reaction kinetics(1)

8/14/2019 Reaction Kinetics(1)

http://slidepdf.com/reader/full/reaction-kinetics1 1/28

1

Reaction

Kinetics (1)

Xuan ChengXiamen University

PhysicalChemistry



2

PhysicalChemistry Reaction Kinetics

)()(23

)(21

322 g NH g H g N →+

For example

)()(21

)( 222 l O H g O g H →+

1/ −∆ mol kJ G or

-16.63

-237.19

Thermodynamics : spontaneous reactions (possible to take place)

Thermodynamics : can’t answer (1) how to make them happen(2) how fast they will take place (3) the reaction mechanism

ReactionKinetics



3

PhysicalChemistry

Reaction Kinetics

)()(23

)(21

322 g NH g H g N →+

)()(21

)( 222 l O H g O g H →+

T , P , catalyst

T , catalyst

Chemical Kinetics :

Chemical Kinetics

The study of the rates and mechanisms of chemical reactions

A reacting system is not in equilibrium

ReactionKinetics



4

PhysicalChemistry Rate of ReactionConsider the homogeneous reaction (occurs entirely in one phase)

b

a

dt dn

dt dn

B

A =/

/

++→++ fF eE bBaA (17.1)

The rate of conversion J

dt dn

f dt dn

edt dn

bdt dn

a J F E B A 1111 ===−=−≡ (17.2)

dt

dn

bdt

dn

a

B A 11 =

At equilibrium, J = 0

ReactionKinetics



5

PhysicalChemistry Rate of Reaction

−=≡

dt dn

aV V J

r A11(17.3)

====−=−=dt F d

f dt E d

edt Bd

bdt Ad

ar

][1][1][1][1(17.4)*

At constant V

The rate of reaction r

mol dm -3 s-1

mol cm -3 s-1

ReactionKinetics



6

PhysicalChemistry Rate Laws

For many reactions

[ ] [ ] [ ]λ β α L B Ak r = (17.5)*

k : rate constant (rate coefficient), k = f (T, P)

α , β , … λ : order or partial order

α + β + … +λ ≡ n : overall order

The expression for r as afunction of concentrations at afixed temperature is called therate law.

ReactionKinetics



7

PhysicalChemistry Reaction Orders

ok r =

[ ] Ak r =

[ ]2 Ak r = [ ] [ ] B Ak r =

[ ] [ ] B Ak r 2= [ ] [ ]2 B Ak r =

[ ] [ ]2−= B Ak r

[ ] [ ]2/1 B Ak r =

[ ][ ] [ ]( )2/11/ B B Ak r −=

Zero-order

First-order

Second-order

Third-order

Negative First-order

1.5-order

No simple order

ReactionKinetics



8

PhysicalChemistry

Rate Laws

Reaction Rate Law

HBr Br H 222 →+ [ ][ ][ ] [ ]

2

2/122/1 Br HBr j

Br H k r

+

=

225242 O NOO N +→

HI I H 222 →+ [ ][ ]22 I H k r =

[ ]52

O N k r =

COCH CHOCH +→ 43 [ ] 2/33CHOCH k r =

ReactionKinetics



9

PhysicalChemistryReaction Mechanisms

322 SO NOSO NO +→+

22 22 NO NOO →+ (17.7)

32222 SOOSO NO

→ +intermediate

2252 42 O NOO N +→

3252 NO NOO N +

23 2 NO NO NO →+2232 NOO NO NO NO ++→+ (17.8)

Step (a)

Step (b)

Step (c)

Elementaryreaction

Reaction actually occurs

ReactionKinetics



10

PhysicalChemistry Measurement of Reaction

Rates

Chemical Method

The concentration of a reactant or product as a function of time

Reaction vessels

At constant T

At intervals Slows down or stopthe reaction

Rapidly analyze chemical

compositions of the mixture

Cooling the sampleremoving a catalystDiluting the mixtureAdding a species

ReactionKinetics



11

PhysicalChemistry

ReactionKinetics



12

PhysicalChemistry Measurement of Reaction

Rates

Physical MethodMeasures a physical property of the reaction system as afunction of time. This allows the reaction to be followedcontinuously as it proceeds.

