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Chapter 13ChemicalKinetics

2008, Prentice Hall

Chemistry: A Molecular Approach , 1 st Ed. Nivaldo Tro

Roy KennedyMassachusetts Bay o!!unity olle"e

#ellesley Hills, M$

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Tro, he!istry% $ Molecular $&&roach 2

' (inetics is the study o) the )actors that a))ectthe s&eed o) a reaction and the !echanis! *y +hich a reaction &roceeds.

' e &eri!entally it is sho+n that there are -)actors that in)luence the s&eed o) areaction%

nature of the reactants,

temperature,

catalysts,

concentration

Kinetics

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Tro, he!istry% $ Molecular $&&roach

/e)inin" Rate

' rate is ho+ !uch a uantity chan"es in a "iven &eriod o) ti!e

' the s&eed you drive your car is a rate the distanceyour car travels !iles3 in a "iven &eriod o) ti!e 1hour3

so the rate o) your car has units o) !i4hr

ti!edistance 5&eed∆

∆=

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Tro, he!istry% $ Molecular $&&roach -

/e)inin" Reaction Rate' the rate o) a che!ical reaction is "enerally !easured in

ter!s o) ho+ !uch the concentration o) a reactantdecreases in a "iven &eriod o) ti!e

or &roduct concentration increases

' )or reactants, a ne"ative si"n is &laced in )ront o) thede)inition

ti!e6reactant7

ti!e6&roduct7

Rate

ti!eionconcentrat

Rate

∆∆−=∆

∆=∆

∆=

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Reaction Rate han"es 9ver Ti!e

' as ti!e "oes on, the rate o) a reaction "enerally

slo+s do+n *ecause the concentration o) the reactants decreases.' at so!e ti!e the reaction sto&s, either *ecause the

reactants run out or *ecause the syste! hasreached e uili*riu!.

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Tro, he!istry% $ Molecular $&&roach :

at t ; 06$7 ; 86B7 ; 86 7 ; 0

at t ; 067 ; 0

at t ; 1:6$7 ; -6B7 ; -6 7 ; -

at t ; 1:67 ; 1

[ ] [ ] [ ]( )

( )( )( )

2.00:10-

Rate

tttRate 1212

=−−=

−−=∆∆= [ ] [ ] [ ]( )

( )( )( )

2.00:18-

Rate

tt$$

t$Rate 1212

=−−−=

−−−=∆∆−= [ ] [ ] [ ]( )

( )( )( )

0:2.00:1

01Rate

tt>>

t>Rate 1212

=−−=

−−=∆∆= [ ] [ ] [ ]( )

( )( )( )

0:2.00:18?

Rate

tt

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Tro, he!istry% $ Molecular $&&roach ?

[ ] [ ] [ ]( )

( )( )( )

12.00:1-:

Rate

tttRate 1212

=−−=

−−=∆∆= [ ] [ ] [ ]( )

( )( )( )

0:2.00:1?:

Rate

tt

t>

Rate12

12

=−−=

−−=∆∆=

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[ ] [ ] [ ]( )

( )( )( )

0:2.00:1:

Rate

tt>

t>

Rate12

12

=−−=

−−=∆∆=

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@

Hy&othetical ReactionRed → Blue

Ti!esec3 Nu!*erRed Nu!*erBlue

0 100 0

8- 1:

10 ?1 2@

1 @ -1

20 0 0

2 -2 8

0 :0 ?0

-0 2 ?

- 21 ?@

0 18 82

in this reaction,one !olecule o) Red turnsinto one !olecule o) Blue

the nu!*er o) !olecules+ill al+ays total 100

the rate o) the reaction can

*e !easured as the s&eed o) loss o) Red !oleculesover ti!e, or the s&eed o)"ain o) Blue !olecules

over ti!e

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Reaction Rate and 5toichio!etry' in !ost reactions, the coe))icients o) the *alanced e uation

are not all the sa!eH2 g 3 A 2 g 3 → 2 H g 3

' )or these reactions, the chan"e in the nu!*er o) !oleculeso) one su*stance is a !ulti&le o) the chan"e in the nu!*ero) !olecules o) another

)or the a*ove reaction, )or every 1 !ole o) H 2 used, 1 !ole o) 2 +ill also *e used and 2 !oles o) H !adethere)ore the rate o) chan"e +ill *e di))erent

' in order to *e consistent, the chan"e in the concentrationo) each su*stance is !ulti&lied *y 14coe))icient

tH 76

21

t76

t7H6

Rate 22∆

∆

+=∆

∆−=∆∆−=

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1-

Hy&othetical Reaction Red → Blue$v". Rate $v". Rate $v". Rate

Ti!esec3

Nu!*erRed

Nu!*erBlue

secintervals3

10 secintervals3

2 secintervals3

0 100 0

8- 1: .2

10 ?1 2@ 2.: 2.@1 @ -1 2.-

20 0 0 1.8 2.1

2 -2 8 1.: 2.

0 : 1.- 1.

