collision theory of bimolecular reactions • arrhenius formula...

物理化學(三) 應用化學系朱超原老師 1

• Collision theory of bimolecular reactions• Arrhenius formula (again)• Fraction number in bimolecular reactions • Unimolecular reactions

• Two-step reactions• More than two-step reactions• Chain reactions

VIII. The chemical reaction mechanismsVIII. The chemical reaction mechanisms


VIIIVIII--5. Two5. Two--step reactionsstep reactions

2HIIH 22 Elementary,Elementary,standard, standard, or ideal case or ideal case

We have extensively studied bimolecular reaction

2222 IHkdtId

dtHd

f

For example

25232 OONO2NO

If elementary

dtOd

dtONd

ONOkdtOd

dtNOd

f252

32

232

21

Experiment

dtONd

ONOkdtOd

f52

323


Two-step elementary reactions

25232 OONO2NO One-step

Real reaction mechanism

(1)

(2)

32 ONO

5223 ONNONO

23 ONO 1k

1k

2k 3NO Reactive intermediate

The steady-state approximation 0teintermedia

dtd

Each step is still elementary


(1)

(2)

1

3231321

32

stepdtNOd

ONOkONOkdtOd

dtNOd

dt

ONdNONOk

dtNOd

dtNOd

step

52232

2

2

3

Overall for intermediate (combine two steps)

02322313213 NONOkONOkONOkdtNOd

Rate law dt

ONdNONOk

dtOd

rate 522323

32221

321 NONOkOk

ONOk


22221

3212 NONOkOk

ONOkkrate

(1)

(2)

32 ONO

5223 ONNONO

23 ONO 1k

1k

2k

Summary

If (1) fast, (2) slow 221

3212 NOOk

ONOkkrate

If (1) slow, (2) fast 22

312 NOk

Okkrate

Experiment support

2313 NOOkdtOd

rate

Rate-limiting step approx. 32 ONO 1k Intermediate or product


Example 23 3O2O

Two-step elementary reactions

MO 3 1k

1k 2k

(1)

(2)

(fast)

(slow)

MOO 2

23 2OOO

intermediate

MOOkMOkdt

ddt

d

stepstep2131

11

2 OO

OOkdt

ddt

d

stepstep32

22

2 OO21

Overall (combine two steps) 0O 322131 OOkMOOkMOkdt

d

OOkOOkMOOkMOkdt

d32322131

2 32O


OOkdt

drate 32

2O31

Rate law

OOkMOk

MOk

322131

MO 3 1k

2k

(1)

(2)

(fast)

(slow)

MOO 2

23 2OOO

Summary

2

23

21

231

22O

31

OO

kOk

Okk

dtd

rate app

1k

Rate-determining step approx.


Calculation of rate constant appkkk

k 11

2

MO 3 1k

2k

(1)

(2)

MOO 2

23 2OOO

The first step (elementary)1k

1

11 k

kK

Calculate equilibrium constantfrom partition function method

The second step (elementary) OOkdt

d32

2O21

Collision theory of bimolecular reactions 2k


PCIIIweek18-1作業

Problem 12.18Page 554


Do not submit your homework papers


VIIIVIII--6. More than two6. More than two--step reactionsstep reactions

productsreactants

Step-1 reaction Step-2 reaction Step-3 reactionStep-4 reaction…

Rate-limiting stepOr Rate-determining step

*Reaction mechanism (from general chemistry, organic chemistry, ….)

