GATE – PSU Chemical Engineering Chemical Reaction Engineering

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Chemical Engineering. Chemical Reaction .... 139. 2004. 139. 2005. 142. 2006. 145. 2007. 147. 2008. 150. 2009. 154. 2010. 156. 2011. 157. 2012. 159. 2013. 161. 2014. 163. 2015. 165. Chapter 12. SOLUTIONS. 167 ... The chemical reaction systems in which the volume of reacting fluid remain constant or have on slightly ...
Revised Study Material

For

GATE – PSU

Chemical Engineering Chemical Reaction Engineering

GATE Syllabus

Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors; Residence time distribution, single parameter model; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.

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TABLE OF CONTENTS Chapter 1

INTRODUCTION 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

Introduction Types of Chemical Reactions Rate of Chemical Reaction Relative Rate of Reaction Factors Affecting the Rate Equation Reaction Mechanism Molecularity Order of Reaction Rate Constant 1.9.1 Arrhenius Theory 1.9.2 Collision Theory 1.9.3 Transition State Theory

2 2 2 3 3 4 4 5 5 6 7 7 8

Chapter 2

HOMOGENEOUS SYSTEM

11 11 12 12 13 13 14 15 17 17 18 20 22 26 27 28 28 29

DESIGN EQUATION

31 31 32 33 35

2.1 Constant Volume System 2.2 Rate Equation for Different Order of Reactions 2.2.1 Zero Order Reaction 2.2.2 First Order Reaction 2.2.3 Second Order Reaction 2.2.4 Third Order Reaction 2.3 Half Life Method 2.4 Rate Equation for Multiple Reactions 2.4.1 Parallel Reactions 2.4.2 Series Reactions 2.5 Reversible Reaction 2.6 Auto Catalytic Reaction 2.7 Variable Volume System 2.7.1 Rate Equation for Different Order of Reactions 2.7.1.1 Zero Order Reaction 2.7.1.2 First Order Reaction 2.7.1.3 Second Order Reaction Chapter 3 3.1 Ideal Batch Reactor 3.2 Flow Parameters 3.3 Ideal CSTR 3.4 Ideal PFR

i

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Chapter 4

MULTIPLE REACTOR SYSTEM 4.1 4.2 4.3 4.4 4.5

CSTR in Series CSTR in Parallel PFR in Series PFR in Parallel Two Different Type of Reactors in Series

39 39 40 40 41 43

Chapter 5

DESIGN OF MULTIPLE REACTION SYSTEM 5.1 Parallel Reactions 5.2 Quantitative Treatment of Product Distribution 5.3 Series Reactions

47 47 49 51

Chapter 6

NON IDEAL FLOW REACTORS 6.1 RTD Measurement 6.1.1 Pulse Input Experiment 6.1.2 Step Input Experiment 6.2 Mean Residence Time 6.3 RTD in Reactors 6.3.1 In CSTR 6.3.2 In PFR 6.4 Reactor Modeling

55 56 56 57 59 62 62 63 64

Chapter 7

EFFECT OF TEMPERATURE AND PRESSURE

7.1 Heat of Reaction 7.2 Equilibrium Constant 7.3 Equilibrium Conversion

65 65 66 66

7.4 Van Hoff Equation 7.5 Relation Between Temperature and Conversion

67 67

7.5.1 For Adiabatic Process 7.5.2 For Non-adiabatic Process

67 68

Chapter 8

HETEROGENEOUS SYSTEM

8.1 Non Catalytic Reaction System 8.1.1 8.1.2 8.1.3 8.1.4 ii

Rate Equation Rate Controlling Concept Rate Equation for Physical Absorption Rate Equation for Absorption with Chemical Reaction

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70 70 70 71 72 74

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8.1.5 Hatta Number 8.2 Catalytic Reaction System