0 ?0 1

-0 2 ? 1 1

- 21 ?@ 0.8

0 18 82 0.: 0.? 1

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1

H2 2H

$v". Rate, M4s $v". Rate, M4s

Ti!e s3 6H27, M 6H 7, M C∆6H274∆t 142 ∆6H 74∆t0.000 1.000

10.000 0.81@

20.000 0.:?0

0.000 0. -@

-0.000 0.--@

0.000 0. :8

:0.000 0. 01?0.000 0.2-?

80.000 0.202

@0.000 0.1:

100.000 0.1


Ti!e s3 6H27, M 6H 7, M C∆6H274∆t 142 ∆6H 74∆t0.000 1.000 0.000

10.000 0.81@ 0. :2

20.000 0.:?0 0.::0

0.000 0. -@ 0.@02

-0.000 0.--@ 1.102

0.000 0. :8 1.2:-

:0.000 0. 01 1. @8?0.000 0.2-? 1. 0:

80.000 0.202 1. @:

@0.000 0.1: 1.:?0

100.000 0.1 1.? 0

5toichio!etry tells us that )orevery 1 !ole4D o) H 2 used,2 !oles4D o) H are !ade.

$ssu!in" a 1 D container, at10 s, +e used 0.181 !oles o)H2. There)ore the a!ount o)H !ade is 2 0.181 !oles3 ;

0. :2 !oles$t :0 s, +e used 0.:@@ !oleso) H 2. There)ore the a!ounto) H !ade is 2 0.:@@ !oles3

; 1. @8 !oles

$v". Rate, M4s

Ti!e s3 6H27, M 6H 7, M C∆6H274∆t0.000 1.000 0.000

10.000 0.81@ 0. :2 0.0181

20.000 0.:?0 0.::0 0.01-@

0.000 0. -@ 0.@02 0.0121

-0.000 0.--@ 1.102 0.0100

0.000 0. :8 1.2:- 0.0081

:0.000 0. 01 1. @8 0.00:??0.000 0.2-? 1. 0: 0.00 -

80.000 0.202 1. @: 0.00-

@0.000 0.1: 1.:?0 0.00 ?

100.000 0.1 1.? 0 0.00 0

The avera"e rate isthe chan"e in theconcentration in a

"iven ti!e &eriod.

n the )irst 10 s, the∆6H27 is C0.181 M,so the rate is

s

M0181.0

s10.000

M181.0

=

−

−


Ti!e s3 6H27, M 6H 7, M C∆6H274∆t 142 ∆6H 74∆t0.000 1.000 0.000

10.000 0.81@ 0. :2 0.0181 0.0181

20.000 0.:?0 0.::0 0.01-@ 0.01-@

0.000 0. -@ 0.@02 0.0121 0.0121

-0.000 0.--@ 1.102 0.0100 0.0100

0.000 0. :8 1.2:- 0.0081 0.0081

:0.000 0. 01 1. @8 0.00:? 0.00:??0.000 0.2-? 1. 0: 0.00 - 0.00 -

80.000 0.202 1. @: 0.00- 0.00-

@0.000 0.1: 1.:?0 0.00 ? 0.00 ?

100.000 0.1 1.? 0 0.00 0 0.00 0

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Tro, he!istry% $ Molecular $&&roach 1:

avera"e rate in a "iven

ti!e &eriod ; − slo&e o)the line connectin" the6H27 &oints and F Aslo&eo) the line )or 6H 7

the avera"e rate )or the)irst 10 s is 0.0181 M4sthe avera"e rate )or the)irst -0 s is 0.01 0 M4sthe avera"e rate )or the)irst 80 s is 0.0108 M4s

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Tro, he!istry% $ Molecular $&&roach 1?

nstantaneous Rate

' the instantaneous rate is the chan"e inconcentration at any one &articular ti!e

slo&e at one &oint o) a curve

' deter!ined *y ta(in" the slo&e o) a line tan"entto the curve at that &articular &oint

)irst derivative o) the )unction)or you calculus )ans

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18

H2 g 3 A 2 g 3 → 2 H g 3 Gsin" 6H 27, theinstantaneous rate at

0 s is%

s

M 0.00?0Rate

s-0M28.0

Rate

=

−−=

Gsin" 6H 7, theinstantaneous rate at

0 s is%

sM 0.00?0Rate

s-0M:.0

21

Rate

=

=

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E 1 .1 C or the reaction "iven, the 6 −7 chan"es )ro!1.000 M to 0.8:8 M in the )irst 10 s. alculate the

avera"e rate in the )irst 10 s and the ∆6HA7.H29 2 aq 3 A

−aq 3 A 2 H

Aaq 3 →

−aq 3 A 2 H 29 l 3

5olve the e uation)or the Rate inter!s o) the chan"e

in concentration o)the Iiven uantity3

5olve the e uationo) the Rate in ter!so) the chan"e in theconcentration )or the

uantity to ind3 )orthe un(no+n value

( )

sMC10-.-0Rate

s10M000.1M8:8.01

t7B61

Rate

×=

−

−=∆

∆

−=

−

( )

( )s

MC

s

MC 108.8010-.-02t

7H6

Rate2t

7H6

t7H6

21

Rate

×−=×−=∆

∆

−=∆∆

∆∆

−=

+

+

+

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Measurin" Reaction Rate' in order to !easure the reaction rate you need to *e

a*le to !easure the concentration o) at least oneco!&onent in the !i ture at !any &oints in ti!e

