Mechanism for nucleophilic substitution and elimination reactions at tertiary carbon in largely aqueous solutions: Lifetime of a simple tertiary carbocation

Article abstract of DOI:10.1021/ja9617451

The rate constants and the yields of the products of the nucleophilic substitution and elimination reactions of 1-(4-methoxyphenyl)-3-methyl-3-butyl derivatives (1-X) have been determined in mostly aqueous solvents, and the absolute rate constant for reac

Full text of DOI:10.1021/ja9617451

11434
J. Am. Chem. Soc. 1996, 118, 11434-11445
Mechanism for Nucleophilic Substitution and Elimination
Reactions at Tertiary Carbon in Largely Aqueous Solutions:
Lifetime of a Simple Tertiary Carbocation
Maria M. Toteva and John P. Richard*
Contribution from the Department of Chemistry, UniVersity at Buffalo, SUNY,
Buffalo, New York 14260-3000
ReceiVed May 23, 1996. ReVised Manuscript ReceiVed September 17, 1996X
Abstract: The rate constants and the yields of the products of the nucleophilic substitution and elimination reactions
of 1-(4-methoxyphenyl)-3-methyl-3-butyl derivatives (1-X) have been determined in mostly aqueous solvents, and
the absolute rate constant for reaction of the simple tertiary carbocation 1+ in 50:50 (v/v) trifluoroethanol/water has
been estimated as ks ) 3.5 × 1012 s-1. Product studies show that the acid-catalyzed reactions of 1-OH and 4-(4-
methoxyphenyl)-2-methyl-1-butene (2) do not proceed exclusively through a common carbocation intermediate 1+.
The observed formation of small amounts of the azide ion adduct 1-N3 likely occurs by a preassociation reaction
mechanism. The reactions of 1-Cl and 1-O2CC6F5 in 50:50 (v/v) trifluoroethanol/water give 39% and 56%,
respectively, of the alkene products of elimination, and the yields of the alkenes are unaffected by the addition of
0.50 M of the good nucleophile N3-. This result is consistent with a concerted unimolecular mechanism for the
elimination reactions of 1-X.
Introduction
alkene product should be formed by proton transfer from the
carbocation to chloride, bromide, or iodide ion leaving groups,
because these anions are less basic than the ethanol solvent
which surrounds the carbocation-leaving group ion pair. Fur-
thermore, there is no experimental evidence that requires that
ion pairs form as intermediates of the elimination reactions of
tert-butyl halides: the decreasing yields of alkene products in
solvents of increasing ionizing power may reflect the higher
polarity of the transition state for solvolysis than of that for a
concerted elimination reaction,6 which would favor formation
of the solvolysis products in the polar solvent water.
The stepwise DN + AN (SN1)1 mechanism for nucleophilic
substitution at tertiary derivatives is strongly favored by the large
steric barrier to concerted bimolecular substitution at tertiary
carbon and the large stabilization of the putative carbocation
intermediate by hyperconjugative electron donation from three
alkyl groups.2 However, there is no consensus about the
dynamics of solvolysis and elimination reactions at tertiary
carbon. In one textbook on physical organic chemistry, it has
been concluded that the solvolysis of tert-butyl derivatives
proceeds through ion pair or ion-molecule pair intermediates
which undergo separation to free species in water,3 and in
another that this classical SN1 mechanism is “now recognized
as an extreme situation, though one which can occur when a
particularly stabilized carbocation such as Ph3C+ is inVolVed”.4
These contradictory conclusions reflect the difficulties in
interpreting results from the literature which pertain to the
lifetime of simple tertiary carbocations in water.
There is no significant common ion inhibition of the reaction
of tert-butyl bromide in 90% acetone in water7 and very little
exchange of 36Cl from Na36Cl into unreacted tert-butyl chloride
during its reaction in methanol8 or of scrambling of 18O between
the bridging and nonbridging positions during the reaction of
18O-labeled tert-butyl p-nitrobenzoate in 80% acetone in
water,9 and the solvolysis of chiral tertiary chlorides proceeds
with partial inversion of configuration in 80% acetone in water10
and in methanol.11 These results are consistent with the
conclusion that the direct reaction of solvent with tertiary
carbocation-leaving group ion pair intermediates of solvolysis
reactions in mostly organic solvents is faster than their separation
to free ions, and that the chloride ion leaving group acts to shield
the ion pair intermediate from frontside attack of solvent.
However, the change to a mostly aqueous solvent will favor
separation of the ion pair intermediates to the free carbocations.
The yields of methylpropene and the solvent adducts from
the reaction of tert-butyl chloride, bromide, and iodide in ethanol
vary with the leaving group, but they are almost constant when
the reactions are carried out in water.5 These results are
consistent with the conclusion that in an organic solvent, where
the diffusional separation of ion pair intermediates is relatively
slow, simple tertiary carbocations undergo deprotonation by the
leaving group within the carbocation-leaving group ion pair,
but that in the highly polar solvent water, the diffusional
separation to free ions is faster than the formation of alkene
products by proton transfer from the carbocation to the leaving
group. However, it is not clear why a significant amount of
Tertiary carbocations will be formed as liberated intermediates
of solvolysis reactions in water provided that the rate constant
(6) Amyes, T. L.; Richard, J. P. J. Am. Chem. Soc. 1991, 113, 8960-
8961.
(7) Bateman, L. C.; Hughes, E. D.; Ingold, C. K. J. Chem. Soc. 1940,
960-966. Bateman, L. C.; Church, M. G.; Hughes, E. D.; Ingold, C. K.;
Taher, N. A. J. Chem. Soc. 1940, 979-1011.
(8) Bunton, C. A.; Nayak, B. J. Chem. Soc. 1959, 3854.
(9) Goering, H. L.; Levy, J. F. J. Am. Chem. Soc. 1962, 84, 3853-3857.
(10) Hughes, E. D.; Ingold, C. K.; Martin, R. J. L.; Meigh, D. F. Nature
1950, 166, 679-680.
(11) Doering, W. v. E.; Zeiss, H. H. J. Am. Chem. Soc. 1953, 75, 4733-
4738.
X Abstract published in AdVance ACS Abstracts, November 1, 1996.
(1) Guthrie, R. D.; Jencks, W. P. Acc. Chem. Res. 1989, 22, 343-349.
(2) Ingold, C. K. Structure and Mechanism in Organic Chemistry, 2nd
ed.; Cornell University Press: Ithaca, 1969.
(3) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic
Chemistry; Harper & Row: New York, 1987.
(4) Isaacs, N. Physical Organic Chemistry, 2nd ed.; Longman Scientific
& Technical: Burnt Mill, 1995.
(5) Cocivera, M.; Winstein, S. J. Am. Chem. Soc. 1963, 85, 1702-1703.
S0002-7863(96)01745-3 CCC: $12.00 © 1996 American Chemical Society

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11435
Scheme 1
from product analysis will be an oVerestimate of the rate
constant ratio for partitioning of the carbocation between
-
reaction with N3 and solvent, and the value of ks (s-1
)
calculated from this observed ratio using kaz ) 5 × 109 M-1
s-1 will then be an underestimate of the reactivity of the
carbocation toward solvent.
In summary, the uncertainty regarding the lifetime of simple
tertiary carbocations in aqueous solvents is due to difficulties
in drawing generalizations from the results obtained in mostly
organic solvents, and to the relative scarcity and sometimes
questionable accuracy of data for the product distributions of
these reactions.25 We report here a comprehensive systematic
study of the kinetics and product distributions of the reactions
of 1-X and 2 in mostly aqueous solvents, which was directed
toward (a) estimating or establishing a limit for the rate constants
for reaction of the simple tertiary carbocation 1+ and the tert-
butyl carbocation with these solvents, (b) characterizing any
for separation of the ion pair to give free ions (k-d′ ≈ 1010 s-1
,
Scheme 1) is larger than that for the direct reaction of solvent
with the ion pair (ks′, Scheme 1). The two best estimates from
the chemical literature of ks ) 4 × 109 s-1 12-14 and ks ) 1010
s-1 15-17 for the rate constant for reaction of the tert-butyl
carbocation with water both suggest that this carbocation will
form as a liberated intermediate of solvolysis reactions in water.
