section
5.2
Thermodynamics
71
products and reactants in the cell can be determined by
use of the common logarithm analogue of Equation (5.1):
AG = AG°' + 2.303
RT
log [products]
[reactants]
If AG is negative, then
under cellular conditions
the re-
action proceeds to form products. The A
G°'
value for a
given chemical reaction may be positive suggesting im-
mediately that the reaction cannot occur (without external
assistance), yet the AG value may be negative indicating
that the reaction can occur under the prevailing concentra-
tions of reactant and products. The reaction of glycolysis,
catalyzed by the enzyme aldolase (Chapter 13), furnishes
a good illustration.
Fructose 1,6-bisphosphate — glyceraldehyde
3-phosphate + dihydroxyacetone phosphate
The
K'
for this reaction at 25°C is 6.7 x 10
- 5
M. We
cq
can calculate AG°' from Equation (5.3):
A
G°'
= -2.303
RT
log
K'tq
=
-2.303 x 1.98 x 10
“ 3
x 298 x log (6.7 x 10“5)
= +5.67 kcal/mol (or + 23.72 kJ/mol).
The positive value for AG0/ indicates that the reaction is
not favored in the forward direction but can proceed in the
reverse direction. Now we calculate the AG value using
the concentration of 50 /xmol/L (or 50 x
1 0
6
M) for both
reactant and product, which is close to their physiological
concentrations:
AG =
AG°' + 2.303RT
x log
[
glyceraldehyde 1 [ dihydroxyacetone
3-phosphate J I
phosphate
[Fructose 1,6-bisphosphate]
= +5.67 kcal/mol + 2.303 x 1.98 x 1(T
3
x 298
[(50 x 10“6) x (50 x 1(T6)]
x log-
(50 x 10-6)
= 5.67 kcal/mol —
5.85 kcal/mol
= -0.18 kcal/mol(or - 0.75 kJ/mol).
The negative value of AG suggests that under physio-
logical conditions the forward reaction is favored, despite
the fact that A G°' is positive. Thus, under physiological
conditions AG values predict better than AG°' values
whether a reaction can occur spontaneously. Similarly,
whereas under certain conditions of reactants and prod-
ucts the conversion of reactant to product is favored (e.g.,
the conversion of fructose
1
,
6
-bisphosphate to glyceralde-
hyde 3-phosphate and dihydroxyacetone phosphate during
glycolysis), the direction of this reaction can be reversed
when appropriate changes occur in the concentrations
of reactants and products (formation of fructose
1
,
6
-
bisphosphate from glyceraldehyde 3-phosphate and di-
hydroxyacetone phosphate during gluconeogenesis). The
same enzyme catalyzes both the forward and the reverse
reactions.
The concept of AG is further clarified by an exam-
ple. Consider a self-operating heat engine that functions
by taking in an agent (e.g., steam) at temperature
T\
and
releasing it at
T2
(7) >
T2).
The heat extracted
(Q)
is con-
verted as efficiently as possible into useful work. If
W
represents the maximum useful work available,
(7i -
T2)
T2
W = Q y
1
2 =Q-Q^
A
A
where
T\
and
T2
are absolute (Kelvin) temperatures.
Unless
T2
= 0 or
T\ =
oo, the useful work is always less
than the total energy supplied by a factor of
Q(T2/T \) =
(Q/T\ )T2.
The ratio
Q/T\
is the entropy (
S
) of the sys-
tem, and the amount of energy unavailable for useful
work
(T2S)
is that which is lost in the process of energy
transfer; it can be thought of as the amount of random-
ness or disorder introduced into the system during the
transfer.
For chemical systems,
G
can be defined by the equa-
tion
G =
H
TS.
Here,
G
(free energy) is analogous to
W,
the maximum useful work available;
H
(enthalpy) is
analogous to
Q,
the heat content of the system at con-
stant pressure;
S
(entropy) is analogous to (
Q /T \
), the
wasted heat energy; and
T
is again the absolute temper-
ature. This relationship
G =
H — TS
is more commonly
used to describe
changes
in these quantities. If a system
goes from state I (with
G =
G\, H
=
H\, S
=
Si)
to state
II
(G = G n ,
H
=
Hu, S
=
Sn)
at constant temperature,
G n - G i
=
(Hn
-
Hi) - T (Su - Si)
or, simply,
AG = A H - T AS.
Since entropy (S) is a measure of disorder (randomness),
it is the energy that is unavailable for useful work. Entropy
values of denatured molecules are high relative to those of
native structures (as in protein dénaturation). In a living
system, entropy is kept at a minimum by utilization of free
energy (G) from outside and by increase in entropy of the
surroundings.
Enthalpy
(H)
is related to the internal energy of a system
by the following equation, where
E
is the internal energy,
P
the external pressure on the system, and
V
the volume
of the system. In terms of changes between states, the
equation becomes
A H = AE
+ A
(PV) = A E
+
P A V
+ VA
P.