' there are t+o +ays o) a&&roachin" this &ro*le! 13 )orreactions that are co!&lete in less than 1 hour, it is *estto use continuous !onitorin" o) the concentration, or

23 )or reactions that ha&&en over a very lon" ti!e,sa!&lin" o) the !i ture at various ti!es can *e used

+hen sa!&lin" is used, o)ten the reaction in the sa!&le issto&&ed *y a uenchin" techni ue

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ontinuous Monitorin"' polarimetry !easurin" the chan"e in the de"ree o)

rotation o) &laneC&olariJed li"ht caused *y one o) theco!&onents over ti!e

' spectrophotometry !easurin" the a!ount o) li"ht o)a &articular +avelen"th a*sor*ed *y one co!&onent

over ti!ethe co!&onent a*sor*s its co!&li!entary color ' total pressure the total &ressure o) a "as !i ture is

stoichio!etrically related to &artial &ressures o) the"ases in the reaction

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5a!&lin"' gas chromatography can !easure the concentrations

o) various co!&onents in a !i ture)or sa!&les that have volatile co!&onentsse&arates !i ture *y adherence to a sur)ace

' dra+in" o)) &eriodic aliquots )ro! the !i ture anddoin" uantitative analysis

titration )or one o) the co!&onents"ravi!etric analysis

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actors $))ectin" Reaction Rate Nature o) the Reactants

' nature o) the reactants !eans +hat (ind o) reactant!olecules and +hat &hysical condition they are in.

s!all !olecules tend to react )aster than lar"e !olecules"ases tend to react )aster than li uids +hich react )aster thansolids

&o+dered solids are !ore reactive than *loc(sL!ore sur)ace area )or contact +ith other reactants

certain ty&es o) che!icals are !ore reactive than otherse."., the activity series o) !etals

ions react )aster than !oleculesno *onds need to *e *ro(en

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Tro, he!istry% $ Molecular $&&roach 2-

' increasin" te!&erature increases reaction rateche!ist s rule o) thu!* C )or each 10 rise in

te!&erature, the s&eed o) the reaction dou*les)or !any reactions

' there is a !athe!atical relationshi& *et+een

the a*solute te!&erature and the s&eed o) areaction discovered *y 5vante $rrhenius+hich +ill *e e a!ined later

actors $))ectin" Reaction RateTe!&erature

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' catalysts are su*stances +hich a))ect the s&eed o)a reaction without being consumed.

' !ost catalysts are used to s&eed u& a reaction,these are called &ositive catalysts

catalysts used to slo+ a reaction are called ne"ativecatalysts.

' ho!o"eneous ; &resent in sa!e &hase' hetero"eneous ; &resent in di))erent &hase' ho+ catalysts +or( +ill *e e a!ined later

actors $))ectin" Reaction Rateatalysts

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' "enerally, the lar"er the concentration o)reactant !olecules, the )aster the reaction

increases the )re uency o) reactant!olecule contactconcentration o) "ases de&ends on the &artial

&ressure o) the "as

hi"her &ressure ; hi"her concentration' concentration o) solutions de&ends on the

solute to solution ratio !olarity3

actors $))ectin" Reaction RateReactant oncentration

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The Rate Da+' the Rate Da+ o) a reaction is the !athe!atical relationshi& *et+een the rate o) the reaction and the concentrations o)

the reactantsand ho!o"eneous catalysts as +ell

' the rate o) a reaction is directly &ro&ortional to theconcentration o) each reactant raised to a &o+er ' )or the reaction aA + bB products the rate la+

+ould have the )or! "iven *elo+n and m are called the orders )or each reactantk is called the rate constant

mnk 6B76$7Rate =

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Reaction 9rder ' the e &onent on each reactant in the rate la+ is

called the order +ith res&ect to that reactant' the su! o) the e &onents on the reactants is

called the order of the reaction

' The rate la+ )or the reaction%2 N9 g 3 A 9 2 g 3→ 2 N9 2 g 3

is Rate ; (6N97 269 27

The reaction issecond order +ith res&ect to 6N97,)irst order +ith res&ect to 69 27,

and third order overall

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Tro, he!istry% $ Molecular $&&roach 2@

5a!&le Rate Da+s

The reaction is autocatalytic, *ecause a &roduct a))ects the rate.H" 2A is a ne"ative catalyst, increasin" its concentration slo+s the reaction.

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Reactant oncentration vs. Ti!e$ → Products

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Hal)CDi)e' the half life , t 1!" , o) a

reaction is the len"tho) ti!e it ta(es )or theconcentration o) the

reactants to )all to Fits initial value' the hal)Cli)e o) the

reaction de&ends onthe order o) thereaction

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>ero 9rder Reactions' Rate ; k 6$70 ; k

constant rate reactions' 6$7 ; Ck t A 6$70' "ra&h o) 6$7 vs. ti!e is strai"ht line +ith

slope # k and y intercept # $A% &

' t ' # $A &%!"( ' when )ate # *!sec, k # *!sec

6$70

6$7

ti!e

s l o & e ; C k

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irst 9rder Reactions

' Rate ; k 6$7' ln6$7 ; C k t A ln6$70 ' "ra&h ln6$7 vs. ti!e "ives strai"ht line +ith

slope # k and y intercept # ln$A% &used to deter!ine the rate constant' t ' # &. 3!k