Rate constants for the reaction of tertiary carbocations with
solvent might be calculated from the azide ion selectivity
determined from product analysis, kaz/ks (M-1), using a diffu-
sional rate constant for the reaction of N3-: kaz ) kT ) 5 ×
109 M-1 s-1 (Scheme 1).18,19 However, this azide “clock”20,21
should be used only when trapping of the free carbocation
(kT[Nu-], Scheme 1) is a step on the pathway to formation of
the azide ion adduct. It is unclear whether the low yields of
the azide ion adduct obtained from nucleophilic substitution at
tertiary derivatives22 represent diffusion-controlled trapping of
a free tertiary carbocation by N3- or the alternative conversion
intermediate that is common to the acid-catalyzed reactions of
1-OH and 2, (c) determining the extent of trapping of the simple
tertiary carbocation 1+ by external nucleophilic reagents in
mostly aqueous solvents, and (d) characterizing the mechanism
of the elimination reactions of 1-X to give alkene products.
-
of an encounter complex of N3 and the substrate to the azide
ion adduct by a preassociation mechanism (Kas, k1′, and kNu′,
Scheme 1).23 The preferred reaction pathway depends on the
balance between the rate constants for the direct reaction of
solvent with the ion pair intermediate (ks′) and its diffusional
separation to give free ions (k-d′).24 If the direct reaction of
solvent with the ion pair is significantly faster than its separation
to free ions (ks′ > k-d′), then the free carbocation will not be
formed and the azide ion adduct must be formed from an
encounter complex between the substrate and the nucleophile
by a preassociation mechanism (Kas, Scheme 1).24 In the case
that the reaction of N3- does occur mainly by a preassociation
mechanism, then the observed value of kaz/ks (M-1) determined
Experimental Section
Syntheses. The materials and procedures for the synthesis of the
following compounds, along with spectral data for these compounds
are given in the Supporting Information: 3-hydroxy-1-(4-methoxyphen-
yl)-3-methylbutane (1-OH), 1-(4-methoxyphenyl)-3-methyl-3-butyl
pentafluorobenzoate (1-O2CC6F5), 4-(4-methoxyphenyl)-2-methyl-1-
butene (2), and 3-chloro-1-(4-methoxyphenyl)-3-methylbutane (1-Cl).
Product Studies. Reactions were carried out at 25 °C and a constant
ionic strength of 0.50 maintained with sodium perchlorate, and product
distributions were determined by HPLC analysis. Reactions were
initiated by making a 100-fold dilution of a solution of substrate in
acetonitrile into the reaction mixture to give a final substrate concentra-
tion of ca. 7 × 10-4 M for the reactions of 1-Cl and 2, or 0.02 M for
the reactions of 1-OH. The reactions of 1-O2CC6F5 in 50:50 (v/v)
TFE/H2O were initiated by making a 50-fold dilution of a solution of
this substrate in acetonitrile into trifluoroethanol, and then mixing the
resulting solution with an equal volume of 1.0 M aqueous sodium
perchlorate to give a final substrate concentration of 0.02 M. 9-Fluo-
renyl methyl ether (3 × 10-5 M) was used as an internal standard to
correct the observed areas of the substrate and product peaks for small
variations in the HPLC injection volume.
(12) McClelland, R. A.; Kanagasabapathy, V. M.; Banait, N. S.; Steenken,
S. J. Am. Chem. Soc. 1989, 111, 3966-3972.
(13) Arnett, E. M.; Hofelich, T. C. J. Am. Chem. Soc. 1983, 105, 2889-
2895.
(14) Boyd, R. H.; Taft, R. W.; Wolf, A. P.; Christman, D. R. J. Am.
Chem. Soc. 1960, 82, 4729-4736.
(15) Chiang, Y.; Chwang, W. K.; Kresge, A. J.; Powell, M. F.; Szilagyi,
S. J. Org. Chem. 1984, 49, 5218-5224.
(16) Chiang, Y.; Kresge, A. J. J. Chem. Soc. 1985, 107, 6363-6367.
(17) Chwang, W. K.; Knittel, P.; Koshy, K. M.; Tidwell, T. T. J. Am.
Chem. Soc. 1977, 99, 3395-3401.
The yields of the products of the spontaneous reactions of 1-O2CC6F5
and 1-Cl were determined during the first 2% of reaction and after at
least ten reaction halftimes, respectively. The yields of the products
of the acid-catalyzed reaction of 1-OH were determined during the
appearance of up to 3% total products, and product yields for the acid-
catalyzed reaction of 2 were determined during the first three halftimes
of the reaction. The conversion of 1-OH (20 mM) or of 2 (20 mM) to
an equilibrium mixture of reaction products in 50:50 (v/v) TFE/H2O
containing 1.00 M HClO4 and 3-(4-methoxyphenyl)-1-propanol (5 ×
(18) McClelland, R. A.; Kanagasabapathy, V. M.; Steenken, S. J. Am.
Chem. Soc. 1988, 110, 6913-6914. McClelland, R. A.; Kanagasabapathy,
V. M.; Banait, N. S.; Steenken, S. J. Am. Chem. Soc. 1991, 113, 1009-
1014.
(19) McClelland, R. A.; Cozens, F. L.; Steenken, S.; Amyes, T. L.;
Richard, J. P. J. Chem. Soc., Perkins Trans. 2 1993, 1717-1722.
(20) Richard, J. P.; Rothenberg, M. E.; Jencks, W. P. J. Am. Chem. Soc.
1984, 106, 1361-1372.
(21) Amyes, T. L.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7888-
7900.
(22) Ta-Shma, R.; Rappoport, Z. J. Am. Chem. Soc. 1983, 105, 6082-
6095.
(23) Jencks, W. P. Acc. Chem. Res. 1980, 13, 161-169. Jencks, W. P.
Chem. Soc. ReV. 1981, 10, 345-375.
(24) Richard, J. P.; Yeary, P. E. J. Am. Chem. Soc. 1993, 115, 1739-
1744.
(25) Dimensionless ratios of kaz/kHOH ) 3.9, 7, 12, 14.5, and 74 have
been reported for the partitioning of the putative intermediate of solvolysis
-
of tert-butyl bromide in aqueous acetone between reaction with N3 and
water. Experimental and typographical errors have been suggested to account
for this range of values, and a “best” value has been identified.22

11436 J. Am. Chem. Soc., Vol. 118, No. 46, 1996
ToteVa and Richard
10-4 M) as an internal standard was monitored by withdrawal of an
aliquot (120 µL) of the reaction mixture at various times, which was
neutralized with 2 M sodium acetate before analysis by HPLC.
HPLC Analyses. The products of the spontaneous reactions of 1-Cl
and 1-O2CC6F5 and the acid-catalyzed reactions of 1-OH and 2 were
separated and quantified by HPLC analysis as described in previous
work.20,26,27 The reaction products were detected at 278 nm, which is
λmax for 1-OH.
were calculated from the ratio of product yields using eq 3. Rate
-
constant ratios (M-1) for partitioning of 1-X between reaction with N3
and solvent were calculated using eq 4, where ∑[1-Solv] is the sum of
the concentrations of the products of the reaction of solvent with 1-X.
A similar equation that treats the elimination reaction as a first-order
process was used to calculate rate constant ratios for partitioning of
1-X between nucleophilic substitution and alkene-forming elimination
reactions.
