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Chem 353 Physical Chemistry II

Chapter 10Chemical Kinetics II.

Composite Mechanism

2013 Fall Semester

Okan Esentürk METU Chemistry Department

Section 2

Ch 10. Chemical Kinetics II. Composite Mechanism

Kinetic reactions:

1) Elementary (simple) reactions

• One-step

• Reactant complex prodcts

direct prodct !ormation t"ro#" acti$ated complex state %it"ot any

complication&

2) 'omposite (complex) Reactions

• Step-%ise or mlti-step reactions

• aority o! c"emical reactions are complex

• Rate is determined *y t"e slo%est reaction called +rate determinin# step, or

+rate controllin# step,

Intro

• 'onsider a rxn

+ → + = • Since t"e rate eation is independent o! . rxn is not a simple reaction *t mst *e a

mlti step rxn&

• ets s##est t"e !ollo%in# mlti-step mec"anism:

→ + → +

• Since t"e slo% rxn determines t"e rate: = • Sc" a mec"anism satis!y t"e rate eation o*ser$ed *y experiment&

Example

! +"#$ → #! + "$ = ! #$ • ! t"is %as a simple rxn t"an rate s"old "a$e *een

= ! #$ !• "ere!ore not a simple reaction *t a composite reaction&

• S##ested mec"anism

1& . slo% rxn*t% 42 and cl

%& + '() → %()+ %'2& . !ast rxn t"at consmes intermediate and reslts 2 and 4'l

%'+'() → '& + %()



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2

Mechanisms are suggestive

• .ll t"e mec"anism t"at satis!ies t"e 5inetic e$idence are st s##esti$e mec"anism&

• .ctal mec"anisms mi#"t *e completely di!!erent&

• "s

A mechanism cannot be proved to be the one with kinetic evidence,

but can be disproved with kinetic evidence.

• t "as o!ten *een !ond t"at a 5inetic mec"anism t"at "as *een accepted !or many

years is pro$ed *y later e$idence to *e ite %ron#&

A reaction of stoichiometry

A+B=Y+Zis found to be second order in A and zero order in B. Suggest a mechanism that is consistent

with this behavior.

Problem 10.4

Solution

fast)(very2Z2Y2BX

slow)(veryX2A

++++→→→→++++

→→→→

Example 10&2

has been studied and the rate equation found to be

Suggest a possible mechanism to explain this behavior.

2

4

6

3

6 I2Fe(CN)2I2Fe(CN) ++++→→→→++++ −−−−−−−−−−−−

0

2

14

6

223

6 ][I][Fe(CN)][I]k[Fe(CN)v −−−−−−−−−−−−−−−−

====

Soltion

• 6otice t"at reaction rate incldes a prodct %/a po%er o! -1&

• "s t"ere mst *e a rxn e& and prodct mst "a$e a coe!!icient o! 1&

• 'onsider a possi*le e& reaction

• #!* mst *e consmed not in rxn rate&

• Rxn (1) cannot *e t"e slo% reaction as *e!ore */c rate en "as prodct $, -.* and reactant $, -/* occrs to t"e second order in rate eation&

• 6ext rxn s"old consme t"e intermediate and s"old *e % / $, -/* to satis!y t"e rate en&

• 7it" s*stittion o! #!* sin# t"e e& constant

−−−−−−−−−−−−−−−−

++++⇔⇔⇔⇔++++ 2

4

6

3

6 )(12)(1)1( I CN Fe I CN Fe

)()()()2(2

4

6

3

62 slow I CN FeCN Fe I ++++→→→→++++

−−−−−−−−−−−−

23

6

2

4

6

]][)([

]][)([K

−−−−−−−−

−−−−−−−−

====

I CN Fe

I CN Fe

])(][[k v 3

622

−−−−−−−−

==== CN Fe I

14

6

2123

62 ])([][])([Kk v −−−−−−−−−−−−−−−−

==== CN Fe I CN Fe

Example 10&3

An investigation was made by M. J. augh and !. ". !alton #J. Amer. $hem. Soc., %&, '(&)*+%&'- of the reaction

of hydrogen chloride with propene at high pressures. hey found that under some circumstances the reaction

was first order in propene and third order in hydrogen chloride/

Suggest a mechanism that is consistent with this result.

3]][[k v HCl propene====

Soltion

• t is not a simple reaction (3

$ + 0 1 → 123)

• "ere cold *e many mec"anism t"at satis!y t"e 5inetic e$idence

• S#esstion:

0 "$ 4 $ ! 5 =$ !

$ !

" $ + 1 4 $61 5! =$6 1

$ 1

7 $ ! + $61→ $/$$$/ + " $ 89

"s = / $ ! $6

$ + : 1 8$/$ = $ !9 → $ /$$$/

Since

$ ! = 5 $ !

and $ 6 = 5! $ 1

= /55! $ / 1



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3

10.1 Evidence for a composite mechanism

• Kinetic en does not correspond to t"e stoic"iometric en&

• 'omplicated concentration dependence o! 5inetic eation sc" as

8 6on-inte#ral po%ers

8 Reactant in denominator

! + ! 4 = ! ! ;!0 + < ; !8 'atalyst in$ol$ement in eation

"!! >?→ "! + ! = !! #*

8 O*ser$ation o! reaction intermediates *y c"emical or spectroscopic met"odsec"anism mst in$ol$e t"e intermediate !ormation t"s 5inetic rxns s"old also in$ol$e t"e

concentration o! intermediates&

Suppose that a reaction of stoichiometry A 0 12 3 4 0 5 is believed to occur by the mechanism

5 is an intermediate. 6rite the expression for the rate of formation of 4.

9ro*lem 10&1

)(

)(2

1

k

k

fast very Z Y B X

slowvery X B A

++++→→→→++++

→→→→++++

Soltion]][[k v 1 B A====

9ro*lem 10&2

Suppose that a reaction A 0 12 3 14 0 17 is believed to occur according to the mechanism

8btain an expression for the rate of formation of the product 4

)(

)(2

2

1

1

k

k

k

slow Z Y B X

mequilibriurapid very X A

++++→→→→++++

⇔⇔⇔⇔

−−−−

Soltion]][[k v 2 B X ====

2 / 1

2 / 1

1

1

2

1

1 ][k

k ][

][

][

k

k A X

A

X

====→→→→====

−−−−−−−−

][][k

k k v 2 / 1

2 / 1

1

12

B A

====

−−−−

10.2 Type of Composite eactions

i& Simltaneos rxns:

ii& Opposin# rxns:

iii& 'onsecti$e rxns:

Reactions are said to ex"i*it !eed*ac5 i! a s*stance

!ormed in one step a!!ects t"e rate o! a pre$ios step&

positi$e !eed*ac5: prodct catalye pre$ios reaction&

ne#ati$e !eed*ac5: prodct dis!a$or pre$ios reaction&

→ → @ + → + $ → ; and ' compete

%/eac" ot"er !or .&

+ A → → B→

→ → B→

10.! ate E"uations for Composite eactions

• 'onsider a rxn *ein# !ormed *y a mec"anism %/elemental steps

A A • Elementary reactions are considered to occr in isolation&

rxn 1: → = rxn 2: ? ! = * rxn 3: → / = ! rxn <: C ? . = *!

• For any species total rate into is t"e sm o! all rates o! rxn

prodcin# t"e species&

• For example: total rate into = or . is

D E = + . = + *! FGH D I = ! = * • otal rate ot o! species is t"e sm o! all rates o! rxn

consmin# t"e species&

D *E = ! + / = * + !

JKL M NONPQR MP SKRT)QPQ QUVW)WXLWVR Y Z [

= Y Z*[ *valid for all the species



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Example* )teady )tate Treatment10.! Consecutive eactions

+ v? → • Bi!!erential rate eations are

] = ] = ] * = ] * ] !

= !

