Chemical KineticsChemical KineticsJens PoulsenJens Poulsen5 x 2 hours5 x 2 hours

Atkins Atkins

Quanta, matter, and Change.Quanta, matter, and Change.

Chapters 19-21.Chapters 19-21.

BA

A reaction may be investigated A reaction may be investigated on several levels…on several levels…

stochiometry:stochiometry:

rate law:rate law:

atomistic:atomistic:

)]([ 52 gONkv

c

b

a

a

kNONONOONNO

kONONONONO

kONNONO

kNONOON

22252

2232

'5232

3252

)()(4)(2 2252 gOgNOgON

Chapter 22: Rates of chemical Chapter 22: Rates of chemical reactions. Concepts:reactions. Concepts:

Defining reaction Defining reaction rates.rates.

Integrated rate Integrated rate laws.laws.

Elementary Elementary reactions.reactions.

Consecutive Consecutive reactions.reactions.

CBA

)exp(][][ 0 ktAA

][][

Akdt

AdvBA

CBA

Start with chemical kineticsStart with chemical kineticson an empirical level:on an empirical level:

Rate equations: How much NRate equations: How much N22OO55 (g) as a function of time etc? (g) as a function of time etc?

No information about reaction mechanismNo information about reaction mechanism(on an atomic scale).(on an atomic scale).

)()(4)(2 2252 gOgNOgON

Experimental techniquesExperimental techniquesconcentrations can be followed by...concentrations can be followed by...

Measuring pressure during Measuring pressure during chemical reaction: chemical reaction:

)()(4)(2 2252 gOgNOgON

Measuring conductivity during Measuring conductivity during chemical reaction: chemical reaction:

)()()()(

)()()(

33

233

aqClaqHaqCOHCH

lOHaqCClCH

Example 19.1Example 19.1monitoring variation in pressure.monitoring variation in pressure.

)()(4)(2 2252 gOgNOgON

.decomposed has that offraction : 52ON

)2

31(

)2

31(

2

1 2 )1(

l tota :Amount

0

2252

npp

nnnn

ONOON

Def. of v - rate of reaction Def. of v - rate of reaction

more generallymore generally

)()()()(2 3 aqHOIaqHaqIOaqHOIO

dt

HOId

dt

Hd

dt

IOd

dt

HOIOdv

][][][][

2

1 3

dt

Dd

ddt

Cd

cdt

Bd

bdt

Ad

av

][1][1][

)(

1][

)(

1

dDcCbBaA

Reaction orderReaction order

Often has reaction rate of formOften has reaction rate of form

Order m with respect to A,..Order m with respect to A,..

Overall order is m+n+..Overall order is m+n+..

..... CBA

...][][ nm BAkv

ExamplesExamplesfirst order reactionfirst order reaction

second order reactionsecond order reaction

zero order reactionzero order reaction

CTgHCkvgCHgHC 062362 700)]([)(2)(

22 )]([)()(2)(2 gNOBrkvgBrgNOgNOBr

kvgNHHN )(2Ironon 3 322

Determination of rate lawDetermination of rate law

isolation methodisolation method: excess of B, C, …: excess of B, C, …

m can be determined etc.m can be determined etc.

method of initial ratesmethod of initial rates: vary the conc. of A, : vary the conc. of A,

B, C, .. B, C, .. In turnIn turn and check how rate changes. and check how rate changes.

..... CBA ...][][ nm BAkv

Integrated rate lawsIntegrated rate laws

First order rateFirst order rate

straight line: straight line: Second order rateSecond order rate

straight line:straight line:

ktAA )]/[]ln([ 0

)exp(][][ 0 ktAA ][][

Akdt

Adv

ktAA 10

1 ][][2][][

Akdt

Adv

ktAA 10

1 ][][

leads toleads to

]][[][

BAkdt

Adv

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

]/[][ln( 00

0

0 ABktAA

BB

Reactions approaching equil.Reactions approaching equil.

]['

][

BkvAB

AkvBA

]['][][

BkAkdt

Ad

Solution:Solution:

Relation between equilibrium constant Relation between equilibrium constant and rate constants.and rate constants.