' the half life of a first order reaction isconstant' the when )ate # *!sec, k # sec 1

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ln6$70

ln6$7

ti!e

s l o & e ; O k

H l)CDi) ) i C9 d R i

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Hal)CDi)e o) a irstC9rder Reactions onstant

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Rate /ata )or- H@ l A H 29 → - H@9H A H l

-ime sec/ $C0 Cl%, *0.0 0.1000

0.0 0.0@0

100.0 0.0820

1 0.0 0.0?-1

200.0 0.0:?1

00.0 0.0 -@

-00.0 0.0--800.0 0.0 :8

800.0 0.0200

10000.0 0.0000

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- H@ l A H 29 → - H@9H A 2 H l

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- H@ l A H 29 → - H@9H A 2 H l

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Tro, he!istry% $ Molecular $&&roach @

- H@ l A H 29 → - H@9H A 2 H l

slo&e ;C2.01 10C

k =

2.01 10 C sC1

s-s1001.2

:@.0

:@.0t

1C

21

=×=

=

−

k

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Tro, he!istry% $ Molecular $&&roach -0

5econd 9rder Reactions

' Rate ; k 6$72

' 146$7 ; k t A 146$70 ' "ra&h 146$7 vs. ti!e "ives strai"ht line +ith

slope # k and y intercept # 1!$A% &used to deter!ine the rate constant

' t ' # 1! ($A &%/

' when )ate # *!sec, k # * 1 · sec 1

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l46$70

146$7

ti!e

s l o & e ;

k

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-2

Rate /ata or 2 N9 2 → 2 N9 A 9 2

Ti!e hrs.3

PartialPressure

N9 2, !!H" ln P N92 3 14 P N92 3

0 100.0 -.:0 0.01000

0 :2. -.1 0.01:00:0 - . .81? 0.02200

@0 .? . ?: 0.02800

120 [email protected] . 81 0.0 -00

1 0 2 .0 .21@ 0.0-000

180 21.? .0?@ 0.0-:00

210 [email protected] 2.@ ? 0.0 200

2-0 1?.2 2.8-? 0.0 800

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Rate /ata Ira&hs or 2 N9 2 → 2 N9 A 9 2

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Tro, he!istry% $ Molecular $&&roach --


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Tro, he!istry% $ Molecular $&&roach -:

/eter!inin" the Rate Da+' can only *e deter!ined e &eri!entally' "ra&hically

rate ; slo&e o) curve 6$7 vs. ti!ei) "ra&h 6$7 vs ti!e is strai"ht line, then e &onent on $ in ratela+ is 0, rate constant ; Cslo&ei) "ra&h ln6$7 vs ti!e is strai"ht line, then e &onent on $ in ratela+ is 1, rate constant ; Cslo&ei) "ra&h 146$7 vs ti!e is strai"ht line, e &onent on $ in rate la+is 2, rate constant ; slo&e

' initial rates *y co!&arin" e))ect on the rate o) chan"in" the initialconcentration o) reactants one at a ti!e

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Tro, he!istry% $ Molecular $&&roach -?

Practice C o!&lete the Ta*le and

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Practice C o!&lete the Ta le and/eter!ine the Rate E uation )or the

Reaction $ → 2 Prod$A%, .*/ $2rod%, .*/ -ime .sec/ ln.$A%/ 1!$A%

0.100 0 0

0.0:? 0

0.0 0 100

0.0-0 1 0

0.0 200

0.02@ 2 0

Practice C o!&lete the Ta*le and

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Tro, he!istry% $ Molecular $&&roach -@

Practice C o!&lete the Ta le and/eter!ine the Rate E uation )or the

Reaction $ → 2 Prod$A%, .*/ $2rod%, .*/ -ime .sec/ ln.$A%/ 1!$A%

0.100 0 0 C2. 10

0.0:? 0.0:: 0 C2.? 1

0.0 0 0.100 100 C .0 20

0.0-0 0.120 1 0 C .2 2

0.0 0.1 - 200 C .- 0

0.02@ 0.1-2 2 0 C .

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Practice C o!&lete the Ta*le and /eter!inethe Rate E uation )or the Reaction $ → 2

Prod

the reaction is second order, Rate ;C∆6$7

∆t; 0.1 6$7 2

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nitial Rate Method' another !ethod )or deter!inin" the order o) a

reactant is to see the e))ect on the initial rate o) thereaction +hen the initial concentration o) thatreactant is chan"ed

for multiple reactants, (eep initial concentration of allreactants constant e8cept oneJero order ; chan"in" the concentration has no e))ect onthe rate)irst order ; the rate chan"es *y the sa!e )actor as theconcentration

dou*lin" the initial concentration +ill dou*le the ratesecond order ; the rate chan"es *y the s uare o) the )actorthe concentration chan"es

dou*lin" the initial concentration +ill uadru&le the rate

E 1 .2 /eter!ine the rate la+ and rate constant )or the

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:

)reaction N9 2 g 3 A 9 g 3 → N9 g 3 A 9 2 g 3

"iven the data *elo+.