• Steady state treatment (>=? is al%ays small

and^ E^_ = u)

\ = ] * ] ! = u

\ = * + ! "en

Z = Zk = w kwP = m& mn l xm*n + m&For !rt"er in!o:

9"ysical '"emistry ed 2A& 'onsecti$e reactions

9eter .t5ins and Glio de 9ala

Suppose that a reaction of stoichiometry A 0 2 3 4 0 7 is believed to occur according to the mechanism. Apply

the steady:state treatment and obtain an expression for the rate.

v? + → + o what expressions does the general rate equation reduce if

a. he second reaction, is slow, the initial equilibrium being established very rapidly;

b. he second reaction is very rapid compared with the first reaction in either direction;

9ro*lem 10&3

Soltion

0]][[k ][k ][k dt

][d211 ====−−−−−−−−====

−−−− B X X A

X

][k k

][k ][

21

1

B

A X

++++

====

−−−−

][k k

]][[k k ]][[k

dt

][dvv

21

21

2 B

B A B X

Z

- Z ++++

================

a&

1

21

k

]][[k k v

-

B A====! k 2>;? is small compared %it" k -1

*& ][k v 1 A====! k 2>;? is $ery lar#e compared %it" k -1

\

\

ate+Controlling #ate+,etermining% )teps10.! Consecutive eactions

. rate controllin# step is t"e one t"at "as stron# in!lence on t"e o$erall rate o! rxn&

Example: + v? → i& ! t * (intermediate = is rapidly con$erted to @)

• "e o$erall rxn rate is determined *y

y + z → { 8|}~•€ F‚ƒ „~G‚~}}…G† |‚ƒ‡9Z = Zk = w kwP = m& mn l xm*n + m&

Z = mn l x

i& * t ! ( → slo%)

• Since t"e rxn 2 is slo% it does not

e!!ecti$ely distr* t"e eili*rim o! 1st&

ˆ = mnm*n = [ l x \ [ = ̂ l x

Z = Zk

= w k

wP = m&

[ = m&

ˆ l x

Example 10&<

he reaction between iodide ions and the cobalt complex $o*$<'811:, for which the stoichiometric

equation is

is believed to go by the mechanism

Assume that the intermediate exists in a steady state, and derive the general rate equation. 6rite the

rate equation for the special cases of low and high iodide concentrations, and decide which is the rate:

controlling step in each case.

O H I CN Co I OH CN Co 2

3

5

2

25 )()( ++++→→→→++++ −−−−−−−−−−−−

−−−−−−−−−−−−

−−−−−−−−

→→→→++++

++++⇔⇔⇔⇔

−−−−

3

5

k 12

5

2

2

5

k

k

2

25

)()(

)()(

2

1

1

I CN Co I CN Co

O H CN CoOH CN Co

Soltion

"e steady-state eation !or 'o('6)A2- is

0]][)([k ])([k ])([k 2

52

2

51

2

251 ====−−−−−−−− −−−−−−−−−−−−

−−−−

−−−− I CN CoCN CoOH CN Co

6ote t"at >42O? is inclded in t"e $ale o! k -1 *ecase as sol$ent its $ale is essentially

constant&

/ /



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][k k

])([k ])([

21

2

2512

5 −−−−

−−−−

−−−−

−−−−

++++

====

I

OH CN CoCN Co

"e #eneral expression !or t"e rate is

][k k

]][)([k k ])(][[k v

21

2

25212

52 −−−−

−−−−

−−−−−−−−

−−−−−−−−

++++

========

I

I OH CN CoCN Co I

]][)([k

k k v 2

25

1

21 −−−−−−−−

−−−−

==== I OH CN Co

! t"e concentration

o! iodide ions is

s!!iciently lo%

reaction 2is rate-controllin# step&

t"e iodide

concentration is

"i#" eno#"

])([k v 2

251

−−−−

==== OH CN Co

reaction 1 is rate-controllin# step&

ate+Controlling #ate+,etermining% )teps10.! Consecutive eactions

• t is easy to ma5e mista5e on determinin# t"e rate controllin# step&(a5e #reat care in identi!yin# a rate controllin# step& .$oid i! it is not strai#"t !or%ard& t is not essential to

determine&)

• "in#s to pay attention

1& Slo%est step may not *e a rate-controllin# stepi&e propa#ation steps o! a c"ain mec"anism %ill proceed at t"e same rate *t one o! t"em may

control t"e rate&

2& t is not possi*le to decide on rate-controllin# step %/ot t"e in!o on relati$e $ales

o! rate constants&

3& n #eneral rate-controllin# step depends on conc& o! reactants&i&e iodide ion concentration in t"e example&

Read pa#e <2H till 10&<

6itro#en pentoxide reacts %it" nitric oxide in t"e #as p"ase accordin# to t"e

stoic"iometric eation

"e !ollo%in# mec"anism "as *een proposed&

.ssme t"at t"e steady-state treatment can *e applied to 6O 3 and deri$e an eation !or t"e rate

o! consmption o! 62OA&

9ro*lem 10&

252 3 NO NOO N ====++++

2

k

3

52

k

32

32

k

52

22

1

1

NO NO NO

O N NO NO

NO NOO N

→→→→++++

→→→→++++

++++→→→→

−−−−

Soltion

"e steady-state eation !or 6O3 is

0]][[k ]][[k ][k 32321521 ====−−−−−−−−−−−−

NO NO NO NOO N

][k ][k

][k ][

221

5213

NO NO

O N NO

++++

====

−−−−

"e rate o! consmption o! 62OA is

][k ][k

]][[k k

][k ][k

]][[k k ][k

]][[k ][k v

221

5221

221

25211521

32152152

NO NO

NOO N

NO NO

NOO N O N

NO NOO N O N

++++

====

++++

−−−−====

−−−−====

−−−−

−−−−

−−−−

−−−−

"e rate o! consmption o! 6O is

][k ][k

]][[k k

]][[k v

221

5221

32

NO NO

NOO N

NO NO NO

++++

====

====

−−−−

"e rate o! !ormation o! 6O2 is

][k ][k

]][[k k 2

][k ][k

]])[[k ][k k ][k

]][[k ]][[k ][k v

221

5221

221

522121521

3232152152

NO NO

NOO N

NO NO

O N NO NO(O N

NO NO NO NOO N O N

++++

====

++++

−−−−++++====

++++−−−−====

−−−−

−−−−

−−−−

−−−−

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12/10/2013

I

"e reaction 26O J O2 → 26O2 is *elie$ed to occr *y t"e mec"anism

.ssme 62O2 to *e in a steady state and deri$e t"e rate eation& nder %"at conditions does t"e rate

eation redce to second-order 5inetics in 6O and !irst-order 5inetics in O 2L

9ro*lem 10&I

2

k

222

k

22

22

k

2

2

2

2

1

1

NOOO N

NOO N

O N NO

→→→→++++

→→→→

→→→→

−−−−

Soltion

"e steady-state eation !or 62O2 is

0]][[k ][k ][k 2222221

2

1 ====−−−−−−−−−−−−

OO N O N NO

][k k

][k ][

221

2

122

O

NOO N

++++

====

−−−−

"e rate is

][k k

][][k k

]][[k vv

221

2

2

21

22222

O

O NO

OO N O

++++

====

========

−−−−

][k k 221 O>>>>>>>>−−−−

1

2

2

21

k

][][k k v

−−−−

====O NO

][k k 221 O<<<<<<<<−−−− 2

1 ][k v NO====

reaction 3 is t"e rate-controllin# step

reaction 1 is t"e rate-controllin# step

9ro*lem 10&10

he following mechanism has been proposed for the thermal decomposition of pure o=one in the

gas phase &‰Š mn→ ‰Š + ‰& + p M‹w ‰+ ‰Š m&→ & ‰&!erive the rate equation.

Soltion

Rate en:^ Œ

^_ = Œ = / !

+ ! /"e steady-state eation !or O is

= Œ = / ! ] ! / = u\ / ! = ! /

\ = / !!/Ž = ! /

S*stittin# into rate o! !ormation o! oxy#en:

Œ = / ! + ! ! / /Œ = / ! + / !

Œ = " / !

10.- ate Constants ate Coefficients and e". constants

'onsider t"e !ollo%in# eili*rim !ormed !rom elementary reactions&

+ v? + "en = * = * ! t"e system is in eili*rim t"en = * t"s = *

\ = * = ‘ b’

!or%ard and re$erse

rxns are elementary

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12/10/2013

H

Example10.- ate Constants ate Coefficients and e". constants

! +"#$ → #! + "$S##ested mec"&

! + #$ v? # + $“”+#$ v? #! + $

.t e& = * and ! = *!

