atkins & de paula: atkins’ physical chemistry 9e

Atkins & de Paula:

Atkins’ Physical Chemistry 9e

Chapter 21: The Rates of Chemical Reactions

Chapter 21: The Rates of Chemical Reactions chemical kinetics, the study of reaction rates. mechanism of reaction, the sequence of elementary steps involved in a reaction. CHEMICAL KINETICS21.1 Experimental techniques real-time analysis, a procedure in which the composition of a system is analysed

while the reaction is in progress.(1)flow method, a procedure in which the composition of a system is analysed as the

reactants flow into a mixing chamber. (2)stopped-flow technique, a procedure in which the reagents are mixed very quickly in

a small chamber fitted with a syringe instead of an outlet tube.

Chapter 21: The Rates of Chemical Reactions(3) flash photolysis, a procedure in which the reaction is initiated by a brief flash of light. quenching methods, techniques based on stopping the reaction after it has been allowed

to proceed for a certain time.(1)chemical quench flow method, a technique in which the reactants are mixed as in the

flow method but the reaction is quenched by another reagent.(2)freeze quench method, a technique in which the reaction is quenched by cooling the

mixture.

Chapter 21: The Rates of Chemical Reactions21.2 The rates of reactions21.2(a) The definition of rate rate of consumption of a reactant R, –d[R]/dt. rate of formation of a product P, d[P]/dt. rate of reaction, v = (1/V)dξ/dt where ξ is the extent of reaction. rate of homogeneous reaction, v = (1/vJ)d[J]/dt. rate of heterogeneous reaction, v = (1/vJ)dσJ/dt. 21.2(b) Rate laws and rate constants rate law, the rate as a function of concentration, v = f([A],[B], ...). rate constant, the constant k in a rate law. hydrogen–bromine reaction: the observed rate law is d[HBr]/dt = kr[H2][Br2]3/2/([Br2] +

kr[HBr]).21.2(c) Reaction order reaction order, the power to which the concentration of a species is raised in a rate law of

the form v = [A]a[B]b... . first-order reaction, a reaction with a rate law of the form v = kr[A]. second-order reaction, a reaction with a rate law of the form v = kr[A]2. overall order, the sum of the orders a + b +..., in a rate law of the form v = kr[A]a[B]b.... zero-order rate law, a rate law of the form v = kr.

Chapter 21: The Rates of Chemical Reactions21.2(d) The determination of the rate law isolation method, a procedure in which the concentrations of all the reactants except one

are in large excess. Pseudo first-order rate law, v = kr[A] with kr = kr[B]0 by maintaining B in large excess.

S. W. Han et al., Chem. Lett., 2007, 36, 1350.

N H 2

O H

N O 2

O H

Nanoparticle Catalyst

0 30 60 90 120 150 180-1.5

-1.0

-0.5

0.0ln

A 4

00

Time (sec)

N O 2

O H

NaBH4

N H 2

O HAgNPs

+

-e-re la y

E (A g )+-1.80 V

E (A g )bulk +0.79 V( 4 A P )

E (4 N P )EA

E (B H )ED 4-

E (A g )n


method of initial rates, a procedure in which the rate is measured at the beginning of the reaction for several different initial concentrations of reactants; v0 = kr [A]0

a

log v0 = log kr + a log [A]0.

Example 21.2

Chapter 21: The Rates of Chemical Reactions21.3 Integrated rate laws integrated rate law, the integrated form of a rate law for concentration as a function

of time. 21.3(a) First-order reactions first-order integrated rate law, -d[A]/dt= kr[A] ln([A]/[A]0) = –krt, [A] = [A]0e–krt. half life, t1/2 = (ln 2)/kr. time constant, the time required for the concentration of a reactant to fall to 1/e of its

initial value,τ = 1/kr.

Example 21.3

Chapter 21: The Rates of Chemical Reactions21.3(c) Second-order reactions second-order integrated rate law, -d[A]/dt= kr[A]2 1/[A] – 1/[A]0 = krt [A] = [A]0/(1 + krt[A]0). half life, t1/2 = 1/kr[A]0. half life for nth-order reaction (n>1), t1/2 = 2n-1-1/(n-1)kr[A]0

n-1.

tkABAABB

xBB

xAA

ABxBxAdx

xbxaabxbdx

xadx

abxbxadx

xbxaabxbxa

tkdtkxBxA

dx

xBxAkdtdxxBxAk

dtAd

BAkdtAdPBA

r

x

r

t

r

x

rdtdxdtAdxAA

r

r

)][]([]/[][]/[][ln

][][ln

][][ln

][][1

)])([]([

constant1ln1ln11))((

111))((

1)])([]([

)])([]([)])([]([][

]][[][;

000

0

0

0

0

0

000

00

0000

00//][][][

000


Check this out!