.0]['

))'(exp('][][ 00

Bforkk

tkkkkAA

'][

]['

][][][][

'

'][][:

00

0

k

k

A

BK

kk

kAAAB

kk

kAAt

eq

eq

eqeq

eq

Disturbing a system in eq:Disturbing a system in eq:

Sudden change in Sudden change in

e.g. by change in T.e.g. by change in T.

BAk

k

'

',kk

dt

dx

dt

Adxkkx

dt

Ad

xBkxAkBkAkdt

Ad

xBBxAA

eqeq

eqeq

][

but '][

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

][][][][

The rate to new equilibrium is The rate to new equilibrium is given by the sum of given by the sum of

))'x(0)exp(-(x(t) )'( tkkxkkdt

dx

',kk

'1

kk

Example 19.4Example 19.4

Calculate the rate constantsCalculate the rate constantsfor water autoprotolysis, given for water autoprotolysis, given

Forward/backward reaction is first/second-Forward/backward reaction is first/second-order, respectively, and T=298 K, pH=7.order, respectively, and T=298 K, pH=7.

BLACK-BOARD!BLACK-BOARD!

2

2 /]][[)()()('

cOHHKaqOHaqHlOH W

k

k

.103737 6 ss

',kk

Temperature dependence ofTemperature dependence ofchemical reactions.chemical reactions.

What can be said about k(T) ?What can be said about k(T) ?

Arrhenius equationArrhenius equation

]][)[( BATkvCBA

)/exp()( RTEATk a

Svante ArrheniusSvante ArrheniusNobel prize 1903.Nobel prize 1903.

interpretationinterpretation

*Reaction coordinate: molecular distortion *Reaction coordinate: molecular distortion along which the reactants become products.along which the reactants become products.

*Transition state = activated complex = climax *Transition state = activated complex = climax of reaction. of reaction.

*Once the reactants have passed the *Once the reactants have passed the transition state, productstransition state, products

are formed.are formed.

)/exp()( RTEATk a ]][)[( BATkvCBA

interpretationinterpretation

Ea: Ea: activation energy (change in potential energy)activation energy (change in potential energy). . Only molecules having kinetic energy larger than Ea Only molecules having kinetic energy larger than Ea

get over barrier.get over barrier.exp(-Ea/RT): fraction of reactants exp(-Ea/RT): fraction of reactants

having enough kinetic energy to pass barrier having enough kinetic energy to pass barrier A: pre-exponential factor: measure of the rate of A: pre-exponential factor: measure of the rate of

collisions collisions

)/exp()( RTEATk a

]][)[( BATkvCBA

exp(-Ea/RT): fraction of reactants having exp(-Ea/RT): fraction of reactants having kinetic energy higher than barrier height Ea.kinetic energy higher than barrier height Ea.

A: proportional to collision frequency.A: proportional to collision frequency.

K(T) = collision frequency timesK(T) = collision frequency times fraction of successful collisionsfraction of successful collisions = A * exp(-Ea/RT)= A * exp(-Ea/RT)

)/exp()( RTEATk a

Accounting for the rate laws. Accounting for the rate laws.

Elementary reactions: The fundamental Elementary reactions: The fundamental “building blocks” of chemical reactions.“building blocks” of chemical reactions.

Describes what happens on an Describes what happens on an atomicatomic scale.scale.

one ethanoate ion collides with one one ethanoate ion collides with one

methyliodide molecule and forms one iodide methyliodide molecule and forms one iodide ion plus one methylethylether….ion plus one methylethylether….

ICHOCHCHOCHCHICH 323233

Elementary reactionsElementary reactions

The molecularity of a reaction: # of The molecularity of a reaction: # of molecules participating.molecules participating.

Unimolecular: one molecule.Unimolecular: one molecule. Bimolecular: two molecules. Bimolecular: two molecules. A unimolecular reaction is first-order.A unimolecular reaction is first-order. A bimolecular reaction is second-order.A bimolecular reaction is second-order.

