Ice 204 Chp3 Non Catalytic Reaction Kinetics

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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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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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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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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# 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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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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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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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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(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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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


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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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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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:


Table 2.10 – Rate Equation for simple reactions

(p 82 Smith – read also p 62 – 74)

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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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- 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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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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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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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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Typical concentration profile in a batch reactor

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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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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:

Ice 204 Chp3 Non Catalytic Reaction Kinetics

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