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Tutorial Chapter 3 : CPE624 (Chain Reactions)

Question 1

Consider the preceding reaction of a general reaction process,

C  B A    which is propogated by a single radical  R . The mechanism is:

 X  Rn

 RC  B R A

 R An

t 

i

,

,

 

  t 

i

n

 Rt t 

 R A p p

n

 Aii

C k r 

C C k r 

C k r 

 

where ni and nt are the number of molecules react in the initiation and termination steps.

By writing the appropriate mass balance for each species involved in the reaction and usingpseudo-steady state approximation on free radical, prove that:

  t it 

n

n

 A p

n

t t 

i C k k n

k r 

 

 

  

 

1

1

 

Question 2

Phosgene, an intermediate in polyurethane monomer, is made by the homogeneous reaction

22  COCl Cl CO    

The elementary steps of this reaction are

Cl COCl Cl COCl 

COCl COCl Cl Cl 

22

2 2 

where all reactions are reversible.(a) Identify initiation, propagation, and termination steps.(b) Show that the rate of this reaction could be

23

2 ]][[   Cl COk r    

(c) Find an expression for the reverse reaction rate.

Question 3

Dimethyl ether decomposes to methane and formaldehyde. It is assumed that the reactionproceeds according to the elementary steps:

323323

332

324333

3333

OCH CH CH OCH CH CH 

 HCHOCH OCH CH 

OCH CH CH OCH CH CH 

OCH CH OCH CH 

 

where the first is the initiation step, the second and third are propagation steps, and thefourth is the termination step. Derive a rate expression for this reaction r = k[CH3OCH3]

n assuming pseudo steady state on radical intermediates.

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 Question 4

Consider the chain reaction A    B + C, which proceeds by the steps

 X  R

 RC  B R A

 R A

 R I 

 ,  

 Rt t 

 R A p p

 Aii

 I iI iI 

C k r 

C C k r C k r 

C k r 

 

The first initiation step occurs by reaction of an initiator I  whose initial concentration is CI0,while the second occurs by decomposition of A whose initial concentration is C A0.

(a) Formulate an expression for the rate of this reaction in terms of C A and CI, assumingCR is small. What are the possible orders of this reaction with respect to C A?

(b) Repeat part (a) assuming the termination step is 2R    X,2

 Rt t    C k r    

(c) For the rate in part (a) calculate C A, CB, and CI versus τ in a CSTR assuming k iI  = 0.What is the conversion when τ ∞  if k il  = 0? 

Question 5

Consider the chain reaction A B + C, which proceeds by the steps

 X  R

 RC  B R A

 R A

 ,

 

 Rt t 

 R A p p

 Aii

C k r 

C C k r 

C k r 

 

with k i  = 0.001 sec-1, kp = 200 liter/mole sec, k t  = 0.01s

-1, and C A0 = 2 moles/liter.(a) Find r(C  A ) assuming the pseudo-steady-state approximation.(b) What residence time will be required in a CSTR for 90% conversion for these kinetics?(c) What residence time will be required in a PFTR for 90% conversion for these kinetics?