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

#rite a "eneral

rate la+includin" allreactants

E a!ine the

data and )indt+o e &eri!entsin +hich theconcentration o)one reactant

chan"es, *ut theotherconcentrationsare the sa!e

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082

. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

o!&arin" E &t 1 and E &t 2, the6N9 27 chan"es *ut the 6 97 does not

mn

k 6 9776N9Rate 2=


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/eter!ine *y+hat )actor theconcentrationsand rates chan"ein these t+oe &eri!ents.

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

2M10.0M20.0

76N976N9

1e &t2

2e &t2 == - 0021.0 0082.0

RateRate

sM

sM

1e &t

2e &t ≈=


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/eter!ine to+hat &o+er theconcentration)actor !ust *eraised to e ualthe rate )actor.

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

2M10.0

M20.0

76N9

76N9

1e &t2

2e &t2 ==- 0021.0

0082.0

Rate

Rate

sM

sM

1e &t

2e &t

≈=

2-2

RateRate

76N976N9

1e &t

2e &t

1e &t2

2e &t2

==

=

n

n

n


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Re&eat )or theother reactants

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

2M10.0M20.0

6 976 97

2e &t

e &t == 1 0082.0 008.0

RateRate

sM

sM

2e &t

e &t ≈=

012

RateRate

6 976 97

2e &t

e &t

2e &t

e &t

==

=

m

m

m

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0


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Tro, he!istry% $ Molecular $&&roach :0



5u*stitute thee &onents intothe "eneral ratela+ to "et the

rate la+ )or thereaction

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

mnk 6 9776N9Rate 2=n ; 2, m ; 0 22

022

76N9Rate6 9776N9Rate

k k

==


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reaction N9 2 g 3 A 9 g 3 → N9 g 3 A 9 2 g 3 "iven the data *elo+.

5u*stitute theconcentrationsand rate )or anye &eri!ent into

the rate la+ andsolve )or k

E &t. Nu!*er

nitial6N9 27, M3

nitial6 97, M3

nitial RateM4s3

1. 0.10 0.10 0.0021

2. 0.20 0.10 0.0082. 0.20 0.20 0.008

-. 0.-0 0.10 0.0

( )1C1C

2s

M

2s

M

22

sM21.0M01.0

0.0021M10.00.0021

1e &t)or76N9Rate

•==

==

k

k

k

Practice C /eter!ine the rate la+ and rate constant )or the

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reaction NH - A1 A N9 2C1 → Ν2 + 2 Η 2Ο"iven the data *elo+.

98pt.:o.

;nitial$: 0+%, *

;nitial$:< " %, *

;nitial )ate,8 1&=/, *!s

1 0.0200 0.200 10.8

2 0.0:00 0.200 2.

0.200 0.0202 10.8- 0.200 0.0-0- 21.:

Practice C /eter!ine the rate la+ and rate constant )or the

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:

reaction NH - A1 A N9 2C1 → Ν2 + 2 Η 2Ο"iven the data *elo+.

98pt.:o.

;nitial$: 0+%, *

;nitial$:< " %, *

;nitial )ate,8 1&=/, *!s

1 0.0200 0.200 10.8

2 0.0:00 0.200 2.

0.200 0.0202 10.8- 0.200 0.0-0- 21.:

order )irst1, 76NHactorRate

108.10

10.21E &t2E &t

Rate,

0200.00:00.0

1E &t2E &t

7,6NHor

-

-

?

?

=∴==

=××=

==

+−−

+

n

nn

Rate ; k 6NH- A7n6N9 2−7m

order )irst1, 22 76N9actorRate

2108.10

10:.21E &t

-E &tRate,

20202.00-0-.0

E &t-E &t

7,6N9or

2

2

?

?

=∴==

=××=

==

−−−

−

m

mm

( )( )

1C1C-2C sM?C

sM?C

2-

sM10?0.2M1000.-

1010.8

M.2000M.020001010.8

1e &t)or76N976NHRate

•×=××

=

=×

=

−

−+

k

k

k

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Tro, he!istry% $ Molecular $&&roach :-

The E))ect o) Te!&erature on Rate' chan"in" the te!&erature chan"es the rate

constant o) the rate la+

' 5vante $rrhenius investi"ated this relationshi&and sho+ed that%

=− RT

E a

e Ak

R is the "as constant in ener"y units, 8. 1- Q4 !ol K3

+here T is the te!&erature in (elvins

A is a )actor called the frequency factor E a is the acti6ation energy , the e tra ener"y needed to startthe !olecules reactin"

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Tro, he!istry% $ Molecular $&&roach ::

$ctivation Ener"y and the$ctivated o!&le

' ener"y *arrier to the reaction' a!ount o) ener"y needed to convert reactants

into the acti6ated comple8a(a transition state

' the activated co!&le is a che!ical s&ecies +ith &artially *ro(en and &artially )or!ed *onds

al+ays very hi"h in ener"y *ecause &artial *onds

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Tro, he!istry% $ Molecular $&&roach :?

so!eriJation o) Methyl sonitrile

!ethyl isonitrile rearran"es to acetonitrile

in order )or the reaction to occur,the H CN *ond !ust *rea( anda ne+ H C *ond )or!

