Lindemann – Hinshelwood Mechanism

A + A → A* +AA* is collisionally activatedwith energy to form products

A* → products

Given enough time, it forms productsin a unimolecular process

A*+A → A* + A*

leaving both with too little energy to decompose.

Unless another collisionremoves the excess energy

' A + A A* + A A* + A A + A

A* P *

a

a

bb

k

k

k d Pk A

dt

Lindemann – Hinshelwood Mechanism

Consider only one species A. This is easy to generalize.

The rate law for formation of A* is2 '[A*] A A A* A* 0a a b

d k k kdt

And with ss approx2

'

AA*

Aa

b a

kk k

or

2

'[ ][P] A*

Aa b

bb a

k k Ad kdt k k

with the result

Lindemann – Hinshelwood Mechanism

2[ ][P] A*' A

a bb

b a

k k Ad kdt k k

This is a reaction with indefinite order. However, if the rate for deactivation of A* is much greater than the unimolecular decay, A* P,

then ka’[A*][A] >> kb[A*] or just ka’[A] >> kb , and we have that

'

[ ][P] [A]a beff

a

k k Ad kdt k

a pseudo first order reaction

Such a reaction goes from 2nd order to 1st order as the pressure increases. This is a very common gas phase mechanism, as collisions supply (take away) energy.

' A + A A* + A activationA* + A A + A deactivation of A* A* P unimolecular decay to product

a

a

b

k

k

k

A B M AB M

Lindemann – Hinshelwood Mechanism

O + NO NO2*

NO2* + M NO2 + M*

Normally, bath gas dominates

Lindemann – Hinshelwood Mechanism

'

[ ][P] A [ ]A

a b

b a

k k Ad k Adt k k

From last time

'

[ ]A

a b

b a

k k Akk k

Giving an effective 1st order k

'1 1[ ]

a

a b a

kk k k k A Rearranging,

1/[A]

1/k

Lindemann – Hinshelwood Mechanism

Catalysis:Energy Profile for a Catalyzed Reaction

The catalyst is unchangedat the end if the reaction

ConcepTest 1Consider a reaction which utilizes a catalyst.

Which of the following statements is false?

A. The catalyst modifies kf and kr.B. The catalyst modifies Ea

C. The catalyst modifies Keq

D. The catalyst modifies the net rate to products compared to that of the uncatalyzedreaction.

Let’s now look at a real catalytic process in our atmosphere.

Hydroxyl radical eats hydrocarbonsin the atmosphere

OH+ CH3CHO H2O + CH3CO

It looks like an elementary Rx, but it can be catalyzedby a single water molecule

E. Vohringer-Martinez et al, Science 315, 497 (2007)

OH+ CH3CHO(H2O) H2O + CH3CO + H2O

How??

Energy Profile for Water Catalyzed ReactionOH+ CH3CHO(H2O) H2O + CH3CO + H2O

E. Vohringer-Martinez et al, Science 315, 497 (2007)

No water With water

Energy Profile for Catalyzed Reaction

Chain ReactionsH2 + Br2 2 HBr

Br2 2 Br initiation

k [H2][Br2]1/21 + [HBr]/m[Br2]

Observed Rate =

Br + H2 HBr + H chain propagation

H + Br2 HBr + Br chain propagation

H + HBr H2 + Br inhibition

Br + Br Br2 termination

Chain ReactionsH2 + Br2 2 HBr

Br2 2 Br initiation: collisional or photolytic

k [H2][Br2]1/21 + [HBr]/m[Br2]

Observed Rate =

Br + H2 HBr + H chain propagation

H + Br2 HBr + Br chain propagation

H + HBr H2 + Br inhibition

Br + Br Br2 termination

Reaction Potential Energy Surfaces

The Born Oppenheimer approximation:

Generally a very accurate approximation, and one of the most important concepts in all of physical

science.

Without it, there would be no chemistry as we know it.

B-O approximation allows the construction of potential energy surfaces for molecules (e.g., AB) and for reactions.

Still too many nuclear degrees of freedom!

Select only important ones

AB A+B