\ = * = “” “}“! ”} b’ ! = !*! = ”! “}# ”} b’ \ 5– = 55! = !**! = ”! “} !! ”} ! b’ "ead p.)>+

S"o% t"at t"e mec"anism

leads to t"e reslt t"at t"e rate eation !or t"e o$erall reaction is v M k >42?>2?&

9ro*lem 10&1<

)(2

)(

)(2

2

2

2

1

1

k

2

2

k

k 2

k

k 2

slow HI I I H

fast I H H I

fast I I

→→→→++++

⇔⇔⇔⇔++++

⇔⇔⇔⇔

−−−−

−−−−

Soltion

1

1

2

2

k

k

][

][

−−−−

====

I

I 2 / 1

2

2 / 1

1

1 ][k

k ][ I I

====

−−−−

2

2

2

2

2

k

k

]][[

][

−−−−

==== H I

I H ]][[k

k

][ 22

2

2 I H I H

====

−−−−

2 / 1

22

2 / 1

1

1

2

22 ]][[

k

k

k

k ][ I H I H

====

−−−−−−−−

"e o$erall rate is

]][[k ]][[k k

k k k ]][[k v 2222

21

21323 I H I H I I H ====

========

−−−−−−−−

. reaction occrs *y t"e mec"anism

and t"e concentration o! = is s!!iciently small compared %it" t"e concentrations o! . and ; t"at t"e steady state

treatment applies& 9ro$e t"at t"e acti$ation ener#y E a at any temperatre is #i$en *y

t"at is is t"e %ei#"ted mean o! t"e $ales E 1JE 2-E -1 and E 1 %"ic" apply respecti$ely to t"e limitin# cases o!

k 1NNk 2 and k 2NNk -1&

9ro*lem 10&11

Z X B A21

1

k k

k →→→→⇔⇔⇔⇔++++

−−−−

21

121211a

k k

Ek )EEE(k E

++++

++++−−−−++++====

−−−−

−−−−−−−−

Soltion

"e steady-state eation !or = is

0])[k k (]][[k 211 ====++++−−−−−−−−

X B A"e rate is 21

1

k k

]][[k ][

++++

====

−−−−

B A X

]][[k ]][[k k

k k ][k v

21

212 B A B A X ====

++++

========

−−−−

21

21

k k

k k k

++++

====

−−−−

)k k ln(k lnk lnk ln 2121 ++++−−−−++++====−−−−

dT

)k k (d

k k

1

dT

k lnd

dT

k lnd

dT

k lnd 21

21

21 ++++

++++

−−−−++++==== −−−−

−−−−

dT

k lnd

k k

k

dT

k lnd

k k

k

dT

k lnd

dT

k lnd

dT

k lnd 1

21

12

21

221 −−−−

−−−−

−−−−

−−−− +

+++

−−−−

++++

−−−−++++====

dT

k lnd

k k

k

dT

k lnd

k k

k

dT

k lnd

dT

k lnd 1

21

12

21

11 −−−−

−−−−

−−−−

−−−−

−−−−

++++

−−−−

++++

++++====

dT

k lndRTE 2

====

21

121211

1

21

12

21

11a

k k

Ek )EEE(k

Ek k

k E

k k

k EE

++++

++++−−−−++++====

++++

−−−−

++++

++++====

−−−−

−−−−−−−−

−−−−

−−−−

−−−−

−−−−

−−−−



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12/10/2013

11

Chain eactions#10./ree+adical eactions%

• Example: ! + ! → " = œ d ; ž œd ;ŸdŽ 80u679From t"e steps Ž = œd = ! ! + / ! ] . 8n9

Ž = ! ! ] / ! ] . = u 8&9Since

^œŽ^_ =0 t"en^œŽ^_ ] ^ œ̂_ = ^ œ̂_ t"s s*tractin# (2) !rom (1) reslts

œd = " / !S*stittion o! >4? yields

œd = " / !5;! ! ! !/ ! + . ! = ! ! ;!80+Ž;!Ž9

0 z•! —→ " z•" z• +“! — “z• +“7 “ + z •!

—B

“z• + z•˜ “ + “ z • —™→8—?9 z• + “! š " z• —›→8—?9 z•!

= "!5;! = " ! *;!

= /;.

Chain eactions#10./ree+adical eactions%

! + ! → " = ! ! ;!0+ ;!Ž 80u679• >4;r? in denominator: n"i*its t"e reaction *y reaction (<)

• >;r2? di$ision o! >4;r?: redces t"e amont o! in"i*ition %it" reaction 3&

• 4;r and ;r2 compete %it" eac" ot"er !or 4 atom&

0 z! —→ " z•" z• +“! — “z• +“7 “ + z •!

—B

“z• + z•˜ “+“z• —™→8—?9 z• + “! š " z• —›→8—?9 z•!

rganic ,epositions#10./ree+adical eactions%

• any reactions in or#anics #oes t"ro#" c"ain reactions&

Ex: Becomposition o! met"ane: $!- → $!. + !

9roposed mec"anism

0 !“- → " “/" “/ + !“- → “. + !“¢7 !“¢ → £&¤¥ + “˜ “ + !“- → ¤& + !“¢ š " !“¢ → .“i

?@nitiation

???..ropagation

????????..ermination

'"ain mec"anism (most o! t"e decomposition !ollo% t"is pat")

Red: maor prodcts

i#"t *le : minor prodcts

Example 10&A

6ork out the expression for the overall rate of the ethane decomposition according to this mechanism, on

the assumption that t he steady:state hypothesis applies to the free radicals $>, $1', and .

Soltion

"e steady-state eations are

0]][[k ][k

0][k 2]][[k ][k ]][[k :0]][[k ][k 2:

624523

2

525624523623152

62326213

====−−−−

====−−−−++++−−−−

====−−−−

H C H H C H for

H C H C H H C H C CH H C for H C CH H C CH for

0][k 2][k 2 2

525621 ====−−−− H C H C 2 / 1

62

2 / 1

5152 ][)k / k (][ H C H C ====

"e rate o! !ormation o! et"ylene is

2 / 1

62

2 / 1

513523 ][)k / k (k ][k v H C H C ========

most experiments "a$e s"o%n t"e reaction to *e o! t"e !irst order

][)k / k (k ]][[k v 62

2 / 1

513

2 / 1

62523 H C H C H C ========modi!ied

\

12/10/2013



12/10/2013

12

Example 10.6

he mechanism originally proposed in +%>) by B 8. "ice and C. D. er=feld for the ethane

decomposition was

*<ote that this differs from the previous scheme only in the chain:ending step.

!erive the rate equation corresponding to this mechanism, assuming the reaction orders to

correspond to the molecularities.

Solution

The steady-state equations are

0]][[k ]][[k ][k :

0]][[k ]][[k ][k ]][[k :

0]][[k ][k 2:

525624523

525624523623252

62326213

====−−−−−−−−

====−−−−++++−−−−

====−−−−

H C H H C H H C H for

H C H H C H H C H C CH H C for

H C CH H C CH for

0]][[k 2][k 2 525621 ====−−−− H H C H C ][k / ][k ][ 525621 H C H C H ====\

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

6241526251

2

5253 ====−−−−−−−− H C H C H C H C

][k k

k k

k 2

k

k 2

k ][ 62

2 / 1

53

41

2

3

1

3

152 H C H C

++++

++++====

rate constant k 1 is $ery small][k k / k k ][ 62

2 / 1

534152 H C )( H C ====

"e rate o! !ormation o! et"ylene '24<is

][k / k k k (][k k / k k (k ][k v 62

2 / 1

543162

2 / 1

53413523 H C ) H C ) H C ============

P #i$es !irst-order 5inetics in a#reement %it" experiment&P t trned ot not to *e t"e correct mec"anism&

P t %as !ond t"at t"e et"yl radical concentration is mc" "i#"er t"an t"e "ydro#en atom concentration&

