Reaction Mechanisms in Inorganic Chemistry

Elementary Reaction Kinetics: A Review of the Fundamentals

The Arrhenius equation

A + B Pk2

2

P[A][B]

dk

dt

Experimental rate law

• Describes temperature dependence of the reaction rate constant.

k2 = A.exp[-Ea/RT]

ln k2 = -(Ea/RT) + constant

Activated Complex Theory (ACT)

1

1

A + B C

C P

k

k

k

Transition state or activated

complex

A +B

P

C ‡G

Reaction coordinate

K‡ = k1/k-1

[P] = [C ]

t

dk

d

Principal aim of kinetics:

Relating experimental (“macroscopic”) rate and equilibrium constants to theoretical (“microscopic”) rate and equilibrium constants

What is the relationship between k2, k‡ and K‡?

2

P[A][B] experimental

dk

dt

P[C ] theory

dk

dt

2[A][B] = [C ]k k

1

1

[C ]

[A][B]

[C ] = [A][B]

kK

k

K

2[A][B] [A][B]

and

k k K

≠ ≠2k =k K

2k k K

and it can be shown (see notes) that

2 exp( / )kT

k G RTh

2 exp( / ) exp( / )kT

k H RT S Rh

Gibbs energy of activation

Entropy of activation

Enthalpy of activation

The Eyring EquationThe Eyring Equation

2 exp( / ) exp( / )kT

k H RT S Rh

2lnk h H S

kT RT R

ln (

kh/

kT)

2

1 /T

2lnk h H S

kT RT R

2ln lnh H S

kkT RT R

So:

2

2

ln

ln

k H

k S

If S‡ increases, ln k2 increases and reaction is entropy driven

If H‡ decreases, ln k2 increases and reaction is enthalpy driven

If S‡ increases, ln k2 increases and reaction is entropy driven

more disordered transition state

If H‡ decreases, ln k2 increases and reaction is enthalpy driven

less energy in total needed to break chemical bonds

2 exp( / ) exp( / )kT

k H RT S Rh

Transition state theory

2 exp( / )ak A E RT

Arrhenius equation

2aH E RT

In solution

Example (p. 1.5)

Excel

Example (p. 1.5)

-38.5

-38

-37.5

-37

-36.5

-36

-35.5

0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405

Example (p. 1.5)

y = -10093x + 2.3527

R2 = 0.9985

-38.5

-38

-37.5

-37

-36.5

-36

-35.5

0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405

Excel

Example (p. 1.5)

Excely = -10093x + 2.3527

R2 = 0.9985

-38.5

-38

-37.5

-37

-36.5

-36

-35.5

0.00375 0.0038 0.00385 0.0039 0.00395 0.004 0.00405

Example (p. 1.5)

Excel

Example (p. 1.5)

Excel

Example (p. 1.5)

So report results as:

H‡ = 84 2 kJ mol-1

S‡ = 20 7 J K-1 mol-1

Example (p. 1.5)

The kinetic salt effect

1

1

A + B Ck

k

Define

C C

A B A

[C ] = =

[A][B]

=

B

aK

a a

K K

But2k k K

So2

Kk k

K

2

Kk k

K

If i = 1 ∀ i, then K = 1 and k2o = k‡K

o2

2

kk

K

From Debye-Hückel theory:

2 1/ 2j jlog Az I

constant charge

I = ½ mjzj2

is the ionic strength

o2

2

kk

K

o2 2

o2 A BC

o 2 2 2 1/ 22

log log log

log log log log

log ( )A B C

k k K

k

k A z z z I

But

A BCz z z

o 2 2 2 1/ 22 2

o 1/ 22

log log ( ( ) )

log 2

A B A B

A B

k k A z z z z I

k Az z I

1/ 22o2

log 2 A B

kAz z I

k

1/ 22o2

log 2 A B

kAz z I

k

A = 0.509 M-½ in aqueous solution at 25 oC

1/ 22o2

log 2 A B

kAz z I

k

o ++

zA = 0 zB = +1

1/ 2

02 2

02 2

2 0

log( / ) 0

( . ., )

A BAz z I

k k

i e k k

log(

/)

kk

220

I1 /2

0

1/ 22o2

log 2 A B

kAz z I

k

+ ++

zA = 1 zB = +1

0 1/ 22 2log( / ) 2k k AI

log(

/)

kk

220

I1 /2

0

2A

The pressure dependence of rate constants

2(ln )V

kP RT

‡

V‡ > 0

‡

V‡ < 0