# 8.27: Untitled Page 216

- Page ID
- 18349

## Chapter 9

*R*

2 *k c*

*c*

HBr

H

Br

2

2

(9‐18)

net rate of production

chemical reaction rate

chemical reaction rate equation

In general, *equations* are unambiguous while *verbal descriptions* can sometimes be misleading. When in doubt, study the *equations*.

Experimental studies of the reaction of hydrogen and bromine to form hydrogen bromide were carried out by Bodenstein and Lind (1907) in a well‐mixed batch reactor, and those experiments indicate that the net rate of production of hydrogen bromide can be expressed as

*k c*

*c*

H2

Br2

Experimental:

*R*

(9‐19)

HBr

1 *k* *c*

*c*

HBr

Br

2

This experimental result is certainly *not consistent* with the chemical reaction rate equation given by Eq. 9‐17, thus the *picture* represented by Eq. 9‐15 is not consistent with the kinetics of the *real* *physical process*. Clearly we need a new picture of the reaction of hydrogen with bromine to form hydrogen bromide, and that new picture is considered in Section 9.3.

Decomposition of azomethane

As another example of an apparently simple reaction, we consider the gas-phase decomposition of azomethane [ (CH ) N ] to produce ethane ( C H ) and 3 2

2

2

6

nitrogen ( N ). This reaction is illustrated in Figure 9‐4 where we have indicated 2

that azomethane appears in both the input and the output streams.

*Figure 9‐4*. Decomposition of azomethane

401

The visual representation of the atomic matrix for this system is given by Molecular species

C H

N

(CH ) N

2

6

2

3 2

2

*carbon*

2

0

2

(9‐20)

*nitrogen*

0

2

2

*hydrogen*

6

0

6

and use of this representation with Axiom II provides

2 0 2

*R * C

0

2 H6

Axiom II:

0 2 2

*R*

0

(9‐21)

N

2

6 0 6

0

*R*

(CH

3 )2 N2

This can be expressed in terms of the *row reduced echelon form* of the atomic matrix to obtain

1 0 1

*R * C H

0

2

6

0 1 1

*R*

0

N2

(9‐22)

0 0 0

0

*R*

(CH

3 )2 N2

and a row‐row partition of this matrix leads to

*R*

C

2 H6

1 0 1

0

*R*

N

(9‐23)

2

0 1 1

0

*R*

(CH

3 )2 N2

Use of the pivot theorem (see Sec. 6.4) allows us to express the net rates of production for ethane and nitrogen in terms of azomethane according to

*R*

C H

1

2

6

*R*

(9‐24)

(CH

3 )2 N2

*R*

1

N

2

*pivot matrix*

and this result leads to the local stoichiometric relations given by Local Stoichiometry:

*R*

*R*

*, *

*R*

*R*

(9‐25)

C2H6

(CH3)2N2

N2

(CH3)2N2

The result for global stoichiometry is based on Eq. 9‐9 that leads to

402