Ener"y Pro)ile )or the

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:8

Ener y Pro)ile )or the so!eriJation o) Methyl sonitrile

$s the reaction *e"ins, the CN *ond +ea(ensenou"h )or the

≡ N "rou& tostart to rotate

the collision frequency is the nu!*er o)!olecules thata&&roach the &ea( in a"iven &eriod o) ti!e

the acti6ation energy is the di))erence inener"y *et+een thereactants and theactivated co!&le

the acti6ated comple8 is a che!ical s&ecies+ith &artial *onds

The $rrhenius E uation%

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Tro, he!istry% $ Molecular $&&roach :@

The $rrhenius E uation%The E &onential actor

' the e &onential )actor in the $rrhenius e uation is a nu!*er *et+een 0 and 1' it re&resents the )raction o) reactant !olecules +ith su))icient

ener"y so they can !a(e it over the ener"y *arrier the hi"her the ener"y *arrier lar"er activation ener"y3, the )e+er!olecules that have su))icient ener"y to overco!e it

' that e tra ener"y co!es )ro! convertin" the (inetic ener"y o)!otion to &otential ener"y in the !olecule +hen the !oleculescollide

increasin" the te!&erature increases the avera"e (inetic ener"y o) the!oleculesthere)ore, increasin" the te!&erature +ill increase the nu!*er o)!olecules +ith su))icient ener"y to overco!e the ener"y *arrier there)ore increasin" the te!&erature +ill increase the reaction rate

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Tro, he!istry% $ Molecular $&&roach ?0

$ h i Pl t

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$rrhenius Plots' the $rrhenius E uation can *e al"e*raically

solved to "ive the )ollo+in" )or!%

( ) A R

E k a ln

T1

3ln +

−=

this e uation is in the )or! y ; ! x A *+here y ; ln k 3 and x ; 14T3

a "ra&h o) ln k 3 vs. 14T3 is a strai"ht line

C8. 1- Q4!ol K3 slo&e o) the line3 ; E a , in Qoules3

e y-interce&t ; A, unit is the sa!e as k 3

E . 1 .? /eter!ine the activation ener"y and )re uency

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)actor )or the reaction 9 g 3 → 9 2 g 3 A 9 g 3 "iven the)ollo+in" data%

Te!&, K k, M C1 sC1 Te!&, K k, M C1 sC1

:00 . ? 10 1 00 ?.8 10 ?

?00 -.8 10 - 1-00 1.- 10 8

800 . 8 10 1 00 2.-: 108

@00 1.?0 10: 1:00 .@ 108

1000 .@0 10: 1?00 .@ 108

1100 1.: 10 ? 1800 8. 10 8

1200 .81 10 ? 1@00 1.1@ 10@


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use as&readsheetto "ra&h

ln k 3 vs.14T3


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Tro, he!istry% $ Molecular $&&roach ?-


E a = ! C R3

solve )or E a

( )!ol(Q

!olQ-

K !olQ-

1.@

[email protected] 1012.1

=

×= ×= •a

a

E

E

A ; e yCinterce&t

solve )or A 11C11

118.2:

sM10:.-

10:.-−•×=

×== A

e A

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$rrhenius E uation%

T+oCPoint or!' i) you only have t+o T, k 3 data &oints, the

)ollo+in" )or!s o) the $rrhenius E uation can

*e used%

( )( ) T T

k

k

xT T R

T T T T

k

k

R x

T T

k

k

R x E a21

2

121

21

21

2

1

12

2

1

lnln11

ln −

••=

•−=−

=

−=

211

2T1

T1ln

R E

k k a

E . 1 .8 The reaction N9 2 g 3A 9 g 3 → 9 2 g 3 A N9 g 3 has a rate

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( )

a

a

a

E

E

E

==×

×=

−=

−•

•

−

•

•

!ol(Q

!olQ

1C-

K !ol

Q

K !olQ

sM

sM

1-10-.1

K 102@0. 1-.8:@.

K 8@1

K ?011

1-.8?.2 :?

ln

1

1C1C

C1C1

constant o) 2. ? M C1·sC1 at ?01 K and :? M C1·sC1 at 8@ K. ind theactivation ener"y in (Q4!ol

!ost activation ener"ies are tens to hundreds o)

(Q4!ol so the ans+er is reasona*le

T1 ; ?01 K, k 1 ; 2. ? MC1

sC1

, T2 ; 8@ K, k 2 ; :? MC1

sC1

Ea, (Q4!ol

Chec(

4olution

Concept 2lan

)elationships

5i6en7ind

E aT1, k 1, T2, k 2

−=

211

2T1

T1ln

R E

k k a

ll h )

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Tro, he!istry% $ Molecular $&&roach ??

ollision Theory o) Kinetics

' )or !ost reactions, in order )or a reaction to ta(e &lace, the reactin" !olecules !ust collide intoeach other.

' once !olecules collide they !ay react to"etheror they !ay not, de&endin" on t+o )actors C1. +hether the collision has enou"h ener"y to

S*rea( the *onds holdin" reactant !oleculesto"etherS

2. +hether the reactin" !olecules collide in the &ro&er orientation )or ne+ *onds to )or!.

