CEE 690K ENVIRONMENTAL REACTION KINETICS Lecture #5 Rate - - PDF document

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CEE 690K

ENVIRONMENTAL REACTION KINETICS

Introduction

David A. Reckhow

CEE690K Lecture #5 1

Updated: 24 September 2013

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Lecture #5

Rate Expressions: Chain Reactions

Brezonik, pp.50-58

Secular Equilibrium

David A. Reckhow

CEE690K Lecture #5

2

 If kii >> ki  The ratio of [B]/[A] approaches a constant  Divide equation for [B] by the equation for [A]  So when kii>>ki, then the exponential approaches zero

t ki

e A A



 ] [ ] [

 

t k t k i ii i

ii i

e e k k A k B

 

   ] [ ] [

 

 

 

t k k i ii i t k t k i ii t k i

i ii ii i i

e k k k e e k k e k A B

   

      1 ] [ ] [

ii i i ii i

k k k k k A B    ] [ ] [

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Example: Radium decay I

David A. Reckhow

CEE690K Lecture #5

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 Natural 226Ra decays as follows:  Radon is used as tracer for vertical mixing from sediments to

water column; Ra is mostly in sediments

 Procedure:

 Collect water column sample & measure purged Rn  Allow sample to reach secular equilibrium and again measure purged Rn  Difference is used to calculate amount of Rn diffused from sediments

Po Rn Ra

ii i

k k 218 222 226

   

t1/2=1620 yr ki=4.28x10-4 yr-1 t1/2=3.8 d ki=6.6x10+1 yr-1

Ra Ra Rn Ra Rn

Radium decay II

David A. Reckhow

CEE690K Lecture #5

4

 How long to wait for secular equilibrium?  % of equilibrium value = 100%(1-e-66t)  92% at 14d  98% at 21d

 

 

 

 

 

t t x t k k i ii i

e e x x Ra Rn e k k k A B

i ii

66 10 28 . 4 66 4 4

1 0000065 . 1 10 28 . 4 66 10 28 . 4 ] [ ] [ 1 ] [ ] [

4

      

       



%

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Chain Reactions I

David A. Reckhow

CEE690K Lecture #5

5



Description

 A multi-step reaction mechanism where the reactants form intermediates that

react with more reactants that yield products plus more intermediates

 Quite common for free radical reactions



Three stages

 Initiation (I)

• initiators

 Propagation (P)

• promotors

 Termination (T)

• scavengers



Evidence

 Induction period  Unusual catalysis or repression  Strange rate equations (product in denominator, fractional order)  Unusual surface effects

Chain Reactions II

David A. Reckhow

CEE690K Lecture #5

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 Simple Generic Cycle P A2 B2 ½ A2 A B

P B A A P A B B P B A A A 2 2

2 2 2 2 2

        

“A” and “B” are reactive intermediates, or chain carriers

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Chain Reactions

David A. Reckhow

CEE690K Lecture #5

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Kinetic Modeling

David A. Reckhow

CEE690K Lecture #5

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 In-class use of Scientist  Consecutive 2nd order reactions

// Example - A --> B --> C Kinetics // This model describes a system having a second order conversion from A to B. // B is subsequently converted to C by another second order reaction. IndVars: TIME DepVars: A, B, C, D Params: A0, D0, KAB, KBC, A' = -KAB*A*D D' = -KAB*A*D-KBC*B*D B' = KAB*A*D - KBC*B*D C' = KBC*B*D // Initial Conditions TIME = 0.0 A = A0 D = D0 B = 0.0 C = 0.0

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David A. Reckhow

CEE690K Lecture #5

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