1

Physical Chemistry

Lecture 6Reaction mechanisms and reaction-velocity predictions

Elementary reactionsReactions of interest are often complexSome reactions do occur in a single step -- elementary reactions Generally involve simple mono- or

bimolecular interactions “Order” (correctly, molecularity) in

elementary reactions is always the stoichiometry number of the reactant

Examples: H2 + O H2OH + Br HBr

“Simple” reaction sequences

Reversible two-step reaction

Irreversible sequential two-step reaction

Irreversible parallel two-step reaction

A B

B C a product

k

k

1

2

( )

A B

B A

k

k

f

r

A B

A C

k

k

1

2

Mathematics of simple reaction sequences

Reversible two-stepBoth first order

Irreversible parallelBoth first order

v k A k A 1 2[ ] [ ]

v k A k Bf r [ ] [ ]

Two-step irreversible process

Both steps first orderExactly solubleGives complex resultCan be understood qualitatively, as well as quantitatively

A B

B C a product

k

k

1

2

( )

Reaction mechanismA description of the course of a reaction that gives a set of elementary reactions Example from Bodenstein’s work:

Reaction mechanisms are not necessarily unique

52

42

32

22

12

5

4

3

2

1 2

vBrBrBrvBrHHBrHvBrHBrBrHvHHBrHBr

vBrBr

k

k

k

k

k

)(2)()( 22 gHBrgBrgH

2

Finding reaction velocityAssuming that every step is elementary allows one to know its rate equationFind expressions for disappearance of reactant or appearance of productInclude terms for every step that affects reactants (or products), with stoichiometryExample from Bodenstein’s work:

5312

432422

][

][][

vvvdt

Brd

vvvdt

HBrdvv

dt

Hd

Reducing rate equations

Eliminate dependence on reactive species (reactive intermediates such as radicals)Use approximations Steady state for reactive species Fast-equilibrium approximation when two

fast steps precede a slow one

Steady-state approximationReactive species have very low concentrationsAfter initiation, this concentration is presumed to be independent of time

Gives relation between velocitiesExample from Bodenstein’s work:

0][

dt

speciesreactived

d Br

dtv v v v v

[ ] 2 2 01 2 3 4 5

Fast-equilibrium approximationOne step containing an intermediate is rate-limitingPrior step is reversible

One presumes a quasi-equilibrium in the first two steps to relate the concentrations

( )

( )

( )

1

2

3

A B C fast

C A B fast

C

Product slow

]][[][][

]][[

][33

2

1 BAKkCkdt

Productd

BA

C

k

kK eqeq

Steady-state rate of formation of HBr

From the reaction mechanism, identify time changes of reactive species and use the steady-state approximation

These two equations give relations0

][

022][

432

54321

vvvdt

Hd

vvvvvdt

Brd

ss

ss

][][

]][[][

][][

423

2/122

2/1

5

221

2/12

2/1

5

151

HBrkBrk

BrH

k

kkH

Brk

kBrvv

ss

ss

Example: H2 + Br2 continuedIdentify the reaction velocity in terms of change of a reactant or product

Substitution gives the final prediction of the steady-state reaction rate by this mechanism

3

5312 ][

v

vvvdt

Brdv

][][

]][[

423

2/322

2/1

5

23

221

HBrkBrk

BrH

k

kkkvss

3

SummaryEvery reaction is described by an equation

“Simple” reaction sequences solved exactlyGenerally, equation like above does NOT describe reaction courseOften cannot get exact time dependence of concentrations for reactions Use a mechanism

Overall reaction expressed in terms of elementary steps Not unique

“Solve” mechanism, using approximations if necessary Rate-limiting steps Steady-state approximation Fast-equilibrium approximation

H gas Br gas HBr gas2 2 2( ) ( ) ( )