### Kinetic Equations

A Mathematica notebook accompanying this article, Kinetics.nb, contains the instructions to process the kinetic input and generate the graphs. To translate the chemical equations into a system of coupled differential equations, the user interface proceeds by identifying the chemical species, by providing initial conditions and the integration time, and by specifying each kinetic step. Every place a user should change information to specify the kinetic system is shown in blue. The detailed procedure is as follows.

#### Elementary Rate Equation for Each Species

The entry of the kinetic equations is now shown by employing reaction 2 as an example, as follows.

2:  + + -> 2 HOBr

The following entries are made for this elementary step:

```

```

The first line is interpreted as follows: "In reaction 2, species #4 (i.e., ) is lost according to a rate law including species #4 (), #1 (), and #3 () with a rate constant of ." The corresponding differential equation is as follows:

This entry is one term in the complete expression for . Reactions 3 to 6 also contribute to .

The six entries in each sublist correspond to the following format:

1.reaction number
2.species number for time-derivative
3."loss" or "production" of species
4.{first species, second species, ... and so on} of kinetic rate equation
5.rate multiplier [account for stoichiometry]
6.rate constant

Reactions that do not fit this mold (e.g., surface reactions) can be manually adjusted in the kinetic equations later.

The complete set of entries corresponding to reactions 1 to 7 of the Belousov-Zhabotinskii chemical mechanism are shown below.

#### Special Instructions

There is occasionally the need for special instructions to be appended to the elementary rate equations. For example, in the Belousov-Zhabotinskii reaction, there is the parameter f. What value should it take?

#### Input Verification

After providing this input to Mathematica, the user verifies the interpretation. The species numbers, labels, and initial concentrations are displayed, as follows:

 1 2 HOBr 3 2 4 5 6 7 Ce(III) 8 Ce(IV) 9 organic

The individual kinetic terms are also displayed, as shown below for sorting by species. A complete kinetic term for the time rate of change of a species is the sum of the individual terms.

 1 0.5 f x 1. [organic][Ce(IV)] 1 1 1 2 d[HOBr]/dt = 2 d[HOBr]/dt = 2 d[HOBr]/dt = 2 d[HOBr]/dt = 3 3 3 3 3 3 4 4 4 4 4 5 5 5 6 6 7 d[Ce(III)]/dt = 1. [organic][Ce(IV)] 7 d[Ce(III)]/dt = 8 d[Ce(IV)]/dt = -1. [organic][Ce(IV)] 8 d[Ce(IV)]/dt = 9 d[organic]/dt = -1. [organic][Ce(IV)]

Converted by Mathematica

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