ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
CHP 3 – NON CATALYTIC & HOMOGENEOUS
REACTION KINETICS
This section covers homogeneous reaction rate expressions, the rates of
irreversible, reversible, and complex reactions
Missen Chapter 4 – 5 + Smith Chapter 2
3.1 Rate of SIMPLE homogeneous reactions – the effect of reactant
concentrations and reaction temperature (T).
kA B C Dα β γ δ+ ⎯⎯→ +
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
The rate law for HOMOGENEOUS reactions :
r [=] mol.V-1.time-1 = k.CAn.CB
m (power law)
* in most cases, ONLY reactant concentrations affect r
** n and m can be different with α and β (for elementary reaction >> n-m =
α-β ; but NOT vice versa)
*** elementary reaction order is normally 1 or 2
**** k, n, and m must be obtained by experiment
***** the relation between each component rates:
n mA B
( )( ) ( ) ( ) k.C CCA B Drr r r rα β γ δ
− −= = = = =
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
k = A.eEaRT
−
(Arrhenius Equation)
NOTE : in addition to the power law (as an empirical rate law) above, there
is also a rate law constructed based on concepts of reaction mechanism.
Such rate law is called fundamental rate law (see Chp 7 Missen). The
latter can be extrapolated outside the experimental conditions range.
eg: ( ) 2( ) 2( )12
Ptg g gCO O CO+ ⎯⎯→
a (fundamental) rate law derived from reaction mechanism is :
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
1/2CO O2
1/2CO O2
k(T).C .C( )[1 + K(T).C '( ).C ]COr
K T− =
+
3.1.1. First Order Reaction
r = k.CA
In constant volume batch reactor, at t = 0 CA = CAo :
A( ) k.CAA
dC rdt
− = − =
CA vs t = ? k = ??
3.1.2. Second Order Reaction
r = k.CA2
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
# in constant volume batch reactor at t = 0 CA = CAo:
2A( ) k.CA
AdC rdt
− = − =
CA vs t = ? k = ??
r = k.CA.CB
## in constant volume batch reactor at t = 0 CA = CAo, CB = CBo:
( ) k.C .AA A B
dC r Cdt
− = − =
CA vs t = ? k = ?? (go to page 14)
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
EXAMPLE # 1:
At 518 oC, acetaldehyde vapor decomposes into methane and carbon
monoxide: COCHCOCH k +⎯→⎯ 43
Hinselwood & Hutchison (1962) carried out an experiment in a constant-volume
batch reactor. The initial pressure of CH3CO was 48.4 kPa, and the following
increases of pressure (ΔP) were noted
t (s) 42 105 242 480 840 1440
ΔP (kPa) 4.5 9.9 17.9 25.9 32.5 37.9
Determine the reaction order, and calculate the rate constant (in pressure and
molar units).
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
3.1.3. Third Order Reaction
r = k.CA2.CB
In constant volume batch reactor at t = 0 CA = CAo, CB = CBo:
2A( ) k.C .A
A BdC r Cdt
− = − =
CA vs t = ? k = ?? >>> Read Missen page 72 – 75 !!
3.1.4. n-th Order Reaction
r = k.CAn
In constant volume batch reactor at t = 0 CA = CAo:
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
A( ) k.CnAA
dC rdt
− = − =
For n = 1 and n ≠ 1 find CA vs t = ? k = ??
SUMMARY:
(i) reaction order 1 or 2 is normally for simple, elementary
reactions
(ii) reaction order 0 is normally NOT observed for reaction in a
single-phase fluid, but it may occur in enzyme reactions and in
the case of gas (solid catalyzed) reactions – refer to Missen Chp
8 & 10
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
(iii) reaction order 3 is rare, but includes: the gas phase reaction
between NO and O2 or H2 or Cl2 or Br2; acids or bases catalyzed
reactions in aqueous phase
(iv) reaction order may be other numbers (even negative!), eg under
certain conditions the decomposition of CH3COH is 3/2-order;
reaction between CO (1-order) and Cl2 (3/2-order) to form COCl2.
