Vicarious Nucleophilic Substitution 239
a reactive short-lived species and that after an initial brief period, its rate of formation and rate of disappearance are just balanced.
Considering the sequence of reactions in Scheme 36.2 and applying the steadystate approximation, the rate law for the VNS reaction will be given by Eq. 36.1:
v =
k1 k2[base]
k -1+ k2[base]
[ nitrobencene][carbanion]
(36.1)
where
kVNS k k
=
k1 k2[base]
k -1+ k2[base]
At this point the reader is encouraged to deduce Eq. 36.1 step by step using the
standard mathematic methodology of the steady-state approximation.
Equation 36.1 suggests a complex kinetic process and explains the observed nonlinear dependence of k VNS
k k
upon the base concentration. However, as shown in the
plot in Fig. 36.1 we can consider two different limiting situations for the reaction,
at low or high base concentration respectively.
At low base concentrations, we can assume that k -1
k k >> k 2
k k [base] and then,
kVNS k k
=
k1 k2[base]
k -1
Considering the equilibrium constant K 1 = k 1 / k -1
k k , the rate law will be reduced
to Eq. 36.2:
v = K1k2[base][nitrobencene][carbanion]
(36.2)
Equation 36.2 refers to a process that prevails when the intermediate V-adduct 1
is formed in a fast pre-equilibrium (K ( ( 1 ). In this instance, the E-elimination step (k 2
k k )
is rate-determining and the rate of the overall VNS reaction will depend linearly
on the concentration (and strength) of the base.
The other limiting situation corresponds to high concentration of base. Under
these circumstances we can consider that k 2
k k [base] >> k -1
k k and Eq. 36.1 will be simplified to Eq. 36.3.
v = k1[nitrobencene][carbanion]
(36.3)
As indicated in Eq. 36.3, at high base concentration the nucleophilic addition
step (k 1 ) is rate limiting. This also means that the E-elimination step (k 2
k k ) is so fast
that the formation of the intermediate V-adduct 1 can be considered an irreversible
process. There is not dependence on the base concentration. From the kinetic
study we can conclude that the VNS reaction has a different rate law (and hence a
different rate-determining step) depending on the concentration of base.
The change in the rate-determining step with the concentration of base is also in
agreement with the observed deuterium KIEs. The experimental data indicate a
decrease from 4.2 (a value typical of a primary KIE) to 0.8 (a secondary KIE
value) with increasing base concentration. If we consider the previous kinetic dis-
a reactive short-lived species and that after an initial brief period, its rate of formation and rate of disappearance are just balanced.
Considering the sequence of reactions in Scheme 36.2 and applying the steadystate approximation, the rate law for the VNS reaction will be given by Eq. 36.1:
v =
k1 k2[base]
k -1+ k2[base]
[ nitrobencene][carbanion]
(36.1)
where
kVNS k k
=
k1 k2[base]
k -1+ k2[base]
At this point the reader is encouraged to deduce Eq. 36.1 step by step using the
standard mathematic methodology of the steady-state approximation.
Equation 36.1 suggests a complex kinetic process and explains the observed nonlinear dependence of k VNS
k k
upon the base concentration. However, as shown in the
plot in Fig. 36.1 we can consider two different limiting situations for the reaction,
at low or high base concentration respectively.
At low base concentrations, we can assume that k -1
k k >> k 2
k k [base] and then,
kVNS k k
=
k1 k2[base]
k -1
Considering the equilibrium constant K 1 = k 1 / k -1
k k , the rate law will be reduced
to Eq. 36.2:
v = K1k2[base][nitrobencene][carbanion]
(36.2)
Equation 36.2 refers to a process that prevails when the intermediate V-adduct 1
is formed in a fast pre-equilibrium (K ( ( 1 ). In this instance, the E-elimination step (k 2
k k )
is rate-determining and the rate of the overall VNS reaction will depend linearly
on the concentration (and strength) of the base.
The other limiting situation corresponds to high concentration of base. Under
these circumstances we can consider that k 2
k k [base] >> k -1
k k and Eq. 36.1 will be simplified to Eq. 36.3.
v = k1[nitrobencene][carbanion]
(36.3)
As indicated in Eq. 36.3, at high base concentration the nucleophilic addition
step (k 1 ) is rate limiting. This also means that the E-elimination step (k 2
k k ) is so fast
that the formation of the intermediate V-adduct 1 can be considered an irreversible
process. There is not dependence on the base concentration. From the kinetic
study we can conclude that the VNS reaction has a different rate law (and hence a
different rate-determining step) depending on the concentration of base.
The change in the rate-determining step with the concentration of base is also in
agreement with the observed deuterium KIEs. The experimental data indicate a
decrease from 4.2 (a value typical of a primary KIE) to 0.8 (a secondary KIE
value) with increasing base concentration. If we consider the previous kinetic dis-