atkins & de paula: atkins physical chemistry 9e chapter 22: reaction dynamics

Atkins & de Paula:

Atkins’ Physical Chemistry 9e

Chapter 22: Reaction Dynamics


REACTIVE ENCOUNTERS22.1 Collision theory rate constant, kr encounter rate minimum energy requirement steric requirement.

RTEr

RTEr

BA

r

a

a

eMTPk

eMTk

MTMTvMTcM

RTc

kv

/2/1

/2/1

2/12/12/12/1

)/(

)/(

[A][B])/()/()/(8

[A][B]P B A

NN

22.1(a) Collision rates in gases collision density, the number of (A,B) collisions in a region of the sample in an interval

of time divided by the volume of the region and the duration of the interval:

22

2122

[A]4

),(,[A][B]8

21

21

AA

AA

BA

BABAAAB

Nm

kTZ

mm

mmddddN

kTZ


22.1(b) The energy requirement

[A][B]8

density,collision

8 frequency,collision

2

21

21

21

21

AAB

BArelAB

ArelAAA

relArel

NkT

Z

cZ

czZ

kTccz

NN

NN

N

2

N

N

rel

rel

ctz

tc

/1

/1/1

tubeofvolume

0

0

a

)()(

energy ofon distributiBoltzmann );([A][B])()(A][d

[A][B])(A][d

εεwhen0)()(d

dfvNk

fNdfvdt

Nvdt

vdt

relAr

Arel

Arel

BArelA NN

N

collision cross-section


)(&0)(

1)(1

occurnot do reactions which above ,

)(

cos

)()(

22max

21

21

,)(22max

max

max

2

222

2

22

212

,21

2

22

,2

21

0

aa

adaa

aBA

BArelBArel

relrelBArelrel

relAr

da

aa

a

d

ad

d

advv

d

advvvv

dfvNk

BArelv ,


RTErelArelAr

kTrel

kTC

a

xe

a

edxxeC

a

edxe

kTakT

kTkTrel

kT

kTddvvkTv

relAr

a

a

a

axaxax

axax

a

ecNdfvNk

ekT

dfv

ekTdede

dekTkT

dekT

dfv

dfdekT

dvvf

de

kTdvvfev

kTdvvf

dfvNk

/

0

/

2/1

0

/2,

/

0

/

0

/

2/1

0

/2/1

2/12/3

0

/2/12/3

2/1/

2/3)2/(,2/2

2/3

0

)()(

8)()(

)(1)(

)(182

)(1

2)()(

)(1

2)(

)2(

2

24)(

24)(

)()(

2

2/12212


22.1(c) The steric requirement steric factor, P = σ*/σ. reactive cross-section, σ*, the area within which a molecule must approach another

molecule for reaction to occur. rate constant from collision theory, harpoon mechanism, a process in which electron transfer precedes atom extraction.

RTEAr

aeNkT

Pk /

2/18

(Exercise Example 22.2!)


22.1(d) The RRK model The Rice–Ramsperger–Kassel model (RRK model), a model that takes into account

the distribution of energy over all the bonds in a molecule.

collision in the availableenergy ; breakage, bond for the requiredenergy ; motion, of modes of # the;

for1)(111

EEs

EEkE

EEk

E

EP b

s

b

s

RRK model

Lindemann-Hinshelwood mechanism

Exp. data for unimolecular isomerization of trans-CHD=CHD

s


22.2 Diffusion-controlled reactions cage effect, the lingering of one molecule near another on account of the hindering

presence of solvent molecules.


22.2(a) Classes of reaction diffusion-controlled limit, a reaction in which the rate is controlled by the rate at which

reactant molecules encounter each other in solution. activation-controlled limit, a reaction in solution in which the rate is controlled by the

rate of accumulating sufficient energy to react.

limit controlled-activation:When

limit controlled-diffusion:When

,[A][B][AB]]P[

[A][B]]AB[0[AB][AB][A][B]

