Elements of
Chemical Reaction Engineering
6th Edition



Home

Essentials of
Chemical Reaction Engineering
Second Edition

  Select  Chapter  >>     TOC     Preface     1     2     3     4     5     6     7     8     9     10     11     12     13     14     15     16     17     18     Appendices  
›

By Chapter Hide

  • Objectives
  • Living Example Problems
  • Extra Help
  • - Summary Notes
  • - LearnChemE Screencasts
  • - FAQs
  • - Interactive Computer Modules
  • Additional Material
  • Self Test
  • i>Clicker Questions
  • Professional Reference Shelf

By Concept Hide

  • Interactive Modules
  • -Web Modules
  • -Interactive Computer Games
  • Living Example Problems

U of M Hide

  • Asynchronous Learning
  • ChE 344
  • ChE 528

Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Learning Resources

Solved Problem - Example CD9-2

   

IMAGE 07eq150.gif

  
   

Using the PSSH, develop a rate law for the rate of formation of HBr for the mechanism given by Equations (CD7-3), (CD7-4), and (CD7-6) through (CD7-8).

  
       
   

Solution

Each reaction is to be considered elementary. First we write down the net rate of formation of the product resulting from all the reaction steps:

  
       








Rate of formation
of HBr

  

IMAGE 07eq151.gif


(CDE7-2.1)



(CDE7-2.2)

 

      

 

  

The intermediate species Brmiddotand Hmiddotare free radicals, which are present in low concentrations and highly reactive. Consequently, the use of the PSSH is justified. We next write the net rate of formation of the intermediate species and set these rates equal to zero (rHmiddot = 0, rBr = 0).

  

 

      

 

  

IMAGE 07eq158.gif

 (CDE7-2.3)


(CDE7-2.4)

 

      

 

  

Adding Equations (CDE7-2.3) and (CDE7-2.4) gives

  

 

      

(Br) as a function of (Br2)

  

IMAGE 07eq159.gif

 (CDE7-2.5)

 

  

Subtracting Equation (CDE7-2.3) from (CDE7-2.2) gives

  
       
   

rHBr= 2k3 (Hmiddot)(Br2)

(CDE7-2.6)
       
   

To eliminate (Hmiddot) from this equation, rewrite Equation (CDE7-2.3) as

  
       
   

IMAGE 07eq161.gif

 (CDE7-2.7)
       
   

and solve for (Hmiddot):

  
       
   

IMAGE 07eq162.gif

 (CDE7-2.8)
       

 

  

To eliminate (Brmiddot), we use Equation (CDE7-2.5) to obtain

  

 

      

(Hmiddot) as a function of reactants and products

  

IMAGE 07eq163.gif

  

 

  

Substituting Equation (CDE7-2.9) into Equation (CDE7-2.6), we see that

 
       
   

IMAGE 07eq164.gif

 (CDE7-2.10)
       
   

We can rewrite Equation (CDE7-2.10) in the form

  
       
   

IMAGE 07eq165.gif

 (CDE7-2.11)
       
   

By comparing Equations (CDE7-2.6) and (CDE7-2.11) we again see that the mechanism produces a rate law consistent with experimental observation!