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Chemical kinetics

Czech chemist

Emil Votoček

1872 - 1950

Collection of Czechoslovak Chemical Communications, 1929

- definition of rates of chemical reactions, reaction orders

- techniques for following concentrations of reactants and products

- elementary reactions and reaction mechanisms

Reaction kinetics – study of reaction rate and time-dependence of

chemical reactions

- mechanisms of chemical reactions

- related processes of reactions: adsorption, dissolution, & others

Kinetics – chemical system far from equilibrium: reaction rates,

concentrations of components, yields of reaction, ... depend on the

reaction time

Catalyzed chemical reactions – change of reaction rates caused by

a change in the reaction mechanism (chemical equilibrium remains

unchanged)

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Applications of chemical kinetics in pharmacy:

Living organisms –non-equilibrium thermodynamic systems

with a number of biochemical reactions under way,

some of which are catalyzed by enzymes

- chemical stability of drugs

- pharmacokinetics of drug action

Example of time-dependence of the contents of a compound in organism:

blood

elimination via excretion

tissue

depot

biotransformation

time

% of dose

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Chemical kinetics

1. Reaction kinetics – kinetics equations for various type of chemical

reactions

2. Theory of chemical kinetics

– molecular mechanism of reactions

– temperature dependence of reaction rates

Basic types of chemical reactions:

– homogeneous reactions – in a single phase (liquid, gas, ...)

– heterogeneous reactions – at a phase boundary (incl. dissolution)

– micro heterogeneous – in colloid systems

12_1575

Time Time

(a) (b) (c)

Course of chemical reaction at molecular level

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Rate of chemical reaction:

DCBA 32

Consider reaction.:

Instantaneous rate:

Consumption of

reactants:

dt

Rd

Formation of

products:

dt

Pd

),( BAR

),( DCP

dt

Bd

dt

Ad

dt

Cd

dt

Dd.2

1.3

1

Instantaneous rate of conversion can be

different for each component:

Extent of chemical reaction:

i

i

i

ii nnn

0

[mol]

Rate of chemical reaction u:

dt

dc

dt

dn

Vdt

d

Vu i

i

i

i

.1

.1.

1.1

- rate of conversion

dt

dn

dt

du i

i

1 1. smol

Rate of chemical reaction in homogeneous solution (volume V)

expressed by means of concentrations:

13. sdmmoldt

dcu i

i

.1

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Time-course of reaction

A B

...... PASimple case:

dt

dc

dt

dcu AA

A

.1

reactant A: 1A

product P: 1Pdt

dc

dt

dcu PP

P

.1

dt

dc

dt

dc PA

Reaction rate can be measured as the change

of reactant/product concentration with the time

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Reaction in gas phase:

dt

dpu A

dt

dpu P

pA, pP – partial pressures

1. sPa

Rate of a heterogeneous chemical reaction occuring on the surface (A)

(corresponding to amount of substance in the volume V):

A

nii Surface density: [mol.m-2]

dt

du i

i

.

1 [mol.m-2.s-1] Reaction rate:

Kinetics of homogeneous reactions

Law of mass action (C.M. Guldberg and P. Waage, 1867).

.....ba

BAku

It was determined experimentaly that the rate of reaction can be

expressed as:

k is the rate constant

rRpPbBaA

... rate of reaction is proportional to the product of concentrations of

reagents at constant temperature

Laws of chemical equilibrium

rate law of the reaction

1)(3)( sdmmol baba

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.....ba

BAku

Rate of chemical reaction :

rRpPbBaA u

rRpPbBaAu

reaction proceeds in both directions

.....rp

RPku

At equilibrium: uu

r

R

p

P

b

B

a

A cckcck ....

b

B

a

A

r

R

p

P

cc

cc

k

k

.

.

k

kKeq

Equilibrium constant of the reaction:

Rate constant & equilibrium constant

C. M. Guldberg and P. Waage, 1867:

In equilibrium concentrations of components of a reaction mixture

will acquire such values that the ratio of concentration of products and

reactants potentiated to stoichiometric coefficients will remain constant,

regardless the initial concentrations

b

B

a

A

r

R

p

Peq

cc

cc

k

kK

.

.

rRpPbBaA

productsBA BA ... ...BAckcu

Overall order of reaction: ...

In simple cases, exponents , , ... are identical with stoichiometric

coefficients of reactants A, B

In general:

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gHBrgBrgH 222

Example:

HBrkBr

BrHku

'

.

2

2/3

22

Uni-directional reaction, reaction order:

rRpPbBaA u

In general: BA ccku ..

a+b molecularity of elementary reaction involved in the

reaction mechanism of complex reactions

+ reaction order (also a non-integer number) corresponds

to empirical rate law, which fits the overall reaction

mechanism

uu

kk

uu

Reactions: zeroth-order kcku A 0.

first-order AA ckcku .. 1

second-order BA ccku ..

2. Acku

third-order DBA cccku ...BA ccku .. 2

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Kinetics of 0-th order reaction:

...... PA catalyst kdt

dcu A

kdtdcA

tc

c

A dtkdcA

A 00

ktcc AA 0

ktcc AA 0

AAP ccc 0Concentration of product:

Concentration of reactant:

ktcP

].[ 13 sdmmol

Reaction rate is independent of concentration:

Zeroth-order reaction:

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Kinetics of 1st order reaction:

... PAA

A kcdt

dcu

kdtc

dc

A

A

tc

c A

A dtkc

dcA

A 00

ktc

c

A

A 0

ln

ktcc AA )(lnln 0

AAP ccc 0 01 A

kt

P cec Concentration of

product:

AA ckcku .. 1

Concentration of

reactant:

Rate of reaction: kt

AA eckkcu 0.