[AB]

process activated :a[AB]PAB

[AB]BAAB

diffusion :d pair,encounter :AB[A][B]ABBA

Kkk

kkkkk

kkkk

kk

kkkkk

dt

d

kk

kkkk

dt

d

kv

kv

kv

ad

darda

drad

da

darra

da

dadd

a

d

d


22.2(b) Diffusion and reaction

AdAd

BAB

ABABB

B

Rr

rB

r

rrr

r

r

B

DNRkDNRkdt

d

DDDD

NDRDRDR

R

D

dr

dDJ

JJR

r

R

r

ba

r

d

rr

d

t

tD

x

cD

t

c

Rrrrr

rr

4]B][A[4]B][A[]P[

stationarynot isA

]B][A[4]B[4]B[4reaction of Rate

]B[]B[ lawfirst sFick' From

A) towardB offlux molar :( 4reaction of Rate

]B[1]B[

]B[ :solution General0]B[2]B[

]B[

;0]B[0]B[

state;steady At

;]B[

]B[

solution!in ABBA

A allfor

2

2

2systemsymmetry y sphericall2

2

2dimension32

2

occurs)reaction wheredistance (the at 0]B[ , as )bulk value is ([B] [B]]B[

distance with thehat variesquantity t a signifies

diffusion) of law second s(Fick'equation diffusion

N


22.3 The material balance equation

3

84

medium) ofviscosity ; radius, ichydrodynam ;,(66

equation;Einstein -Stokes usingBy

21 RT

DNRkRRR

RRR

kTD

R

kTD

AdBA

BAB

BA

A

!y!numericallequation balance material thesolvecan wecases, generalFor

)([J] reaction; No

reaction nofor :J][]J[[J] ;convection No

equation balance material J];[J][J][J][

reaction chemical Including

J][J][J][

convection includingequation diffusion the:equationdiffusion dGeneralize

4/2/1

0

2

2

2

2

2

Dtx

tk

r

eDtA

n

e

kx

vx

Dt

xv

xD

t

r


TRANSITION STATE THEORY transition state theory (or activated complex theory, ACT), a theory of rate constants

for elementary bimolecular reactions. transition state, the arrangement of atoms in an activated complex that must be

achieved in order for the products to form.

22.4 The Eyring equation

‡‡θ

‡‡‡

‡θ

‡]J[

θ‡‡

[A][B]

]C[PC

[A][B]]C[

CBA‡

Kkp

RTkkv

kv

Kp

RT

pp

ppK

rr

RTp

BA

C

J

Our task!!


22.4(a) The rate of decay of the activated complex transmission coefficient, κ, the constant of proportionality between the rate of passage

of the complex (k‡) through the transition state and the vibrational frequency along the reaction coordinate (‡); k‡ = κ‡.

22.4(b) The concentration of the activated complex

discarded) C of mode al vibrationonewith ; (

complex. theof modesother theallfor function partition thedenotes where

11

11

1formation;product toleads which vibrationspecificfor function Partition

)B()A()C(&bar 1where

‡‡‡/θB

θA

θ

C‡‡‡

‡

CC‡C

‡‡

‡

/

00‡

00/

θB

θA

θ

C‡/

J

θmJ,

0‡

‡‡‡

‡

0‡

0

J

KKeqq

qNKK

h

kTK

qqh

kTq

h

kT

kTh

qkTh

eq

EEEEpeqq

qNKe

N

qK

RTEA

kTh

rRTEARTE

A

r

rr


22.4(c) The rate constant

difficult!very complex activated of structure and shape, size, theknow tohave we,For

equation Eyring ;

θ

C

‡

C

‡θ‡

‡‡θ

‡

‡

‡

q

Kh

kTK

p

RT

h

kTK

p

RTkkr

22.4(d) The collision of structureless particles

02

8

/22

/2

3

C

BA/2θ

m3

C

3B

3A

θ

C

2

3

C

θm

2θ

C2

~θ

C

‡

θθ

m2/1J

J3J

θmθ

J

,8

22

,,

2mode rotatioal toscorrespond B),(ACBA

)2(

/2/1

0

0

‡

0

‡

‡

‡

‡

2

‡

EErerkT

N

eIkT

Nh

kTe

IkT

V

N

p

RT

h

kTk

mmmmm

mmrI

VIkTqq

p

RTV

kTm

hVq

ra

eNkT

kRTE

A

RTEA

RTEAr

BABA

BA

IBhc

RTaEAr

r

rr


22.4(e) Observation and manipulation of the activated complex Na+I- decay

Photoreaction of IH∙∙∙OCO van der Waals complex IH∙∙∙OCO HOCO resembles the activated complex of H + CO2[HOCO] ‡ HO+CO