21.4 Reactions approaching equilibrium21.4(a) First-order reactions close to equilibrium

b

b

a

a

eqreqr

r

r

eq

eq

rr

reqeq

rr

req

rr

tkkrr

rrrrr

rr

r

r

kk

kk

KreactiongeneralFor

BkAksamebemustratesreverseforwardmequilibriuat

kk

AB

K

kkAkAAB

kkAkAt

Akk

ekkA

AkAkkAAkAkdtAd

BkAkdtAd

BkvABAkvBA

rr

,

][][;&

][][

][][][][][][;

][][

][])[(])[]([][][

][][][][][

00

0

0

)(

00


21.4(b) Relaxation methods relaxation, the return to equilibrium. temperature jump, a procedure in which a sudden temperature rise is imposed and

the system returns to equilibrium. pressure-jump techniques, as for temperature jump, but with a sudden change in

pressure.

rrt

rreqreqr

rr

eqeq

rreqreqr

kkexx

equationaldifferentiorderstisabovedtdx

dtAd

xkkxBkAxkdtAd

BkAkdtAd

xBBAxA

constratenewarekkBkAkmequilibriunewthetoreadjustssystemjumptempAfter

/1

1][

)()]([)][(][

][][][

][][,][][

.)&(][][,.

/0

Chapter 21: The Rates of Chemical Reactions21.5 The temperature dependence of reaction rates Arrhenius equation, ln k = ln A – Ea/RT. pre-exponential factor (frequency factor), the parameter A in the Arrhenius equation. activation energy, the parameter Ea in the Arrhenius equation; the minimum kinetic

energy for reaction during a molecular encounter. Arrhenius parameters, the parameters A and Ea. generalized activation energy, Ea = RT2(d ln k/dT). activated complex, the cluster of atoms that corresponds to the region close to the

maximum potential energy along the reaction coordinate. transition state, a configuration of atoms in the activated complex which, if attained,

leads to products.


ACCOUNTING FOR THE RATE LAWS21.6 Elementary reactions elementary reaction, a single step in a reaction mechanism.

H + Br2 HBr + Br molecularity, the number of molecules coming together to react in an elementary

reaction. reaction order, the power to which the concentration of a species is raised in a rate

law of the form v = [A]a[B]b... ; an empirical quantity, and obtained from the experimental rate law.

unimolecular reaction, an elementary reaction involving a single reactant molecule. bimolecular reaction, an elementary reaction involving the encounter of two reactant

molecules.

CH3I(alc) + CH3CH2O-(alc) CH3OCH2CH3(alc) + I-(alc)Mechanism: CH3I + CH3CH2O- CH3OCH2CH3 + I-, a single elementary stepRate law: v=kr[CH3I][CH3CH2O-]


21.7 Consecutive elementary reactions consecutive first-order reactions, a sequence of first-order reactions.

00

0

0

0

][1][][][][][

])[(][

][][][

][][

][][][

][][],[][

Akk

ekekPAPIA

Aeekk

kI

eAkIkdt

Id

IkdtPd

IkAkdt

Id

eAAAkdtAd

PIA

ab

tkb

tka

tktk

ab

a

tkab

b

ba

tka

kk

ab

ba

a

a

ba

Chapter 21: The Rates of Chemical Reactions steady-state approximation (or quasi-steady-state approximation, QSSA) the rates

of change of concentrations of all reaction intermediates are negligibly small: d[I]/dt 0 and their concentrations are low.

induction period, the initial stage of a reaction during which reaction intermediates are formed.

