70
chapter 5
Thermodynamics, Chemical Kinetics, and Energy Metabolism
to measure, however, and molar concentrations are com-
monly used in their place. Since concentration and activity
are almost equal in dilute solutions and many biological
reactions occur at low concentrations, this approximation
is valid.
A physical interpretation of AG° can be obtained
by noting that if [products]/[reactants] = 1, then AG =
A
G°.
AG° is the amount of useful work that can be ob-
tained by conversion of
1
mol of each reactant in its stan-
dard state to
1
mol of each product in its standard state.
The standard free-energy change for a reaction is also
useful for predicting whether a reaction will occur under
standard conditions. If A
G°
< 0, the reaction will occur
spontaneously provided standard conditions prevail; if
AG° > 0, the reaction will not occur by itself. It is AG,
however, that determines whether or not a reaction will
occur under conditions different from the standard state,
such as those existing within a cell, for two reasons.
1. Most solutes are present at fairly low concentrations
(< 0.1 M) and water is present at high concentration
(55.6 M for pure water); the water concentration is
thus assumed to be constant. If water enters into a
reaction, it is incorporated into
K
eq; if
Keq
is
determined at pH 7.0, it is indicated by
K
'q.
2. If H+ or OH- participates in a reaction, its
concentration influences AG°. Since most biological
reactions occur in systems buffered to pH ~ 7, it is
useful to define A
G°'
as the value of AG° measured
at pH = 7.0, i.e., where [ //+] = 10
- 7
M. AG°' values
can be compared to each other but not to values of
A G°.
Therefore, for biochemical systems, Equation (5.2)
can be written as
AG°' = -2.303
RT
log
K'eq
(5.3)
Substituting for
R
= 1.987 x 10
- 3
kcal • mol-1- deg
- 1
(8.314 x 10
" 3
kJ • mol
- 1
• deg-1) and
T =
298 K (i.e.,
273 + 25°C),
[in kcal/mol] AG°' —
—1.36 log M'q;
or
K'
=
10-ACGi.36
c4
[in kcal/mol]AG°' = -5.69 log
K'eq,
or
K'eq =
K nAG°'A
69
(
5
.
4
)
From Equation (5.4), at 25°C, each —
1.36 kcal/mol value
of A
G°'
corresponds to a factor of
1 0
in the equilibrium
constant in favor of product formation (Table 5-1). As
K'eq
increases, the value for AG°' decreases and the tendency
for reactions to occur increases spontaneously. Thus, we
can calculate AG°' by knowing
K'
and the temperature at
TABLE 5-1
Relationship between Standard Free Energy Change
(AG
0’)
and Equilibrium Constant (K'eq) at pH 7.0
and 25°C*
K'ec
AG0'
kcal/mol
kJ/mol
1 0 - 6
8.18
34.22
1 0 - 5
6.82
28.53
1 0 - 4
5.46
22.84
1 0 - 3
4.09
17.11
1 0 - 2
2.73
11.42
1 0 - 1
1.36
5.69
1
0
0
1 0
-1.36
-5.69
1 0 2
-2.73
-11.42
1 0 3
-4.09
-17.11
1 0 4
-5.46
-22.84
1 0 5
-6.82
-28.53
1 0 6
-8.18
-34.22
*K'
= 10 AG°
1,36
when AG° is expressed in kcal/mol at 25°C.
K'eq = 10_AG<>
5
69
when AG0" is expressed in kJ/mol at 25°C.
which
K'eq
is determined. In living systems, chemical reac-
tions rarely reach complete equilibrium states but do attain
near-equilibrium and nonequilibrium conditions. These
conditions are maintained by utilizing energy from the ex-
ternal source. In a metabolic pathway, one of the nonequi-
librium reactions usually becomes the rate-determining
step of that pathway and its regulation provides direction-
ality to the pathway. In a reaction sequence
A ^ B t^ C A - "
the reaction A —> B can be prevented from reaching
near-equilibrium by removing B (converting it to C) as
fast as it can be made from A. However, the conver-
sion of B to C may attain near-equilibrium. The near-
equilibrium reactions are reversible and allow for re-
versal of the biochemical pathway. All reactions in the
body are interrelated and the system as a whole is in
a
steady-state condition,
with individual reactions op-
erating in either near- or nonequilibrium conditions. A
change in concentration of any component (product of
one reaction used as reactant in another reaction) shifts
the concentration of all other components linked to it by
means of a sequence of chemical reactions, resulting in
the attainment of a new steady state.
The value of AG for a nonequilibrium system can be
determined from AG0', and the actual concentrations of
