66
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
in which V is the volume of the container and the other symbols are
the same as we have used before in Eq. 130. Expressions for the partition functions are derived from quantum and statistical-mechanical
theory. Since the equilibrium constant for any system can be expressed
in terms of the partition functions of the molecules concerned, Eq. 137
can be written
k
' = *(f)Fj£h-.e
-
E
°
/RT
(141)
Here F* is the partition function per unit volume of the activated complex; F A and F B are the partition functions of the reactants; and E 0 is
the difference in zero-level energy, e.g., the activation energy at absolute zero which has merely been taken out of the partition functions.
Physical data necessary for computing partition functions may be obtained from spectroscopy, and from a knowledge of the mass and structure of the reacting molecules.
From Eq. 138 and 139 it is apparent that the term {F
% /F A F B · · · )
in Eq. 141 involves principally the entropy of activation, AS*. Frequently, especially for unimolecular reactions, the activated complex is
a looser structure than the reactants and the entropy of activation is
positive. In some reactions, however, the activated complex is a more
rigid structure than the reactants, and the entropy of activation is negative. The specific rate in all cases, when the transmission coefficient κ is
unity, depends upon the product of the exponential terms involving
entropy and heats of activation, or in other words, upon the free energy
change in passing from the normal state to the activated complex, the
rate of decomposition of the activated complex always being equal to
kT/h.
C. APPLICATION OF ABSOLUTE REACTION RATE THEORY TO
BIOLOGICAL PROCESSES
1. Importance of the Activation Energy
The cardinal role played by the free energy of activation in rate
processes, as clearly revealed by absolute rate theory, affords a fundamental way of viewing many reactions. Consider, for example, the
hydrolysis reaction of ATP presented in an earlier section. In terms of
rate theory, the reaction may be written
ATP + H 2 0 ^±
H
Enz · · · ATP · . · θ/
H
► ADP + P t
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
in which V is the volume of the container and the other symbols are
the same as we have used before in Eq. 130. Expressions for the partition functions are derived from quantum and statistical-mechanical
theory. Since the equilibrium constant for any system can be expressed
in terms of the partition functions of the molecules concerned, Eq. 137
can be written
k
' = *(f)Fj£h-.e
-
E
°
/RT
(141)
Here F* is the partition function per unit volume of the activated complex; F A and F B are the partition functions of the reactants; and E 0 is
the difference in zero-level energy, e.g., the activation energy at absolute zero which has merely been taken out of the partition functions.
Physical data necessary for computing partition functions may be obtained from spectroscopy, and from a knowledge of the mass and structure of the reacting molecules.
From Eq. 138 and 139 it is apparent that the term {F
% /F A F B · · · )
in Eq. 141 involves principally the entropy of activation, AS*. Frequently, especially for unimolecular reactions, the activated complex is
a looser structure than the reactants and the entropy of activation is
positive. In some reactions, however, the activated complex is a more
rigid structure than the reactants, and the entropy of activation is negative. The specific rate in all cases, when the transmission coefficient κ is
unity, depends upon the product of the exponential terms involving
entropy and heats of activation, or in other words, upon the free energy
change in passing from the normal state to the activated complex, the
rate of decomposition of the activated complex always being equal to
kT/h.
C. APPLICATION OF ABSOLUTE REACTION RATE THEORY TO
BIOLOGICAL PROCESSES
1. Importance of the Activation Energy
The cardinal role played by the free energy of activation in rate
processes, as clearly revealed by absolute rate theory, affords a fundamental way of viewing many reactions. Consider, for example, the
hydrolysis reaction of ATP presented in an earlier section. In terms of
rate theory, the reaction may be written
ATP + H 2 0 ^±
H
Enz · · · ATP · . · θ/
H
► ADP + P t