9.9: Untitled Page 225

Chapter 9

Elementary chemical reaction rate equation I:

I

R

  k c c

(9‐82c)

A

I A B

Elementary reference chemical reaction rate I:

r

 k c c

(9‐82d)

I

I A B

Here we should note that Eq. 9‐82c has the same form as Eq. 9‐18. In this case the term on the left hand side is an elementary rate of production while the term on the right hand side is referred to as an elementary chemical reaction rate. To illustrate the relation to Eq. 9‐18 we express Eq. 9‐82c as

I

R



 k c c

A

I A B





(9‐83)

elementary rate of production

elementary chemical reaction rate







elementar

y chemical reaction rate equation

In Eq. 9‐82d we have defined an elementary reference chemical reaction rate that is designated by r , and we will choose a similar reference quantity for each I

chemical kinetic schema. The units of these reference quantities are moles ( volume  time) and they will be designated by r , r and r . These I

II

III

reference chemical reaction rates will always be positive, and they must be distinguished from r , r , r , etc. that were used in Chapter 4 (see Eq. 4‐6) to A

B

C

represent the net mass rate of production of species A, B, C, etc.

Moving on to the second elementary step indicated by Eq. 9‐81b, we create a set of results analogous to Eqs. 9‐82 that are given by:

k II

Elementary chemical kinetic schema II:

C  B 

 E

(9‐84a)

Elementary stoichiometry II:

II

II

II

R

 R ,

R

  R II

(9‐84b)

C

B

C

E

Elementary chemical reaction rate equation II:

II

R

  k c c

(9‐84c)

C

II B C

Elementary reference chemical reaction rate II:

r

 k c c

(9‐84d)

II

II B C

Finally we examine the third elementary step indicated by Eq. 9‐81c in order to obtain the following relations

k III

Elementary chemical kinetic schema III:

C  D 

 A  B

(9‐85a)

Reaction Kinetics

419

Elementary stoichiometry III:

III

III

III

III

III

III

R

 R

,

R

  R

,

R

  R

(9‐85b)

C

D

C

A

C

B

Elementary chemical reaction rate equation III:

III

R

  k c c

(9‐85c)

C

III C D

Elementary reference chemical reaction rate III:

r

 k c c

(9‐85d)

III

III C D

The net rate of production for each molecular species is given in terms of the elementary rates of production according to

I

II

III

Species A:

R

 R  R  R

(9‐86a)

A

A

A

A

I

II

III

Species B:

R

 R  R  R

(9‐86b)

B

B

B

B

I

II

III

Species C:

R

 R  R  R

(9‐86c)

C

C

C

C

I

II

III

Species D:

R

 R  R  R

(9‐86d)

D

D

D

D

I

II

III

Species E:

R

 R  R  R

(9‐86e)

E

E

E

E

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

Species A:

R

  r  0  r

(9‐87a)

A

I

III

Species B:

R

  r  r  r

(9‐87b)

B

I

II

III

Species C:

R



r

 r

 r

(9‐87c)

C

I

II

III

Species D:

R



r

 0  r

(9‐87d)

D

I

III

Species E:

R



0  r

 0

(9‐87e)

E

II

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

420