0

000

0

][1][

])[1(][[P]

step!gdeterminin ratetheis;][][][

])[(][])[/(][

0][][][

Akk

ekekP

AedteAk

IAAkIkdtPd

Aeekk

kIAkkI

IkAkdt

IdPIA

ab

tkb

tkakk

tkt tka

kab

tktk

ab

akkba

ba

kk

abab

aa

a

baab

ba


validation of steady-state approximation (QSSA)

000

0

0

0

0

])[1(][[P];

][1][;

])[/(])[/(][;

])[(][;

][][;&

AedteAkQSSA

Akk

ekekPExact

eAkkAkkIQSSA

Aeekk

kIExact

eAAQSSAExact

PIA

tkt tka

ab

tkb

tka

tkbaba

tktk

ab

a

tk

kk

aa

ab

a

ba

a

ba

ab kk 20


An example of steady-state approximation

ba

bacaa

ba

abaa

c

bcb

k

k

k

k

kkONkkONNOkNONOkONk

dtONd

NOkkONkNONONOkNONOkONk

dtNOd

ONkNONOkNOONNOkNONOk

dtNOd

NONONOONNO

NOONONONO

ONNONO

NONOON

gOgNOgON

c

b

a

a

][2]][[]][[][][])[(

][][0]][[]][[][][][

]][[][0]][[]][[][NO and NO tes;intermedia

)()(4)(2

52523252

52

2

523323252

3

52

325232

3

22252

2232

5232

3252

2252


rate-determining step, the step in a mechanism that controls the overall rate of the reaction; commonly but not necessarily the slowest step.

Chapter 21: The Rates of Chemical Reactions pre-equilibrium, a state in which an intermediate is in equilibrium with the reactants

and which arises when the rates of formation of the intermediate and its decay back into reactants are much faster than its rate of formation of products.

a

bar

kk

ba

barr

ba

abaa

b

ba

a

babrrbb

a

a

ba

kkkk

kkkkkBAk

dtPd

kkBAkIIkIkBAk

dtId

IkdtPd

kk

kkkKkkBAkBAKkIk

dtPd

kk

BAIK

kkwhenPIBA

ba

],][[][

]][[][0][][]][[][

][][assumingnot

],][[]][[][][]][[

][;


Examples of reaction mechanisms21.8 Unimolecular reactions Lindemann–Hinshelwood mechanism, a theory of ‘unimolecular’ reactions.

a

barrba

ab

bab

ab

a

baa

b

a

a

kkkkAk

dtPdAkAAk

AkkAkkAk

dtPd

AkkAkA

AkAAkAkdtAd

AkdtAdPA

AAkdtAdAAAA

AkdtAdAAAA

],[][];[]][[

][][][][

][][][

0][]][[][][

][][

]][[][

][][

22

2

2

Chapter 21: The Rates of Chemical Reactions Test of Lindemann–Hinshelwood mechanism

linestraightA

againstk

plottheoryofTest

Akkkk

kAkkAkkkAk

dtPd

reactionorderndAkAkk

AkkdtPd

kAkAkAAkAofconcLow

r

aba

a

rab

barr

aab

ba

baba

][11;

][11

][][],[][

A offormaiton r bimolecula theis step gdeterminin-rate A, ofion concentrat lowAt

!2;][][

][][

][][]][[;.

22

activation energies of composite reactions

)()()()(

))(( /)}()()({/)(

/)(/)(

aEbEaEE

eA

AAeA

eAeAkkkk

aaaa

RTaEbEaE

a

baRTaE

a

RTbEb

RTaEa

a

bar

aaa

a

aa


21.9 POLYMERIZATION KINETICS stepwise polymerization, a polymerization reaction in which any two monomers present

in the reaction mixture can link together at any time and the growth of the polymer is not confined to chains that are already forming.

chain polymerization, a polymerization reaction in which an activated monomer attacks another monomer, links to it, then that unit attacks another monomer, and so on.

stepwise polymerization

chain polymerization

Chapter 21: The Rates of Chemical Reactions21.9(a) Stepwise polymerization degree of polymerization, the average number of monomer residues per polymer

molecule, n = 1/(1 – p), where p is the average number of monomers per polymer molecule; n = 1 + krt[A]0.

