10.3.6 Rate Laws Derived from the Pseudo-Steady-State Hypothesis (PSSH)
by H. Scott Fogler
Essentials of Chemical Reaction Engineering
- Title Page
- Copyright Page
- Dedicated to
- Contents
- Preface
- About the Author
- Chapter 1. Mole Balances
- Chapter 2. Conversion and Reactor Sizing
- Chapter 2. Conversion and Reactor Sizing
- 2.3.1 CSTR (Also Known as a Backmix Reactor or a Vat)
- 2.3.2 Tubular Flow Reactor (PFR)
- 2.3.3 Packed-Bed Reactor (PBR)
- 2.5.1 CSTRs in Series
- 2.5.2 PFRs in Series
- 2.5.3 Combinations of CSTRs and PFRs in Series
- 2.5.4 Comparing the CSTR and PFR Reactor Volumes and Reactor Sequencing
- 2.6.1 Space Time
- 2.6.2 Space Velocity
- Chapter 3. Rate Laws
- Chapter 4. Stoichiometry
- Chapter 5. Isothermal Reactor Design: Conversion
- Chapter 6. Isothermal Reactor Design: Molar Flow Rates
- Chapter 7. Collection and Analysis of Rate Data
- Chapter 8. Multiple Reactions
- Chapter 8. Multiple Reactions
- 8.1.1 Types of Reactions
- 8.1.2 Selectivity
- 8.1.3 Yield
- 8.2.1 Modifications to the Chapter 6 CRE Algorithm for Multiple Reactions
- 8.3.1 Selectivity
- 8.3.2 Maximizing the Desired Product for One Reactant
- 8.3.3 Reactor Selection and Operating Conditions
- 8.5.1 Complex Reactions in a PBR
- 8.5.2 Multiple Reactions in a CSTR
- Chapter 9. Reaction Mechanisms, Pathways, Bioreactions, and Bioreactors
- Chapter 9. Reaction Mechanisms, Pathways, Bioreactions, and Bioreactors
- 9.1.1 Pseudo-Steady-State Hypothesis (PSSH)
- 9.1.2 Searching for a Mechanism
- 9.1.3 Chain Reactions
- 9.2.1 Enzyme–Substrate Complex
- 9.2.2 Mechanisms
- 9.2.3 Michaelis–Menten Equation
- 9.2.4 Batch Reactor Calculations for Enzyme Reactions
- 9.3.1 Competitive Inhibition
- 9.3.2 Uncompetitive Inhibition
- 9.3.3 Noncompetitive Inhibition (Mixed Inhibition)12
- 9.3.4 Substrate Inhibition
- Cell Growth and Division
- 9.4.1 Cell Growth
- 9.4.2 Rate Laws
- 9.4.3 Stoichiometry
- 9.4.4 Mass Balances
- 9.4.5 Chemostats
- 9.4.6 CSTR Bioreactor Operation
- 9.4.7 Wash-Out
- Chapter 10. Catalysis and Catalytic Reactors
- Chapter 10. Catalysis and Catalytic Reactors
- 10.1.1 Definitions
- 10.1.2 Catalyst Properties
- 10.1.3 Catalytic Gas-Solid Interactions
- 10.1.4 Classification of Catalysts
- Where Are We Heading?
- 10.2.1 Step 1 Overview: Diffusion from the Bulk to the External Surface of the Catalyst
- 10.2.2 Step 2 Overview: Internal Diffusion
- 10.2.3 Adsorption Isotherms
- 10.2.4 Surface Reaction
- 10.2.5 Desorption
- 10.2.6 The Rate-Limiting Step
- 10.3.1 Is the Adsorption of Cumene Rate-Limiting?
- 10.3.2 Is the Surface Reaction Rate-Limiting?
- 10.3.3 Is the Desorption of Benzene Rate-Limiting?
- 10.3.4 Summary of the Cumene Decomposition
- 10.3.5 Reforming Catalysts
- 10.3.6 Rate Laws Derived from the Pseudo-Steady-State Hypothesis (PSSH)
- 10.3.7 Temperature Dependence of the Rate Law
- 10.4.1 Deducing a Rate Law from the Experimental Data
- 10.4.2 Finding a Mechanism Consistent with Experimental Observations
- 10.4.3 Evaluation of the Rate Law Parameters
- 10.4.4 Reactor Design
- 10.5.1 Overview
- 10.5.2 Chemical Vapor Deposition
- Chapter 11. Nonisothermal Reactor Design–The Steady State Energy Balance and Adiabatic PFR Applications
- Chapter 11. Nonisothermal Reactor Design–The Steady State Energy Balance and Adiabatic PFR Applications
- 11.2.1 First Law of Thermodynamics
- 11.2.2 Evaluating the Work Term
- 11.2.3 Overview of Energy Balances
- 11.3.1 Dissecting the Steady-State Molar Flow Rates to Obtain the Heat of Reaction
- 11.3.2 Dissecting the Enthalpies
- 11.3.3 Relating ΔHRx(T), , and ΔCP
- 11.4.1 Adiabatic Energy Balance
- 11.4.2 Adiabatic Tubular Reactor
- 11.5.1 Equilibrium Conversion
- 11.5.2 Reactor Staging
- Chapter 12. Steady-State Nonisothermal Reactor Design—Flow Reactors with Heat Exchange
- Chapter 12. Steady-State Nonisothermal Reactor Design—Flow Reactors with Heat Exchange
- 12.1.1 Deriving the Energy Balance for a PFR
- 12.2.1 Co-Current Flow
- 12.2.2 Counter Current Flow
- 12.3.1 Applying the Algorithm to an Exothermic Reaction
- 12.3.2 Applying the Algorithm to an Endothermic Reaction
- 12.4.1 Heat Added to the Reactor,
- 12.5.1 Heat-Removed Term, R(T)
- 12.5.2 Heat-Generated Term, G(T)
- 12.5.3 Ignition-Extinction Curve
- 12.6.1 Energy Balance for Multiple Reactions in Plug-Flow Reactors
- 12.6.2 Parallel Reactions in a PFR
- 12.6.3 Energy Balance for Multiple Reactions in a CSTR
- 12.6.4 Series Reactions in a CSTR
- 12.6.5 Complex Reactions in a PFR
- Chapter 13. Unsteady-State Nonisothermal Reactor Design
- Appendices
- Appendix A. Numerical Techniques
- Appendix B. Ideal Gas Constant and Conversion Factors
- Appendix C. Thermodynamic Relationships Involving the Equilibrium Constant
- Appendix D. Nomenclature
- Appendix E. Software Packages
- Appendix F. Rate Law Data
- Appendix G. Open-Ended Problems
- Appendix H. How to Use the DVD-ROM
- Index
- About the DVD-ROM
- Footnotes
10.3.6 Rate Laws Derived from the Pseudo-Steady-State Hypothesis (PSSH)
In Section 9.1 we discussed the PSSH, where the net rate of formation of reactive intermediates was assumed to be zero. An alternative way to derive a catalytic rate law rather than setting
is to assume that each species adsorbed on the surface is a reactive intermediate. Consequently, the net rate of formation of species i adsorbed on the surface will be zero:
The PSSH is used when more than one step is rate limiting. The isomerization example shown in Table 10-4 is reworked using the PSSH in the DVD-ROM.
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