62
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
formulation of the so-called Arrhenius equation which is usually written
in the form
k = Ae~
E /
RT
(127)
where k is the specific rate constant, E is the heat constant between
activated and inert molecules (usually termed the energy of activation),
R is the gas constant, T the absolute temperature, and A is the so-called
frequency factor. The Arrhenius equation is generally accepted as the
relationship representing the temperature dependence of specific reaction rates of most chemical reactions and of many biological processes.
Provided the temperature range is not large, E and A may be taken as
constant. The energy of activation, E, represents the energy that the
molecule in the initial state of the process must acquire before it can
take part in the reaction. In its simplified form, therefore, the problem
of making absolute calculations of reaction rates involves two independent aspects: the determination of the energy of activation and of
the frequency factor. The rate constant is also a function of pressure.
This is not taken into account in the Arrhenius equation but is in absolute rate theory.
B. ABSOLUTE REACTION RATE THEORY
The method of calculating the frequency factor A using the "theory
of absolute reaction rates" (18) is based on the fundamental concept
that reactants combine to form a critical intermediate, called the actitivated complex, to which equilibrium theory may be applied. If one
plots on independent coordinates all of the distances which must be
specified to fix the potential energy of the activated complex, and in an
independent direction plots the corresponding energy, then a potential
surface in configuration space is obtained which is similar to an ordinary landscape. On such a surface basins correspond to compounds,
and saddle points in the passes between the low regions correspond to
activated complexes. If, from an initial low region, one climbs to the
pass and then descends by the "water course" into the adjoining low
region, this path corresponds to the reaction coordinate. A plot of energy against distance along the reaction coordinate for any reaction has
the general appearance as shown in Fig. 4.
The activated complex is to be regarded as an ordinary molecule,
possessing all the usual thermodynamic properties, with the exception
that motion in one direction, i.e., along the reaction coordinate, leads
to decomposition at a definite rate. With these assumptions, it is possible to derive the concentration of and the rate at which the activated
complexes pass through the critical activated configuration by statistical
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
formulation of the so-called Arrhenius equation which is usually written
in the form
k = Ae~
E /
RT
(127)
where k is the specific rate constant, E is the heat constant between
activated and inert molecules (usually termed the energy of activation),
R is the gas constant, T the absolute temperature, and A is the so-called
frequency factor. The Arrhenius equation is generally accepted as the
relationship representing the temperature dependence of specific reaction rates of most chemical reactions and of many biological processes.
Provided the temperature range is not large, E and A may be taken as
constant. The energy of activation, E, represents the energy that the
molecule in the initial state of the process must acquire before it can
take part in the reaction. In its simplified form, therefore, the problem
of making absolute calculations of reaction rates involves two independent aspects: the determination of the energy of activation and of
the frequency factor. The rate constant is also a function of pressure.
This is not taken into account in the Arrhenius equation but is in absolute rate theory.
B. ABSOLUTE REACTION RATE THEORY
The method of calculating the frequency factor A using the "theory
of absolute reaction rates" (18) is based on the fundamental concept
that reactants combine to form a critical intermediate, called the actitivated complex, to which equilibrium theory may be applied. If one
plots on independent coordinates all of the distances which must be
specified to fix the potential energy of the activated complex, and in an
independent direction plots the corresponding energy, then a potential
surface in configuration space is obtained which is similar to an ordinary landscape. On such a surface basins correspond to compounds,
and saddle points in the passes between the low regions correspond to
activated complexes. If, from an initial low region, one climbs to the
pass and then descends by the "water course" into the adjoining low
region, this path corresponds to the reaction coordinate. A plot of energy against distance along the reaction coordinate for any reaction has
the general appearance as shown in Fig. 4.
The activated complex is to be regarded as an ordinary molecule,
possessing all the usual thermodynamic properties, with the exception
that motion in one direction, i.e., along the reaction coordinate, leads
to decomposition at a definite rate. With these assumptions, it is possible to derive the concentration of and the rate at which the activated
complexes pass through the critical activated configuration by statistical