Page 228 - Thermodynamics of Biochemical Reactions

228 Mathematica Solutions to Problems

it involves an important issue that often arises in enzyme-catalyzed reactions, and that is the problem of water as a reactant in
dilute aqueous solutions. The problem is that the activity of water is taken as unity by convention, and so its concentration
does not appear in the expression for the apparent equilibrium constant. The conservation matrix at constant pH is
G6P H2 0 Glu Pi
A= C 6 0 6 0
0 9 1 6 4
P 1 0 0 1
Since the activity of water is taken as unity in dilute aqueous solutions independent of the extent of reaction, the Hz 0 column
and the oxygen row must be deleted from the conservation matrix:
G6P GIU Pi
A'= C 6 6 0
P 1 0 1

Therefore the conservation matrix is given by

as= ({6t 6, O}, (1, 0, I}};
The standard transformed Gibbs energies of the reactants at 298.15 K, pH 7, and 0.25 M ionic strength are

glucose6ghos /. gH + 7 /. is + 0.25

-1318.92

glucose /. gH -+ 7 /. is + 0.25
-426.708

pi /. pH -+ 7 /. is + 0.25

-1059.49

h20 /. gH+ 7 /. is + 0.25
-155.658

The standard further transformed Gibbs energies of formation in kJ rno1-l are

glucose6phoSft= -1318.92 -9 (-155.66)

82.02

glucoseft = -426.71 - 6 (-155.66)
507.25

pift = -1059.49 - 4 (-155.66)

-436.85
The equilibrium composition is calculated using

equcalcc [as, - {82.02, 507.25, -436.85) I (0.1, 0, 011
8.314510.29815
{0.0000919341, 0.0999081, 0.0999081)