply the
number of reacting species (atoms, ions or
molecules) involving in an elementary step
of reaction which must collide
simultaneously in order to bring out a
chemical reaction
Let us consider the following reactions,
90. 12/05/20
A unimolecular reaction occurs when
a molecule rearranges itself to produce
one or more products. An example of
this is radioactive decay, in which
particles are emitted from an atom.
Other examples include cis-trans
isomerization, thermal decomposition,
ring opening, and racemization
Unimolecular reaction
92. Molecularity vs. Order
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
94. 1.
2.
Practice Problems
1. Order of reaction = 1/2 + 2 = (1 + 4)/2 = 5/2 = 2.5.
2. Rate = k [X]2
The concentration of [X] is made to increase 3 times
Rate = k [3X]2
then rate will increase by 9 times as it is an exponential
factor.
So the rate of formation of Y will increase by 9 times
95. 12/05/20
NEED OF INTEGRATED RATE EQUATION
We have already noted that the concentration
dependence of rate is called differential rate
equation.
It is not always convenient to determine the
instantaneous rate, as it is measured by
determination of slope of the tangent at point ‘t’ in
concentration vs time plot (Fig. 4.1).
This makes it difficult to determine the rate law and
hence the order of the reaction.
In order to avoid this difficulty, we can integrate the
differential rate equation to give a relation between
directly measured experimental data, i.e.,
concentrations at different times and rate constant.
97. 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
115. 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
117. Half-Life of a Reaction
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.
121. 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].
128. 2 A first order reaction has rate
constant 1.15 x10-3 s-1 .How long
will 5g of this reactant take to reduce
3g?
Given,
k=1.15 x 10-3 g
R 5
]
[ 0 g
R 3
]
[
]
[
]
[
log
303
.
2 0
R
R
t
k
]
[
]
[
log
303
.
2 0
R
R
k
t
131. 5 Time required to decompose
SO2Cl2 to half of its initial amount is
60 minutes. If the decomposition is a
first order reaction, calculate the rate
constant of the reaction?
2
1
693
.
0
t
k
60
2
1
,
t
given
60
693
.
0
k
60
*
60
693
.
0
k
1
4
10
*
925
.
1
s
k
132. 6 For the reaction: 2A+ B-----A2 B,
the rate=k[A][B]2 with k=2.0*10-6
mole-2 L2 s-1 .Calculate the initial rate
of the reaction when [A]=0.1 mole L-1
,[B]=0.2 mole L-1 .Calculate the rate
the reaction after [A] is reduced to
0.06 mole L-1 .
133. 2
]
[
]
[ B
A
k
rate
2
6
]
2
.
0
[
*
1
.
0
*
10
*
0
.
2
rate
1
1
9
10
*
0
.
8
S
moleL
rate
When [A] is reduced from 0.1 to 0.06 ie
0.1-0.06=0.04 of A reacts with B.
B=1/2*0.04=0.02 ie 0.2-0.02=0.18 of B
remains.
2
]
[
]
[ B
A
k
rate
2
6
]
18
.
0
[
]
06
.
0
[
10
*
2
rate
1
1
9
10
*
89
.
3
s
moleL
rate
134. 7 The half life period for radioactive
decay of C14 is 5730 years. An
archaeological artifact containing
wood had only 80% of the C14 found
in a living tree. Estimate the age of the
sample.
years
t 5730
2
1
100
]
[ 0
R 80
]
[
R
2
1
693
.
0
t
k
years
k
5730
693
.
0
1
0001209
.
0
years
k
136. 8 The rate constant for a first order
reaction is 60 S-1 .How much time will
it take to reduce the initial
concentration of the reactant to its
1/16th value.?
]
[
]
[
log
303
.
2 0
R
R
k
t
1
]
[ 0
R 16
/
1
]
[
R
16
1
1
log
60
303
.
2
t
138. 9 . A first order reaction takes 40 min
for 30% decomposition. Calculate half
life period for first order reaction.
100
]
[ 0
R 70
30
100
]
[
R
]
[
]
[
log
303
.
2 0
R
R
t
k
1
3
min
10
*
918
.
8
k
]
7
log
10
[log
40
303
.
2
k
70
100
log
40
303
.
2
k
1549
.
0
*
40
303
.
2
k
1
min
008918
.
0
k
140. 10. For a first order reaction show
that time required for 99% completion
is twice the time required for the
completion of 90 % of reaction.
100
]
[ 0
R 1
99
100
]
[
R
]
[
]
[
log
303
.
2 0
R
R
k
t
1
100
log
303
.
2
%
99
k
t
10
log
2
*
303
.
2
%
99
k
t )
1
(
2
*
303
.
2
%
99
k
t
141. 100
]
[ 0
R
similarly
10
90
100
]
[
R
]
[
]
[
log
303
.
2 0
%
90
R
R
k
t
10
100
log
303
.