]][[/][

][/][

BAkdtAdPBA

AkdtAdPA

Elementary reactionsElementary reactions

If we know a reaction is single-step and If we know a reaction is single-step and bimolecular we can write down a rate bimolecular we can write down a rate equation directly:equation directly:

Same applies to unimolecular reactions...Same applies to unimolecular reactions...

]][[/][ BAkdtAdPBA

Elementary reactionsElementary reactions

On the other hand, consider the reaction On the other hand, consider the reaction

A rate law of formA rate law of form

does does notnot imply the reaction to be simple bi- imply the reaction to be simple bi-molecular:molecular:

]][[/][ BAkdtAd

)()()( gPgBgA

PBA

Example. Example.

)]()][([ 2 gOgHBrkv

Consecutive elementary Consecutive elementary reactionsreactions

example: enzyme/substrateexample: enzyme/substrate

PIAba kk

Solving time-dependence of Solving time-dependence of [P]. [P].

BLACK-BOARD!BLACK-BOARD!

PIAba kk

0][)exp()exp(

1][ Akk

tkktkkP

ab

abba

Consecutive reactionsConsecutive reactions

Qualitative time-dependence ofQualitative time-dependence of

[A], [I] and [P].[A], [I] and [P].

Steady State approx.Steady State approx.VERY IMPORTANT!!VERY IMPORTANT!!

The higher the molecularity, the more The higher the molecularity, the more complex mathematics when solving rate complex mathematics when solving rate equations. equations. Need approximation.Need approximation.

Introduce Introduce steady state approximationsteady state approximation::

PIAba kk

ab kkdt

IdI 0

][0][

Steady state approx. continued.Steady state approx. continued.

More generally: all intermediates More generally: all intermediates

are assumed to have negligible concentration are assumed to have negligible concentration and rate of change of concentration:and rate of change of concentration:

0][,,...0][,0][ 21 nIII

nIII ,...,, 21

0][

,.....,0][

,0][ 21

dt

Id

dt

Id

dt

Id n

Apply steady state approx.Apply steady state approx.to consecutive reaction.to consecutive reaction.

PIAba kk

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

/][][0][][][

AtkkAkIkdt

Pd

kAkIIkAkdt

Id

aaab

baba

0

00

0

][

][ 0

0

]))[exp(1(][

]))[exp(1(][][

])[exp(][

])[exp(][][][

0

AtkP

AtkPP

AtkkdtPd

AtkkAkIkdt

Pd

a

a

aa

P

P

s

aaab

Steady state example.Steady state example.

Two intermediates: NO and NOTwo intermediates: NO and NO33.

)()(4)(2 2252 gOgNOgON

c

b

a

a

kNONONOONNO

kONONONONO

kONNONO

kNONOON

22252

2232

'5232

3252

]][[]][[00/][

]][)[(][00/][

5232

32'

523

ONNOkNONOkdtNOd

NONOkkONkdtNOd

cb

baa

Hence..[Hence..[exerciseexercise]:]:

]][[

]][[][/][

52

32'

5252

ONNOk

NONOkONkdtONd

c

aa

)/(][2/][ '5252 baba kkONkkdtONd

Rate determining stepRate determining stepExample. when kExample. when kaa<k<kb b thenthen

may be treated as a simple may be treated as a simple reaction: reaction:

””the principle of the rate the principle of the rate determining step”determining step”

PIAba kk

PAak

Proof:Proof:When kWhen kaa<k<kb b thenthen

becomes becomes

as expectedas expected

0][)exp()exp(

1][ Akk

tkktkkP

ab

abba

t

a

AA

AtkP

][][

][)exp(1][

0

0

Rate determining step – Rate determining step – in generalin general

If one elementary step in a reaction is If one elementary step in a reaction is slower than others then this step controls slower than others then this step controls the rate of the overall reaction.the rate of the overall reaction.

The slow step is rate determining if it can’t The slow step is rate determining if it can’t be sidestepped.be sidestepped.

Once the rate determining step is found, the Once the rate determining step is found, the rate expression can be written down rate expression can be written down immediately. immediately.

Example.Example.

Even if kEven if kaa<< k<< kb b the upper reaction may be sidestepped if the upper reaction may be sidestepped if kkaa<k<ka’a’ and k and kaa<k<kb’b’. Then. Then

is is notnot rate determining. rate determining.

