9.12: Untitled Page 228

Chapter 9

SCHEMA IV

k IV

Elementary chemical kinetic schema IV:

H  HBr 

 H  Br (9‐100a)

2

IV

IV

IV

IV

R

 R

,

R

  R

Elementary stoichiometry IV:

H

HBr

H

H2

(9‐100b)

IV

IV

R

  R

H

Br

Elementary chemical reaction rate equation IV:

IV

R

  k c c

(9‐100c)

H

IV H HBr

Elementary reference chemical reaction rate IV:

r

 k c c

(9‐100d)

IV

IV H HBr

SCHEMA V

k V

Elementary chemical kinetic schema V:

2Br



 Br

(9‐101a)

2

V

R

Elementary stoichiometry V:

Br

V

  R

(9‐101b)

2

Br

2

Elementary chemical reaction rate equation V:

V

R

  k

2

c

(9‐101c)

Br

V Br

Elementary reference chemical reaction rate V:

r

 k c 2

(9‐101d)

V

V Br

We begin our analysis of Eqs. 9‐96 by listing the net molar rates of production of all five species in terms of the elementary rates of reaction according to I

II

III

IV

V

R

 R

 R

 R

 R

 R

(9‐102a)

Br2

Br2

Br2

B 2

r

Br2

Br2

I

II

III

IV

V

R

 R

 R

 R

 R

 R

(9‐102b)

H2

H2

H2

H2

H2

H2

I

II

III

IV

V

R

 R

 R

 R

 R

 R

(9‐102c)

HBr

HBr

HBr

HBr

HBr

HBr

I

II

III

IV

R

 R

 R

 R

 R

 R V

(9‐102d)

H

H

H

H

H

H

I

II

III

IV

V

R

 R

 R

 R

 R

 R

(9‐102e)

Br

Br

Br

Br

Br

Br

At this point we can use the elementary chemical reaction rates to express the net rates of production according to

Reaction Kinetics

425

R

  r  0  r

 0  1

Br

r

(9‐103a)

2

I

III

V

2

R



0  r

 0  r

 0

(9‐103b)

H2

II

IV

R



0  r

 r

 r

 0

(9‐103c)

HBr

II

III

IV

R



0  r

 r

 r

 0

(9‐103d)

H

II

III

IV

R

 2 r  r  r

 r

 r

(9‐103e)

Br

I

II

III

IV

V

In matrix form these representations for the net rates of production are given by

 R



 r 

2

Br

1

0 1

0

1 2 





 I 





 R



H

0





1

0

1

0

r II 

2













 R

r

HBr 

  0

1

1 1

0   III 

(9‐104)













R

0

1 1 



1

0 



r

H 

 IV 









2

1

1

1



R



1  





r

Br 

 V 

The compact form of this lengthy algebraic result can be expressed as R

 M r

(9‐105)

M

in which R is the column matrix of all net rates of production, M is the M

mechanistic matrix, and r is the column matrix of elementary chemical reaction rates. These quantities are defined explicitly by

426