Module 2 :
Kinetics of
Homogenous
Reactions
Prepared by :
Ma. Junallie F. Pomperada, RChE, MENG-ChE, PhD-TM
Ideal Flow or
Contacting Patterns
for Ideal Reactors
Batch Reactor
Uniform composition everywhere in the reactor, but the
composition changes with time.
Steady-state flow
Fluid passes through the reactor with
no mixing of earlier and later entering
fluid, and with no overtaking (as if the
fluid moved in single file through the
reactor).
Uniformly mixed, same
composition everywhere,
within the reactor and at
the exit.
Rate Law

The rate law will give -rA = [kA(T)][fn(CA,CB,…)]

Rate law gives the relationship between the reaction rate
and concentration.

k= specific reaction rate determined by Arrhenius equation
E
k  Ae
RT
where
E = activation energy
R = universal gas constant
T = temperature
A = frequency factor
* k and A units depends on
overall reaction order
Rate Law

For a reaction given below:
aA + bB  cC + dD
rA
rB rC rD

 
a b c
d

Example:
2NO + O2 →2NO2
rNO rO2 rNO2


 2 1
2
Self Test
Write the rate law for the elementary liquid phase reaction;
3A  2B  4C
solely in terms of conversion(-rA as a function of X). The feed to the
batch reactor is equal molar A and B with C BO = CA0 = 2 mol/dm3
and kA= 0.01 (dm3/mol)41/s.
a) What is the rate law?
b) What is the concentration of A and B at any time t?
a)
 rA  kCA CB
3
2
b) Liquid phase,V=V0 (no volume change)
The Rate Equation
For a single – phase reaction:
aA + bB
-rA = -
1 dNA
V dt
=
rR + sS
(amount of A disappearing),
(volume)(time)
mol
m3 -s
Note: rate of consumption/formation of a species is an intensive
measure
Note: Rate of reaction is influenced by the composition and energy of the
material. Energy is the random kinetic energy of molecules, light intensity
within the system which will affect bond energy between atoms, magnetic
field intensity, etc…..focusing on effect of temperature.
-rA =
temperature
ƒ dependent
terms
where:
concentration
a
kC
=
=
A
dependent
terms
-ra = mol/m3.s
k = (mol/m3)1-as-1
a = reaction order
E = activation energy
k0e-E/RT = temperature dependent term
k0e-E/RTCAa
Concentration-Dependent Term

Depends on type of reaction which is also in
turn dependent on the form and number of
kinetic equations used to describe the
progress of the reaction.

The temperature must be held constant (or
assumed constant) throughout the reaction
when determining the concentration
dependent term of the rate equation.
Temperature-Dependent Term
Rate Constant, k
units:
nth order = (time)-1 (concentration)1-n
1st order = (time)-1
Reaction Rate Constant

At temperature T0,
k (T0 )  Ae
E
RT0
E
k (T )  Ae
RT
At temperature T,
Taking the ratio to obtain,
k (T )  k (T0 )e
A+B
H
E
C
R
Reaction Coordinate
E 1 1 
  
R  T0 T 
Activation Energy: defined as
the energy that must be
overcome in order for a
chemical reaction to occur.
Why is there an Activation
Energy?


the molecules need energy to distort or stretch their bonds in
order to break them and to thus form new bonds
as the reacting molecules come close together they must
overcome both steric and electron repulsion forces in order to
react
Final Note:
By increasing the temperature we increase the kinetic
energy of the reactant molecules which can in turn be
transferred to internal energy to increase the stretching
and bending of the bonds causing them to be in an
activated state, vulnerable to bond breaking and
reaction.
Activation Energy is the minimum amount of energy
required to initiate a chemical reaction.
Temperature Dependency from
Arrhenius’ Law
k = koe-E/RT
where: ko - frequency factor or pre-exponential
factor
E - activation energy of the reaction
ln (r2/r1) = ln(t1/t2) = ln(k2/k1)
= E/R (1/T1 - 1/T2)
Plot of Arrhenius’ Law
Low E
200
High E
100
ln k
50
20
Slope = E/R, K
10
5
2000 K
1000 K
463 K
1/T
376 K
Activation Energy & Temperature Dependency