PIAba kk

PIAba kk ''

'

IAak

Preequilibria.Preequilibria.

Assume A and B are in eq. then Assume A and B are in eq. then

PIBAbak

ak

k

'

]][[][/][

]][[

]['

BAKkIkdtPd

k

kK

BA

IK

bb

a

a

Example. Analysing pre-eq. by Example. Analysing pre-eq. by steady state.steady state.

we do not assume eq. we do not assume eq.

PIBAbak

ak

k

'

''

'

]][[/][

]][[][

0][]][[][/][

][/][

ab

ba

ab

a

aab

b

kk

BAkkdtPd

kk

BAkI

IkBAkIkdtId

IkdtPd

When pre-eq exists kWhen pre-eq exists kbb<k<ka’a’

result. analysis eq-pre old the

]][[]][[/][

''a

ba

ab

ba

k

BAkk

kk

BAkkdtPd

PIBAbak

ak

k

'

Unimolecular reactions.Unimolecular reactions.Lindemann Hinshelwood Lindemann Hinshelwood

mechanism.mechanism.

Found to involve bimolecular step, how can it be Found to involve bimolecular step, how can it be first order?first order?

The reaction is not given by an elementary first The reaction is not given by an elementary first order mechanism.order mechanism.

Can be described by the Lindemann Hinshelwood Can be described by the Lindemann Hinshelwood mechanism. mechanism.

][ 632363 HCcyclokvCHCHCHHCcyclo

Lindemann HinshelwoodLindemann Hinshelwood

2][][

Akdt

AdAAAA a

ka

]][[][

'

'

AAk

dt

AdAAAA a

ka

][][

Ak

dt

AdPA b

kb

Use steady state...Use steady state...

If kIf kbb is small: k is small: kbb << k << ka’ a’ [A][A] then first-then first-

order reactionorder reaction

][

][][

0][]][[][][

'

2

2'

Akk

AkA

AkAAkAkdt

Ad

ab

a

aab

'

][][

a

ab

k

Akk

dt

Pd

][

][][0][

][

'

2

Akk

Akk

dt

PdAk

dt

Pd

ab

abb

On the other hand at low On the other hand at low pressure:pressure:

Since the reactionSince the reaction

becomes ”bottleneck”. becomes ”bottleneck”.

2][][

Akdt

Pda

2][][

Akdt

AdAAAA a

ka

Define effective rate constant:Define effective rate constant:

Lindemann Hinshelwood Lindemann Hinshelwood mechanism gives linear plotmechanism gives linear plot

][

][with

][][][

][

][

][][

'

''

2

Akk

AkkK

AKAAkk

Akk

Akk

Akk

dt

Pd

ab

ab

ab

ab

ab

ab

ba

a

a kk

kA

kdt

PdAK '11 ][

1][/][

The kinetics of complex reactionsThe kinetics of complex reactions

Chain reactionsChain reactions ExplosionsExplosions Catalysis (enzymes)Catalysis (enzymes)

What is a chain reaction?What is a chain reaction?

Example, thermal Example, thermal decomposition of ethanal: decomposition of ethanal:

Elementary reactions Elementary reactions (Rice-Herzfeld):(Rice-Herzfeld):

Chain carriers are CH3 Chain carriers are CH3 and CH3CO radicalsand CH3CO radicals

)()()( 43 gCOgCHgCHOCH

23333

333

333433

333

][2:nterminatio

][' :npropagatio

]][[ :npropagatio

][ :initiation

CHkvCHCHCH

COCHkvCHCOCOCH

CHOCHCHkvCOCHCHCHOCHCH

CHOCHkvCHOCHCHOCH

t

p

p

i

Derivation of rate law:Derivation of rate law:

Steady state:Steady state:

Add these together:Add these together:

0][]][[][

0][][

]][[][][

3'

333

233

'

3333

COCHkCHOCHCHkdt

COCHd

CHkCOCHk

CHOCHCHkCHOCHkdt

CHd

pp

tp

pi

][][][][0 332

33 CHOCHk

kCHCHkCHOCHk

t

iti

Insert into Insert into

As observed experimentally.As observed experimentally.

