Kinetics of reaction in solution

Solvent effects

1) Solvation of reactant

2) Catalysis

3) Intermolecular reaction (ions, polar reactant)

4) Diffusion (solvent viscosity)

5) Hydrogen bond

Change mechanism

1) Solvent effects on rate constants

CH3I + Cl CH3Cl + I

solvent HCONH2 HCONHCH3 HCON(CH3)2

k/ dm3 mol-1 s-

1

510-5 1.4 10-4 0.4

The reaction rate depends strongly on the solvent used.

Solvent effect on activation energy

standard Solvent A Solvent B

A B AB P

Bk Tk K

h B exp

k T Gk

h RT

y

A BΔ Δ Δ Δr f f fG G G G y y y y

For evaluation of solvent effect

,0 m,Sr m f m fG G G y y y

,0 ,

0

exp f m f m SSG Gk

k RT

y y

0

Δ(Δ )ln S mk G

k RT

y

+2 5 3 2 5 2 5 4(C H ) N C H I (C H ) N I

Solvents 102k / dm3mol-1s-1

Hexane 0.00018

Benzene 0.0058

chlorobenzene 0.023

nitrobenzene 70.1

If the polarity of product is higher than that of reactants, higher polar solvent benefits the reaction.

C

Br3

Br1

Br2

1.788

2.6552.314

2.591 O

Br2 Br1C

Br3

O1

O2O3

2.479

2431

1.914

2.990

1.929

1.776

Br2

Br1

C

Br3

O2.120

2.969

1.765

2.133

CBr1

Br2

Br3

O2

O1

2.468

2.0272.944

1.817

Br2

Br1

C

Br3

O1

O2

2.275

2.739

1.9142.431

1.988

Br2

Br1 C

Br3

O1

O2

O3

2.828

2.401

1.869

1.910

2.660 2.268

Br

Br

O

C

2) Catalysis of water

3) Effect of ionic strength-primary/kinetics salt effect

For ionic reactions in solution, activity coefficients must be

taken into consideration. Therefore, the apparent rate

constant depends on the ionic strength of the solution.

A B A BA B (A B) PZ Z Z Z k

Bc

k Tk K

h

1

A B A B

( )na c

aK K c

a a

y

1B A B A B0( )n

s a

k Tk c K k

h

y

For dilute solution ln A Z Z I

A B0

log 2skZ Z A I

k

Effect of ionic strength on the rate of reaction between two ions.

+4: Co(NH3)5Br2+ + Hg2+

+2: S2O82- + I

+1: [NO2NCO2C2H5] + OH

0: CH3COOC2H5 + OH

-1: H2O2 + H+ + Br

-2: Co(NH3)5Br2+ + OH

0.0

-0.2

-0.4

0.2

0.4

0.6

0.0 0.1 0.2 0.3I

0

log sk

k

A substantial amount of inert salt (supporting electrolyte) was added to keep the ionic strength and therefore the activity coefficient of the solution essentially constant.

4) Cage effect

Solvent cage: capture reactant molecules

Diffuse in or out, from or to other solvent cages.

Once reactant molecules meet in one solvent cage through diffusion (an encounter), they will be trapped in the cage for a relatively long time during which they collide repeatedly with each other (collision), providing more chance to react.

Within a solvent cage (for 1~100 ns), two reactant molecules can collide 10 ~105 times.

Does viscosity of solvent affect collision in the solvent cage?

Experimental evidence: photolysis of CH3NNCH3 and CD3NNCD3 in gaseous phase and in solution. Given by Lyon and Levy in 1961.

The process can be represented as

A + B → {AB} → products

in which the {AB} term represents the caged reactants including th

e encounter pair and the activated complex.

10-12 ~ 10-10 s, collides for 10 ~ 105 times.

Ere > Ediff. Reaction control.

Ediff. > Ere, diffusion control.

5) Diffusion-controlled reactions

,

,

A+B [A : B]

[A : B] P

d in

d out

r

k

k

k

diffusion

reaction

, ,

[A:B][A][B] [A:B] [ : B] 0

dt d in d out r

dk k k A

,

,

[A][B][A:B] d in

d out r

k

k k

,

,

[A:B] [A][B] [A][B]r d inr

d out r

k kr k k

k k

,

,

[A][B]r d in

d out r

k kr

k k

Discussion:

,d out rk k ,

,

[A][B] [A][B]r d inr d

d out

k kr k K

k

If reaction is much slow than diffusion, activation control or kinetics control

,d out rk k , [A][B]d inr k ,d ink k

If diffusion is much slow than reaction, diffusion control

For activation control

Resembles gaseous reaction, no effect of solvent.

media gas CS2 C6H6 C2H5OH

106 k/ dm3 mol-1 s-1

6 6 10 20

2

Solvent effect on reaction between species of low polarity is weak.

For diffusion control

Fickian first law B Bdn dcDA

dt dx Flux

D diffusion coefficient with unit of m2s-1.

6Bk T

Dr

For spherical particle, Einstein-Storks equation

For second-order reaction 2AB4 B

B

dNr r D

dx

Integration yields A B B B4 ( )r r r D N

A B A B A B A B4 ( )( ) dr r r D D N N k N N

A B A B4 ( )( )dk r r D D

For second-order reaction

4 ( )d A B ABk D D r f f is electrostatic factor.

Diffusion-Limited Rate Constants, Slow reactions

BA B

A B

1 14 ( ) ( )

6d

k Tk r r

r r

BA B

A B

1 14 ( ) ( )

6d

k Tk r r

r r

If rA = rB

B8

3d

k Tk

exp aE

ART

B8exp

3a

d

Ek Tk

A RT

For diffusion, Ea 10 kJmol-1

4． Reactions in Solution 4.1 General Properties of Reactions in Solutions4.2 Diffusion-Limited Rate Constants, Slow reactions4.3 Effect of Ionic Strength on Reactions between Ions4.4 Linear Free-Energy Relationships

J.H. Espenson, Chemical Kinetics and Reaction Mechanisms, 2nd Ed (McGraw-Hill, New York, 1995)

Stochastic and Dynamic Views of Chemical Reaction Kinetics in SolutionsAuthor:A. KuznetsovISBN-10: 2-88074-379-6ISBN-13: 978-2-88074-379-6Published in: January 1999