Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of

chemical reactions and the design of the reactors in which they take place.

Lecture 14

Today’s lecturePseudo Steady State Hypothesis (PSSH)

Net Rate of Reaction of Active Intermediates is Zero

Hall of Fame Reaction: 2NO +O2 2NO2

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An active intermediate is a molecule that is in a highly energetic and reactive state It is short lived as it disappears virtually as fast as it is formed. That is, the net rate of reaction of an active intermediate, A*, is zero.The assumption that the net rate of reaction is zero is called the Pseudo Steady State Hypothesis (PSSH)

3

4

Example

CBA

The rate law for the reaction

rA kCA

2

1 k CA

is found from experiment to be

How did this rate law come about? Suggest a mechanism consistent with the rate law.

5

For reactions with active intermediates, the reaction coordinated now has trough in it and the active intermediate, A*, sits in this trough

A*k1

k2

k3

A+A B+C

A+A

+A

6

AAA*A 2 2k

r2A* k2CA*CA

CB*A 3 3k

r3A* k3CA*

A*AAA 1 1k

r1A* k1CA2

Solution

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Rates:Laws:

r1A* k1CA2Reaction (1)

(1)

r2A* k2CACA*Reaction (2)(2)

r3A* k3CA*Reaction (3)(3)

r1A r1A* , r3B r3A*Relative Rates:But C*A cannot be measured since it is so small

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k3 is defined w.r.t. A*

CA* k1CA

2

k 3 k 2CA

Net Rates: Rate of Formation of Product

rB r3B r3A* k3CA* (4)

*A3*A2*A1*A*A rrrrr (5)

k1CA2 k2CACA* k3CA* 0 (6)

CA*Solving for

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Pseudo Steady State Hypothesis r*A = 0

Substituting for in Equation (4) the rate of formation of B is

CA*

rB k1k 3CA

2

k 3 k 2CA

(8)

rA

1

rB1

CBA

Relative rates overall

rA rB k1k3CA

2

k3 k2CA

(9)10

For high concentrations of A, we can neglect with regard to , i.e.,

3kA2Ck

3A2 kCk

and the rate law becomes

Apparent first order.

rA k1k3

k2CA kCA (10)

11

A23 Ckk

For low concentrations of A, we can neglect with regard to k3, i.e.,

and the rate law becomes

2A1

2A

3

13A Ck2C

kkkr (11)

Apparent second order.Dividing by k3 and letting k’=k2/k3 and k=k1 we have the rate law we were asked to derive

A

2A

A Ck1kCr

(12)

A2Ck

12

What about AA kCr

CBA )4(

AAA*A )3(

IAI*A )2(

I*AIA )1(

4

3

2

1

k

k

k

k

Active Intermediates

)InertI(C̀k1

kCrA

AA

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Why so many Reactions Follow Elementary Rate Laws

22 O2NONO CkCr

The reaction 2NO +O2 2NO2

has an elementary rate law

However… Look what happens to the rate as the temperature is increased.

Active Intermediates / Free Radicals (PSSH)

-rNO2

T14

Hall of Fame Reaction

Why does the rate law decrease with increasing temperature?

Mechanism:*3

k2 NOONO 1 (1)

2k*

3 ONONO 2 (2)

2k*

3 NO2NONO 3 (3)

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Write Rate of formation of Product rNO2

Note: k3 is defined w.r.t. NO2

NONOkCCkr *33NONO33 *

3

21ONO11 ONOkCCkr2

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Assume that all reactions are elementary reactions, such that:

21NO11NO1ONOkrrr *

3*3

*32NO22NO2

NOkrrr *3

*3

NONOk21r

2rr *

33NO33

NO3 *3

*3

NONOk21NOkONOkr *

33*3221NO*

3

*3

*3

*3

*3 NO3NO2NO1NO

rrrr

The net reaction rate for NO3* is the sum of the individual reaction rates for NO3*:

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rNO3

* 0

NONOk21NOkONOk0 *

33*3221

NO

2kkNOONOk0 3

2*321

NO

2kk

ONOkNO3

2

21*3

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Pseudo Steady State Hypothesis (PSSH)The PSSH assumes that the net rate of species A* (in this case NO3

*) is zero.

NO

2kk

ONOkNO3

2

21*3

Pseudo Steady State Hypothesis (PSSH)

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]NO[

2kk

ONOkkNO3

2

22

312

Pseudo Steady State Hypothesis (PSSH)

22RT

EEE

2

312

2

2

31NO ONOe

AAAONO

kkkr

312

2

312 EEE

NO2kk 3

2

The result shows why the rate decreases as temperature increases.20

-rNO2

T

End of Lecture 14

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