2
%
90
k
t
10
log
303
.
2
%
90
k
t )
2
(
303
.
2
%
90
k
t
Equation (1) is divided by (2)
2
303
.
2
*
2
*
303
.
2
k
k
t
%
90
%
99
t
t
%
90
*
2
%
99
t
t
142. 11. The following results have been
obtained during the kinetic studies of
the reaction:
D
C
B
A
2
Experiment [A]/M [B]/M Initial rate of formation of
D/moleper litre per minute
1 0.1 0.1 6.0*10-3
2 0.3 0.2 7.2*10-2
3 0.3 0.4 2.88*10-1
4
0.4 0.1 2.40*10-2
143. Determine the rate law and rate constant for the
reaction.
y
x
B
A
k
rate ]
[
]
[
)
3
(
)
2
(
exp and
eriment
from
y
x
y
x
k
k
eriment
eriment
)
2
.
0
(
)
3
.
0
(
)
4
.
0
(
)
3
.
0
(
10
*
2
.
7
10
*
88
.
2
)
2
(
exp
)
3
(
exp
2
1
y
y
)
2
.
0
(
)
4
.
0
(
4 y
)
2
(
4
y
)
2
(
)
2
( 2
2
y
150. 12. The following data were
obtained during first order thermal
decomposition of SO2 Cl2 at
constant volume.
SO2 Cl2 (g)-----SO2 (g) + Cl2 (g)
Experiment Time/S-1 Total Pressure/atm
1 0 0.5
2 100 0.6
Calculate the rate of the reaction when total
pressure is 0.65 atm.
152. SO2 Cl2 (g)-----SO2 (g) + Cl2 (g)
0.5 atm 0 0
0.5 - x x x
P total = 0.5 – x + x + x = 0.5 + x
0.6 = 0.5 + x
x = 0.6 - 0.5 = 0.1
Now, pi = 0.5 atm and p (at time 100 S)
=0.5 - x
153. Now, pi = 0.5 - x = 0.5 - 0.1 = 0.4 atm
p
pi
t
k log
303
.
2
4
.
0
5
.
0
log
100
303
.
2
k
25
.
1
log
100
303
.
2
k
25
.
1
log
100
303
.
2
k
155. P = 2* 0.5 - 0.65
P = 1 - 0.65
Rate = K (PSO2 Cl2 )=
P = 0.35 atm
Rate = 2.23*10-3 *0.35
Rate = 7.8*10-4 atm s-1
156. 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 )
158. Solution
1)
For first order reaction,
k=(2.303/t) log [a]/[a−x]
t=(2.303/k) log [a]/[a−x]
a=1 a−x=1−3/4=1/4
k=2.4×10−3 s−1, t=(2.303/2.4×10-3)log(1/(1/4))
=(2.303/2.4×10-3)log4
= 578 s
159. 2 . A first order reaction takes 40 minutes for 30 %
completion . calculate its t1/2 value.
Ans : Let a be 100 the initial concentration.
After 40 minutes,30% has reacted, so x is 30.
a-x=70
k=(2.303/t)log[a]/[a-x])
k=(2.303/40)log100/70
k=8.92×10−3/min
The half life period, t1/2=0.693/k
=77.7 min.
161. 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
162. 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 increae
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.
163. 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.
168. 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.
170. 12/05/20
An activated
complex is an
intermediate
state that is
formed during
the conversion
of reactants
into products.
An activated
complex is the
structure that
results in the
maximum
energy point
along the
reaction path.
175. 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.
176. 12/05/20
Most of the chemical reactions are
accelerated by increase in temperature.
For example, in decomposition of N2O5,
the time taken for half of the original
amount of material to decompose is
EFFECT OF TEMPERATURE ON THE RATE OF REACTION
177. 12/05/20
12 min at 500C,
5 h at 250 C and
10 days at 0 C.
At Zero degree Celsius How long will it take to
complete?
At 25 degree Celcius How long will it take to
complete?
At 50 degree celcius, how long will it take to complete?
181. 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
182. 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 = ̶ Ea/2.303R
The temperature dependence of the rate of a chemical reaction
can be accurately explained by Arrhenius equation
Effect of temperature on rate of chemical
reaction
or
Arrhenius equation
190. Effect of temperature on rate of chemical
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
191. Plot of ln k vs 1/T is a straight line & slope =-Ea/R
Effect of temperature on rate of chemical
reaction
192. -Ea/RT
k = A.e
a
2
1 1 2
E
k 1 1
or log = -
k 2.303 R T T
Effect of temperature on rate of chemical
reaction
195.
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.
Illustrative Example
Solution:
196. 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).
197. 12/05/20
The rate of a reaction can be increased by adding a suitable
catalyst. A catalyst is a substance which increases the rate of a
chemical reaction but it is not used up (remains chemically
unchanged at the end). It provides an alternative reaction pathway
of lower activation energy.
201. 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.