Page 29 - Introduction to chemical reaction engineering and kinetics

1.4 Aspects of Kinetics 11

(2) The construction of the formula matrix A by the statement:

MatrixForm[Transpose[A = (C2H6, H2, C2H4, CH4, C2H2}]]

which is followed by the response:

2 0 2 1 2
6 2 4 4 2

(3) The reduction of A to the unit-matrix form A* by the statement:

RowReduce[ %]

which is followed by the response:

1 0 1 1/2 1
0 1 - 1 1/2 - 2

(4) Obtaining the chemical equation(s):

C = rank (A) = 2

(the number of l’s in the unit submatrix on the left). The columns in the unit sub-
matrix represent the components, C,H, and H, (in that order) in this case. Each of
the remaining three columns gives the values of the stoichiometric coefficients of
the components (on the left side) in a chemical equation involving 1 mole of each
of the noncomponents (on the right side) in the order in the list above. Thus, the
maximum number of linearly independent chemical equations is

The set of three equations is

+lC,H, - lH, = lC,H,

1 1
++Hh + ZHZ = lCH,

+lC,H, - 2H, = lC,H,

This is referred to as a canonical form of the set, since each equation involves exclusively
1 mole of one noncomponent, together with the components as required. However, we
conventionally write the equations without minus signs and fractions as:

C,H, = H, + C,H, (4

C2H, + H2 = 2CH, (JV

C,H, = 2H, + C,H, CC)

This set is not unique and does not necessarily imply anything about the way in which
reaction occurs. Thus, from a stoichiometric point of view, (A), (B), and (C) are properly
called equations and not reactions. The nonuniqueness is illustrated by the fact that any