Chemistry 232

Kinetics of Complex Reactions

Chain Reactions

Classifying steps in a chain reaction. Initiation

C2H6 (g) 2 CH3•

Propagation Steps C2H6 + •CH3 •C2H5 + CH4

Branching Steps H2O + •O• 2 •OH

Chain Reactions (Cont’d)

Retardation Step HBr + H• H2 + Br•

Terminations Steps 2 CH3CH2• CH3CH2CH2CH3

Inhibition Steps R• + CH3• RCH3

The H2 + Br2 Reaction

The overall rate for the reaction was established in 1906 by Bodenstein and Lind

HBrkBr

BrHk

dt

HBrd/

2

23

22

The Mechanism

The mechanism was proposed independently by Christiansen and Herzfeld and by Michael Polyani.

Mechanism Rate Laws

BrBr 22

HHBrHBr 2

BrHBrBrH 2

BrHHBrH 2

2BrBrBr

211 Brkv 222 HBrkv HBrkv 222 HBrHkv 33

244 Brkv

Using the SSA

Using the SSA on the rates of formation of Br• and H•

HBrkkBr

BrHkkk

dt

HBrd

/2

32

23

224

122

Hydrogenation of Ethane

The Rice-Herzfeld Mechanism

Mechanism

362 2CHHC423362 CHCHCHCHHC

HCHCHCHCH 2223

22333 HCHCHHCHCH 6223 HCHCHCH

Rate Laws for the Rice-Herzfeld Mechanism

The rate laws for the elementary reactions are as follows.

6211 HCkv

36222 CHHCkv

2322 CHCHkv 3322 // CHCHHkv

2333 CHCHHkv

Explosions

Thermal explosions Rapid increase in the reactions rate with

temperature. Chain branching explosions

chain branching steps in the mechanism lead to a rapid (exponential) increase in the number of chain carriers in the system.

Photochemical Reactions

Many reactions are initiated by the absorption of light.

Stark-Einstein Law – one photon is absorbed by each molecule responsible for the primary photochemical process.

IvI I = Intensity of the absorbed radiation

Primary Quantum Yield

Define the primary quantum yield,

absorbed photons of #

productsprimary of #

Define the overall quantum yield,

absorbed photons of #

react that molecules reactant of #

Photosensitization

Transfer of excitation energy from one molecule (the photosensitizer) to another nonabsorbing species during a collision..

HHgHHHg

HHgHHg

HgHgnm

2

2

254

2

Polymerization Kinetics

Chain polymerization Activated monomer attacks another

monomer, chemically bonds to the monomer, and then the whole unit proceeds to attack another monomer.

Stepwise polymerization A reaction in which a small molecule

(e.g., H2O) is eliminated in each step.

Chain Polymerization

The overall polymerization rate is first order in monomer and ½ order in initiator.

The kinetic chain length, kcl Measure of the efficiency of the chain

propagation reaction.

produced centres active of #

consumed units monomer of #

i

pkcl v

v

Mechanism

InitiationI 2 R•

Or

M + R• M1 • Propagation

M + M1• M2 •

M + M2• M3 •

M + M3• M4 •Etc.

Ikv ii

Rate Laws

1npp MMkv

Mechanism (Cont’d)

Termination

M + M3• M4 •

2 Mkv tt

Note – Not all the initiator molecules produce chainsDefine = fraction of initiator molecules that produce chains

Ikdt

Mdi2

Return to Kinetic Chain Length

We can express the kinetic chain length in terms of kt and kp

2

1

21

2

2

2

ti

p

t

pkcl

kk

IMk

Mk

MMk

Stepwise Polymerization

A classic example of a stepwise polymerization – nylon production.NH2-(CH2)6-NH2 + HOOC-(CH2)4COOH

NH2-(CH2)6-NHOC-(CH2)4COOH + H2O

After many stepsH-(NH-(CH2)6-NHOC-(CH2)4CO)n-OH

The Reaction Rate Law

Consider the condensation of a generic hydroxyacid

OH-M-COOH Expect the following rate law

COOHOHkv polypoly

The Reaction Rate Law (Cont’d)

Let [A] = [-COOH] A can be taken as any generic end

group for the polymer undergoing condensation.