(v) reaction rate may also depend on the product concentration; if
the order is + the effect is known as autocatalysis, but if the
order is – the effect is called product inhibition (common in
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
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catalytic reaction). This effect can be known if measurements at
low reactant-conversions are conducted. Refer to Missen Chp 8
3.1.5. Effect of T
T affects the rate as indicated in Arrhenius equation. The values of A
and EA may be estimated using the linearized form
1ln k = ln A - ( )EaR T
EXAMPLE # 2:
Determine the Arrhenius parameters for the reaction
2 4 4 6 6 1kC H C H C H+ ⎯⎯→ 0
ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
The following data was collected by Rowley & Steiner (1951):
T (K) k (L.mol-1.s-1) T (K) k (L.mol-1.s-1)
760 0.38 863 3.12
780 0.56 866 4.05
803 0.94 867 3.47
832 1.57 876 3.74
822 1.34 894 5.62
823 1.23 921 8.20
826 1.59
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
3.2 Rate of REVERSIBLE homogeneous reactions
Many reactions are reversible, in which reaction thermodynamics apply
(remember Chapter 2!). The rate only measures changes PRIOR TO the
equilibrium condition. In the way to equilibrium, the rate diminishes and near
equilibrium r ≈ 0. Examples of reversible reactions:
14 10 4 11
k
kn C H i C H
−⎯⎯→− −←⎯⎯ 0
22 2 32
12
k
kSO O SO
−⎯⎯→+ ←⎯⎯
33 3 2 3 33
k
kCH COOCH H O CH COOH CH OH
−⎯⎯→+ +←⎯⎯
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
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t (h) 0 1 2 3 4 ∼
100CA/CA0 100 72.5 56.8 45.6 39.5 30
Following data were obtained at a certain T from a constant-volume batch
reactor:
The isomerization of A to D follows first order in both directions
1
1
k
kA D
−⎯⎯→←⎯⎯
find the values of k1 and k-1.
EXAMPLE # 3:
ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
Table 2.10 – Rate Equation for simple reactions
(p 82 Smith – read also p 62 – 74)
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
3.3 Rate of COMPLEX homogeneous reactions
Types of complex reactions:
- Parallel reactions, eg:
2 5 2 4 2C H OH C H H O→ +
2 5 2 4 2 C H OH C H O H→ +
6 5 2 3 6 4 2 2 2( )C H NO HNO o C H NO H O+ → − +
6 5 2 3 6 4 2 2 2( )C H NO HNO m C H NO H O+ → − +
6 5 2 3 6 4 2 2 2( )C H NO HNO p C H NO H O+ → − +
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
- Series reactions, eg:
3 2 4 2( )CH CO CH CH CO→ +
2 2 412
CH CO C H CO→ +
- Series & reversible, eg:
2 5 2 4 212
N O N O O→ +
2 4 2 2N O NO⎯⎯→←⎯⎯
- Series & parallel, eg:
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
4 2 2CH O HCHO H O+ → +
2 21/ 2HCHO O CO H O+ → +
4 2 2 22 2CH O CO H O+ → +
NOTE:
For a complex reaction system, we can find the maximum number of linearly
independent chemical equations (TTSL reaction in Azas TK). The number tells
us the minimum number of species that need to be analyzed in a kinetic study.
However, those equations have NOTHING to do with the kinetics (real
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
reactions or mechanism). But, they can be useful for mass balance purposes.
3.3.1 Parallel reactions
Read 5.2.1 Missen p 90!!
The (most common) conversion, yield and selectivity in parallel reactions:
A B P+ →
A B S+ →
Conversion = 0
0
( )A AC C−
AC Selectivity to P = 0( )
P
A AC C− C
0
P
A
CYield of P = C Yield = conversion x selectivity
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
EXAMPLE # 4:
Describe how experiments in a constant-volume batch reactor should be
carried out to measure k1 and k for these 1st order parallel reactions: 2
A B C→ + r = k1.CAB
A D E→ + rD = k2.CA
3.3.2 Series reactions
1 2k kA B C⎯⎯→ ⎯⎯→
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
EXAMPLE # 5:
Describe how experiments in a constant-volume batch reactor should be
carried out to measure k1 and k2 for a 1st order series reactions?
HOMEWORK
1. For the series reaction above, calculate the time at which the CB is
maximum, and what is the CB maximum if initially CA = CA0 and CB = CC = 0.
2. An elementary reversible liquid phase reaction 1
1
k
kA R
−⎯⎯→←⎯⎯ is carried out
isothermally in a constant-volume batch reactor. After 8 minutes, A
conversion is 1/3 and at equilibrium A conversion is 2/3. Calculate the
rate constants.
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ICE 204 – KINETIKA & KATALISIS – CHAPTER 3
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3.3.3 Series-parallel reactions (see Levenspiel, Chemical Reaction Engineering, 3rd edition,
p 188 & 190)
1kA B R+ ⎯⎯→
2kR B S+ ⎯⎯→
If the individual reactions follow 1st order in respect to each reactant:
CA0 – CA = CR – CR0 + CS – CS0 CB0 – CB = CR – CR0 + 2(CS – CS0)
(-rA) = k1.CA.CB rR = k1.CA.CB - k2.CR.CB
(-rB) = k1.CA.CB + k2.CR.CB rS = k2.CR.CB
MORE EXERCISES: Hill examples 5-1, 5-3 up to 5-6
Mol balances:
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