75 75

8.2.1 Steps of Catalytic Reaction 8.2.2 Rate Equation for Pore Diffusion and Surface Reaction 8.2.3 Effectiveness Factor 8.2.4 Characteristic Length 8.2.5 Thiele Modulus 8.2.6 For Strong Pore Diffusion Resistance 8.3 Effective Diffusivity 8.4 Design Equation for Reactors Containing Porous Catalyst

76 77 79 80 81 81 82 83

8.5 Activity of Catalyst 8.6 Deactivation of Catalyst

84 84

Chapter 9 LEVEL 1 LEVEL 2

86 106

UNSOLVED QUESTIONS

127

QUESTIONS (2004 TO 2015)

139 139 142 145 147 150 154 156 157 159 161 163 165

SOLUTIONS

167

Chapter 10

Chapter 11 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Chapter 12

iii

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CHAPTER 2

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• HOMOGENEOUS SYSTEM

2.1 CONSTANT VOLUME SYSTEM The chemical reaction systems in which the volume of reacting fluid remain constant or have on slightly changes throughout the reaction are called Constant Volume Systems or Constant Density Systems. The rate of disappearance of reactant A is 1 𝑑𝑁𝐴

−𝑟𝐴 = − 𝑉

Ci =

𝑑𝑡

𝑁𝑖 𝑉

Ni = Ci.V 𝑟𝑖 = 𝑟𝑖 =

1 𝑑(𝐶𝑖 .𝑉) 𝑉 1 𝑉

𝑑𝑡 𝑑𝐶𝑖

[𝑉

𝑑𝑡

+

𝑑𝑉 𝑑𝑡

]

For constant volume second term is zero 𝑟𝑖 = 

1 𝑑𝐶𝑖 𝑉 𝑑𝑡

FRACTIONAL CONVERSION OF A 𝑋𝐴 = 𝑋𝐴 =

𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴 𝑓𝑒𝑑 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐴 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝑁𝐴𝑜

Moles of A reacted = N AO X A Material balance A unreacted

= A initially fed – A reacted

N A  N AO  N AO X A N A  N AO 1  X A 

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CA 

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N A N AO 1  X A   V V

C A  C AO 1  X A 



FOR A CHEMICAL REACTION aA  bB  cC  dD

Moles of A reacted = NA0XA moles of B reacted =

b  mole of A reacted a

Similarly moles of C formed c N C = N co    N AO X A a c N co    N AO X A N a Cc= c = V V

c Cc= Cco +   C AO X A a C D = C DO +  d / a  C A0 X A



FOR FLOW SYSTEM For the flow system concentration is defined as the ratio molar flow rate and volume of the system. C A  FA / V FA  FAO 1  X A  C A  C AO 1  X A 

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2.2 RATE EQUATION FOR DIFFERENT ORDER OF REACTIONS

2.2.1 ZERO ORDER REACTION For any zero order reaction having rate constant k K P A 

The rate of reaction is 𝐶

−𝑟𝐴 = −

𝑑𝐶𝐴 𝑑𝑡

= 𝑘𝐶𝐴0 = 𝑘

𝑡

𝐴 ∫𝐶 −𝑑𝐶𝐴 = ∫0 𝑘𝑑𝑡 𝐴𝑜

𝐶𝐴0 − 𝐶𝐴 = 𝑘𝑡 In terms of conversion 𝐶𝐴𝑜 𝑋𝐴 = 𝑘𝑡 2.2.2 FIRST ORDER REACTION The first order liquid phase reaction having rate constant k K P A 

The rate of disappearance of component A is −𝑟𝐴 = −

𝑑𝐶𝐴 𝑑𝑡

= 𝑘𝐶𝐴𝑛 = 𝑘𝐶𝐴

Where n = 1 for first order Integrate both sides 𝐶𝐴 −𝑑𝐶𝐴

∫𝐶

𝐶𝐴

𝐴𝑜

𝑡

= ∫0 𝑘𝑑𝑡

ln(𝐶𝐴0 /𝐶𝐴 ) = 𝑘𝑡 In terms of conversion 1

ln (1−𝑋 ) = 𝑘𝑡 𝐴

13

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Where CA0 and CA are initial and final concentration of reactant A