][][][][0 332

33 CHOCHk

kCHCHkCHOCHk

t

iti

2/33

334

][

]][[][

COHCHk

kk

COHCHCHkdt

CHd

t

ip

p

Key elements of chain reactionKey elements of chain reaction

Initiation: involves formation of Initiation: involves formation of chain carrierschain carriers propagation: done by propagation: done by chain carrierschain carriers Termination: chain carriers are ”destroyed”.Termination: chain carriers are ”destroyed”.

New example:New example:

Initiated by heat. Initiated by heat. )(2)()( 22 gHBrgHgBr

New example:New example:

Complicated rate law:Complicated rate law:

Can be explained by postulating Can be explained by postulating

a chain reaction mechanism.a chain reaction mechanism.

)(2)()( 22 gHBrgHgBr

]['][

]][[][

2

2/322

HBrkBr

BrHk

dt

HBrd

Mechanism: collision inducedMechanism: collision induced

Retardation step: A product is Retardation step: A product is removed.removed.

Chain carriers are H and Br radicals.Chain carriers are H and Br radicals.

22

2

22

22

2

][ :nTerminatio

]][[ :nRetardatio

]][[' :nPropagatio

]][[ :nPropagatio

2:Initiation

BrkvBrBrBr

HBrHkvBrHHBrH

BrHkvBrHBrBrH

HBrkvHHBrHBr

MBrMBr

t

r

p

p

Steady state analysis.Steady state analysis.Rate ofRate of formationformation

Steady-state:Steady-state:

]][[]][[']][[][

22 HHBrkBrHkBrHkdt

HBrdrpp

0][][2

]][[]][[']][[]][[2][

0]][[]][[']][[][

2

222

22

MBrk

HHBrkBrHkBrHkMBrkdt

Brd

HHBrkBrHkBrHkdt

Hd

t

rppi

rpp

Adding these two equations giveAdding these two equations give

Inserting the expression for Br Inserting the expression for Br radical into first eq. givesradical into first eq. gives

2/12

22 ][][0][][2]][[2 Br

k

kBrMBrkMBrk

t

iti

][]['

][][

][2

22/1

2

HBrkBrk

HBrkk

k

Hrp

t

ip

Substituting into rate expression givesSubstituting into rate expression gives

Which has the same form as the Which has the same form as the experimental rate law providedexperimental rate law provided

])['/(][

]][[2

]][[]][[']][[][

2

2/322

22

HBrkkBr

BrHkk

k

HHBrkBrHkBrHkdt

HBrd

pr

t

ip

rpp

)'/('2 prt

ip kkkk

kkk

ExplosionsExplosions

An explosion is a rapidly An explosion is a rapidly accellerating reaction arising accellerating reaction arising from a rapid increase in reaction from a rapid increase in reaction rate with increasing rate with increasing temperature temperature

.. moreeven rises T reaction faster even

rises T c)(exothermiheat releasingreaction fast

Example Example

Has not been fully understod. # Chain carriers Has not been fully understod. # Chain carriers grow exponentially.grow exponentially.

)(2)(2)( 222 gOHgHgO

]['

][2

1 :nterminatio

]][['

]][[ :branching

]][[ :npropagatio

:initiation

22

2

22

22

222

2

HkvMHOMOH

HkvHwallH

HOkvHOHHO

HOkvHOOHO

OHHkvOHHOHH

vconstvHHH

t

t

b

b

p

init

Occurence of explosion given by explosion region Occurence of explosion given by explosion region (regions of T,p).(regions of T,p).

chain carriers are chain carriers are Branching: one chain Branching: one chain

carrier becomes two or carrier becomes two or more.more.

OOHH ,,

If T is low, rate constants are If T is low, rate constants are too small.too small.

If p is low, the reaction rates, If p is low, the reaction rates, v, are too low due to v, are too low due to infrequent collisions.infrequent collisions.

ExampleExampleShow that an explosion happens Show that an explosion happens

when rate of chain branching when rate of chain branching

exceeds that of chain termination.exceeds that of chain termination.

