72
chapter 5
Thermodynamics, Chemical Kinetics, and Energy Metabolism
At constant pressure, AP = 0 and
A H =
A
E
+
PAV.
If, in addition, the volume is constant, then
AV =
0 and
AH = AE.
In many biological reactions,
AV = AP =
0. Consequently, for a change of state, the maximum
amount of energy that can be released as heat
(AH)
is
equal to
AE,
the change in the internal energy of the
system.
A H
can be measured by burning the particular com-
pound in a bomb calorimeter at constant pressure. The
heat released is measured as the rise in temperature of
a large water bath surrounding the combustion chamber.
The values so obtained indicate the total energy available
in a compound when it is completely oxidized. Factors that
usually contribute to AH under these conditions are the
heat of fusion (melting), the heat of vaporization (boiling),
and the heat of combustion (bond making and breaking).
The first two factors are important, for example, if at the
standard temperature (25°C) a solid is combusted to a com-
bination of liquids and gases, as in the examples below.
Just as with AG,
AH
for a process is equal to
—AH
for the reverse process:
Nemst equation:
Eh = E°'
+
2.303
RT
nF
log
(electron acceptor)
(electron donor)
where
Eh
= observed potential,
E°' =
standard redox po-
tential,
R =
gas constant (8.31 J deg
- 1
• mol),
T
= temper-
ature in Kelvin,
n =
number of electrons being transferred,
and
F
= the
(96,487 J/V). It is evident
from the Nemst equation that
Eh
=
E°'
when [electron
acceptor] = [electron donor]. Thus, the
E°’
value repre-
sents the midpoint in a redox reaction, which is analogous
to the measurement of the pK' value of a weak acid, HA,
when [A- ] = [HA] (see discussion of the Henderson-
Hasselbalch equation in Chapter 1). In this manner,
E°'
values for many redox reactions of biochemical impor-
tance have been determined (Chapter 14).
A
half-reaction
is a reaction in which electrons or hy-
dride ions are written explicitly. Values of
and
E°'
are
tabulated with the half-reactions for which they are mea-
sured. For example,
E°'
= -0.32 V
A H
(liquid —>■
gas)
= — AH
(gas -> liquid)
A H
(liquid —> solid) =
—A H
(solid
—>
liquid)
A H
(making a bond) =
— AH
(breaking the same bond).
A H
values for various food substances and their applica-
tion to human energy metabolism are discussed later in
this chapter.
A number of processes in living systems result in the
transfer of electrons (oxidation and reduction) and can be
understood in thermodynamic terms.
Oxidation
is the loss
of electrons or hydride (H~) ions (but not hydrogen [H+]
ions) by a molecule, atom, or ion.
Reduction
is the gain
of electrons or hydride (H_) ions by a molecule, atom, or
ion. Transfer of one hydride ion results in the transfer of
two
electrons.
The amount of work required to add or remove electrons
is called the
electromotive potential or force
(
em f
) and is
designated
E.
It is measured in volts (joules per coulomb,
where a coulomb is a unit of electric charge or a quantity
of electrons).
The standard emf,
(or, at pH 7,
E°'),
is the emf
measured when the temperature is 25°C and the materials
being oxidized or reduced are present at concentrations
of 1.0 M. In biological systems,
E°'
is most commonly
used
. 1
The emf measured for an oxidation-reduction
(redox)
reaction under nonstandard conditions,
Eh,
is
mathematically related to the emf measured for the
same reaction under standard conditions,
E°',
through the
and
H
2
O -» ^ 0
2
+ 2H+ +
2e~
E°' = -
0.816 V
are half-reactions because they show electrons
(e )
or hy-
dride ions (H_). NADH and NAD+ are abbreviations for
reduced and oxidized forms of nicotinamide adenine dinu-
cleotide (whose structure is given in Chapter
6
and whose
metabolic functions are discussed elsewhere).
Alternatively, these half-reactions can be written as
NAD+ + H_ —>■
E°' =
+0.32 V
2e~
+ 2H+ + ^ 0
2
-> H20
E°' =
+0.816 V.
Reversing the direction of a reaction changes the sign of
the potential charge (just as with
AG
and
AH).
The oxidation potential is a measure of the ease of re-
moval of electrons from a material compared to the ease of
removal of electrons from hydrogen in the half-reaction:
H
2
-* 2H+ +
2e~
E° =
0.00 V.
in this reaction is defined as zero when H
2
gas is at
1.0 atm, [H+] is 1.0 M (i.e., pH 0), and the temperature is
25°C, thus fixing the scale of
value for other reactions.
If it is easier to remove electrons from a material,
E°'
will
be negative; if it is harder,
E°'
will be positive.
for the
hydrogen half-reaction is used as the zero point even when
reference is made to
E°'
values. Thus,
H
2
-+ 2H+ +
2e~
E°'
= -0.42 V.
'Some texts use the notation
E '0
for the standard oxidation-reduction
^
easier to remove electrons from hydrogen (and pro
potential.
duce H+) when [H+] = 10
- 7
M than when [H+] = 1.0 M.