The temperature dependency of reactions is determined by the
activation energy and the temperature level of the reaction.
Findings from Arrhenius’ Equations:
1. A plot of ln k vs. 1/T from Arrhenius’ Law gives a straight line, with
large slope for large E and small slope for small E.
2. Reactions with high activation energies are very temperaturesensitive; reactions with low activation energies are relatively
temperature insensitive.
3. Any given reaction is much more temperature sensitive at low
temperature than at high temperature.
4. The value of the frequency factor ko, does not affect the
temperature sensitivity of a reaction.
Sample Problem


The rule of thumb that the rate of reaction doubles for a 10 °C
increase in temperature occurs only at a specific temperature for a
given activation energy. Develop a relationship between the
temperature and activation energy for which the rule of thumbs
holds. Neglect any variation of concentration with temperature.
Determine the activation energy and frequency factor from the
following
K (min-1)
0.001
0.050
T(°C)
60.0
100.0
Temperature Dependency from
Thermodynamics
For an elementary, reversible reaction such as
A⇄R
∆Hr
d  ln K  H

dT
RT
From Van Hoff’s Equation
r
2
d  ln K  H r

dTd ln K  HRT 2
dT

r
RT 2
where: K = Kc = [R]/[A] = k1/k2
then
d  ln k1  d  ln k2  H r


dT
dT
RT 2
Temperature Dependency from
Thermodynamics
which yields the following relationships
d  ln k1  E1
d  ln k2  E2
 2 and
 2
dT
RT
dT
RT
where: E1 – E2 = ∆Hr
Temperature Dependency from Collision
Theory
For the bimolecular collisions of like molecules in a gas
Z AA   n
2 2
A A
2
4 kT
N
  A2 6
MA
10
4 kT 2
CA
MA
where: ZAA is the number of collisions of
A with A per sec per cc
Temperature Dependency from Collision
Theory
For the bimolecular collisions of unlike molecules in a
gas
 1
1 
  A B 

 1  1  
 n
 AnB 8 kT


Z

n
n
8

kT
 M



2
M

 2 
B 
 M  M A
2
Z AB
2
A
AB
B
A B
A
2
 1
1 
  A B  N

8 kT 

C ACB

6
2

 10
 MA MB 
2
Z AB
B
Temperature Dependency from Collision
Theory
Thus rate of reaction is
1 dN A
1000  RTE
rA  
 kC ACB  Z AB
e
V dt
N
  A B  N
2
rA  

2

3
10

 1
1   RTE
8 kT 

e C AC B
 MA MB 
Temperature Dependency from Collision
Theory
σ – diameter of a molecule, cm
M – molecular weight/N, mass of a
molecule, g
N – Avogadro’s Number, 6.023 x 1023
molecule/mole
CA – concentration of A, mole/liter
nA – NCA/103, no. of molecules of A per cc
k – Boltzmann Constant, R/N = 1.38 x 10-16
erg/mole.ºK
Temperature Dependency from
Transition-state Theory



A more detailed mechanism on how reactants
form products.
Pictures how reactants combine to form unstable
intermediates called activated complexes
which decompose spontaneously to form the
products.
Assumes that equilibrium occurs between
reactants and intermediates at all times and that
the rate of decomposition of the activated
complexes is the same for all reactions.
Temperature Dependency from
Transition-state Theory
For the forward elementary reaction of a
reversible reaction
k1
A + B ⇄ AB
∆Hr
k2
The conceptual scheme is
k3
A + B ⇄ AB* → AB
k4
k5
Single and Multiple Reactions

Single Reaction – a single stoichiometric
equation and a single rate equation are chosen
to represent the progress of the reaction.

Multiple Reaction – more than one
stoichiometric equation is chosen to represent
the observed changes and more than one
kinetic expression is needed to follow the
changing composition of all the reaction
components.
Types of Multiple Reactions
1) Series Reactions
A
R
S
2) Parallel Reactions
a) Competitive
R
b) Side by Side
c) Complicated
A
R
A+B → R
B
S
R+B→ S
A
S
reaction is parallel with
respect to B but in series with
respect to A, R & S
Elementary and Non-elementary
Reactions

Elementary Reactions – reactions in
which the rate equation corresponds to a
stoichiometric equation.

