一日一句 - shandong universitycourse.sdu.edu.cn/download2/20190923214456354.pdf · kinetics of...

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一日一句

Chapter X

Kinetics of Complex Reactions

Outside classroom reading:

Levine: p.559 17.9

§10.1 Typical complex reactions

The kinds of typical complex reactions

2) Parallel Reaction

Compteting reaction

1 2A B Ck k

3) Consecutive Reaction

1) Opposing Reaction

Reversible reaction


The most simple complex reaction is composed of two elementary steps.

10.1.1 Opposing Reaction / reversible reaction

The forward and the backward / reverse reaction take place simultaneously.

for opposing reaction consisting of elementary

reactions:

[A] [B]a br k

[G] [H]g hr k As reaction proceeds, r+ increases while r

decreases. When r+ becomes equal to r,

equilibrium is reached.

[A] [B] [G] [H]a b g hk k

[G] [H]

[A] [B]

g h

ca b

kK

k

k

kKc

The connection between the equilibrium

constant (Kc) and the rate coefficients of

simple reactions. This relation, named as

kinetic equilibrium constant.

Can we extend this discussion to ammonia synthesis?


For first-first order opposing reaction:

(2) rate equation

t = 0 a 0

The total rate is

xkxakdt

dx )(

e e( )k a x k x e

e

( )k a xk

x

Under equilibrium conditions

e

e

( )x xdxk a

dt x

t = te a-xe xe

t = t a-x x


e e

e

ln( )

x xk

at x x

e e

e

ln( )

a x xk

at x x


k+ and k can be determined by measuring

x at t and at equilibrium concentration.

Principle of relaxation method for

studying fast reaction


e e

e

ln( )

x xk

at x x

e e

e

ln( )

a x xk

at x x

e

e

1ln

( )

xk k

t x x

e

e

ln ( )( )

xk k t kt

x x

Why?


1-2 opposing reaction

2-2 opposing reaction

Other opposing reactions

10.1.2 Competing reaction/Parallel reaction

1

[B][A]

dk

dt

2

[C][A]

dk

dt

))(()()( 2121 xakkxakxakdt

dx

21 kk When )(1 xakdt

dx

When 21 kk )(2 xakdt

dx

The rate of parallel reaction is determined

mainly by the faster one.

HCOOH

CO2 + H2

CO + H2O


))(( 21 xakkdt

dx

Integration of the equation yields:

tkkxa

a)(ln 21

])(exp[)( 21 tkkaxa

A B C

a 0 0

a-x y z x = y + z

)(1 xakdt

dy

)(2 xakdt

dz

For production of B and C:

])(exp[ 211 tkkakdt

dy



])(exp[)( 21 tkkaxa

]})(exp[1{ 21

21

1 tkkkk

aky

2

1

k

k

z

y selectivity of the reaction.

]})(exp[1{ 21

21

2 tkkkk

akz

A

B

C

t

c



(2) Optimal temperature for better selectivity

A B A1 Ea, 1

A C A2 Ea, 2



(3) Selectivity of catalyst

HCOOH

CO2 + H2

CO + H2O

(4) Main reaction and Side reaction:

reaction with higher k is taken as the main

reaction, while others side reactions.

Reaction that produces the demanded product

is the main reaction.

product

consumed

nS

nSelectivity:



10.1. 3 Consecutive reaction

Some reactions proceed through the formation of intermediate.

CH4 + Cl2 CH3Cl CH2Cl2 CHCl3 CCl4

A B C

a = x + y + z

General reaction

1 2A B Ck k

t = 0 a 0 0

t = t x y z

xkdt

dx1

tkx

a1ln

ykxkdt

dy21 yk

dt

dz2


)exp( 1tkax

)exp()exp( 21

12

1 tktkkk

aky

)exp(

)exp(1

2

12

1

1

12

2

tkkk

k

tkkk

k

az

1 2A B Ck k



shows that the intermediate’s concentration

rises from zero to a maximum and then drops

back to zero as A is depleted and C dominates

in the mixture.

)exp()exp( 21

12

1 tktkkk

aky

If C is the demanded product, the reaction time should be prolonged. If B is the

demanded product, the reaction should be interrupted at optimum time, i.e., tmax.

0dt

dy

21

21max

)/ln(

kk

kkt

At tmax, the concentration of B = ?



k2/k1 1/5 5 10 100 103 108

tmax 2.01 0.40 0.25 0.047 710-3 10-7

ymax/a 0.67 0.13 0.08 7 10-3 10-3 0

Ea,1Ea,2 -0.4 4.0 5.7 11.5 17.2 46.1

When k2 >> k1, ymax would be very small,

and the tmax would be very short.

2 1

2 1

max

ln( k / k )t

k k

0dt

dy

2

2 11

2

k

k k

max

ky a( )

k


k2/k1

increases


Physical meaning of k2 >> k1

B that is difficult to form but easy to

decompose is a active intermediate (Such

as active atom: Cl, H, etc., radicals: CH3•,

H2C:, C+, C-, etc., activated molecules: A*),

it is difficult to form but easy to

decompose to product.

For consecutive reaction with large k2/k1

ratio, once the reaction take place, the active

intermediate (B) rapidly attains its maximum

concentration and its concentration keeps

nearly unchanged during the whole reaction.

0dt

dy

Steady-state approximation

1 2A B Ck k



)exp()exp(1 2

12

11

12

2 tkkk

ktk

kk

kaz

1 21 2

2 1

Zdc ak kexp( k t ) exp( k t )

dt k k

When k2 >> k1

1 1Zdc

ak exp( k t )dt

The total rate is determined mainly by k1

When k2 << k1

2 2Zdc

ak exp( k t )dt

The total rate is determined mainly by k2

The rate of the overall consecutive reaction depends only on the smaller rate constant

(rate-determining step).



Rate-determining step (r. d. s.): the step with the slowest rate.



The rate of the elementary step with the lowest rate constant, i.e., r.d.s., can be used to

express the actual rate of the overall reaction.



Summary:

1. Deduce the rate law of typical complex reactions;

2. Explain the rate characteristics of typical complex reactions;

3. Judge the key step to accelerate the overall reactions;

4. Explain the principles and validity of pre-equilibrium (fast equilibrium), steady-state

and rate-determining step approximations;

5. Explain the principle for relaxation method to determine the reaction rate of rapid

reaction.

6. Design possible ways to alter the selectivity of reactions;

7. Judge the possible r. d. s..


一日一句 - shandong universitycourse.sdu.edu.cn/download2/20190923214456354.pdf · kinetics of...

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