Page 30 - Introduction to chemical reaction engineering and kinetics

12 Chapter 1: Introduction

one of these three linearly independent equations can be replaced by a combination of
equations (A), (B), and (C). For example, (A) could be replaced by 2(B) - (A):

2H, + C,H, = 2CH,, CD)

so that the set could consist of(B), (C), and (D). However, this latter set is not a canonical
set if C,H, and H, are components, since two noncomponents appear in (D).

There is a disadvantage in using Muthematica in this way. This stems from the arbi-
trary ordering of species and of elements, that is, of the columns and rows in A. Since
columns are not interchanged to obtain A* in the commands used, the unit submatrix
does not necessarily occur as the first C columns as in Example 1-3. The column inter-
change can readily be done by inspection, but the species designation remains with the
column. The following example illustrates this. (Alternatively, the columns may be left
as generated, and A* interpreted accordingly.)

Using Mathematics, obtain a set of chemical equations in canonical and in conventional
form for the system

{(CO,, H,O, H,, CH,, CO), (H, C, 0))

which could refer to the steam-reforming of natural gas, primarily to produce H,.

SOLUTION

Following the first two steps in the procedure in Example 1-3, we obtain

(1) (2) (3) (4) (5)
0 2 2 4 0

A< ( 1 2 1 0 0 0 1 1 1 1
0
Here the numbers at the tops of the columns correspond to the species in the order given,
and the rows are in the order of the elements given. After row reduction, Mathematics
provides the following:

(1) (2) (3) (4) (5)
0 0 1 4 1
1 0 0 1 1
A*= ( 0 1 0 - 2 - 1 1
This matrix can be rearranged by column interchange so that it is in the usual form for A*;
the order of species changes accordingly. The resulting matrix is

(3) (1) (2) (4) (5)
0 0 4 1
1 0 1 1
**= ( ; 0 0 1 - 2 - 1 1