Page 318 - Thermodynamics of Biochemical Reactions

318 Matheniatica Solutions to Problems

5.1 (a) Carry out the operations involved in equations 5.1-12 to 5.1-27 using MathematicaR. (b) Carry out the operations
involved in equations 5.1-22 to 5.1-26. (c) Calculate the amounts of the components C, H, and 0 for a system containing
one mole of each of the five species. (d) Calculate the amounts of the components CO, H2, and CH4 for the system contain-
ing one mole of each of the five species.

(a) Equations 5.1-12 to 5.1-20
The conservation matrix is given by

TableForm [a]
1 0 1 0 1
0 2 4 2 0
1 0 0 1 2

The stoichiometric number matrix is given by

TableForm[nul
-1 -1
-3 1
1 0
1 -1
0 1
The matrix product is given by

TableForm[a.nul

0 0
0 0
0 0

The canonical form of the conservation matrix is

TableForm[ared=RowReduce[all
1 0 0 1 2
0 1 0 3 2
0 0 1 -1 -1
The matrix product using the row reduced form of the conservation matrix isactivated by using a period.

TableForm [ared. nu1
0 0
0 0
0 0

Thus the row reduced form represents the conservation relations equally well.
Calculate a basis for the nullspace of the conservation matrices a.