The alcohol (1-OH) and the disubstituted alkene (2) products of the
reactions of 1-X were identified by comparison of their HPLC retention
times with those of authentic materials. The ethers 1-OMe and
1-OCH2CF3 were identified as the peaks which appear during reaction
of 1-X in mixed MeOH/H2O and TFE/H2O solvents, respectively. The
trisubstituted alkene 3 was identified as the additional product peak
that appears during the acid-catalyzed reactions of 1-OH and 2 and
the spontaneous reactions of 1-Cl and 1-O2CC6F5.
kNu1/kNu2 ) ([1-Nu1][Nu2])/([1-Nu2][Nu1])
kaz/ks ) [1-N3]/(Σ[1-Solv][N3-])
(3)
(4)
The integrated HPLC peak areas and the rate constant ratios
calculated directly from the ratios of product peak areas are reproducible
to better than (5% and (10%, respectively. The product rate constant
ratios for reaction of N3- are estimated to be accurate to ( 20%, because
the yields of the azide ion adduct 1-N3 were determined from the
difference between the normalized areas of the product peaks for
reactions in the presence and absence of this nucleophile (see above).
Kinetic Studies. Kinetic studies were carried out at 25 °C and a
constant ionic strength of 0.50 maintained with sodium perchlorate.
The reactions of 1-Cl were initiated by making a 100-fold dilution
of a solution of substrate in acetonitrile into the reaction mixture to
give a final substrate concentration of ca. 6 × 10-4 M. Reactions in
the presence of perchlorate, lyoxide, and halide ions were monitored
spectrophotometrically by following the increase in absorbance at 234
nm. Reactions in 50:50 (v/v) MeOH/H2O in the presence of N3- were
monitored by following the protonation of a phenoxide anion indicator
(8 × 10-4 M) at 290 nm.30 Argon was bubbled through both the
aqueous salt solutions (1.0 M) and the methanol cosolvent immediately
before preparation of the mixed solvent used in the phenoxide indicator
assay, in order to minimize the amount of dissolved oxygen in the final
solvent. In most cases this eliminated the downward drift in the end
points for these reactions, which is probably due to oxidation of
phenoxide ion. In cases where the end point was unstable, it was
calculated by adding 3% to the change in A290 observed after five
reaction halftimes. Observed first-order rate constants, kobsd (s-1), for
the reaction of 1-Cl were calculated from the slopes of semilogarithmic
plots of reaction progress against time, which were linear for at least
three reaction halftimes. The values of kobsd were reproducible to within
(5%.
The reactions of 1-O2CC6F5 in 50:50 (v/v) TFE/H2O were carried
out as described for the product studies. The relative concentrations
of products (Σ[P]) and substrate ([S]0) were monitored by HPLC
analyses during the first 2% of this reaction, and kobsd was determined
as the slope of a plot of Σ[P]/[S]0 against time.
The acid-catalyzed reactions of 1-OH and 2 in 50:50 (v/v) TFE/
H2O were carried out as described for the product studies. The first-
order rate constant for conversion of 1-OH to 1-OCH2CF3 was
determined as the slope of a linear plot of A1-OTFE/A1-OH against time
during the first 12% of the approach to an equilibrium concentration
of 1-OCH2CF3, where A1-OTFE and A1-OH are the integrated HPLC
peak areas for 1-OCH2CF3 and 1-OH, respectively. The first-order
rate constant for the disappearance of 2 was determined as the slope
of a semilogarithmic plot of reaction progress against time which
covered three reaction halftimes.
When the reactions of 1-Cl and 1-O2CC6F5 were carried out in the
presence of increasing concentrations of NaN3, there was no change in
the normalized peak area for 3, but there was an increase in the
normalized area of the peak for 2 that was identical, within experimental
error, with the accompanying decrease in the sum of the normalized
peak areas for the solvent adducts (1-Solv). This suggests that 1-N3
and 2 have nearly identical retention times. A partial resolution of the
peaks for 1-N3 and 2 was achieved by use of very long HPLC analysis
times, but these conditions were not practical for the routine determi-
nation of product yields. The extinction coefficients of 1-Solv and
1-N3 at 278 nm are identical (see below). Therefore, the peak areas
for 1-N3 were estimated as either (a) the difference between the sum
of the normalized areas for the solvent peaks (1-Solv) for reactions in
-
the presence and absence of N3 or (b) the difference between the
normalized peak areas for the mixture of 1-N3 and 2 for reactions in
the presence of N3- and the peak area for 2 for reactions in the absence
of N3-. As required by mass balance, there is good agreement between
these two determinations.
The ratios of product yields were calculated using eq 1, where A1
and A2 are the HPLC peak areas for the products P1 and P2 and ꢀ2/ꢀ1
is the ratio of the extinction coefficients for P2 and P1 at 278 nm, the
[P]1/[P]2 ) (A1/A2)(ꢀ2/ꢀ1)
(1)
wavelength used for these analyses. A ratio of ꢀ1-OH/ꢀ1-Cl ) 1.0 was
determined from HPLC analysis using authentic 1-OH and 1-Cl, and
-
ratios of ꢀ1-OH/ꢀ1-X ) 1.0 were used for the N3 (1-N3) and alkoxide
ion (1-OMe and 1-OCH2CF3) adducts, because it has been shown in
previous work that, at λmax, the extinction coefficients of R-substituted
4-methoxybenzyl alcohols do not change when the hydroxy group is
replaced by azido or simple alkoxy groups.20,27-29 A ratio of ꢀ1-OH/ꢀ2
) 1.0 at 278 nm was determined by showing that the decrease in the
normalized HPLC peak area for 2 during its acid-catalyzed (0.50 M
HClO4) reaction in 50:50 (v/v) TFE/H2O is identical, within experi-
mental error, with the increase in the sum of the normalized peak areas
for the reaction products, which are mostly the solvent adducts 1-OH
and 1-OCH2CF3 (97%). A ratio of ꢀ1-Cl/ꢀ3 ) ꢀ1-OH/ꢀ3 ) 0.82 was
calculated using eq 2, where A1-Cl is the initial normalized HPLC peak
area for 1-Cl, and A1-Solv, A2, and A3 are the final normalized peak
areas of the products of the complete reaction of 1-Cl in 50:50 (v/v)
MeOH/H2O. The 7% increase in absorbance that is observed when
the reaction of 1-Cl in 50:50 (v/v) TFE/H2O is followed spectropho-
tometrically at 278 nm is consistent with the conclusion that the
extinction coefficient for 3 at 278 nm is slightly larger than that for
1-Cl.
Results
The first-order rate constants for the reaction of 1-Cl at 25
°C in 50:50 (v/v) TFE/H2O, determined by monitoring the
increase in absorbance at 234 nm, are kobsd ) 3.1 × 10-4 s-1 (I
) 0.50, NaClO4) and 2.1 × 10-4 s-1 (I ) 0). Figure 1 shows
the dependence of kobsd/k0 for the reaction of 1-Cl at 25 °C on
the concentration of added Cl- in 50:50 (v/v) MeOH/H2O (I )
0.50, NaClO4) and on the concentration of added Cl- or Br- in
50:50 (v/v) TFE/H2O (I ) 0.50, NaClO4), where k0 is the rate
constant for reaction in the absence of added halide ion.
ꢀ1-Cl/ꢀ3 ) (A1-Cl - A1-Solv - A2)/A3
(2)
Calculation of Rate Constant Ratios. Dimensionless rate constant
ratios for the reactions of 1-X with nucleophilic reagents Nu1 and Nu2
(26) Richard, J. P.; Amyes, T. L.; Jagannadham, V.; Lee, Y.-G.; Rice,
D. J. J. Am. Chem. Soc. 1995, 117, 5198-5205.
(27) Richard, J. P. J. Am. Chem. Soc. 1989, 111, 1455-1465.
(28) Richard, J. P.; Amyes, T. L.; Vontor, T. J. Am. Chem. Soc. 1992,
114, 5626-5634.
(29) Richard, J. P.; Jagannadham, V.; Amyes, T. L.; Mishima, M.; Tsuno,
Y. J. Am. Chem. Soc. 1994, 116, 6706-6712.
(30) Amyes, T. L.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7900-
7909.

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11437
Figure 3. The dependence of kobsd/k0 and the fractional yields of
nucleophilic substitution and elimination products (fP) for the reaction
of 1-Cl on the concentration of added N3 in 50:50 (v/v) MeOH/H2O
at 25 °C and I ) 0.50 (NaClO4), where k0 is the rate constant for
reaction in the absence of added N3-. Key: [, kobsd/k0; b, total fractional
yield of 1-OH and 1-OMe; 2, fractional yield of 1-N3; 9, total
fractional yield of 2 and 3.