22.5 Thermodynamic aspects22.5(a) Activation parameters

RSRS

RTERSr

ar

aRTE

r

RTHRSr

STHGRTGr

steric

a

a

ePBeeA

eBeek

RTHET

kRTEAek

p

RT

h

kTBeBeke

p

RT

h

kTk

KRTG

//2

//2

‡2/

θ// termS into absorbed is /

θ

‡‡

‡‡

‡

‡‡‡‡‡‡

2ln

ln ,activation ofenergy Gibbs

correlation analysis, a procedure in which ln K (=-ΔrGθ/RT) is plotted against ln k (proportional to -Δ‡G /RT).

liner free energy relation (LFER), a linear relation obtained in correlation analysis; reaction becomes thermodynamically more favorable.


22.5(b) Reactions between ions kinetic salt effect, the effect of a change in ionic strength on the rate constant of a reaction.

2/1

BA0

2/12BA

2B

2A

0

2/12BAC

2/12BB

2/12AA

02/1-

01 when

‡

BA

Cθ‡

BA

C‡‡

2log

)(loglog

)(log

loglog

C),25at aq.for 0.509 ,log( law limiting ckeluH-Debye From

[A][B]]P[

[A][B]

]C[]C[

]P[

‡

‡0

‡‡

IzAzk

IzzzzAkk

IzzA

IAzIAz

AAIzz

K

kk

K

Kkkk

dt

d

Kc

Kaa

aKk

dt

d

r

rr

rr

Kkkrr

r

Exercise Example 22.3!


THE DYNAMICS OF MOLECULAR COLLISIONS22.6 Reactive collisions22.6(a) Experimental probes of reactive collisions infrared chemiluminescence, a process in which vibrationally excited molecules emit

infrared radiation as they return to their ground states.IR chemiluminescence

O+CSCO+S


laser-induced fluorescence (LIF), a technique in which a laser is used to excite a product molecule from a specific vibration–rotation level and then the intensity of fluorescence is monitored.


multiphoton ionization (MPI), a process in which the absorption of several photons by a molecule results in ionization.

resonant multiphoton ionization (REMPI), a technique in which one or more photons promote a molecule to an electronically excited state and then additional photons are used to generate ions from the excited state.

A laser pulse excites electrons in a semiconductor surface (10 layers C 60 on a Cu(111) substrate) which in turn pass their energy to adsorbed molecules (NO). REMPI measures the motion of the desorbed molecules.


reaction product imaging, a technique for the determination of the angular distribution of products.

Reaction products detected in the Streamer Chamber when a 1.1-GeV-per-nucleon beam of holmium-165 collided with a holmium-165 target at the Bevalac.


22.7 Potential energy surfaces potential energy surface, the potential energy as a function of the relative positions of

all the atoms taking part in the reaction.

HA + HB-HC HA-HB + HC


saddle point, the highest point on a potential energy surface encountered along the reaction coordinate.



Example of potential energy surfaces.

Ultrafast reaction dynamics of the complete photo cycle of an indolylfulgimide studied by absorption, fluorescence and vibrational spectroscopy


22.8 Some results from experiments and calculations




http://random.chem.psu.edu/movies/REACT.MPG

http://random.chem.psu.edu/movies/NONREACT.MPG


22.8(a) The direction of attack and separation

300


22.8(b) Attractive and repulsive surfaces attractive surface, a potential energy surface in which the saddle point occurs early on

the reaction coordinate. repulsive surface, a potential energy surface in which the saddle point occurs late on the

reaction coordinate.

attractive surface repulsive surface

H + Cl2 HCl +Cl


22.8(c) Classical trajectories direct mode process, a bimolecular process in which the switch of partners takes place

very rapidly. complex mode process, a bimolecular process in which the activated complex survives

for an extended period.

direct mode process complex mode process

atkins & de paula: atkins physical chemistry 9e chapter 22: reaction dynamics

Documents

reaction slide

reaction dynamics slide

reaction products

reaction dynamics saddle

activated complex slide

correlation analysis

h c slide

e chapter