P "s t"e termination process '24AJ'24A mst *e more important t"an '24AJ4&

6hen ethanal *acetaldehyde decomposes thermally the main products are methane and carbon monoxide,

and under usual conditions the order of reaction is +.'. A variety of experimental evidence has shown that

the reaction occurs to a large extent by the mechanism

"e steady-state eation !or '43 is0][k ][k ]][[k ][k

2

343333231 ====−−−−++++−−−− CH COCH CHOCH CH CHOCH

"e steady-state eation !or '43'O is

0][k ]][[k 33332 ====−−−− COCH CHOCH CH

0][k ][k 2

3431 ====−−−− CH CHOCH 2 / 1

3

2 / 1

4

13 ][

k

k ][ CHOCH CH

====

"e rate o! c"an#e o! t"e concentration o! met"ane %"ic" is approximately t"e rate

o! c"an#e o! t"e concentration o! acetalde"yde

2 / 3

3

2 / 1

4

12332 ][k

k k ]][[k v CHOCH CHOCH CH

========

Example 10&

\

"e #as-p"ase reaction

proceeds *y a !ree-radical c"ain reaction in %"ic" t"e c"ain propa#ators are 'l and '43 (*t not 4) and t"e

c"ain endin# step is 2'l→'l2& 7rite t"e mec"anism identi!y t"e initiation reaction and t"e c"ain-propa#atin#

steps and o*tain an expression !or t"e rate o! t"e o$erall reaction&

9ro*lem 10&H

HClClCHCHCl 342 +→+

Soltion

"e mec"anism is

2

k

3

k

23

3

k

4

k

2

1

3

2

1

2

)(

)(

)(2

ClCl

n propagatiochainClClCH ClCH

n propagatiochainCH HClCH Cl

initiationClCl

−−−−

→→→→

++++→→→→++++

++++→→→→++++

→→→→

12/10/2013



/ /

13


0]][[k ]][[k :

0][k 2]][[k ]][[k ][k 2:

233423

2

12334221

====−−−−

====−−−−++++−−−−−−−−

ClCH CH ClCH For

ClClCH CH ClClClFor

0][k 2][k 2 2

121 ====−−−−−−−− ClCl

2 / 1

2

2 / 1

1

1 ][k

k ][ ClCl

====

−−−−

][][k

k k ]][[k vv 4

2 / 1

2

2 / 1

1

1242 CH ClCH Cl

HCl

============

−−−−

"e rate o! reaction is t"e rate o! t"e !ormation o! 4'l:

10. 3hotochemical eactions#adiation Chemical xns%

• Re!ers to t"e reactions occr *y radiation! + $! ¦§ "$ j ¨ ¨3• Radiation can *e eit"er particle or electroma#netic

9articles: Q (4e nclei) (electron) cat"ode ray (electron) *eam o! electrons `a–dbe©b `a babdcªElectroma#netic: R Dis D x-Rays -rays

"adiation chemical rxn/ "i#" ener#y radiation t"at reslts in !ormation o! ions&

hotochemical rxn/ lo%er ener#y radiation t"at doe not !orm ions&

hotochemical treshold/ lo%est !reency or "T#"est %a$elen#t" at %"ic" t"e rxn occr&

10. 3hotochemical eactions #Cont$d%

• 9"otoc"emical rxn example:$/$$/ +j¨ → $/$$/ « → $ + "$/- $ery s"ort li!e-time o! excited molecles (C10-I s)

- one-to-one correspondence o! a*sor*ed p"otons to nm*er o! excited molecles&

he law of photochemical equivalance/

t"e rate o! !ormation o! prodcts are proprtional to t"e nm*er o! p"otons

a*sor*edaccordin# to t"e stoic"iometric relations&

• ena*les to calclate rate !rom reslts o! optical measrements

• "e la% is not applica*le i! t"e reaction is not elementary *t a composite one&

• Uield %ill *e less t"an t"e calclated one&

10. 3hotochemical eactions #Cont$d%

• 9"oton yield (or antm yield or ant e!!iciency) ¬¬ = 322 j ®®

• + mol photon 3 + mol einstein

• @s it possible to have ¯ 9 +

Ues& One p"oton may lead to prodction o! more t"an one mole o! prodcts&

Ex: "# +j° → ! + #! ¬ = "ec": “” + ±° → + #“ + # → ! + #” + # → #! 6ot a c"ain reaction

6o cycle

- 7it" a c"ain rxn ¬ cold *e $ery lar#e&

Ex:! + $! + j° → "$ ¬ = 10

12/10/2013



1<

The photochemical 42 5 6r2 eaction10. 3hotochemical eactions

Ex: "! + ! → ""ermal rxn rate: = œ d ;ž ²³´ ;µ³´Ž9"otoc"emical rxn:

= ¶

œ

>;

ž ²³´ ;µ¶³´Ž%"ere : intensity o! t"e li#"t&

- Similarity s##est t"at only t"e initiation rxn is di!!erent&

0 z! + ±° —→ " z" z +“! — “z +“7 “ + z ! —B “z + z˜ “+ “z —™→8—?9 z• + “! š " z —›→8—?9 z•!

????????@nitiation

?.ropagation

*??.."etardation

????????.ermination

a: ntensity o! t"e li#"t a*sor*ed (einsteins/dm3)

einsteins: moles o! p"oton

42 5 6r2 eaction#Cont$d%10. 3hotochemical eactions

Ex: "! + ! → "- Steady state approximationH z

H‚ = z! ”· ] ! z “! + / “ z! + . “ “ z ] ¢ ! = u

Since t"e p"oton is only a*sor*ed *y ;r2 in t"e !irst reaction t"an ¸ ³´¸¹ *y rxn 1 is t%ice t"e

li#"t a*sor*ed/s or z! ”· = " #e"en

¸ ³´¸¹ = "”· ] ! z “! + / “ z! + . “ “ z ] ¢ ! = u.lso

¸ ²̧¹ = ! z “! ] / “ z! ] . “ “z = u"”· ] ¢ ! = u \ = " #e¢

;!

0 z! + ±º —→ " z" z +“! — “z +“7 “ + z ! —B “z + z˜ “ + “ z —™→8—?9 z• + “! š " z —›→8—?9 z•!

12/10/2013



1A

42 5 6r2 eaction#Cont$d%10. 3hotochemical eactions

Ex: "! + ! → "- "s H “zH‚ = = ! z “! + / “ z! ] . “ “z.#ain

¸ ²³´¸¹ ] ¸ ²̧¹ = ¸ ²d¸¹ \ ¸ ²³´¸¹ = " / “ z!S*stittin# ¸ ²̧¹ and sol$in# !or >4? reslts = œ »¼½›

;B d ž™œdŽ

= "/ ! ! "#e¢ ;!/ ! + .Ž z! = "! "¢ ;! ! #e;!/ ! + .Ž = ¾ ! #e;!0+ ;!Ž

0 z! + ±º —→ " z" z +“! — “z +“7 “ + z !

—B

“z + z˜ “ + “ z —™→8—?9 z• + “! š " z —›→8—?9 z•!

3hotosensiti7ation10. 3hotochemical eactions

Sensiti=ation: t"e action or process o! ma5in# sensiti$e or "ypersensiti$e

hotosensiti=ation: process o! initiation o! a rxn *y a*sorption o! li#"t *y one species and

trans!errin# ener#y to anot"er&

Ex: Excitation o! O2 in tmor treatment&

- se o! mercry $apor in 42 to #enerate atomic 4&

- Ena*les to se con$enient and stron# mercry emission line (2A3&nm) to excite&

- Excited 4# atoms li$es lon# and collides %it" 42 and trans!er its ener#y !or dissociation&

“ ¿ i +j° "šÀ67 → « ¿ /1 « + ! → + " « + ! → + - @n and 'd atoms "a$e also *een sed&

lash 3hotolysis10. 3hotochemical eactions

• 9lse met"od

• . !las" o! "i#" intensity s"ort (time) plse o! li#"t irradiates t"e sample and reslts

!ormation o! atoms and molecles

• Rxns o! t"ose !ollo%ed %/!ast spectroscopic tec"nies

• ay *e also re!erred as +plse and pro*e, met"od

• 9ro*e plse intensity is mc" lo%er t"an t"e pmp and is sally in Dis R or 4

• oday iti is possi*le to stdy do%n to attosecond (10-1Is)

Free-radical li!e-times (!e% !s to µs)

Becay o! excited species (ps to ns)

9re c"emical processes sally reire ns resoltion

Sol$ent reor#aniations ener#y distri*tions or ot"er processes may "appen in ps time

scale&

• Read till 10&H 'atalysis

10.8 Catalysis

'atalyst

• a s*stance t"at increases t"e rate o! reaction %it"ot modi!yin# t"e o$erall Vi**s

ener#y c"an#e o! t"e reaction&

• t is not consmed *y t"e reaction

• t s"old not "a$e any permanent c"emical c"an#e

• . catalyst mst in!lence t"e !or%ard and re$erse rates in t"e same proportion&Ex:

con$ersion o! starc" into s#ars t"e rate o! %"ic" is in!lenced *y acids

decomposition o! "ydro#en peroxide in!lenced *y !erric ions and

!ormation o! ammonia in t"e presence o! spon#y platinm&

'atalysis: c"an#e in t"e rate o! a rxn %/participation o! a catalyst

n"i*itor: s*stance t"at decreases t"e rate o! a rxn&

12/10/2013



1

10.8 Catalysis

'atalyst

• a s*stance t"at increases t"e rate o! reaction %it"ot modi!yin# t"e o$erall Vi**s

ener#y c"an#e o! t"e reaction&

it #i$es no ener#y to t"e system t"ere!ore "a$e no in!lence on t"e position o!