Note 1 –OH for each –COOH

2Ak

AOHkv

poly

polypoly

The Reaction Rate Law (Cont’d)

If the rate constant is independent of the molar mass of the polymer

opoly

o

opoly

ot

Atk

A

COOHtk

COOHCOOH

1

1

The Fraction of Polymerization

Denote p = the fraction of end groups that have polymerized

o

to

A

AAp

opoly

opoly

Atk

Atkp

1

Statistics of Polymerization

Define Pn = total probability that a polymer is composed of n-monomers

ppP nn 11

The Degree of Polymerization

Define <n> as the average number of monomers in the chain

t

o

A

A

pn

1

1

Degree of Polymerization (cont’d)

The average polymer length in a stepwise polymerization increases as time increases.

opoly

opoly

opoly

Atk

Atk

Atk

pn

1

11

1

1

Molar Masses of Polymers

The average molar mass of the polymer also increases with time.

Two types of molar mass distributions. <M>n = the number averaged molar mass

of the polymer. <M>w = the mass averaged molar mass

of the polymer.

Definitions of <M>n

Two definitions!

J JJ

on

Mnn

MpM

1

11

Mo = molar mass of monomer n = number of polymers of mass Mn

MJ = molar mass of polymer of length nJ

Definitions of <M>w

<M>w is defined as follows

J JJ

JJ

j

xnow

Mn

Mn

pxMpM n 1221

Note - xn the number of monomer units in a polymer molecule

The Dispersity of a Polymer Mixture

Polymers consists of many molecules of varying sizes.

Define the dispersity index () of the mass distribution.

n

w

M

M

Note – monodisperse sample ideally has <M>w=<M>n

The Dispersity Index in a Stepwise Polymerization

The dispersity index varies as follows in a condensation polymerization

n

w

M

M1

Note – as the polymerization proceeds, the ratio of <M>w/<M>n approaches 2!!!

Mass Distributions in Polymer Samples

For a random polymer sample

09 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

Monodisperse Sample

Polydisperse Sample

Molar mass / (10000 g/mole)

Pn

Types of Catalyst

We will briefly discuss three types of catalysts. The type of catalyst depends on the phase of the catalyst and the reacting species. Homogeneous Heterogeneous Enzyme

Homogeneous Catalysis

The catalyst and the reactants are in the same phase

e.g. Oxidation of SO2 (g) to SO3 (g)

2 SO2(g) + O2(g) 2 SO3 (g) SLOW

Presence of NO (g), the following occurs.NO (g) + O2 (g) NO2 (g)

NO2 (g) + SO2 (g) SO3 (g) + NO (g) FAST

SO3 (g) is a potent acid rain gas

H2O (l) + SO3 (g) H2SO4 (aq) Note the rate of NO2(g) oxidizing

SO2(g) to SO3(g) is faster than the direct oxidation.

NOx(g) are produced from burning fossil fuels such as gasoline, coal, oil!!

Heterogeneous Catalysis

The catalyst and the reactants are in different phases adsorption the binding of molecules on a

surface. Adsorption on the surface occurs on

active sites Places where reacting molecules are

adsorbed and physically bond to the metal surface.

The hydrogenation of ethene (C2H4 (g)) to ethane

C2H4 (g) + H2(g) C2H6 (g) Reaction is energetically favourable

rxnH = -136.98 kJ/mole of ethane. With a finely divided metal such as Ni

(s), Pt (s), or Pd(s), the reaction goes very quickly .

There are four main steps in the process the molecules approach the surface; H2 (g) and C2H4 (g) adsorb on the surface;

H2 dissociates to form H(g) on the surface; the adsorbed H atoms migrate to the adsorbed C2H4 and react to form the product (C2H6) on the surface

the product desorbs from the surface and diffuses back to the gas phase

Simplified Model for Enzyme Catalysis

E enzyme; S substrate; P product

E + S ES ES P + E

rate = k [ES] The reaction rate depends directly on

the concentration of the substrate.

Enzyme Catalysis

Enzymes - proteins (M > 10000 g/mol) High degree of specificity (i.e., they will

react with one substance and one substance primarily

Living cell > 3000 different enzymes

The Lock and Key Hypothesis

Enzymes are large, usually floppy molecules. Being proteins, they are folded into fixed configuration.

According to Fischer, active site is rigid, the substrate’s molecular structure exactly fits the “lock” (hence, the “key”).

The Lock and Key (II)