Figure 1. The dependence of kobsd/k0 for the reaction of 1-Cl on the
concentration of added X- at 25 °C and I ) 0.50 (NaClO4), where k0
is the rate constant for reaction in the absence of added halide ion.
Key: b, effect of added Cl- in 50:50 (v/v) MeOH/H2O; 9, effect of
added Cl- in 50:50 (v/v) TFE/H2O; 2, effect of added Br- in 50:50
(v/v) TFE/H2O.
-
Table 1. Product Rate Constant Ratios for the Partitioning of 1-X
between Reaction with Azide Ion and Solvent at 25 °C and I )
0.50 (NaClO4)a
kaz/ksb
kaz/
kHOH
kaz/
kROH
c
d
substrate
1-Cl
solvent
50:50 (v/v)
trifluoroethanol/water
50:50 (v/v)
methanol/water
50:50 (v/v)
(M-1
0.38
)
13
15
11
14e
19f
10e
0.41
0.31
g
1-O2CC6F5
trifluoroethanol/water
a The rate constant ratios are estimated to be accurate to (20% (see
Experimental Section). b Rate constant ratio for partitioning between
reaction with azide ion and solvent, calculated using eq 4. c Dimen-
sionless ratio of second-order rate constants for reaction with azide
ion and water, calculated using eq 3. d Dimensionless ratio of second-
order rate constants for reaction with azide ion and ROH, calculated
using eq 3. e ROH ) CF3CH2OH. f ROH ) MeOH. g Determined from
the product yields during the first 2% of the reaction.
of a phenoxide anion indicator at 290 nm, and on the product
yields, determined by HPLC analysis, for the reaction of 1-Cl
at 25 °C in 50:50 (v/v) MeOH/H2O (I ) 0.50, NaClO4), where
-
k0 is the rate constant for reaction in the absence of added N3
.
Figure 2. The dependence of kobsd/k0 and the fractional yields of
substitution and elimination products (fP) for the reaction of 1-Cl on
the concentration of added HO- in 50:50 (v/v) MeOH/H2O at 25 °C
and I ) 0.50 (NaClO4), where k0 is the rate constant for reaction in the
absence of added HO-. Key: [, kobsd/k0; b, fractional yield of 1-OH;
2, fractional yield of 1-OMe; 9, total fractional yield of 2 and 3.
Rate constant ratios for partitioning of 1-Cl between reaction
with N3- and with solvent, calculated from the product yields,
are reported in Table 1. These ratios were calculated by treating
the reactions of solvent either as a first-order process (kaz/ks,
M-1) using eq 4, or as bimolecular reactions of methanol and
water (kaz/kMeOH and kaz/kHOH) using eq 3. Azide ion (up to
0.50 M) has no effect on the total yield of 25% of the alkenes
2 and 3 from the reaction of 1-Cl in this solvent, and the
observed product rate constant ratios kaz/ke (M-1, not reported)
for partitioning of 1-Cl between formation of the azide ion
adduct and elimination to form alkenes decrease with increasing
concentrations of N3-. Table 1 also gives the product rate
constant ratios for the reaction of 1-Cl with N3- and solvent in
50:50 (v/v) TFE/H2O (I ) 0.50, NaClO4) at 25 °C; there is
also no effect of N3- on the yields of 2 and 3 from the reaction
of 1-Cl in this solvent. Nucleophile selectivities kaz/kHOH
Figure 2 shows the effect of increasing concentrations of
added lyoxide ion on kobsd/k0 and on the product yields,
determined by HPLC analysis, for the reaction of 1-Cl at 25
°C in 50:50 (v/v) MeOH/H2O (I ) 0.50, NaClO4), where k0 is
the rate constant for reaction in the absence of added lyoxide
ion. The addition of 0.25 M lyoxide ion has no effect on the
product distribution for the reaction of 1-Cl in the presence of
-
0.25 M N3 in this solvent.
Figure 3 shows the effect of increasing concentrations of
added N3- on kobsd/k0, determined by monitoring the protonation

11438 J. Am. Chem. Soc., Vol. 118, No. 46, 1996
ToteVa and Richard
Table 2. Yields of the Products of the Spontaneous Reactions of 1-X and the Acid-Catalyzed Reactions of 1-OH and 2 in Mixed Alcohol/
Water Solvents at 25 °C and I ) 0.50 (NaClO4)
yield of product (%)a
solvent
TFE/H2O
50:50 (v/v)
substrate
1-Cl
1-O2CC6F5
1-OHc
2d
1-Cl
1-OHc
2d
1-Cl
1-OHc
2d
1-Cl
1-OHc
2d
1-Cl
1-OHc
2d
1-OH
1-OCH2CF3
1-OMe
2
3
50
35
12
9.3
58
10
13
30
13
26
26
29
3.4
18
21
3.9
23
27
3.5
15
54
b
87
54
MeOH/H2O
50:50 (v/v)
21
66
32
2.7
12
6.1
7.2
13
64
51
MeOH/TFE/H2O
5:45:50 (v/v/v)
9.8
47
7.7
3.3
24
2.6
2.2
24
14
15
83
74
TFE/H2O
20:80 (v/v)
6.8
22
95
75
2.7
15
48
MeOH/TFE/H2O
2:18:80 (v/v/v)
0.88
8.6
1.4
6.9
20
94
1.8
2.6
a Product yields were determined by HPLC analysis at 278 nm and are given to two significant figures. b Product yields determined during the
first 2% of the reaction. c Acid-catalyzed reaction in the presence of 0.50 M HClO4. These yields were determined by short extrapolations to zero
time of plots of product yield against time during appearance of up to 3% total products. d Acid-catalyzed reaction in the presence of 0.50 M
HClO4. Product yields were determined during the first three halftimes of the reaction.
Scheme 2
determined in these experiments fall within the broad range of
values reported for the reactions of tert-butyl derivatives.25
The first-order rate constant for the reaction of 1-O2CC6F5
at 25 °C in 50:50 (v/v) TFE/H2O (I ) 0.50, NaClO4), determined
by following the formation of products during the first 2% of
reaction, is kobsd ) 7.1 × 10-8 s-1. There is no detectable
change in kobsd ((5%) for this reaction when the concentration
(Table 2) is only 2-3%. A similar procedure was used to
determine the initial yields of the products of the acid-catalyzed
reactions of 1-OH in other mixed alcohol/H2O solvents (Table
2). Rate constant ratios for partitioning of 1-OH between
nucleophilic substitution and elimination (Scheme 2A), calcu-
lated from the product yields in Table 2, are given in Table 3.
The change in the observed yields of the products of the acid-
catalyzed reaction of 2 at 25 °C in 50:50 (v/v) TFE/H2O
containing 0.50 M HClO4 is e10% during the first three
halftimes of the reaction (Table 1S, Supporting Information).
The yields of the products of the reaction of 2 in several mixed
alcohol/H2O solvents are given in Table 2. Rate constant ratios
for partitioning of 2 between nucleophilic addition of solvent
and isomerization (Scheme 2B), calculated from the product
yields in Table 2, are given in Table 3.
-
of N3 is increased from zero to 0.50 M, and the yields of the
alkenes 2 and 3 are also independent of the concentration of
-
N3
.
Rate constant ratios for partitioning of 1-O2CC6F5
-
between reaction with N3 and solvent, calculated from the
product yields using either eq 3 or 4, are reported in Table 1.
Table 2 gives the yields, determined by HPLC analysis, of
the products of the spontaneous solvolysis and elimination
reactions of 1-Cl and 1-O2CC6F5 in several mixed alcohol/water
solvents. Rate constant ratios for partitioning of 1-X between
nucleophilic substitution and elimination (Scheme 2A), calcu-
lated from the product yields in Table 2, are given in Table 3.