2.2.3 SECOND ORDER REACTION Case 1: The second order reaction with single reactant K 2A  P

−𝑟𝐴 = −

𝑑𝐶𝐴 𝑑𝑡

= 𝑘𝐶𝐴2

𝐶𝐴 −𝑑𝐶𝐴

∫𝐶

𝐴𝑜

𝐶𝐴2

𝑡

= ∫0 𝑘𝑑𝑡

1 1 − = 𝑘𝑡 𝐶𝐴 𝐶𝐴𝑜 In terms of conversion 1 𝑋𝐴 ( ) CAo 1 − 𝑋𝐴 = 𝑘𝑡 Case 2: Second order reaction with two reactants A and B K P A + B 

dCA  KCACB Let M = CB 0 / CA0 dt where M be the molar ratio  rA  

14

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2.2.4 THIRD ORDER REACTION K P 3A  dC rA   A  kC A3 dt

 dC    A   kdt int egrate both sides  C A0  1 1 1   2  2   kt 2  C A C A0   1 1  2 kt =  2  2   C A C A0 

Similarly, For nth order reaction

15

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2.3 HALF LIFE METHOD The half life is the time required for 50% conversion or to reduce concentration to half of its initial concentration The reaction order & rate constant of a reaction can be determined from the data of half life of reaction as a function of initial concentration.

t1/2

2 

n 1

 1

C1Ao n

k (n  1)

 t1/2  C1Ao n

 t1/ 2 1st order 





t1/2 (S)

ln(CAo/ CA) CAo- CA

-ln(1-XA) CAoXA

1 1 − 𝐶𝐴𝑜 𝐶𝐴

1 𝑋𝐴 ( ) 𝐶𝐴𝑜 1 − 𝑋𝐴

0.693/k 𝐶𝐴𝑜 2𝑘 1 𝐶𝐴𝑜 . 𝑘

n

Kt mol / m3s

1 0 2

Where t1/2 = Half life time



0.693 K

when 𝐶𝐴 =



Kt mol / m2s

𝐶𝐴𝑜 2

Example 2.1 The half life of a first order liquid phase reaction is 30 sec, than rate const (k) in min-1 is (a) 0.0231

(b) 0.602

(c) 1.386

(d) 2

Solution:

16

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For first order reaction we know, 0.693 k 0.693 0.693 k   t1 / 2 30 / 60 t1 / 2 

 k  1.386 min 1

Example 2.2 For a certain reaction A → B, rate is first order if C A = low, rate is zero order if C A =High. Possible expression for such case:  K1C A2  (a) rA =    1  K 2C A 

2

(b) rA 

K1C A2

1  K 2C A 

2

 K C2 1 A (c) rA    1  K C  2 A 

2

 K 1C A  (d) rA    1  K 2C A  

Example 2.3 The liquid phase reaction being carried out in a constant volume batch reactor, k = 0.01 s-1, C A0  1 mol / m3 , t =100 sec than CA=? (a )

1 mol / m 3 e

(b) 2.3 mol / m3

(c) e mol / m3

 P , t1 / 2  Example 2.4 For the liquid phase reaction, A  (a) 1.5

(b) 1

(c) 0.5

(d ) 0.1 mol / m3 1 CAo

 n? (d) -1.5

Solution: for nth order reaction we know, t1 / 2  C 1Ao n 1/2  t1 / 2  C 1Ao n  C Ao

 n  1.5

2.4 RATE EQUATION FOR MULTIPLE REACTIONS 2.4.1 Parallel Reactions/competing reaction The reactant A undergoes two simultaneous reaction giving product R and S 17

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rS k 1  rR k 2

Knowing both slopes, we get the value of individual rate constant

18

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