eili*rim& (catalyst is nc"an#ed at t"e end o! t"e reaction)

∆V is t"e same %it" or %it"ot a catalyst&

ÁÂ f = ]@Ã 5 t"s e& constant is also t"e same&

5 =

? *ot" rate const& s"old *e a!!ected in t"e same proportion&

10.8 Catalysis

'atalyst

• .n extremely small amont o! a catalyst may case a considera*le increase in t"e rate

o! a reaction

Ex: >'olloidal 9t? M 10-I mol&dm-3 "a$e si#ni!icant e!!ect on decomposition o! "ydro#en

peroxide&

• E!!ecti$eness o! a catalyst may *e expressed *y its trno$er nm*er

2¨ 2® = fÄ ©ÅÆ©_de_b ŸfÇb–ÅÇb© ^b–fŸÈf©b^Ÿ`aÅ_b «aÅŸÆbd fÄ –e_eÇª©_

Bepends on temperatre and s*strate concentration&

1181→→→→118081 turnover number is ' million

10.8 Catalysis

'atalyst

• E!!ecti$eness #enerally measred in terms o! rate coe!!icient&

• Rate o! a catalyed rxn is proportional to t"e concentration o! t"e catalyst&

= $ +i

•

i : rate o! a reaction %it"ot catalyst&

• . catalyst sally lo%ers acti$ation *arrier

*y permittin# t"e rxn to occr *y a lo%er

ener#y rxn pat"&

• n"i*itors do not increase t"e *arrier&

"ey eit"er destroy t"e catalyst or remo$e

acti$ated complex or !ree radicals or ot"er rxn

intermediates t"at %old lead to prodcts&

%%%&ic&ed

Figure 10.5

9cid 6ase Catalysis10.8 Catalysis

• First in 1II< *y Ost%ald and later *y .rr"enis t %as realied t"at t"e reactions catalyed

*y an acid %ere independent o! t"e natre o! t"e anion and is proportional to its electrical

condcti$ity "ence its acidic stren#t" >4J?

• Similarly rate o! reactions t"at are catalyed *y al5alis are proportional to t"e

concentration o! al5ali *t %as independent o! its natre t"s acti$e species is >O4-?

• "s 4J and O4- are t"e e!!ecti$e species in acid or a *ase catalyed rxns&

• n s!!iciently stron# acid soltions %"ere >O4-? is lo% eno#" to "a$e no catalytic acti$ity

= œÉ ž ÊŽ Ê + A Êž + * Êž A 123 Rate constant

!or 4J catalyed

rxn

'oncentration

o! s*strate

12/10/2013



1


• Rxn t"at do occr *y t"e catalysis o! 4J and O4- ions and also %it"ot catalyst

= i Ê + œÉ ž Ê + Œœ? * ÊŽZ = mp + m%É %ž + m‰%? ‰%* ËŽ

• Remem*er: >4J?>O4-? M K% MN >O4-?M K%/>4J?

* = 5Ì

ž \ = i + œÉ ž + Œœ?5Ì

ž Í jj 33 36

= i + œÉ

ž

Žž = 5Ì* \ = i + œÉ 5Ì* + Œœ?*Ž Î jj ®3 36 = i + Œœ?*Ž


• For rxns %it" catalysis is lar#ely *y 4J ions&

= œÉ ž \ }~† = }~†œÉ + }~† žÏÐÑm = )KÒm%É ] T%

.t constant lo# 5 $s p4 "as -1 slope&

• Similarly !or rxn %it" catalysis is lar#ely *y O4- ions&

ÏÐÑm = )KÒm‰%?

] T‰%.t constant lo# 5 $s p4 "as J1 slope

• iddle re#ion s"o%s t"e rate o! spontaneos

reaction&

Digure +E.(

"e re#ion %"ere

catalytic acti$ity isminimal t"s 50 can

*e determined&

= i


• ! t"e rate o! t"e spontaneos reaction is s!!iciently slo%

"oriontal part o! t"e cr$e does not exist& ()

• ! œÉ is ne#li#i*ly small lo% p4 re#ion is not !ond ()

• ! Œœ? is ne#li#i*ly small "i#" p4 re#ion is not !ond& ()

Example: reaction *et%een acetone and iodine in aeos soltion&$/$$/ + #! → $/$$!# + #• Rate is linear in acetone and acid

• Rate o! reaction is independent o! 2 concentration

• ;r2 reaction proceeds %it" t"e same rate

• l2 (or ;r2) mst *e in$ol$ed in !ast step t"s "as no e!!ect on t"e rate

Digure +E.(

he following is a slightly simplified version of the mechanism proposed in +%>& by F. C. "ollefson and ". D.

Daull #J Amer. $hem. Soc., '%, (1'*+%>&- to explain the iodine:cataly=ed decomposition of acetaldehyde/

Apply the steady:state treatment to @, $>$8, and $> and obtain an expression for the rate.

9ro*lem 10&2A

Soltion

)3(0]][[k ][k :

)2(0][k ]][[k :

)1(0][k ]][[k ]][[k ][k :

34333

33323

2

1343221

====−−−−

====−−−−

====−−−−++++−−−−−−−−

HI CH COCH CH For

COCH I CHOCH COCH For

I HI CH I CHOCH I I For


][k

k ][ 2

2 / 1

1

1 I I

=====>=>=>=>

−−−−

][][k

k k ]][[k k vv 3

2 / 1

2

2 / 1

1

123233

CHOCH I I CHOCH CO][CH CO

================

−−−−

0][k ][k )3()2()1( 2

121 ====−−−−====++++++++−−−− I I

12/10/2013



1I

9ro*lem 10&2I

"e !ollo%in# mec"anism "as *een proposed !or t"e al5aline "ydrolysis o! 'o(643)A'12J&

.ssme 'o(643)<(642)'lJ and 'o(643)<(642)2J to *e in t"e steady state and deri$e an expression !or t"e rate o!

reaction& Experimentally t"e rate is proportional to >'o(64)A'12J? >O4-? does t"is !act tell s anyt"in# a*ot "e

relati$e ma#nitdes o! t"e rate constant&

Soltion

SM'o(643)A'l2J

=M'o(643)<(642)'lJ

UM'o(643)<(642)2J

++++

−−−−

−−−−

→→→→

++++→→→→

++++→→→→++++

2

53

k

k

2

k

)()(3

2

1

OH NH CoY

ClY X

O H X OH S

Steady-state eations are

0][k ][k :

0])[k k ([k :

32

211

====−−−−

====++++−−−−−−−−

−−−−

Y X Y For

X ]S][OH X For

21

321

21

1

k k

)[k k k ][

k k

[k ][

++++

====

++++

====

−−−−

−−−−

−−−−

−−−−

]S][OH / (Y

]S][OH X

21

213

k k

[k k ][k v

++++

========

−−−−

−−−− ]S][OH Y

"e dependence o! v on >S? and >O4-? is independent o! t"e relati$e ma#nitdes o! t"e rate constants&

++++

−−−−

−−−−

→→→→

++++→→→→

++++→→→→++++

2

53

k

k

2

k

)()(3

2

1

OH NH CoY

ClY X

O H X OH S

6ronsted elationship10.8 Catalysis

• 'atalysis *y an acid or a *ase in$ol$e proton trans!er

• E!!ecti$eness depends on its acid or *ase stren#t"

• .cid/;ase stren#t" is measred *y its dissociation

e = Âe 5eÓ Ô 5eÓ

Õ 3 3 36Ö× 36 8 Ø Ö Ø 09Âe×$}~†e = }~†Âe + Ö } ~† 5e = }~†Âe ] Ö 5e

• Similarly !or a *ase Æ = ÂÆ 5ÆÙ j u Ø Ú Ø 0}~†Æ = }~†ÂÆ + Ú } ~† 5Æ = }~†ÂÆ ] Ö 5Æ

6ronsted elationship10.8 Catalysis

Remem*er: Ka K* MK%

• For an acid %/more t"an one ionia*le proton (polyprotic acids)

e = Âe 5 Ó Æ = ÂÆ 5Æ

ÙÛ × - j 3 Ü× - 33

12/10/2013



1H

9ro*lem 10&30

he following results have been obtained by !. ". !ahlberg and D. A. Gong #J. Amer. $hem. Soc., '%,

>H1'*+%&>- for the base:cataly=ed enoli=ation of >:methyl acetone.

