section
5.2 Thermodynamics
69
FIGURE 5-2
Energy diagram for a thermodynamically unfavorable forward chemical
reaction,
W + X
—»■
¥ + Z . A G '
= free-energy of activation, and AG =
free energy difference between reactants and products that has a positive
value (Gy + z —
Gw + x > 0).
FIG URE 5-3
Energy diagram showing the reduction in free energy of activation
(A G ')
in an enzyme-catalyzed reaction. The free-energy difference between
reactant and product (AG) is
unchanged.
favorable
and that
the reaction can occur spontaneously.
If a chemical reaction has a positive AG value (as in
Figure 5-2), the reaction is
thermodynamically unfavor-
able
and can occur only with the assistance of an exter-
nal source of energy (e.g., coupling of an unfavorable re-
action with a favorable one); such a reaction is termed
endergonic.
An enzyme accelerates a chemical reaction by
de-
creasing AG',
which is usually accomplished by provid-
ing an alternate pathway for the reaction (Figure 5-3).
While
AG'
is decreased by the enzyme, the
AG
value
(i.e., free-energy difference between reactant and prod-
uct) is
unchanged.
In enzyme catalysis, the reactant is
termed
substrate.
The ability of an enzyme to decrease the
AG'
value is illustrated by hydrogen peroxide decompo-
sition (
2
H
2
O
2
—> 2H20 + O
2
). In the absence of catalase,
AG’
for the reaction is 18 kcal • mol
- 1
(79.3 kJ • mol-1),
whereas in the presence of catalase,
AG'
is 7 kcal • mol
- 1
(29.2 kJ • mol- 1). A calorie is the amount of heat required
to raise the temperature of 1
g of water by 1°C (from
14.5°C to 15.5°C). One kilocalorie (kcal) is 1000 calo-
ries. A joule (J) is the amount of energy required to apply
a force of 1 N (newton) over a distance of 1 m. One kilo-
joule (kJ) is 1000 J (1 kcal = 4.184 kJ).
For a reversible chemical reaction, the dependence of
AG on the temperature and concentration of reactants and
products is given by the expression
AG = AG° + RT In
[products]
(5.1)
where AG° is the standard free-energy change in calo-
ries per mole of reactant consumed; R is the gas constant
(1.987 x 10
- 3
kcal • mol-
1
-deg-1); T is the absolute tem-
perature in degrees Kelvin (= °C + 273); In is the natu-
ral logarithm (base
e);
and [products] and [reactants] are
the corresponding molar concentrations (for solvents and
solutes) or pressures in atmospheres (for gases).
Since at equilibrium AG = 0, this equation can be
written
л г „
p-ri
U
r
[products]
A
G
— —R T \n KQQ
where л еа =
-------------.
4
q
[reactants]
Note that the standard free-energy change is proportional
to the absolute temperature and the equilibrium constant,
Кщ.
The equilibrium constant depends only on the tem-
perature of the system. This equation provides a way of
determining A G° from equilibrium concentration data.
Another commonly used form is
AG° =
— RT
(In 10) (log
Keq) =
-2.303
RT
log Keq
(5.2)
where log means logarithm (base
1 0
).
The standard state for AG° is one in which the temper-
ature is 25°C, all gases are present at pressures of 1 atm,
all liquids and solids are pure (i.e., not mixtures), and all
solutes have unit activity. Activity is similar to concentra-
tion but takes into account interactions of solute molecules
with each other and with the solvent. Activities are difficult
[reactants]