Half live of reaction t1/2 – time of conversion of ½ of the

initial amount of reactant 2

0AA

cc

kt

AA ecc .0

2/1.2

00 kt

AA ecc

kt

2ln2/1

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Reaction of 1st order:

612661262112212 OHCOHCOHOHC

Hydrolysis of saccharose (at acidic pH):

saccharose glucose fructose

sacchOHsacch ckcdt

dcu .2

sacchsacchOH ckccku '.. 2

Bimolecular reaction of first order – pseudo unimolecular reaction

The order of reaction decreases if one of the reactants is in excess amount so

that its concentration can be considered to remain constant during the reaction.

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Kinetics of reactions of 2nd order:

BA ccku ..

... PBA

dt

dc

dt

dcu BA If cA=cB=c:

2kcdt

dc

tc

c

dtkc

dc

0

2

0

ktcc

0

11

ktcc

0

11

0

0

1 ktc

cc

...2 PA

Half-life of reaction of 2nd order:

Half-life t1/2 – time required for conversion of

½ of the reagents 2

0cc

ktcc

0

11

2/1

00

12kt

cc

0

2/1

1

kct

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BA ccku ..If cA cB

cA0, cB0 – initial concentrations x – concentration of molecules

which reacted in time t

xcc AA 0

xcc BB 0

dt

dx

dt

dcA

BAA cckdt

dcu ..

xcxckdt

dxBA 00 .

ktcc

cc

cc AB

BA

AB

0

0

00

ln1

tcckcc

ccAB

AB

BA00

0

0ln

t1/2 is different for A and B

... PBA

Reaction of 2nd order:

22 22 ONONO

ktcc

0

11

Alkalic hydrolysis of ethyl acetate:

OHHCCOONaCHNaOHHCOOCCH 523523

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0th order:

1st order:

2nd order:

ktcc AA 0

ktcc AA )(lnln 0

ktcc

0

11

kdt

dcA

kcku A 0.

Acku .

AA kcdt

dc

2. Acku 2kc

dt

dc

13. sdmmol

1s

131 sdmmol

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Summary:

Reaction: zeroth order kcku A 0.

first order AA ckcku .. 1

second order BA ccku ..

2. Acku

third order DBA cccku ... BA ccku .. 2

time [h]

Determination of reaction order:

nkcdt

dcu

cnku logloglog

General case of kinetic equation:

log c

log

u

log k

ntg

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-2.4 -2.2 -2 -1.8 -1.6 -1.4

log [J]0

-6.8

-6.4

-6

-5.6

-5.2

-4.8

log

u0

log u0 = 2.00 * log[J]0 - 1.84

Initial reaction rate u0 depends on the initial concentration [J]0

as follows: [J]0 (103 mol.dm-3) u0 (107 moldm-3s-1)

5,0 3,6

8,2 9,6

17 41

30 130

00 ]log[loglog Jnku

Example:

2n

11384,1 014,010 smoldmk

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Methods for monitoring the kinetics of chemical reactions:

are based on following the concentration changes, e.g.

- absorption of light - UV spectroscopy:

gHBrgBrgH 222 E.g.

- total pressure measurement (for reactions in gas phase)

- conductometry, potenciometry:

aqClaqHaqCOHCHOHaqCClCH 33233E.g.

gOgNOgON 2252 42 E.g.

- NMR, gas chromatography, titration ...

Techniques:

- flow method

- real time analysis

Flow method: Stopped-flow technique:

Monitoring the kinetics of fast chemical reactions:

„continuous flow“ and „stopped flow“

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Temperature dependence of reaction rate:

Arrhenius equation

Reaction rates and rate constant depend on temperature

In general reaction rate increases with increasing temperature

(not always)

Arrhenius equation:

RT

EAk aexp.

Ea – activation energy of reaction (typically 10 – 200 kJmol-1)

A – pre-exponential factor (dimension of k)

RT

EAk a lnln

Ea , A – Arrhenius parameters

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Activation energy:

Large value of Ea means that rate constant k strongly

depends on temperature T

Ea = 0 – reaction rate is independent of temperature

Ea < 0 – reaction rate decreases with increasing

temperature (reaction proceeds with a complex reaction

mechanism)

Activation energy corresponds to a minimum

kinetic energy of reactants, which is required

for the formation of products

Mechanisms of chemical reactions:

- collision theory

- theory of activated complex

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Collisions must have sufficient kinetic energy

A2 + B2 2 AB

Too slow

Fast

Reactants Activated complex Products

Effective collision

separation

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Questions:

• define rate of chemical reactions, reaction order, molecularity and half-life of

reaction

• explain law of mass action and define rate laws for different orders of reactions

• write the time-dependence of reactant concentration of zeroth-order and first-order

reaction and plot the graphs

• write the time-dependence of reactant concentration of first-order and

second-order reaction and plot the graphs

• explain methods for experimental determination of rate constants of chemical

reactions and show an example of first-order rate constant derivation

• define temperature-dependence of rates of chemical reactions

• explain the meaning of activation energy and its relationships to mechanisms of

chemical reactions