Although the terms transition state and activated complex are often used synonymously, the transition state does not have a chemically significant life time. Consider the reaction
A + B
C P
(33.1)
In the equation (32.1), C is the activated complex which forms the products P with a unimolecular rate constant k
d [ C ] / dt = k [ C ]
(32.2)
The concentration of C is expressed in terms of the concentrations of A and B through the proportionality,
[ C ] = K [A] [B]
(33.3)
substituting eq. (33.3) into (33.2), we have
d [ C ] dt = k 2 [A] [B] where k 2 = k K
33.4
We now will determine the values of the constants k and K. It should be obvious that the process represented in Eq. (33.3) is not a regular equilibrium process because, as the products are formed, [A] and [B] are decreasing with time and [C] is not increasing with time since the collisions responsible for the formation of C are themselves decreasing in frequency as the reaction evolves. Although transition state theory has contributed enormously to the growth of chemical kinetics, this is one of its weak links.
The activated complex can exhibit several motions such as translations, rotations and vibrations, since it has a finite life time. The motion leading to the product is assumed to be a specific vibration with a frequency . This vibrational motion is along the reaction coordinate is equated to the constant k.
C
P 
. This vibrational motion is along the reaction coordinate is equated to the constant k