More accurate and less tedious

IR UV-VIS ESR NMR ESCA

ReactionKinetics



14

PhysicalChemistry First-Order Reactions

Suppose the reaction P aA → is first-order with [ ] Ak r =

====−=−=dt F d

f dt E d

edt Bd

bdt Ad

ar ][1][1][1][1

(17.4)*

[ ] [ ] [ ]λ β α L B Ak r = (17.5)*

[ ] [ ] Ak dt Ad

ar =−= 1

(17.10)

define ak k A ≡ [ ] [ ] Ak dt Ad A−=/ (17.11)

[ ] [ ] dt k A Ad A−=/

[ ] [ ] ∫ −=∫ 21

21 / dt k A Ad A

ReactionKinetics



15

PhysicalChemistry First-Order Reactions

[ ] [ ] ∫ −=∫ 21

21 / dt k A Ad A

(17.12)[ ] [ ]( ) )(/ln 1212 t t k A A A −−=

(17.13)[ ][ ]

t k A A

Ao

−=ln

if t t =2[ ] [ ]o A A =1 at 01 =t [ ] [ ] A A =

2 atand

[ ] [ ] t k o

Ae A A−

= (17.14)*

The concentration of A (and r) decreases exponentially withtime for a first-order reaction.

[ ] [ ] Ak dt Ad

ar =−= 1 (17.10)

Integrated ratelaw

ReactionKinetics



16

First-order reaction: ln[A] vs t

First-Order ReactionsPhysical

Chemistry

[ ] [ ] t k o

Ae A A−

= (17.14)*

[ ] [ ] t k A A Ao −= lnln

[ A ] / [ A ] o

t First-order reaction: [A]/[A] o vs t

[ ][ ]

t k

o

Ae A

A −=

L n

[ A ]

t

[ ] [ ] t k A A Ao =/ln

ReactionKinetics



17

First-Order ReactionsPhysical

Chemistry

2/1t Half-life:

2/1t t = o A A ][2/1][ =

(17.13)[ ][ ] t k A A Ao

−=ln

2/1][][2/1

ln t k A

A A

o

o−=

693.02ln2/1 ==t k A First-order reaction (17.15)*

2/12/1ln t k A−=

The time needed for [A] to drop to half its value

Ak t /693.02/1 = Independent of [A] o

A useful indication for the chemical reactionrate

ReactionKinetics



18

Second-Order ReactionsPhysical

Chemistry

22

2

][A P2A )2(

A][B][ PBA )1(

k r

k r

= →

= → +

[ ] [ ]21 Ak

dt Ad

ar =−= (17.10)

define ak k A ≡ [ ] [ ]2/ Ak dt Ad A−= (17.11)

[ ] [ ]2 Ak

dt

Ad A−=

[ ][ ] ∫ −=∫ 2

12

1 21

dt k Ad A

A

ReactionKinetics



19


Chemistry

[ ] [ ])(

1112

21t t k

A AA −−=− (17.16)

A plot of 1/[ A] versus t gives a strait line of slope k A if

ak k A ≡ (17.17)[ ] [ ][ ]o A

o At k

A A

+=1

[ ] [ ] ∫ −=∫ 2

1

2

1 2

1dt k Ad

A A

[ ] [ ]t k

A A Ao

=− 11

[ ]2 Ak r =

ReactionKinetics



20

{[A] -1 }

{t }

Second-order reaction: 1/[A] vs t


Chemistry

(17.16)[ ] [ ]t k

A A Ao =−11

[ ] [ ]t k

A A Ao +=11

2/1t Half-life:

2/1t t = o A A ][2/1][ =

Ao k At

][1

2/1 =

Second-order reaction with

r = k[A] 2

ReactionKinetics



21


Chemistry

Ao k At

][

12/1 = Second-order reaction with r = k[A] 2

Ak t 2ln2/1 = First-order reaction with r = k[A]

productsbBaA →+ [ ] [ ] B Ak r −=

[ ] [ ] [ ] B Ak dt Ad

a −=1 (17.18)