Answer:Answer:

Focus only on the rate of prod of Focus only on the rate of prod of

chain carrier as important. Rate of chain carrier as important. Rate of change of chain carrier:change of chain carrier:

H

]][][['][]][['

]][[]][[][

22

22

OMHkHkHOk

OHkHOHkvHdt

d

ttb

bpini

Example Example Steady state approximation:Steady state approximation:

Then chain carrier production rate isThen chain carrier production rate is]['/]][[][

]/[]][[2][

0]][[']][[][

0]][[']][[]][[][

22

22

22

222

HkHOkO

HHOk

kOH

HOkHOkOdt

d

HOkHOkHOHkOHdt

d

bb

p

b

bb

bbp

]])[][['][2(][ 22 HOMkkOkvHdt

dttbini

ExampleExamplewrite:write:

Then chain carrier production rate isThen chain carrier production rate is

rate. branchingchain measuring][2 2Okk bbranch

termbranchtkk

termbranch

init

termbranchtkk

branchterm

init

kkekk

vHb

kkekk

vHa

termbranch

branchterm

)1(][)

)1(][)

)(

)(

rate.on terminatimeasuring]][[ 2' MOkkk ttterm

])[(][ HkkvHdt

dtermbranchini

Homogeneous catalysisHomogeneous catalysis

A catalyst lowers the activation energy for a A catalyst lowers the activation energy for a reaction.reaction.

It is not consumed in the reaction (reforms in It is not consumed in the reaction (reforms in the end).the end).

Examples are enzymes, metal catalysts etc.Examples are enzymes, metal catalysts etc. Homogeneous catalysis: the catalyst exists Homogeneous catalysis: the catalyst exists

in same phase as reactants.in same phase as reactants.

Example: Example:

as catalyzed by bromide ions.as catalyzed by bromide ions.

Notice that bromide reappears in the end.Notice that bromide reappears in the end.

)()(2)(2 2222 gOlOHaqOH

)(

]][[

]][/[][

2322

23223

22323232223

fastBrOOHOHHOBr

BrOHkvOHHOBrBrOH

OHOHOHKOHOHOHOH

EnzymesEnzymes

Enzymes (E) are Enzymes (E) are biological catalysts.biological catalysts.

Typical proteins.Typical proteins. Contains an active site Contains an active site

that binds substrate (S):that binds substrate (S): Induced fitInduced fit model: S model: S

induces change in E induces change in E and and

only then do they fit only then do they fit together. together.

EPESSE

Michaelis Menten mechanism.Michaelis Menten mechanism.Three exp. observationsThree exp. observations

i) For a given amount of S, the rate of product i) For a given amount of S, the rate of product formation is proportional to [E].formation is proportional to [E].

ii) For a give amount of E and low values of [S], ii) For a give amount of E and low values of [S], the rate of product formation is proportional to [S].the rate of product formation is proportional to [S].

iii) For a given amont of E and high values of [S], iii) For a given amont of E and high values of [S], the rate of product formation reaches a max. the rate of product formation reaches a max. value, v(max), and becomes independent of [S].value, v(max), and becomes independent of [S].

i) and ii) - but not iii) - is consistent withi) and ii) - but not iii) - is consistent with

Michaelis-Menten explains i)-iii)Michaelis-Menten explains i)-iii)

leads toleads to

]][[ ESkvEPSE

b

aa

kEPES

kkESSE

',

][

]][[

]/[1

][][

0

0

ES

SEK

SK

EkESkv M

M

bb

Proof.Proof.

Steady state approx.:Steady state approx.:

thenthen

DefineDefine

UseUse

][

]][['

ES

SE

k

kkK

a

baM

0][][']][[][

ESkESkSEkdt

ESdbaa

ba

a

kk

SEkES

'

]][[][

excessin substrate ][][][][][ 00 SSESEE

)]/[1]([])/[1]([][ 00 SKESSKESE MM

thenthen

Then i)-iii) is correct. show!Then i)-iii) is correct. show!