$atalyst $l$1$88:

$>$88:

8)1:

K aImol dm:> +.>%××××+E:> +.HE××××+E:' (.1'××××+E:H

k Idm> mol:+ s:+ +.)+××××+E:> +.>)××××+E:1 E.1(

Bstimate the 2ronsted coefficientββββ.

Soltion

a

14

bK

10K

−−−−

====

slopeMβ

β ββ β

bbb KGk ====

Dor the oxidation of molecular hydrogen by dichromate ions cataly=ed by Ag0 ions, A. . 6ebster and J. alpern #J.

hys. $hem., (E, 1HE*+%'(- obtained the rate equation

he existence of two terms suggests that two mechanisms are occurring in parallel. Suggest the two mechanisms,

applying the steady:state treatment to obtain the term in the rate equation.

9ro*lem 10&33

]Ag['']H[

]Ag][H[']Ag][H[k

2

222

2 +

+

+

+

+=

k

k v

Soltion

Ag AgH or H Ag Ag AgH

H AgH H Ag

AgH H Ag

++++++++→→→→++++

++++⇔⇔⇔⇔++++

→→→→++++

++++++++++++

++++++++

++++++++

2

22

2

2

!ollo%ed *y t"e rapid reaction o! t"e dic"romate ion

('r2O2-) *y t"e .#4J ion

!ollo%ed *y t"e rapid reaction o! t"e dic"romateion ('r2O

2-) *y t"e .# or .#4J ion

En7yme Catalysis10.8 Catalysis

• Enymes proteins are *iolo#ical catalysts&

• ;e"a$ior is similar to t"e catalytic action o! acids and *ases *t is considera*ly

complicated&

• n #eneral t"e mec"anism is $ery complicated&

• Simplest cases are t"e ones %it" a sin#le s*strate&

Ex: 4ydrolysis o! an ester&

"e rate

o $aries linearly %it" >S? at lo% concentrations (1st order)

o *ecomes independent o! s*strate concentration

(ero-order 5inetics) at "i#" concentrations&

o "is type o! *e"a$ior %as !irst explained in 1H13

*y eonor ic"aelis and ad & enten

in terms o! t"e mec"anism. #eneral trend o! t"e dependence

on s*strate concentrat ion

Figure 10.7

Ý + Ë mnvm?n ÝË

ÝËm&

→ Ý + k


Bn=yme cataly=ed single substrate rxns/

• n #eneral >S? NN >E?

• "s >ES? CC >S?

•^ Þß

^_is $ery small and can *e assmed to *e ero&

• 9ossi*le to apply t"e steady-state treatment àÊ = à Ê ] * àÊ ] ! àÊ = u \ à = * àÊ + ! àÊÊŽ • >E? in t"is eation is t"e concentration o! t"e !ree enyme and it may *e $ery mc" less

t"an t"e total concentration >E?0 o! enyme since mc" o! t"e enyme may *e in t"e !orm

o! ES&

à i = à + àÊ \ àÊ = à i ÊŽ* + ! + ÊŽ

Ý + Ë mnvm?n ÝËÝË m&→ Ý + k

12/10/2013



20




• á±ƒ •F‚ƒ …|

=

= ! àÊ = ! à i ÊŽ

*

+ !

+

ÊŽ = ! à iÊŽ* + !

+ÊŽZ = â ËˆR + ËŽ Ô â = m& Ý p ˆR = m*n + m&mn 8ãWSäMQ)WN SK‹NPM‹P9



Z = â ËˆR + ËŽ Ô â = m & Ý p ˆR = m*n + m&mn 8ãWSäMQ)WN SK‹NPM‹P9• imitin# cases:

9 Ê t 5Ÿ \ = å ßæçž ß = è = ! à i ES *rea5do%n determines t"e rate (rxn 2) (rate-limitin# step)

9 Ê r 5Ÿ \ = å ßæçž ß = æç à i Ê = ?ž à i Êno rate-controllin# step

9 Ê = 5Ÿ \ = å ßßŽž ß = å! Êic"aelis constant is t"e s*strate concentration

at %"ic" t"e rate is one-"al! t"e limitin# rate&



• "e mec"anism

Ý + Ë mnvm?n ÝË m&→éê ÝË¾8→ ë 9 mŠ→ Ý + kalso #i$es t"e same type o! rate eation (%it" one or many more intermediates ES ESW

ESWWX)&

• ! ic"aelis eation applies *t t"e mec"anism is n5o%n t"en t"e rate en cold *e

Z = â ËˆR + ËŽ = m& Ý p ËˆR + ËŽ KL Z = mS Ý p ËˆR + ËŽ5c : catalytic constant

Example 10&H

he following data apply to an en=yme:cataly=ed reaction

#S-Imol dm:> "ate, v Imol dm:>s:+

1.'××××+E:) 1.>××××+E:)

'.E××××+E:> &.H××××+E:)

he concentration of the en=yme is 1 g dm:> and its molecular weight is 'EEEE. Assume the Michaelis:

Menten equation to apply and calculate Michaelis constantK m, the limiting rate, V , and the rate

coefficientk c .

Soltion

][K

][Vv

m S

S

++++

====

4

m

44

105.2K

105.2V1032

−−−−

−−−−

−−−−

××××++++

××××××××====××××.

3

m

34

100.5K

100.5V1087

−−−−

−−−−

−−−−

××××++++

××××××××====××××.

134

34

m

10928V

10207K

−−−−−−−−−−−−

−−−−−−−−

××××====

××××====

sdmmol.

dmmol.

35

1

3

0 10450000

2][ −−−−−−−−

−−−−

−−−−

××××======== dmmolmolg

dmg E

1

35

134

0

c 3.22104

1092.8

][

Vk

−−−−

−−−−−−−−

−−−−−−−−−−−−

====

××××

××××=========>=>=>=> s

dmmol

sdmmo

E

Y

12/10/2013



21

Example 10&10

Suppose that an en=yme system, involving a single substrate, proceeds by t he simple Michaelis:Menten

mechanism. Suppose that kinetic measurements are carried out, at a single temperature, with a particular

substrate S and with a substrate S on which an isotopic substitution has been made.a. Suppose first that separate kinetic measurements are made with S and S. @n terms of the kinetic

parameters k c

and K m

, what will be the ratio of rates at very low, and at very high, substrate concentrations;

b. Suppose instead that competitive isotope effects are studied, i.e., the two substrates S and S are present

together. 6hat will then be the ratio of rates at the two limits;

Soltion

=>=>=>=>==== ][][K

k v

0

m

2 S E

a&at lo% s*strate concentrations

m

*

2

*

m2

*

Kk

Kk

v

v====

at "i#" s*strate concentrations

=>=>=>=>==== 02 ][k v E *

2

2

*k

k

v

v====

*&

products E ES S E

products E ES S E

*

*++++→→→→⇔⇔⇔⇔++++

++++→→→→⇔⇔⇔⇔++++

21

2

21

2

k *

k

k

*

k k

k

"e total enyme concentration is ][][][][ *

0 ES ES E E ++++++++====

0][k ][k ]][[k 211 ====−−−−−−−−−−−−

ES ES S E

0dt

][d====

ES

0][k ][k ]][[k **

2

**

1

**

1 ====−−−−−−−−−−−−

ES ES S E 0

dt][d

*

==== ES

][k

][k ][k ][

1

21

S

ES ES E

++++====

−−−−

])[k k (k

]][)[k k (k ][

*

2

*

11

*

21

*

1*

S

S ES ES

++++

++++====

−−−−

−−−−

)K] /[K][1] /[K]([][ *

mm

*

m0 S S S ES E ++++++++====

1

21m

k

k k K

++++====

−−−−

*

1

*

2

*

1*

mk

k k K

++++====

−−−−

*

mm

*

m

0

K] /[K][1] /[K

][][

S S S

E ES

++++++++

====

"e rate o! !ormation o! prodct !rom S is

)K / ][K / ][1(K

][][k

K] /[K][1] /[K

][k ][k v

*

m

*

mm

02

*

mm

*

m

022

S S

S E

S S S

E ES

++++++++

====

++++++++

========

"e rate o! !ormation o! prodct !rom SZ is

)K / ][K / ][1(K

][][k

][K

][K

K] /[K][1] /[K

][k ][k v *

m

*

m

*

m

*

0

*

2

*

m

*

m

*

mm

*

m

02*

2

*

S S

S E

S

S

S S S

E ES

**

++++++++====

++++++++========

t !ollo%s t"at t"e ratio o! rates at eal concentrations o! S and SZ is

m

*

2

*

m2

*

m

*

2

m2

*Kk

Kk

K / k

K / k

v

v========

he following is a simplified version of the mechanism that has been proposed by . heorell and 2ritton

$hance for certain en=yme reactions involving two substrates A and 2.