00

0

0

0

0

0

0

2

][11

1][][ tion;polymeriza of degree

][1][

][][][

condensedCOOHofp,fraction,][1

][][

])[]([][]][[dt

d[A]COOH-R-HO COOH-R-HOFor

AtkpA

AN

AtkAtk

AAAp

AtkAA

COOHAAkAOHk

r

r

r

r

rr

Chapter 21: The Rates of Chemical Reactions21.9(b) Chain polymerization

][2][

]][[

nPropagatio (b))(

step gdetermininrate;][Initiation (a)

CHXCHXCHCHCHXCHXCHCH

1

32

21

1

22222

IfkdtMd

MMkvMMM

MMMMMM

fastMRMIkvRRI

iproduction

ppnn

ii

2

2

][2][nsfer)(chain tra

tionation)(dispropor][on) terminati(mutual

nTerminatio (c)

MkdtMd

MMMMMMMM

MkvMMM

tdepletion

nn

mnmn

ttmnmn

][][][][]][[

][][0][2][2][

2/12/1

2/12

MIkMIkfkkMMkv

IkfkMMkIfk

dtMd

rt

ippp

t

iti

rate of chain polymerization


kinetic chain length, v, the ratio of the number of monomer units consumed per activated centre produced in the initiation step; v = k[M][I]–½.

2/1

2/1212/1

][][

2

]][[22

))((]][[][2][

][2]][[

radicals of production of ratechains ofn propagatio of rate

produced centers activated of #consumed unitsmonomer of #

2/12/1

IMkvN

kfkkkIMkMkMk

MkMMk

v

v

v

r

tiprr

IkfkM

t

p

t

p t

i

Chapter 21: The Rates of Chemical Reactions21.10 PHOTOCHEMISTRY primary process, a process in which products are formed directly from the excited

state of a reactant. secondary process, a process in which products originate from intermediates formed

directly from the excited state of a reactant.


21.10(a) The primary quantum yield primary quantum yield, ϕ, the number of photophysical or photochemical events that

lead to primary products divided by the number of photons absorbed by the molecule in the same interval, ϕ = v/Iabs.

iii

iabsi abs

i

rPICfPICf

i abs

i

ii

abs

vvvI

Iv

orIv

Iv

1

11

1

absorbedlight ofintensity process of rate

absorbed photons of #events of #

Chapter 21: The Rates of Chemical Reactions21.10(b) Mechanism of decay of excited singlet states

ICISCf

f

ICISCf

f

abs

ffICISCfabs

ICISCfabsICISCfabs

ICISCf

tt

ICISCfICISCf

abs

ISCISC

ICIC

fff

absabsi

kkkk

SkkkSk

Iv

SkkkI

SkkkISkSkSkIdtSd

kkkeSS

SkkkSkSkSkS

IS

SkvTS

SkvSS

SkvhvSS

IvShvS

])[(][

])[(

0])[(][][][][

1][][

])[(][][][][ ofdecay of rate

:][ offormation of rate

][:crossing mIntersyste

][:conversion Internal

][:ceFluorescen

:Absorption

0/

00

Chapter 21: The Rates of Chemical Reactions21.10(c) Quenching quenching, shortening of the lifetime of an excited state. Stern–Volmer equation, φf,0/φf = 1 + τ0kQ[Q].

equationr SternVolme];[1

][1][

quencherwithout ;

quencherwith ;][

0]])[[(][

]][[:Quenching

00,

0,

0,

Qk

Qkkk

kk

Qkkkkkkk

k

kkkk

Qkkkkk

SQkkkkIdtSd

SQkvQSQS

Qf

f

ICISCf

Q

f

QICISCf

ICISCf

f

f

f

ICISCf

ff

QICISCf

ff

QICISCfabs

QQ

Stern–Volmer plot


Modified Stern–Volmer equation

][11

][1

11

0

000,

0,0

Qk

Qk

k

kkkkkk

kkk

Q

Qf

f

f

f

f

f

fICISCf

f

ICISCf

Example 21.9

Q: Fe(OH2)63+


Three common mechanism of quenching

QSorQSQS

QSQS

QSQS

:ransferElectron t

:nsferenergy tra Resonance

:ondeactivati lCollisiona

21.10(d) Resonance energy transfer Förster theory, a theory of resonance energy transfer, - efficiency (ηT =1-φf,0/φf); ηT 1/R6 [ηT = R0

6/(R06 + R6)].

- hdonor h acceptor


fluorescence resonance energy transfer (FRET), a technique used to measure distances in biological systems.

ηT = R06/(R0

6 + R6)

7.9 nm

Protein rhodopsin

ηT =1-φf,0/φf

atkins & de paula: atkins’ physical chemistry 9e

Documents