The variation with time of the yields of the products of the
acid-catalyzed reaction of 1-OH, determined during the ap-
pearance of up to 3% total products, at 25 °C in 50:50 (v/v)
TFE/H2O containing 0.50 M HClO4 is shown in Table 1S of
the Supporting Information. The small changes in the apparent
product yields over time are due to the acid-catalyzed reaction
of 2. Table 2 gives the initial yields of the products that were
determined by a linear extrapolation of product yields to zero
time. The absolute difference between the yields of 2 (11%)
and 1-OCH2CF3 (60%) observed at early reaction times and
their yields determined by extrapolation of the data to zero time
The first-order rate constant for the acid-catalyzed conversion
of 1-OH to 1-OCH2CF3, determined under initial velocity
conditions, at 25 °C in 50:50 (v/v) TFE/H2O containing 0.50
M HClO4 is kh ) 1.5 × 10-7 s-1. This can be converted to the
second-order rate constant for the acid-catalyzed cleavage of
1-OH to give the carbocation 1+, kH ) 1.8 × 10-6 M-1 s-1
,
using eq 5 ([H+] ) 0.50 M) and 6, which were derived for the
kh(1/fp)
kH )
(5)
(6)
0.50 M
k2
kTFE[TFE] kTFE[TFE]
kHOH[HOH]
kTFE[TFE]
k3
1/fp ) 1 +
+
+

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11439
Table 3. Product Rate Constant Ratios for the Spontaneous Reactions of 1-X and the Acid-Catalyzed Reactions of 1-OH and 2 in Mixed
Alcohol/Water Solvents at 25 °C and I ) 0.50 (NaClO4) (Scheme 2)
rate constant ratioa
k2/kMeOH
(M)
k3/kTFE
(M)
k3/kMeOH
(M)
b
b
b
c
solvent
TFE/H2O
50:50 (v/v)
substrate
1-Cl
1-O2CC6F5
1-OHd
2d
kHOH/kMeOH
kHOH/kTFE
kMeOH/kTFE
k2/kTFE (M)
k3/k2
1.1
0.92
7.6
22
1.6
15
19
3.4
2.3
2.0
0.89
2.1
2.1
MeOH/H2O
50:50 (v/v)
1-Cl
1-OHd
2d
1-Cl
1-OHd
2d
1-Cl
1-OHd
2d
1-Cl
1-OHd
2d
1.1
4.2
2.3
10
2.4
1.7
4.0
1.5
11
2.8
0.70
0.90
0.83
MeOH/TFE/H2O
5:45:50 (v/v/v)
1.2
1.4
1.2
4.0
8.6
1.9
6.2
1.6
15
1.7
1.8
3.5
2.8
13
6.3
2.8
17
0.60
2.4
1.4
TFE/H2O
20:80 (v/v)
5.6
2.6
2.3
2.4
2.2
1.9
MeOH/TFE/H2O
2:18:80 (v/v/v)
0.94
0.74
2.0
1.8
3.9
7.7
2.0
3.9
1.1
8.7
2.7
0.91
2.2
2.4
4.8
3.5
2.9
a Calculated from the product yields in Table 2. Rate constants are defined in Scheme 2. b Dimensionless ratio of second-order rate constants,
calculated using eq 3. c Dimensionless ratio of first-order rate constants, calculated as the ratio of the yields of 3 and 2 (Table 2). d Acid-catalyzed
reaction in the presence of 0.50 M HClO4.
Table 4. Equilibrium Constants for Interconversion of the
Products of the Acid-Catalyzed Reactions of 1-OH and 2 at 25 °C
in 50:50 (v/v) Trifluoroethanol/Water (Scheme 4)a
Scheme 3
equilibrium constantb
c
KTFE
0.11
d
K2
K3
1.1 × 10-3
1.1 × 10-2
10
mechanism shown in Scheme 3. A value of fp ) 0.17 for the
fractional yield of 1-OCH2CF3 from partitioning of 1+ was
estimated from the relative yields of 1-OCH2CF3, 2, and 3 from
the reaction of 1-OH and with the assumption that the rate
constant ratio for partitioning of the intermediate of the acid-
catalyzed reaction of 1-OH between reaction with water and
trifluoroethanol is equal to kHOH/kTFE ) 1.1 determined for the
spontaneous reaction of 1-Cl (Table 3).31 By comparison, a
value of kH ) 4 × 10-6 M-1 s-1 has been determined for the
acid-catalyzed cleavage of tert-butyl alcohol to form the tert-
butyl carbocation in water.14
d
e
Kiso
falk ) 0.011f
fRSolv ) 0.989g
a Equilibria were established in solutions that contained 1.0 M HClO4.
The reactions of 1-OH and 2 lead to the same equilibrium mixture of
products. b The equilibrium constants are defined in Scheme 4. c Ratio
of the concentrations of 1-OCH2CF3 and 1-OH at equilibrium. d Ratio
of the concentrations of the respective alkene and the solvent adduct
1-OH at equilibrium. e Ratio of the concentrations of the trisubstituted
alkene 3 and the disubstituted alkene 2 at equilibrium. f The total
fraction of the alkenes 2 and 3 at equilibrium. g The total fraction of
the solvent adducts 1-OH and 1-OCH2CF3 at equilibrium.
The first-order rate constant for the disappearance of 2 at 25
°C in 50:50 (v/v) TFE/H2O containing 0.50 M HClO4 is kh )
4.0 × 10-5 s-1. This can be converted to the second-order rate
constant for the protonation of 2 to give 1+, kH ) 8.1 × 10-5
M-1 s-1, using eq 5 with fp ) (1.0 - 0.016) ) 0.984, where
0.016 is the fraction of the carbocation intermediate 1+ that
partitions to reform 2. This fraction was calculated from the
yield of 3.4% of 3 from the acid-catalyzed reaction of 2 (Table
2) and the rate constant ratio k3/k2 ) 2.1 for the formation of 3
and 2 from the acid-catalyzed reaction of 1-OH in 50:50 (v/v)
TFE/H2O (Table 3).
Scheme 4
The reaction of 1-OH or of 2 for 6 days at 25 °C in 50:50
(v/v) TFE/H2O containing 1.0 M HClO4 leads to the formation
of the same ((5% in the yield of the individual products)
equilibrium mixture of 1-OH, 1-OCH2CF3, 2, and 3 (Scheme
4). Table 4 gives the equilibrium constants for the acid-
catalyzed interconversion of 1-OH, 1-OCH2CF3, 2, and 3
shown in Scheme 4 that were calculated from the relative
concentrations of these species at chemical equilibrium. The
value of K2 ) 1.1 × 10-3 for the interconversion of 1-OH and
2 in 50:50 (v/v) TFE/H2O (Table 4) is larger than the K ) 1.3
× 10-4 values reported for the dehydration of tert-butyl alcohol
to give methylpropene in water.32
Discussion
The addition of a â-(4-methoxybenzyl) group to tert-butyl
chloride to give 1-Cl leads to a small decrease in the first-order
rate constant for reaction at 25 °C in 50:50 (v/v) TFE/H2O (I
) 0), from kobsd ) 9 × 10-4 s-1 for tert-butyl chloride33 to 2.1
× 10-4 s-1 for 1-Cl (Results), which can be attributed to the
polar effect of the electron-withdrawing 4-methoxybenzyl group.
There is no nucleophilic assistance to the ionization of 1-Cl by
(32) Eberz, W. F.; Lucas, H. J. J. Am. Chem. Soc. 1934, 56, 1230-
1234.
(33) Estimated by linear interpolation from kobsd ) 7.3 × 10-4 and 1.6
× 10-3 s-1 for reaction of tert-butyl chloride in TFE/H2O (I ) 0) containing
40 wt % and 50 wt % water, respectively,34 to 50:50 (v/v) TFE/H2O, which
contains 42 wt % water.
(31) The very weak Brønsted base Cl- should have little or no effect on
the relative reactivity of water and trifluoroethanol toward the carbocation
intermediate 1+ of these reactions.