Assume that the substrates A and 2 are in excess of B so that the steady:state treatment can be applied to BAand B7, and obtain an expression for the rate.

9ro*lem 10&<0

ZEEZ

YEZBEA

EAAE

3

2

1

1

+→

+→+

⇔+

−

k

k

k

k

Soltion

Steady-state eation !or E.:

0]][[k ][k ]][[k 211 ====−−−−−−−−−−−−

B EA EA A E

Steady-state eation !or E@:

0][k ]][[k 32 ====−−−− EZ B EA

][][k

][k k ][

1

21 EA A

B E

++++====

−−−−

]][[k

k ][

3

2 EA B EZ ====

12/10/2013



22

][][][][ 0 EZ EA E E ++++++++====

][][k

][k k ][

1

21 EA

A

B E

++++====

−−−−

]][[k

k ][

3

2 EA B EZ ====

++++++++

++++====

−−−−

3

2

1

210

k

][k 1

][k

][k k ][][

B

A

B EA E

]][[k k ][k k ][k k k k

]][[][k k k

k

][k 1

][k

][k k

]][[k ]][[k v

21323131

0321

3

2

1

21

022

B A B A

B A E

B

A

B

E B B EA

++++++++++++

====

++++++++++++

========

−−−−

−−−−

6hen an inhibitor @ is added to a single:substrate en=yme system, the mechanism is sometimes

his is known as a competitive mechanism, since S and @ compete for sites on the en=yme.

a. Assume that the substrate and inhibitor are present in great excess of the en=yme, apply the steady:state

treatment, and obtain the rate equation.

b. 8btain an expression for the degree of inhibition defined as

where v is the rate in the presence of inhibitor and v E is the rate in its absence.

9ro*lem 10&<1

0

0

v

vv −=ε

Soltion

Steady-state eation !or ES:

0])[k k (]][[k 211 ====++++−−−−−−−−

ES S E

Steady-state eation !or E:

0][k ]][[k ii ====−−−−−−−− EI I E

][][k

k k ][

1

21 ES S

E ++++

==== −−−−

]][[][k k

)k k (k ]][[

k

k ][

1i

21i

i

i I ES S

I E EI −−−−

−−−−

−−−−

++++========

][][][][ 0 EI ES E E ++++++++====

++++

++++++++++++

====

−−−−

−−−−−−−−

][k k

])[k k (k 1

][k

k k ][][

1i

21i

1

210

S

I

S ES E

][K

][1K

][][k

k k

])[k k (k ][

k

k k

][][k

][k k

])[k k (k 1

][k

k k

][k ][k v

i

m

02

1i

21i

1

21

02

1i

21i

1

21

022

S I

S E

I S

S E

S

I

S

E ES

++++

++++

====++++

++++++++++++

====++++

++++++++++++

========

−−−−

−−−−−−−−

−−−−

−−−−−−−−

a&

*&

][K

][1K

][K

K

][K

][1K

][K1

][][k

][K

][K

][1K

][][k 1

v

v1

v

vv

i

m

i

m

i

m

m

02

m

i

m

02

00

0

S I

I

S I

S

S E

S

S I

S E

++++

++++

====

++++

++++

++++−−−−====

++++⋅⋅⋅⋅

++++

++++

−−−−====−−−−====−−−−

====ε εε ε

he following Kping:pongK mechanism appears sometimes to apply to an en=yme:cataly=ed reaction between

two substrates A and 2 to give the final products 4 and 7/

@t can be assumed that the substrates are present in great excess of the en=yme and that steady:state condition

apply. 8btain an expression for the rate of reaction.

9ro*lem 10&<A

Soltion

Steady-state eation !or E.:

0])[k k (]][[k 211 ====++++−−−−−−−−

EA A E

Steady-state eation !or E.W:

0]]['[k ][k 32 ====−−−− B EA EA

][][k

k k ][

1

21 EA A

E ++++

==== −−−−

]]['[k

k ][

2

3 B EA EA ====

Steady-state eation !or E.W;:

0]'[k ]]['[k 43 ====−−−− B EA B EA ]]['[k

k ]'[

4

3 B EA B EA ====

12/10/2013



23

]'[]'[][][][ 0 B EA EA EA E E ++++++++++++====

++++++++++++++++====

−−−−

4

3

2

3

2

3

1

210

k ][k 1

k ][k

k ][k

][k )k k (]'[][ B B B

A EA E

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

]][[][k k k k

k

][k 1

k

][k

k

][k

][k

)k k (

][][k ]]['[k v

42312143421

04321

4

3

2

3

2

3

1

21

033

B A B A

B A E

B B B

A

B E B EA

++++++++++++++++

====

++++++++++++++++

========

−−−−

−−−−

12/10/2013



1

Chem 353 Physical Chemistry II

Chapter 10

Chemical Kinetics II.Composite Mechanism

2013 Fall Semester

Okan Esentürk METU Chemistry Department

Section 2

10.11 Mechanisms of Macromolecule Formation

• Macromolecule: a substance having a molecular weight of more than 10000.

• Polymer: a molecule of general formula Mn re!eating n i"entical units of M#monomer$

• %t is no longer necessary to have Mn to "efine as a substance as !olymer.

&'am!le: ste!(growth !olymers #con"ensation elimination of water$

)o!olymers #two "ifferent units$ !roteins #having 20 "ifferent amino aci"s$

• )lassification of !olymers #accor"ing to their !re!aration$:

i. *""ition !olymers #usually from free ra"icals$

ii. Ste!(growth !olymers #ste! by ste! formation of a chain by con"ensation reaction$

Addition Polymers10.11 Mechanisms of Macromolecule Formation

• +sually !referre" for olefinic substances such as ethylene an" styrene

• Pro"uce" by free ra"ical initiation of atoms or molecules

• %nteraction of free ra"icals with unsaturate" monomer

• *""ition to the multibon"region − + = → − − − − − − + = → − − − − − −• &very ste! !ro"uces a new larger ra"ical an" reaction continues till termination.

• ,a"ical formation ,: thermally by a catalyst !hoto( or ra"iation(chemical !rocesses.

Step-Groth Polymeri!ation10.11 Mechanisms of Macromolecule Formation

• Ste! by ste! formation of a chain by elimination of a small molecule li-e 2

con"ensation reaction

• Example: ethylene glycol +succinic acid

+ → + • ew larger molecule also has ( an" ) functional gru!s to react further.

• Process can continue in"efinitely forming a large co!olymer.

• )atalyst #aci"s or bases$ is a common choise to initiate reaction.

• &'am!le: Formation of nylon #rea" the boo-$

12/10/2013



2

Ionic Polymeri!ations10.11 Mechanisms of Macromolecule Formation

• )ationic or anionic "e!en"ing on the ion ty!es involve".

• Polymeriation in solution is usually carrie" out by a mechanism involving formation of

ion interme"iates.

• )atalyse" by aci"s or bases.

• ,ate "e!en"s on the "ielectric constant of the solvent.

• )ationic !olymeriation is initiate" by formation of a com!le' #4SM56($ of an aci"#M5$

an" solvent #S$ interaction.

• *nionic !olymeriation is initiate" by "issociation of base #72$ into ions #7 2($

• )ontinue by interaction of of com!le' or the negative ions of base with "oule bon".

"#i$in%" Polymers10.11 Mechanisms of Macromolecule Formation

• *nionic !olymeriation has no termination ste! thus reaction may continue till the

monomer is consume".

• *""ition of new monomer may initiate the reaction an" !olymeriation.