E)) i lli i

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E))ective ollisions' collisions in +hich these t+o conditions are

!et and there)ore lead to reaction3 are calledeffecti6e collisions

' the hi"her the )re uency o) e))ectivecollisions, the )aster the reaction rate

' +hen t+o !olecules have an e))ectivecollision, a te!&orary, hi"h ener"y unsta*le3che!ical s&ecies is )or!ed C called anacti6ated comple8 or transition state

E))ective ollisions

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Tro, he!istry% $ Molecular $&&roach ?@

E))ective ollisionsKinetic Ener"y actor

)or a collision to leadto overco!in" the

ener"y *arrier, thereactin" !olecules!ust have su))icient(inetic ener"y so that+hen they collide itcan )or! theactivated co!&le

E)) i lli i

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E))ective ollisions9rientation E))ect

ollision Theory and

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ollision Theory andthe $rrhenius E uation

' A is the )actor called the frequency factor andis the nu!*er o) !olecules that can a&&roachoverco!in" the ener"y *arrier

' there are t+o )actors that !a(e u& the )re uency)actor the orientation factor p/ and thecollision frequency factor z /

RT E

RT E aa

pzee Ak −−

=

=

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9rientation actor

' the &ro&er orientation results +hen the ato!s areali"ned in such a +ay that the old *onds can *rea( andthe ne+ *onds can )or!

' the !ore co!&le the reactant !olecules, the less)re uently they +ill collide +ith the &ro&er orientation

reactions *et+een ato!s "enerally have p ; 1reactions +here sy!!etry results in !ulti&le orientationsleadin" to reaction have p sli"htly less than 1

' )or !ost reactions, the orientation )actor is less than 1)or !any, p 1there are so!e reactions that have p U 1 in +hich an electronis trans)erred +ithout direct collision

Reaction Mechanis!s

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Reaction Mechanis!s' +e "enerally descri*e che!ical reactions +ith an

e uation listin" all the reactant !olecules and &roduct!olecules' *ut the &ro*a*ility o) !ore than !olecules collidin" at

the sa!e instant +ith the &ro&er orientation andsu))icient ener"y to overco!e the ener"y *arrier isne"li"i*le

' !ost reactions occur in a series o) s!all reactionsinvolvin" 1, 2, or at !ost !olecules

' descri*in" the series o) ste&s that occur to &roduce theoverall o*served reaction is called a reactionmechanism

' (no+in" the rate la+ o) the reaction hel&s us understandthe se uence o) ste&s in the !echanis!

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Tro, he!istry% $ Molecular $&&roach 8-

$n E a!&le o) a Reaction Mechanis!' 9verall reaction%

H2 g 3 A 2 l g 3 → 2 H l g 3 A 2 g 3 ' Mechanis!%

13 H2 g 3

A l g 3

→

H l g 3

A H g 3

23 H g 3 A l g 3 → H l g 3 A 2 g 3

' the ste&s in this !echanis! are elementarysteps , !eanin" that they cannot *e *ro(endo+n into si!&ler ste&s and that the !oleculesactually interact directly in this !anner +ithoutany other ste&s

Ele!ents o) a Mechanis!

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H2 g 3 A 2 l g 3→ 2 H l g 3 A 2 g 313 H2 g 3 A l g 3→ H l g 3 A H g 323 H g 3 A l g 3→ H l g 3 A 2 g 3

Ele!ents o) a Mechanis!nter!ediates

' notice that the H is a &roduct in 5te& 1, *ut then areactant in 5te& 2' since H is !ade *ut then consu!ed, H does not

sho+ u& in the overall reaction

' !aterials that are &roducts in an early ste&, *ut then areactant in a later ste& are called intermediates

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Molecularity' the nu!*er o) reactant &articles in an ele!entary

ste& is called its molecularity

' a uni!olecular ste& involves 1 reactant &article' a *i!olecular ste& involves 2 reactant &articles

thou"h they !ay *e the sa!e (ind o) &article

' a ter!olecular ste& involves reactant &articlesthou"h these are e ceedin"ly rare in ele!entary ste&s

R t D + ) El ! t 5t &

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Rate Da+s )or Ele!entary 5te&s' each ste& in the !echanis! is li(e its o+n little

reaction +ith its o+n activation ener"y and o+nrate la+

' the rate la+ )or an overall reaction !ust *edeter!ined e &eri!entally

' *ut the rate la+ o) an ele!entary ste& can *ededuced )ro! the e uation o) the ste&

H2 g 3 A 2 l g 3→ 2 H l g 3 A 2 g 313 H2 g 3 A l g 3→ H l g 3 A H g 3 Rate ; k 16H276 l723 H g 3 A l g 3→ H l g 3 A 2 g 3 Rate ; k 26H 76

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Rate Da+s o) Ele!entary 5te&s

Rate /eter!inin" 5te&

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Tro, he!istry% $ Molecular $&&roach 8@

Rate /eter!inin" 5te&' in !ost !echanis!s, one ste& occurs slo+er than the

other ste&s' the result is that &roduct &roduction cannot occur any)aster than the slo+est ste& the ste& deter!ines therate o) the overall reaction

' +e call the slo+est ste& in the !echanis! the ratedetermining stepthe slo+est ste& has the lar"est activation ener"y

' the rate la+ o) the rate deter!inin" ste& deter!ines therate la+ o) the overall reaction

$nother Reaction Mechanis!