)]/[1/(][][ 00 SKEkESkv Mbb

)]/[1/(][][ 00 SKEES M

Alternative formula:Alternative formula:

Plot of 1/v against 1/[S] gives straight Plot of 1/v against 1/[S] gives straight line for MM mechanism.line for MM mechanism.

Plot is called Plot is called Lineweaver-Burk plotLineweaver-Burk plot

max0max

0

max

][

111

]/[1][

v

K

Svv

SK

vESkv

M

Mb

0max ][Ekv b

Determine enzyme parameters.Determine enzyme parameters.

Lineweaver-Burke plot Lineweaver-Burke plot givesgives

and and

From knowing total From knowing total enzyme concentration enzyme concentration we calc.we calc.

Cannot determine Cannot determine

max/ vKm

0max ][Ekv b

bm kK ,

aa kk ',

max0max

0

max

][

111

]/[1][

v

K

Svv

SK

vESkv

M

Mb

Catalytic constant.Catalytic constant.

gives the number gives the number of ”turn overs” pr. unit of ”turn overs” pr. unit time. This number – time. This number – with units of pr time – with units of pr time – is called the catalytic is called the catalytic constant,constant,

b

aa

kEPES

kkESSE

',

bk

catk

Catalytic efficiency.Catalytic efficiency.

Catalytic efficiency: measure of overall Catalytic efficiency: measure of overall enzym efficiency equalsenzym efficiency equals

effective rate constant for overall effective rate constant for overall reactionreaction

b

aa

kEPES

kkESSE

',

M

b

M

bb

ba

ab

K

k

SEK

kk

kk

kSEkv

]][['

]][[ [ES]

If enzyme is very If enzyme is very efficient then kb is efficient then kb is large. Thenlarge. Then

ka is determined by ka is determined by diffusion.diffusion.

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1198 1010 sMka

Enzyme inhibitionEnzyme inhibition

An inhibitor reduces rate of product An inhibitor reduces rate of product formation by binding to E, ES or both, formation by binding to E, ES or both, thereby decreasing [ES] and hence product thereby decreasing [ES] and hence product formation. formation.

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New rate of product formation.New rate of product formation.

Maximum velocity is no longer obtainable Maximum velocity is no longer obtainable when competitive inhibition occurs.when competitive inhibition occurs.

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Proof:Proof:

Introduce conservation Introduce conservation of enzyme molcs:of enzyme molcs:

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Different types of inhibitionDifferent types of inhibition

Case 1: meaning only EI not ESICase 1: meaning only EI not ESI

is formed. Once EI is formed, S cannot bind is formed. Once EI is formed, S cannot bind to E. Termed to E. Termed competitive inhibitioncompetitive inhibition. .

Case 2: meaning that only ESI Case 2: meaning that only ESI not EI is formed. I can only bind to E if S is not EI is formed. I can only bind to E if S is already present i.e. ES. ESI does not lead to already present i.e. ES. ESI does not lead to product. Termed product. Termed uncompetitive inhibitionuncompetitive inhibition. .

1'1

1'1

Different types of inhibitionDifferent types of inhibition

Case 3: meaning that both EI Case 3: meaning that both EI and ESI are formed. Inhibitor binds to a site and ESI are formed. Inhibitor binds to a site different from the active site in both cases. different from the active site in both cases. EI cannot bind S. Termed EI cannot bind S. Termed non-competitive non-competitive inhibitioninhibition. .

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How to determine How to determine

Do a unhibited exp. with S & E and find Do a unhibited exp. with S & E and find vmax and Km.vmax and Km.

Add inhibitor with known conc. and plot Add inhibitor with known conc. and plot Lineweaver-Burk from which and Lineweaver-Burk from which and thereby can be determined.thereby can be determined.

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Example of use of competitive Example of use of competitive inhibition.inhibition.

To kill bacteria (B). B To kill bacteria (B). B has enzyme dihydro- has enzyme dihydro- pteroate synthease pteroate synthease producing folate which producing folate which is crucial for survival of is crucial for survival of B. B.

Active substrate p-Active substrate p-aminobenzoic acid.aminobenzoic acid.

Inhibitor Sulfanilamide.Inhibitor Sulfanilamide.