76
chapter 5
Thermodynamics, Chemical Kinetics, and Energy Metabolism
This reaction is first order with respect to A, first order with
respect to B, and second order overall. Most reactions are
zero, first,
or
second
order.
The concept of reaction order can be related to the
number of molecules that must collide simultaneously for
the reaction to occur. In a
first-order reaction,
no colli-
sions are required (since only one reactant molecule is
involved). Every molecule with sufficient free energy to
surmount the activation barrier may spontaneously con-
vert to products. In a second-order reaction, not only
must two molecules have enough free energy but they
also must collide with each other for the products to
form. A third-order reaction requires the simultaneous
meeting of three molecules, a less likely event. Reac-
tions of orders higher than second are seldom encoun-
tered in simple chemical conversions. Higher apparent or-
ders are encountered, however, in some cases in which
an overall rate equation is written for a process that pro-
ceeds in several steps via one or more intermediates.
In such situations, the individual steps seldom involve
a third- or higher order process. Therefore, for a chem-
ical reaction consisting of multiple steps, the order of
the reaction provides information about the overall rate
equation but does not provide information regarding the
number of atoms or molecules that must actually col-
lide to form products during each step. This informa-
tion is obtained by knowing the molecularity of the re-
action, which is defined as the number of molecules that
come together in a reaction. In a single-step reaction, the
molecularity (which is the same as the order of reaction)
determines the exponents in the rate equation. In a mul-
tistep reaction sequence, each step has unique molecular-
ity; knowing this provides information about the reaction
mechanism.
Zero-order reactions can be explained in two ways.
In a process that is truly zero order with respect to all
reactants (and catalysts, in the case of enzymes), either
the activation energy is zero or every molecule has suffi-
cient energy to overcome the activation barrier. This kind
of reaction is rare in homogeneous reactions in gases or
solutions.
Alternatively, a reaction can be zero order with respect
to one or more (but not all) of the reactants. This kind
of reaction is important in enzyme kinetics and assays
of enzymes of clinical importance (Chapter
8
). If one of
the reactants (or a catalyst, such as an enzyme) is lim-
ited, then increasing the availability (concentrations) of
the other reactants can result in no increase in the velocity
of the reaction beyond that dictated by the limiting reagent.
Hence, the rate is independent of the concentrations of the
nonlimiting materials and zero-order with respect to those
materials.
Theoretically all reactions are reversible. The correct
way to write A -> B, then, is
ki
A ^ B
k~\
where
ki
is the rate constant for the conversion of A to B,
and
i is the rate constant for the reverse reaction, i.e.,
conversion of B to A. The reaction is kinetically reversible
if
k\ = k -
1
; it is irreversible for all practical purposes
(i.e., the reverse reaction is so slow that it can be ignored)
if
k-\
<<C
k\.
The rate of a reversible reaction is written
d m
V
=
-
7
^ = k
1
[A]-k_
1
[B],
dt
For the reversible reaction,
k,
A + B ^ C + D
k
-1
d[products]
d\C]
d[D]
dt
dt
dt
= *,[A][B]-*_,[C][D].
Kinetic schemes can become complicated with many
linked reactions and intermediates. Kinetics are important
in biological systems, however because enzymes make re-
versible many otherwise kinetically irreversible reactions.
The rate at which a reaction will proceed (measured
by
k)
is directly related to the amount of energy that must
be supplied before reactants and products can be inter-
converted. This
activation energy
(Eu)
comes from the
kinetic energy of the reactants. This energy may be trans-
lational and rotational (needed if two molecules must col-
lide to react) or vibrational and electronic (useful when
one molecule rearranges itself or eliminates some atoms
to form the product). The larger the activation energy, the
slower the reaction rate and the smaller the rate constant.
A
Ea
is a free energy, so it contains both
AH
and
AS
terms. Not only must the reactants have enough energy
(AH)
to make and break the requisite bonds, but they
must also be properly oriented (AS) for the products to
form.
The Arrhenius equation expresses the relation between
rate constants and activation energies:
k — A ■
e~E'/RT
where
Es
is the Arrhenius activation energy in calories
per mole;
R
is the gas constant (1.987 calories mole
- 1
degrees K 1);
T
is the absolute temperature (K); A is the
Arrhenius pre-exponential factor, a constant;
k
is the rate
constant; and
e
is 2.71828, the base of the natural loga-
rithms. This equation is empirical, whereas
Ea,
the free
energy of activation, is a theoretical concept, derived from
