# 9.1: Untitled Page 217

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## Chapter 9

### Global Stoichiometry:

R

R

*, *

R

R

(9‐26)

C2H6

(CH3)2N2

N2

(CH3)2N2

The relation between local and global stoichiometry is illustrated in Figure 9‐5.

The fact that these two relations are identical in form is based on the *assumption* that only azomethane, ethane, and nitrogen are present at both the *local level* and the *macroscopic level*. At this point we accept Eqs. 9‐25 and 9‐26 as being valid; however, we note that the principle of stoichiometric skepticism discussed in Sec. 6.1.1 should always be kept in mind. As we did in the case of the hydrogen bromide reaction, we begin with the simplest possible chemical kinetic schema given by

*k*

Local chemical kinetic schema:

(CH ) N

C H N

(9‐27)

3 2

2

2

6

2

This schema suggests that a molecule of azomethane spontaneously decomposes into a molecule of ethane and a molecule of nitrogen, and this decomposition is illustrated in Figure 9‐6. On the basis of the chemical kinetic schema indicated *Figure 9‐5*. Local and global stoichiometry for decomposition of azomethane by Eq. 9‐27 and illustrated in Figure 9‐6, the local rate equation for the production of ethane takes the form

Local chemical reaction rate equation:

*R*

*k c*

(9‐28)

C2H6

(CH3)2N2

*Reaction Kinetics *

403

Here the rate constant, *k*, is a parameter to be determined by experiment and should not be confused with the rate constant that appears in Eq. 9‐17 for the production of hydrogen bromide. The result given by Eq. 9‐28 is not in agreement with experimental observations (Ramsperger, 1927) which indicate that the reaction is *first order* with respect to azomethane at high concentrations and *second order* at low concentrations. The experimental observations can be expressed as

2

*k *[ *c*

]

(CH ) N

Experimental:

3 2 2

*R*

C2H6

1

(9‐29)

*k* *c*(CH3)2N2

in which *k* and *k* are not to be confused with the analogous coefficients in Eq. 9‐19.

*Figure 9‐6*. Spontaneous decomposition to leading to products The experimental results represented by Eq. 9‐19 and Eq. 9‐29 indicate that both reaction processes are more complex than suggested by Figure 9‐3 and by Figure 9‐6. The fundamental difficulty results from the fact that global observations cannot necessarily be used to correctly infer local processes, and we need to explore the local processes more carefully if we are to correctly predict the forms given by Eq. 9‐19 and Eq. 9‐29. In order to do so, we need to examine mass action kinetics in more detail and this is done in subsequent paragraphs.

*9.1.1* *Local and elementary stoichiometry*

The concept of *local stoichiometry* was introduced in Chapter 6, identified above by Eq. 9‐3 and repeated here as

*A * *N*

Axiom II:

*N R*

0 *, *

*J * 1 *, * 2 *,...,T *

(9‐30)

*JA A*

*A * 1

404