11440 J. Am. Chem. Soc., Vol. 118, No. 46, 1996
ToteVa and Richard
the 4-methoxyphenyl group to form the arenium ion 4, because
no nucleophilic assistance by formation of a phenonium ion
was observed in earlier studies of the reaction of MeO-5,35 and
intramolecular nucleophilic displacement to form four-mem-
bered rings is typically 102-103-fold slower than the corre-
sponding displacement reactions to form three-membered
rings.36 The concentrations of 1+ and the arenium ion 4 at
Scheme 5
data establish a linear logarithmic relationship (eq 7) between
log ks ) -0.53 log kobsd + 10.6 (7)
chemical equilibrium depend on the balance between the
stabilization of 1+ obtained from intramolecular addition of the
4-methoxyphenyl group to the tertiary carbocation and the ca.
26 kcal/mol of strain energy in the four-membered ring of 4.37
However, the stabilization obtained from addition of the
4-methoxyphenyl group to the tertiary cationic center must be
significantly smaller than 26 kcal/mol, because the addition of
water to 1+ form the neutral alcohol 1-OH, which is thermo-
dynamically more stable than 4, is favored by only by 23 kcal/
mol.38 Similar arguments exclude the more unlikely possibility
of participation by C-1 of the 4-methoxyphenyl ring as a
Brønsted base in intramolecular deprotonation of 1+ to form
alkenes.39 We conclude that there is no internal nucleophilic
assistance to the ionization of 1-Cl to form 1+, and that this
carbocation exists essentially exclusively in the open form as a
simple tertiary carbocation.
Estimated Rate Constants for Reactions of Tertiary
Carbocations. The rate constants ks (s-1) for reaction of this
solvent with a series of ring-substituted cumyl carbocations were
determined in previous work, by using the reaction of N3- with
the carbocation as a “clock” for the slower reaction of solvent.42b
The extended Hammett relationship established by these data
was then extrapolated to give estimated rate constants for the
reactions of cumyl carbocations with solvent which were too
large to determine using the azide ion clock method.42a,b These
kobsd (s-1) for reaction of ring-substituted cumyl chlorides in
50:50 (v/v) TFE/H2O6 and the values of ks (s-1) for reaction of
the corresponding cumyl carbocations (Scheme 5). The values
of kobsd for reaction of 1-Cl and tert-butyl chloride in 50:50
(v/v) TFE/H2O at I ) 0 (see Experimental Section) were
substituted into eq 7 to give estimated values of ks ) 3.5 ×
1012 s-1 and 1.6 × 1012 s-1 for reaction of 1+ and the tert-
butyl carbocation, respectively, with this solvent. This estimate
of ks for reaction of the tert-butyl carbocation with solvent is
more than 100-fold larger than the best available literature
estimates of this rate constant cited in the introduction.12,15,16
We prefer the estimate made in this work to the earlier estimates
because of the close structural similarity between cumyl
chlorides, which were used to establish the linear relationship
given by eq 7, and simple tertiary alkyl chlorides. By contrast,
one of the earlier estimates of the lifetime of the tert-butyl
carbocation required extrapolation of a rate-equilibrium relation-
ship established for oxocarbenium ions,15,16 and the other12 was
based on the extrapolation of a linear logarithmic relationship
between equilibrium constants for formation of highly resonance-
stabilized triarylmethyl carbocations in water and in the gas
phase.13
We are interested in understanding the factors which deter-
mine when a kinetic barrier appears for the reaction of
carbocations with nucleophilic solvents, and the factors which
control the height of that barrier.43 The data in this work suggest
that the requirement for the partial loss of stabilizing hyper-
conjugative interactions between the â-hydrogens and the
cationic center in the transition state for the nucleophilic addition
of aqueous solvents to simple tertiary alkyl carbocations does
not create a large kinetic barrier to this reaction.
(34) Shiner, V. J., Jr.; Dowd, W.; Fisher, R. D.; Hartshorn, S. R.; Kessick,
M. A.; Milakofsky, L.; Rapp, M. W. J. Am. Chem. Soc. 1969, 91, 4838-
4843.
(35) The small 1.5-fold difference in kobsd for reaction of H-5 and MeO-5
is consistent with only a small inductive effect of the 4-MeO substituent
on the reaction, and it shows that there is no significant movement of positive
charge from the developing carbocation onto the aromatic ring [Brown, H.
C.; Kim, C. J. J. Am. Chem. Soc. 1968, 90, 2082-2096].
The estimated rate constants for reaction of the tert-butyl
carbocation and 1+ with solvent, ks ≈ 1012 s-1, are larger than
both the rate constant for their diffusional encounter with
external nucleophilic reagents, kT[Nu-] ≈ (5 × 109 M-1
s-1)[Nu-] (Scheme 1),18,19 and that for reorganization of the
local solvation shell by the dielectric relaxation of solvent (kreorg
(36) (a) Kirby, A. AdV. Phys. Org. Chem. 1980, 183-278. (b) Knipe,
A. C.; Stirling, C. J. M. J. Chem. Soc. B 1968, 67-71. (c) Bird, R.; Knipe,
A. C. J. Chem. Soc., Perkin Trans. 2 1973, 1215-1220.
(37) Winnik, M. C. Chem. ReV. 1981, 81, 491-524.
(38) Calculated from pKR ) -16.7 for 1+ which was determined in this
work.
(39) There will be no significant intramolecular proton transfer to C-1
of the 4-methoxyphenyl ring in the presence of the fast competing proton
transfer and nucleophilic addition reactions of solvent for the following
reasons: (i) This site is much more weakly basic than solvent: A pKa of
-6.74 has been determined for protonation of methoxybenzene at oxygen
[Arnett, E. M.; Wu, C. Y. J. Am. Chem. Soc. 1960, 82, 5660-5665], and
the pKa for protonation of C-4 of the aromatic ring must be even more
negative than this. (ii) Proton transfer between two carbon atoms is
intrinsically slower than proton transfer between carbon and an electrone-
gative atom such as oxygen (see ref 41b, p 166). (iii) The effective molarities
for intramolecular proton transfer reactions are generally close to unity,36a
so that there is no large kinetic advantage to intramolecular deprotonation
of 1+.
(42) (a) Richard, J. P.; Amyes, T. L.; Vontor, T. J. Am. Chem. Soc. 1991,
113, 5871-5873. (b) The azide “clock” assumes a value of kaz ) 5 × 109
M-1 s-1 for diffusion-limited trapping of carbocations by N3-. This
assumption has been verified by direct measurement of second-order rate
constants for the diffusion-limited reaction of N3 with triarylmethyl,18
-
diarylmethyl,18 and R-substituted 4-methoxybenzyl19 carbocations. The rate
constants for these diffusion-limited reactions range from 5 × 109 to 7 ×
109 M-1 s-1, which sets an error limit of e40% for the value of ks calculated
from the N3 selectivity kaz/ks (M-1). (c) This relationship has been
-
determined using the following data, where X indicates the benzene ring
substituent(s) (Scheme 5): X ) 3-F, log kobsd ) -0.92, log ks ) 11.1; X
(40) Saunders, W. H. J. Am. Chem. Soc. 1994, 116, 5400-5404.
(41) (a) Kresge, A. J. Acc. Chem. Res. 1975, 8, 354-360. (b) Bernasconi,
C. F. AdV. Phys. Org. Chem. 1992, 27, 119-238.
) 4-NO2, log kobsd ) -3.63, log ks ) 12.3; X ) 3,5-(CF3), log kobsd
-4.50, log ks ) 13.1.
(43) Richard, J. P. Tetrahedron 1995, 51, 1535-1573.
)

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11441
≈ 1011 s-1).44 They suggest that the ion pair or ion molecule
intermediates of the reactions of simple tertiary derivatives
undergo direct reaction with a molecule of solvent within the
solvation shell that is present at the time of their formation,
Scheme 6
with ks′ ≈ ks ) kreorg
,
56 and that there is no significant chemical
reaction between these intermediates and bulk solvent, because
ks′ > k-d ≈ 1010 s-1
.