• Polymers forme" by anionic !olymeriation are calle" 8living8 !olymers by Michael

Swarc.

• ,eaction may terminate by im!urities.

,ea" !90(9;

Free &adical Polymeri!ation10.1' Kinetics of Polymeri!ation

• <he general mechanism ? → initiation #!"#$ = %&$

+' → + ' → (−−−−−−−−)* + ' → ) chain p,opagation -.p/01 + 02 → 3142 termination #-t$

• <he stea"y(state e=n for ,1>

%& − 56 ' − 57 8 9):;)< =


• Similarly the stea"y(state e=n for ,2>

56 ' − 56 ' − 57 8 9):;

)<

= •

the stea"y(state e=n for ,n>56 )* ' − 56 ) ' − 57 ) 8 9):;)< =

• %nfinitely many e=uations whose summation is e=ual to ero.

%& − 57 8 );

)< =

• The rate of initiation is equal to the sum of the rates of all the terminations.

? → + ' → +' → (−−−−−−− −)* + ' → )

01 + 02 → 3142

12/10/2013



3


• <he rate of "isa!!erance of monomer is the sum of all the rates of

all the !ro!agations>

− > '># = 569':89):;)<

Since %& − 57 );)< = @ );)< = ABCDE

<hus the rate of "isa!!erance of the monomer>

− F GFH = IJ KLIH MEN 9G:

? → + ' → +' → (

−−−−−−− −)* + ' → )01 + 02 → 3142


−F G

FH = IJ KL

IH

MN

GSpecial case KL − F GFHi$ thermal initiation

%nitial ra"ical

formation reaction

may be secon" or"er.

5& ' 56 5&57 '

ii$ with a catalyst

Might involve

interaction with a

catalyst

5&4M64)6

56 5&

57

' (E

E

iii$ !hotochemical

,ate of initiation may

sim!ly be the intensity

of the light

% 56 O57 9':

Condensation Polymeri!ation10.1' Kinetics of Polymeri!ation

• ,ate "etermine" by following the concentration of functional grou!s #( ()$

• ?et c0 be the initial conc. an" c be conc. at the time t of the functional grou!s.

• <hus

− >P># = 5P Q&7R &)&7&ST UV)WX PY − PP PY• ,ea"ing !9@(!9AA

( Section 10:13

Kinetics of (lectrode &eactions10.1) (lectrochemical *ynamics

Overvoltage (overpotential) : Z = [ −[!$\• a!!lie" voltage amount over the reversible #e=uilibrium$ voltage for the

electrochemical reaction to occur.

• "e!en"s on the cell es!ecially the electro"es

•"evelo!s as a result of electro"e !olariation:B concentration !olariation ( mass trans!ort limite"

B a"sor!tion/"esor!tion !olariation ( rate of surface attach/"etachment

B charge(transfer !olariation ( rate of re"o' reaction

B reaction !olariation ( rate of re"o' reaction of interme"iate in re"o' reaction

• *no"ic overvoltage: *n electrolytic cellCs ano"e is more !ositive using more energy

than thermo"ynamics re=uire.

• )atho"ic overvoltage: *n electrolytic cellCs catho"e is more negative using more energy

than thermo"ynamics re=uire.

ver!otential is an electrochemical term that

refers to the !otential "ifference #voltage$

between a half(reactionCs thermo"ynamically

"etermine" re"uction !otential an" the !otential

at which the re"o' event is e'!erimentally

observe".4Di-i6

12/10/2013



9


Overvoltage (overpotential) : Z = [ −[!$\• <he overvoltage values "ue to the "e!osition !rocess of metals are small .

• vervoltage relate" to the hy"rogen evolution at catho"e is given in <able 10.1.

• y"rogen over!otential

1. Eiffusion of from bul- to the electro"e.

2. Eischarge of the iion to form atom.

3. Formation of hy"rogen molecule at the electro"e.

9. Formation of hy"rogen gas #"esor!tion$

The most slowest step will control the overall rate of the electrochemical reaction


Overvoltage (overpotential) : Z = [ −[!$\• concentration !olariation : "iffusion of ions to the surface controls the overall rate an"

causes the overvoltage #"iffusion control$.

• hy"rogen overvoltage

• the rate is usually controlle" by the "ischarge at the catho"e of hy"rogen ions by

electrons from the metal.

• <affel e=n: relation btw overvoltage an" current "ensity #i/*$Z = " +] ln^* an" b are constants for a given system.


Overvoltage (overpotential) : Z = [ −[!$\• at the e=uilibrium or reversible voltage #Z 0$

( the rate of "e!osition of ions at an electro"e is e=ual to the rate of reioniation of the

"e!osite" substance

( the net rate of "e!osition an" therefore the net current is ero.

• Dhen the a""itional voltage #the overvoltage$ is a!!lie" #Z _ 0$

( the rate of "e!osition is increase"

( the rate of the reverse reaction is "ecrease"

( net "e!osition.

( the greater the overvoltage the greater the current.^` = ^Y$bEd7 "e> ^f = ^Y $* *a b)

Figure 10.11


Overvoltage (overpotential) : Z = [ − [!$\

• Forwar" current: ^` = ^Y$abcEd7 an" reverse current: ^f = ^Y $* *a bcEdg

• et current: ^ = ^̀ − ^f = ^Y-$abcEdg − $* *a bcEdg/

• ?imiting cases:

( o overvoltage Z 0

then both e'!onential terms are ero.

( ?arge overvoltage

then the secon" term becomes ero.

Figure 10.11

12/10/2013



;


Overvoltage (overpotential) : Z = [ −[!$\( ?arge overvoltage

then the secon" term becomes ero. <hus^ = ^Y$bEdg

Z =h

ijln

^

^Y

= −h

ijln ^Y

h

ijln ^

• <he same form as <afel &=n. #Z = " ]ln^ $

•

i: symmetry factor

• i can be calculate" using <afel e=n.

Figure 10.12


Overvoltage (overpotential) :

• i reers to the symmetry factor an" results from neutraliation of an by an electron

at the electro"e surface.

• * more general e'!erssion is

Z =h

kjln

^

^Y= −

h

kjln ^Y

h

kjln ^

• k is transfer coefficient.

Figure 10.12

(lectro+inetic (ffects, he (lectric doule layer10.1) (lectrochemical *ynamics

• ature of the interface between the electro"e an" the solution "etermines the -inetics

of the elecro"e !rocesses.

• %nterface "etermines the movement of !articles an" the solvent in the fiel".

• &lectric "ouble layer: a thin layer of solution #two o!!ositely charge"

layers$ at the electro"e.

• First theory of the layer: elmholt mo"el #a simle mo"el$

( Surface of soli" is !ositively #or negatively$ charge"

( * unimolecular layer of o!!osing charges will be attracte" to the surface.

( * fixed double layer is forme" #a ca!acitor$.

( Potential "ifference between layers = m

oop

( * is usually aroun" 0.3nm.Figure 10.12

<he elmholt

Mo"els


• Secon" theory of the "ouble layer: Eiffuse Eouble ?ayer #Gouy()ha!man Mo"el$

( %m!rove" by consi"ere" more than Hust a sim!le layer of of ions on the solution si"e.

( Solution si"e of the interface has a Ioltman "istribution of the ions.

( <hermal agitation !ermits the ion movement.

( <he "istribution of the o!!osivetly charge" ions is stillnot uniform "ue to the fiel".

( <hic-ness of the "ouble layer is inversely !ro!ortional to the conc.

#0.001 M solution (J thic-ness is K100nm$

( Potential "ifference between layers = mF

oop qr-*s/

( Dhen t = " u = mF

oop

vw$!$

x = > , effective thickness of the double layer

Figure 10.12

Eiffuse Eouble

?ayer

12/10/2013




• <hir" theory of the "ouble layer: combination #tto Stern$

( )ombine" the fi'e" "ouble layer an" "iffuse "ouble layer

( Fi'e" layer with a thic-nessof a

( * "iffuse layer with a thic-ness of '

( Ietter than others.

( ,ea" !9@;(9@A

Figure 10.12

)ombination

10.9. <he !olymeriation of styrene 4M6 catalye" by benoyl !ero'i"e 4)6 obeys a -inetic

e=uation of the form:

y > '># = 5 ' (E E

btain an e'!ression for the -inetic chain length in terms of 4M6 4)6 an" the rate constants

for initiation !ro!agation an" termination.

ch10 chemicalkinetics ii pchem 353.pdf

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