No-need to consider step 4 and after

***The steady-state approximation 0teintermedia

dtd

**Each step is elementary reaction


2252 ONO4O2N Example

Proposed mechanism

2232 NOONONONO

52ON1k

1k32 NONO

2k

23 NO2NONO 3k

(1)

(2)

(3)

fast

fast

slow

NO3NO and intermediates

0NONO3 dt

ddt

d


(1)

(2)

(3)

fast

fast

slow

0NO 333223215213 NONOkNONOkNONOkONkdtd

3215211

3NO NONOkONkdt

d

step

1

3222

3 NONO

stepstep dtdNONOk

dtd

2

333

3 NONO

stepstep dtdNONOk

dtd

Overall (combine three steps)

0NO 33322 NONOkNONOkdtd

322321521 2 NONOkNONOkONk

3221

5212

NONOkk

ONk

NONOkk

23

2


52ON1k

32 NONO (1)1k

Rate law

32152152ON

NONOkONkdt

drate

322321521 2 NONOkNONOkONkrate

3221

5212

NONOkk

ONk

5221

5221522

2ONONk

kkONkk

dtd

rate app

2252 ONO4O2N


Example productBA 3

Rate law 3BAkrate app

Find mechanism

BGGBFFBA

321 fast

fast

slowGF and intermediates

FkBAkdtFd

step11

1

1

222

stepstep dt

GdGkBFkdtFd

BGkdtGd

step3

2


02211 GkBFkFkBAkdtFd

0322 BGkGkBFkdtGd

Overall (combine three steps)

BGkGkBFk 322

BGkFkBAk 311

GBkkBFk

32

2

FBkkBkk

kBAk

32

223

11

Approxi.

F

Bkkk

k

BAk

2

2

231

1 Gk

BFk

22

1

1k

BAk


Rate law

FBA

BGkFkBAkdt

Adrate 311

31

1

2

23 BAk

kkk

krate

appk


Example productDFB

Rate law aabaapp DFBkrate Find mechanism

bBaA

DAFB21

slow, rate-limiting

fast

A intermediate DAkFBkdt

Ad

step11

1

bastep

BAkdt

Ada 22

1

0211 ba BAakDAkFBkdtAd

Overall


Rate lawDAFB

ba BAakDAkFBkdtFdrate 211

approxi ADk

FBk

11

baaa

BDF

kkakrate

1

12

appk


2223 OO2H4NO4HNO Example

Proposed mechanism

3HNOHO

3HNO1k

1k2NOHO

2k

(1)

(2)

fast

slow

HO intermediates 2131

1NOHOkHNOkHO

stepdtd

322

HNOHOkHO stepdt

dOverall

0HNOHOkNOHOkHNOkHO 322131 dtd


Rate law

3HNO1k

1k2NOHO

3221312 HNOHOkNOHOkHNOk dtNOdrate

HOHNOkNOk

HNOk

3221

31

HONOkHNOk

21

31

2

23

1

12 NO

HNOkk

k

rate

appk

Experiment observes


PCIIIweek18-2作業


Problems 12.2412.31

Page 555



VIIIVIII--7. Chain reactions7. Chain reactions

2HBrBrH 22 Reaction

Empirical Rate law

2

2/1222/1 BrHBrk

BrHkdtHd

rateb

a

Proposed chain reaction mechanism

BrHBrBrH3

HHBrHBr22BrBr1

2

2

2

fast

fast

slow

General chemistry


Chain carriers BrH and intermediates 2121

121 BrkBrk

dtBrd

step

1

2222

stepstep dt

HdHHBrkHBrkdtBrd

(1)

(2)

(3) 3

232

stepstep dt

BrdBrHkdtHd

Overall 02 232222121 BrHkHHBrkHBrkBrkBrkdtBrd

023222 BrHkHHBrkHBrkdtHd


HHBrHBr 2Rate law

232222 BrHkHHBrkHBrkdtHdrate

HBrkHBrk

HBrk

23222

23 BrHkrate

BrBrkk

2/12

1

1

2/32

232

22

1

13 BrBrkHBrk

Hkkk

krate


2/32

232

22

1

13 BrBrkHBrk

Hkkk

krate

2

2/122/1 BrHBrk

BrHkrate

b

a

Compare

21

1 kkk

k a

3

2kk

k b


PCIIIweek18-3作業



collision theory of bimolecular reactions • arrhenius formula...

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