Chloride ion is approximately 100-fold more reactive than
water toward stable carbocations (kCl/ks ≈ 100 M-1),45,46 so that
the chemical barrier to collapse of a contact ion pair between
Cl- and 1+, in which the Cl- is correctly aligned to allow
reaction to give 1-Cl, should be even smaller than the barrier
to the reaction of solvent with the carbocation. Therefore, the
rate constant for the reaction of Cl- within the ion pair 1+‚Cl-
will lie close to the vibrational limit of 1013 s-1, so that this ion
pair may not exist as an intermediate in a potential well for the
time of even one bond vibration (≈10-13 s).23 By comparison,
Abraham has estimated a barrier of ∆Gq ) 5 ( 5 kcal/mol for
collapse of the contact ion pair between Cl- and the tert-butyl
carbocation to give tert-butyl chloride.47 The results reported
here suggest that the barrier to collapse of the contact ion pair
1+‚Cl- to give 1-Cl is much smaller than 5 kcal/mol. For
example, the Eyring equation [ln k ) ln (kBT/h) - (∆Gq/RT)]
predicts a barrier of ∆Gq ) 1.1 kcal/mol for a reaction with a
rate constant of 1012 s-1 at 25 °C.
Estimated Equilibrium Constants for Formation of Ter-
tiary Carbocations. The estimated rate constant for conversion
of an ion-molecule pair between 1+ and solvent, in which the
solvent molecule is orientated to allow its reaction with 1+ to
give the solvent adduct, is ks ≈ 1012 s-1 (see above). Therefore,
the rate-limiting step for reaction of 1+ with a molecule of water
within the solvation shell which surrounds this carbocation at
the time of its formation as an intermediate in the acid-catalyzed
reaction of 1-OH (Scheme 3) must be the rotation of a water
molecule into a reactive orientation, with a rate constant similar
to that for the dielectric relaxation of water (ks ) kreorg ≈ 1011
s-1).44 This value of ks ) kHOH[HOH] ) 1 × 1011 s-1 and kH
) 1.8 × 10-6 M-1 s-1 for the acid-catalyzed cleavage of 1-OH
were substituted into eq 8 that was derived for Scheme 3, to
give an estimated value of pKR ) -16.7 for the simple tertiary
carbocation 1+ in 50:50 (v/v) TFE/H2O. Similarly, the value
product distributions of the acid-catalyzed reactions of 1-OH
or 2 in aqueous solvents, because these reactions are expected
to proceed through tertiary carbocation intermediates that are
virtually identical (1+, Scheme 6).
The data in Table 2 show that the reactions of 1-OH and 2
in several mixed alcohol/water solvents give different relatiVe
yields of the solvolysis and elimination reaction products. Since
the major fate of 1+ generated from the acid-catalyzed cleavage
of 1-OH is its “invisible” reaction with water to regenerate
1-OH (Scheme 3), these differences are best illustrated as
differences in the product rate constant ratios k3/kTFE (M), k3/
kMeOH (M), and kMeOH/kTFE given in Table 3. These data require
the following: (a) that 1-OH and 2 do not undergo exclusive
reaction through a common, identical, reaction intermediate 1+,
and (b) that the rate constant ratios for partitioning of 1+ in
nucleophilic solvents cannot be easily determined from these
product studies.
This failure, in very favorable circumstances, to observe acid-
catalyzed reactions of 1-OH and 2 through a common tertiary
carbocation intermediate 1+ emphasizes the fleeting lifetime of
such carbocations, and the resulting difficulties in the determi-
nation of the distribution of the products of their reaction in
aqueous solution. The observed differences in the relative yields
of the products from the acid-catalyzed reactions of 1-OH and
2 might be explained by the following:
(1) There may be differences in the composition and reac-
tivity of the solvation shell which surrounds 1+ at the time of
its formation from the respective substrates (Scheme 6).
However, the data in Table 3 require that such differences be
maintained even in 20:80 (v/v) TFE/H2O and 2:18:80 (v/v/v)
MeOH/TFE/H2O (Table 3) which contain 94 mol % water.
(2) Acid-catalyzed nucleophilic substitution of solvent at
1-OH proceeds by partitioning of the nonselective carbocation
1+, because tertiary aliphatic carbon is extremely resistant to
concerted nucleophilic substitution. A significant fraction of
the reaction of the acid-catalyzed addition of solvent to 2 may
occur by a concerted reaction mechanism, because of the greater
steric ease of concerted nucleophilic addition of solvent at the
planar sp2 carbon of 2 than at the tertiary carbon of 1-OH. The
larger nucleophilic selectivity kMeOH/kTFE ) 4 for the acid-
catalyzed reaction of 2 in 5:45:50 (v/v/v) MeOH/TFE/H2O
compared to the acid-catalyzed reaction of 1-OH for which
kMeOH/kTFE ) 1.2 (Table 3) shows that the former reaction
proceeds through a transition state in which the bonding to the
incoming nucleophile is stronger than for addition of solvent
to the nonselective carbocation 1+. This is consistent with
stabilization of the transition state by the incoming nucleophile,
whose addition to 2 is concerted with proton transfer to carbon.
Reactions of 1-X in the Presence of Nucleophilic Reagents.
(a) Chloride Ion. The kinetic data for the reaction of 1-Cl in
the presence of increasing concentrations of Cl- serve to
illustrate the difficulty in distinguishing chloride common ion
and induced common ion inhibition49 of solvolysis from specific
Cl- salt effects.
pKR ) log (kH/kHOH[HOH])
(8)
of ks ) kHOH[HOH] ) 1 × 1011 s-1 and kH ) 4.0 × 10-6 M-1
s-1 for the acid-catalyzed exchange of 18O from H218O into
tert-butyl alcohol14 gives pKR ) -16.4 for the tert-butyl
carbocation in water. This is more negative than the earlier
estimates of pKR ) -1513 and -15.548 for the tert-butyl
carbocation, which were obtained by extrapolation of linear free
energy correlations between data for reactions in the gas phase13
or organic solvents48 and H2O.
Acid-Catalyzed Reactions of 1-OH and 2. One of the goals
of this work was to determine rate constant ratios for the
partitioning of 1+ which were free of the effects of the presence
of an anionic leaving group in an ion pair reaction intermediate.
In principle, this can be accomplished by determining the
(44) Giese, K.; Kaatze, U.; Pottel, R. J. Phys. Chem. 1970, 74, 3718-
3725. Kaatze, U. J. Chem. Eng. Data 1989, 34, 371-374. Kaatze, U.; Pottel,
R.; Schumacher, A. J. Phys. Chem. 1992, 96, 6017-6020.
(45) Bailey, T. H.; Fox, J. R.; Jackson, E.; Kohnstam, G.; Queen, A. J.
Chem. Soc., Chem. Commun. 1966, 122-123.
(46) Royer, R. E.; Daub, G. H.; Van der Jagt, D. L. V. J. Org. Chem.
1979, 44, 3196-3201.
(47) Abraham, M. H. Prog. Phys. Org. Chem. 1974, 11, 1.
(48) Wayner, D. D. M.; McPhee, D. J.; Griller, D. J. Am. Chem. Soc.
1988, 110, 132-137.