Three variables

ReactionKinetics

h l



22


Chemistry

products B A →+0=t

[ ] [ ] [ ] B Ak

dt

Ad −=

x=0 when t =0

[ ]o A [ ]o B

t t = [ ] x A o − [ ] x B o −

0

x

[ ] [ ][ ] [ ]( )[ ]( ) x B x Ak B Ak dt Ad oo −−−=−= [ ] dt

dxdt Ad −=

[ ]( )[ ]( ) x B x Ak dt dx

oo −−=

[ ]( )[ ]( ) kdt x B x A

dx

oo=−− [ ]( )[ ]( ) ∫ =∫ −−

t x

ookdt

x B x Adx

00

ReactionKinetics

h i l



23


Chemistry

[ ]( )[ ]( )kt kdt

x B x A

dx t x

oo=∫ =∫

−− 00

[ ]( )[ ]( ) [ ] [ ] [ ]( ) [ ]( )dx x B x A A B x B x A

dx x

oooo

x

oo∫ −−−−=∫ −− 00

111

[ ] [ ][ ]

[ ][ ]

[ ]

−−

−−= x B

B x A

A A B o

o

o

o

oolnln

1

[ ] [ ][ ]

[ ][ ]

[ ] kt x B B

x A A

A B o

o

o

o

oo =

−−

−− lnln1

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

kt A A B B

A B o

o

oo=

− /

/ln

1 [ ] [ ] x A A o −=[ ] [ ] x B B

o −=

(17.22)’

ReactionKinetics

Ph i l



24


Chemistry

[ ]( )[ ]( ) [ ]( )kt kdt

x A

dx

x B x A

dx t x

o

x

oo =∫ =∫ −=∫ −− 00 20

[ ]( ) [ ] [ ]kt

A x A x A

dx

oo

x

o

=−−=∫ −

110 2

If [A] o=[B] o

[ ] [ ]kt

A A o=− 11

(17.23)’

2/1t Half-life:

2/1t t = o A A ][2/1][ =

[ ]o

Ak t

12/1 =

ReactionKinetics

Ph i l



25

Third-Order ReactionsPhysical

Chemistry

[ ] [ ]3 Aak dt Ad −=

[ ][ ]

dt k A

Ad A−=3 [ ] [ ]

t k A A

Ao

211

22 =−

[ ] [ ] [ ] B Aak dt Ad 2−= [ ] [ ] [ ]2 B Aak dt Ad −=[ ]

[ ] [ ] [ C B Aak dt Ad

−=

(Problems 17.17 and 17.24)

[ ] [ ][ ]( )2/1221 o

o

Akt

A A+

= (17.24)

ReactionKinetics

Ph i l



26

nth-Order ReactionPhysical

Chemistry

Consider

[ ] ×− −1)1( no An

[ ] [ ]n A Ak dt Ad −= (17.25)

Integration gives[ ]

[ ]∫ −=∫ 21

21 dt k

A

Ad An (17.26)

[ ] [ ]t k

n A A

A

no

n−=+−

− +−+−

1

11For n ≠ 1 (17.27)

[ ][ ]

[ ] t k n A A A

Ano

n

o)1(1 1

1

−+=

−

−For n ≠ 1 (17.28)

ReactionKinetics

Ph i l



27

nth-Order ReactionPhysical

Chemistry

[ ] Ano

n

k Ant

1

1

2/1)1(

12−

−

−−= (17.29)For n ≠ 1

[ ] [ ] t k oAe A A −= For n = 1 (17.30)

2/1t Half-life:

2/1t t = o A A ][2/1][ =

Ak t 2ln

2/1 =

[ ][ ]

∫ −=∫ 21

21 dt k

A

Ad An (17.26)

[ ] [ ] t k A A Ao =−[ ]

A

ok

At

22/1 = For n = 0

ReactionKinetics

Ph i l



28

Homework Physical

Chemistry

Page 591

Prob. 17.5Prob. 17.6

Prob. 17.8

Prob. 17.10

ReactionKinetics

reaction kinetics(1)

Documents