Lecture 28 : Elementary Reactions and Reaction Mechanisms
Figure 28.1 The concentrations of [A], [B] and [C] as a function of time [ all relative to [A]0 ) for a consecutive reaction
A
B
C. The time over which the steady state approximation is valid is shown between dashed vertical lines.
After the first few moments, the concentration of [B] reaches a nearly steady value, at which d[B]/dt = 0. Substituting this in (28.5), we get for the steady state concentration of
B, d [B] /d t = 0
(28.10a)
[B] = ( k a / k b ) [ A ]
(28.10b)
and now (28.6) can be very easily integrated to get
(28.11)
this is a much simpler equation than eq (28.9) and far easier to obtain than (28.9) and is valid for a major part (except the very initial part and the tail end of time) of the reaction time. Indeed, (28.11) is a special case of (28.9) when ka >> kb. Equations ( 28.8 ) and ( 28.9 ) could be easily derived because of simplicity of A
B
C . In complex reactions, it is not possible to get integrated concentrations of reactive intermediates and approximations regarding the concentrations of intermediates (such as eq 28.10b) are extremely useful in obtaining final approximate rate expressions.
b) Preequilibria.
Consider the following sequence of reactions
A + B
(AB)
C
(28.12)
Here, the intermediate (AB) reaches an equilibrium with the reactants as in
K eq = {[A B ] / [A] [B] } eq = k f / k r
(28.13)
Eq (28.13) would be exactly true if AB does not react further to give products C. But if k p is small, eq ( 28.13 ) is valid quite well for a considerable length of time and this is known as preequilibrium. The formation of the product C is now described by
d [C] / dt = kp [ A B] = kp K [A] [ B ] = k [A] [ B]
(28.14)
with the final rate constant k = kp kf / kr and the reaction is second order overall.
We can now incorporate these approximations in getting suitable expressions for integrated rate laws in complex reaction schemes.
B
C. The time over which the steady state approximation is valid is shown between dashed vertical lines. 
B
C . In complex reactions, it is not possible to get integrated concentrations of reactive intermediates and approximations regarding the concentrations of intermediates (such as eq 28.10b) are extremely useful in obtaining final approximate rate expressions. 
(AB)
C 