Non-elementary Reactions – there is no
direct correspondence between
stoichiometry and rate.
Representation of an Elementary
Reaction
using partial pressure (for gaseous reactions only)
rA  kP PAa PBb .....PDd
zero order: -rA = k
1st order: -rA = kCA
2nd order: -rA = rR = k1CA2
Representation of a Nonelementary Reaction
Stoichiometry:
N2  3H 2  2 NH 3
N 2  H 2  2
NH 3 


 k1
 k2
2
3
 NH 3 
H2  2
3
Rate Equation:
rNH3
Note: the non-match between stoichiometry and rate
equation dictates that a multi-step reaction
model should be developed
Molecularity and Order of the
Reactions
Molecularity – concept only applies to elementary
reactions
– equals to the total number of molecules
involved in the reaction
− always assumes an integral value
Order of the Reaction – the powers to which the
concentrations are raised in the
rate equation
- can be a fraction and need not
always be an integer
- empirically determined
Reaction Order

Rate law is a behavior of a reaction.

Consider the following reaction:
aA + bB  cC + dD
The rate law may be written as Power Law Model:


 rA  kCA CB
where
k = specific reaction rate
 = order with respect to A
 = order with respect to B
+ = overall order
Reaction Order
In the previous example, i.e.,
aA + bB  cC + dD
The rate law was written as:
(-rA) = k CA CB
Elementary Rate Law
 if the Stoichiometry
coefficients are the same
as the individual reaction
order of each species.
 H2 +I2  2HI
(rHI) = k CH2 CI2
Non-elementary Rate Law
 CO+CI2→COCI2
 This rxn is 1st order with
respect to CO, 3/2 order
with respect to CI2 and 5/2
order overall.
 rCO  kCCOCCI3/ 22
Self Test
1)
What is the reaction rate law for the reaction
A+1/2 BC if the reaction is elementary? What is rB? What is rC ?
 rA  kCAC B1/ 2
rA
rB

1 1/ 2
1
k
rB  rA   C AC B1/ 2
2
2
rC
rA

1
1
rC   rA  kCAC B1/ 2
Self Test
2) Calculate the rates of A, B, and C for the reaction A+1/2 BC in a
CSTR where the concentrations are CA = 1.5 mol/dm3, CB = 9 mol/dm3 and
kA = 2 (dm3/mol)(1/2)(1/s).
  dm 3
 rA   2
  mol

mol
 rA  9
dm 3
mol
rB  4.5
dm 3
mol
rC  9
dm 3
1/ 2



1  
mol   mol 
1.5
9
3 

s 
dm   dm 3 

1/ 2
Kinetic Models for
Nonelementary Reactions
Key Assumption:
It is a sequence of elementary reactions in
which the amounts of intermediates
formed are non-measurable or nonobservable because their amounts are
negligible, thus what are observed are the
initial reactants and final products only
(which appears to be a single reaction).
Example:
A2  B2  2 AB

 2 A*
A2 


 AB  B *
A*  B2 


 AB
A*  B * 

Note: The components with asterisks refer
to the unobserved intermediates
Types of Reaction
Intermediates
Free Radicals
free atoms or larger fragments of stable molecules
that contain one or more unpaired electron(s)
generally unstable and highly reactive
the free radical is designated by a dot on its chemical
symbol
Examples: CH3•, C2H5•, I•, H•, CCl3•
Ions and Polar Substances
electrically charged atoms,
molecules, or fragments of molecules
that acts as active intermediates
Examples: N3-, Na+, OH-, NH4+,
CH3OH2+, I-
Molecules
A
R
S
Transition Complexes
strained bonds, unstable forms of
molecules, or unstable association of
molecules which resulted from
numerous collisions between reactant
molecules
Reaction Schemes
Nonchain Reactions – the intermediate is
formed in the first reaction and disappears
as it reacts further to give the products
reactants → (intermediates)*
(intermediates)* → products
Chain Reactions – the intermediate is formed in
the first reaction called the chain initiation step,
combines to form product and more
intermediates in the chain propagation step and
is destroyed in the chain termination step
reactant → (intermediate)*
(intermediate)* + reactant → (intermediate)* + product
(intermediate)* → product
initiation
propagation
termination
Note: in the propagation step, the intermediate is not consumed but acts
as a catalyst for the conversion of the material
Any Questions?
- The End -