Page 28 - Introduction to chemical reaction engineering and kinetics

10 Chapter 1: Introduction

involved, their molecular formulas, and a method of solving the linear algebraic equa-
tions for the atom balances, which is achieved by reduction of the A matrix to A*. We
illustrate the procedure in the following two examples, as implemented by the com-
puter algebra software Muthematica3 (Smith and Missen, 1997).4 (The systems in these
examples are small enough that the matrix reduction can alternatively be done read-
ily by hand manipulation.) As shown in these examples, and also in Example 1-2, the
maximum number of linearly independent chemical equations required is5

R = N-rank(A) = N-C (1.4-9)

A proper set of chemical equations for a system is made up of R linearly independent
equations.

The dehydrogenation of ethane (C,H,) is used to produce ethylene (C,H,), along with Hz,
but other species, such as methane (CH,) and acetylene (C,H,), may also be present in
the product stream. Using Muthematica, determine C and a permissible set of components,
and construct a set of chemical equations to represent a reacting system involving these
five species.

SOLUTION

The system is formally represented by a list of species, followed by a list of elements, both
in arbitrary order:

W,H,, Hz> C,H,, CH,, C,H,), CC, W)

The procedure is in four main steps:
(1) The entry for each species (in the order listed) of the formula vector formed by the
subscripts to the elements (in the order listed):

C2H6 = {2,6}
H2 = {0,2}

C2H4 = {2,4}

CH4 = {1,4}
C2H2 = {2,2}

3Muthematica is a registered trademark of Wolfram Research, Inc.
4Any software that includes matrix reduction can be used similarly. For example, with Maple (Waterloo Maple,
Inc.), the first three steps in Example 1-3 are initiated by (1) with (linalg): ; (2) transpose (array ([list of species
as in (l)])); (3) rref (“). In many cases, the matrix reduction can be done conveniently by hand manipulation.
?hemical reaction stoichiometry is described more fully on a Web site located at http://www.chemical-
stoichiometry.net. The site includes a tutorial and a Java applet to implement the matrix reduction method used
in the examples here.