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Tro, he!istry% $ Molecular $&&roach @0

$nother Reaction Mechanis! N9 2 g 3 A 9 g 3 → N9 g 3 A 9 2 g 3 Rate o*s ; k 6N9 272

13 N9 2 g 3 A N9 2 g 3 → N9 g 3 A N9 g 3 Rate ; k 16N9 272 slo+23 N9 g 3 A 9 g 3 → N9 2 g 3 A 9 2 g 3 Rate ; k 26N9 76 97 )ast

The )irst ste& in this !echanis!is the rate deter!inin" ste&.

The )irst ste& is slo+er than the

second ste& *ecause itsactivation ener"y is lar"er.

The rate la+ o) the )irst ste& isthe sa!e as the rate la+ o) theoverall reaction.

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Validatin" a Mechanis!

' in order to validate not &rove3 a !echanis!,t+o conditions !ust *e !et%

1. the ele!entary ste&s !ust su! to the overallreaction

2. the rate la+ &redicted *y the !echanis! !ust *e consistent +ith the e &eri!entallyo*served rate la+

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Mechanis!s +ith a ast nitial 5te&

' +hen a !echanis! contains a )ast initial ste&, the rateli!itin" ste& !ay contain inter!ediates

' +hen a &revious ste& is ra&id and reaches e uili*riu!,the )or+ard and reverse reaction rates are e ual so theconcentrations o) reactants and &roducts o) the ste& arerelated

and the &roduct is an inter!ediate

' su*stitutin" into the rate la+ o) the R/5 +ill &roduce arate la+ in ter!s o) Wust reactants

$n E a!&le

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$n E a!&le

2 N9 g 3⇔ N 29 2 g 3 ast

H2 g 3 A N29 2 g 3→ H 29 g 3 A N29 g 3 5lo+ Rate ; k ! 6H276N29 27H2 g 3 A N29 g 3 → H 29 g 3 A N2 g 3 ast

k 1

k -1

2 H 2 g 3 A 2 N9 g 3 → 2 H 29 g 3 A N2 g 3 Rate o*s ; k 6H276N972

)or 5te& 1 Rate )or+ard ; Rate reverse

2

1

122

221

2

1

6N97796N796N6N97

−

−==

k k k k

222

1

12

221

122

2222

776N96HRate

76N976HRate

7976N6HRate

−

−

=

=

=

k k k

k k

k

k

E 1 .@ 5ho+ that the &ro&osed !echanis! )or thereaction 2 9 3 → 9 2 3 !atches the o*served rate la+

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Tro, he!istry% $ Molecular $&&roach @-

reaction 2 9 g 3 9 2 g 3 !atches the o served rate la+Rate ; k 69 7269 27C1

9 g 3⇔ 9 2 g 3 A 9 g 3 ast

9 g 3 A 9 g 3→ 2 9 2 g 35lo+ Rate ; k ! 69 7697

k 1

k -1

)or 5te& 1 Rate )or+ard ; Rate reverse

1

21

1

211

776969697

769769769

−

−

−

=

=

k

k

k k

1C2

2

1

12

1C2

1

12

2

769769Rate

776969769Rate

769769Rate

−

−

=

=

=

k k k

k k

k

k

t l t

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atalysts' catalysts are su*stances that a))ect the rate o) a reaction

+ithout *ein" consu!ed' catalysts +or( *y &rovidin" an alternative !echanis!

)or the reaction+ith a lo+er activation ener"y

' catalysts are consu!ed in an early !echanis! ste&,then !ade in a later ste&

!echanis! +ithout catalyst

9 g 3 A 9 g 3→ 2 9 2 g 3 V. 5lo+

!echanis! +ith catalyst

l g 3 A 9 g 3⇔ 9 2 g 3 A l9 g 3 ast

l9 g 3 A 9 g 3→ 9 2 g 3 A l g 3 5lo+

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Tro, he!istry% $ Molecular $&&roach @:

9Jone /e&letion over the $ntarctic

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atal sts

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atalysts

' homogeneous catalysts are in the sa!e &hase asthe reactant &articlesl g 3 in the destruction o) 9 g 3

' heterogeneous catalysts are in a di))erent &hasethan the reactant &articles

solid catalytic converter in a car s e haust syste!

Ty&es o) atalysts

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Tro, he!istry% $ Molecular $&&roach @@

Ty&es o) atalysts

t l ti H d " ti

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atalytic Hydro"enationH

2; H

2 A H

2 X H H

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EnJy!es

' *ecause !any o) the !olecules are lar"e andco!&le , !ost *iolo"ical reactions re uire acatalyst to &roceed at a reasona*le rate

' &rotein !olecules that catalyJe *iolo"icalreactions are called en>ymes

' enJy!es +or( *y adsor*in" the su*stratereactant onto an active site that orients it )orreaction

E J ! C5 * t t Bi di "

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EnJy!eC5u*strate Bindin"Doc( and Key Mechanis!

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