Lecture 14 Thursday 2/21/08

Pseudo Steady State Hypothesis

(PSSH)

Net Rate of Reaction of Active Intermediates is Zero

Hall of Fame Reaction: 2NO +O2 2NO2

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)

rA* riA 0

Example

The rate law for the reaction

is found from experiment to be

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

A BC

rA kCA

2

1 k CA

For reactions with active intermediates, the reaction coordinated discussed in Chapter 3 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

Solution

(1)

(2)

(3)

AAk1 A *A

A *Ak2 AA

A *k3 BC

r2A* k2CA*CA

r3A* k3CA*

r1A* k1CA2

RatesLaws

Reaction (1) (1)

Reaction (2) (2)

Reaction (3) (3)

Relative Rates

(4)

r1A* k1CA2

r2A* k2CACA*

r3A* k3CA*

r1A r1A* , r3B r3A*

Net Rates: Rate of Formation of Product

(4)

(5)

(6)

Solving for

(7)

rB r3B r3A* k3CA*

rA* r1A* r1A* r2A* r3A*

k1CA2 k2CACA* k3CA* 0

CA* k1CA

2

k 3 k 2CA

CA*

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

(8)

Relative rates overall

(9)

CA*

rB k1k 3CA

2

k 3 k 2CA

A BC

rA

1

rB1

rA rB k1k3CA

2

k3 k2CA

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

and the rate law becomes

(10)

Apparent first order.

k 3

k 2CA

k2CA k3

rA k1k3

k2

CA kCA

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

and the rate law becomes

(11)

Apparent second order

Dividing by and letting and we have the rate law wewere asked to derive

(12)

k 3 k 2CA

rA k3k1

k3

CA2 2k1CA

2

rA kCA

2

1 k CA

k3

k k 2

k 3

k k1

Active Intermediates

A → B + C

Propose a mechanism

Treat each step as elementary

But C*A cannot be measured since it is so small

The rate law found experimentally matches this proposed reaction mechanism

A

AA Ck

kCr

`1

2

CBA

AAAA

AAA

k

k

k

3

2

1

* )3(

* )2(

* )1(

*3

*3*3

*3A

*2*2

21*1

C

B :Product

ABAAA

ABAA

AA

CkrrCkr

CkrCkr

Ckr

B+CA+A

A*

A

A

A

A

A

AA

A

AA

AAAAA

AAAAAAAA

Ck

kC

Ckk

Ck

Ckk

Ckkr

Ckk

CkC

CkCCkCkrPSSH

CkCCkCkrrrr

`11

0 ,0set 2

32

21

23

213

23

21*

*3

*2

21*

*3

*2

21*3*2*1*

What about

A

AAAA Ck

kCrkCr

`1

CBA

IAIA

IAIA

k

k

k

3

2

1

* )3(

* )2(

* )1(

CBA

AAAA

IAIA

IAIA

k

k

k

k

4

3

2

1

)4(

* )3(

* )2(

* )1(

2NO + O2 → 2NO2

Product NO2

NONONO

k

NONO

k

ONONO

k

CCkrNONON

CkrONON

CCkrNOON

*3

*2

3

*3

*2

2

2*3

1

332*3

222*3

11

*32

2O )3(

O )2(

O )1(

22

2

2

2*3

*3

*32

*3

*332

2

2

31

3232

231

32

1

321

33

2

Chigh at very except k 2

0

22

ONONO

NO

ONONO

NO

ONO

NO

NONONOONONO

NONONONO

CCk

kkr

kCkk

CCkkr

Ckk

CCkC

CCkCkCCkr

CCkrr