11442 J. Am. Chem. Soc., Vol. 118, No. 46, 1996
ToteVa and Richard
Figure 1 (b) shows that the addition of 0.50 M Cl- leads to
no detectable common ion inhibition of the reaction of 1-Cl in
50:50 (v/v) MeOH/H2O (I ) 0.50, NaClO4). However, the
replacement of 0.50 M sodium perchlorate with 0.50 M sodium
chloride results in a 30% decrease in kobsd for reaction of this
substrate in 50:50 (v/v) TFE/H2O (Figure 1, 9). By contrast,
when sodium chloride is the only salt present, kobsd for reaction
of 1-Cl in this solvent remains constant (kobsd ) 2.1 × 10-4
s-1) when the concentration of this salt is increased from 0 to
0.50 M. The decreases in kobsd that are observed when
perchlorate ion is replaced by Cl- in 50:50 (v/v) TFE/H2O
(Figure 1, 9) might be attributed to perchlorate-ion-induced
common ion inhibition of the reaction of 1-Cl.49 However, these
decreases are more likely due to differences in the specific
perchlorate and halide ion salt effects on kobsd, for the following
reasons: (a) Sodium bromide and sodium chloride lead to
similar decreases in kobsd for reaction of 1-Cl at constant ionic
strength of 0.50 maintained with sodium perchlorate (Figure
1).50 (b) There are only low yields of the azide ion adduct 1-N3
Scheme 7
-
H2O (I ) 0.50, NaClO4) when the concentration of N3 is
increased from 0 to 0.50 M. This is accompanied by the
formation of 13% of the azide ion adduct 1-N3 at the expense
of the solvent adducts, but there is no change in the total yield
of 25% of the alkenes 2 and 3 (Figure 3). We attribute the
very small (<0.1 kcal/mol) stabilization of the transition state
-
from the trapping of 1+ by the good nucleophile N3 (below),
so that there should be little or no common ion inhibition of
the reaction of 1-Cl from trapping of 1+ by Cl-, which is more
-
for the reaction of 1-Cl by 0.50 M N3- to either a specific N3
-
weakly nucleophilic than N3
.
-
(b) Lyoxide Ion. Figure 2 shows that there is no change in
the product distribution of the reaction of 1-Cl in 50:50 (v/v)
MeOH/H2O when the concentration of lyoxide ion is increased
from 0 to 0.50 M (I ) 0.50, NaClO4), but that there is an
accompanying 23% decrease in kobsd for this reaction (Figure
2, [), which can be attributed to a specific lyoxide ion salt
effect. An increase from 0 to 0.75 M sodium hydroxide also
has no effect on the relative yields of the solvolysis and
elimination products of the reaction of 2-chloro-2-methyl-1-
phenylpropane (H-5) in 25% acetonitrile in water.51
salt effect or to a very weak bimolecular reaction of N3 with
1-Cl. The absence of any detectable increase in kobsd for the
reaction of 1-O2CC6F5 in 50:50 (v/v) TFE/H2O when the
concentration of N3 is increased from 0 to 0.50 M (Results)
shows that there is also no significant bimolecular nucleophilic
substitution reaction of N3 with this substrate. Rate constant
ratios for the reaction of 1-Cl and 1-O2CC6F5 with N3 and
solvent, calculated from the yields of the N3 and solvent
adducts using eq 3 or eq 4, are reported in Table 1. The
-
-
-
-
dimensionless selectivities kaz/kHOH for the reaction of 1-X in
mixed alcohol/water solvents (Table 1) are close to kaz/kHOH
)
General base catalysts and lyoxide ion often cause an increase
in the fractional yield of alkene from the partitioning of
R-methylbenzyl carbocations between loss of a proton and
capture by solvent, because these bases provide stronger
catalysis of the deprotonation of the carbocation than of the
nucleophilic addition of solvent.52-55 By contrast, lyoxide ion
leads to no detectable change in the total yields of 25% of the
alkenes 2 and 3 and 75% of the solvent adducts 1-OH and
1-OMe from the reaction of 1-Cl in 50:50 (v/v) MeOH/H2O
(Table 2 and Figure 2). This does not result from catalysis by
lyoxide ion of both the deprotonation of 1+ and its capture by
solvent, because the addition of 0.25 M lyoxide ion also has no
effect on the product distribution of the reaction of 1-Cl in the
presence of 0.25 M N3- in this solvent (Results), for which the
7.2% yield of the azide ion adduct 1-N3 is formed at the expense
of only the solvent adducts. We conclude that the reactions of
the carbocation 1+ are so fast that it undergoes no detectable
competing bimolecular reaction with lyoxide ion.
19 determined for the reaction of H-5 in 25% acetonitrile in
water.51
We now consider the detailed mechanism for the formation
of the small amounts of the azide ion adduct 1-N3 from the
reactions of 1-Cl and 1-O2CC6F5 (Table 1). The yield of 1-N3
from the diffusion-controlled trapping of the ion pair 1+‚X- to
give the triple ion complex N3-‚1+‚X- (kd[Nu-], Scheme 1) is
negligible even at the highest concentration of N3- used in our
experiments, because the first-order rate constant for this
reaction, kd[N3-] ≈ (5 × 109 M-1 s-1) (0.50 M),18,19,42c is much
smaller than the estimated rate constant ks′ ≈ ks ) 1011 s-1 for
the direct reaction of solvent with the ion pair (see above).
Therefore, the possibility of diffusional encounter of the ion
pair 1+‚X- with N3- to give the triple ion complex N3-‚1+‚X-
has been omitted from Scheme 7.30,56 The remaining possibili-
ties are that 1-N3 is formed either by trapping of the free
carbocation 1+ (k1, k-d′ and kT[N3-], Scheme 7), or by a
preassociation mechanism through the association complex
N3-‚1-X (Kas, k1′, and kNu′, Scheme 7).23,42,57 The following
observations are consistent with the conclusion that the ion pair
intermediates 1+‚X- of the reactions of 1-X are so reactive that
they undergo little or no diffusional separation to the free
carbocation (ks′ > k-d′, Scheme 7), so that most or all of the
observed azide ion adduct must be formed by a preassociation
mechanism.23
(c) Azide Ion. Figure 3 ([) shows that there is a 10%
increase in kobsd for the reaction of 1-Cl in 50:50 (v/v) MeOH/
(49) Winstein, S.; Klinedinst, P. E., Jr.; Robinson, G. C. J. Am. Chem.
Soc. 1961, 83, 885-895. Vitullo, V. P.; Wilgis, F. P. J. Am. Chem. Soc.
1981, 103, 880-883.
(50) 1-Br is too reactive to accumulate during the reaction of 1-Cl in
the presence of NaBr because kobsd values for reaction of tert-butyl bromide
in mixed aqueous/organic solvents are ca. 40-fold larger than those for
reaction of tert-butyl chloride under the same conditions [Harris, J. M.;
Mount, D. L.; Smith, M. R.; Neal, W. C., Jr.; Dukes, M. D.; Raber, D. J.
J. Am. Chem. Soc. 1978, 100, 8147-8155].
(51) Thibblin, A. J. Am. Chem. Soc. 1989, 111, 5412-5416.
(52) Richard, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1984, 106, 1373-
1383.
(53) Thibblin, A. J. Chem. Soc., Perkin Trans. 2 1986, 321-326.
(54) Thibblin, A. J. Am. Chem. Soc. 1987, 109, 2071-2076.
(55) Thibblin, A. J. Phys. Org. Chem. 1989, 2, 15-25.
(1) There is no decrease in the product rate constant ratio
kaz/ks (M-1) for the reaction of 1-Cl when the nucleophilicity
(56) Richard, J. P. J. Org. Chem. 1992, 57, 625-629.
(57) There should be no significant formation of the solvent adducts from
reaction of the triple ion complex N3-‚1+‚X-, because the chemical
-
reactivity of N3 within this complex is much greater than that of the
surrounding solvent molecules.

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11443
of the solvent is increased by replacing TFE in 50:50 (v/v) TFE/
H2O by methanol (Table 1). This is inconsistent with the
formation of 1-N3 and 1-Solv by trapping of a diffusionally-
equilibrated carbocation intermediate, because an increase in
the nucleophilicity of the solvent would lead to an increase in
the rate constant for the activation-limited reaction of solvent
(ks), but to little or no change in kT for the diffusion-limited
reaction of N3-, resulting in an overall decrease in the observed
azide ion selectivity kaz/ks (M-1). For example, there is a large
decrease from kaz/ks ) 105 to 10 M-1 for reaction of the 1-(4-
methoxyphenyl)ethyl carbocation when the solvent is changed
from 50:50 (v/v) TFE/H2O to 50:50 (v/v) MeOH/H2O.20 The
almost identical product rate constant ratios kaz/ks (M-1) for the
reaction of 1-Cl in these solvents (Table 1) strongly suggest
that the yield of the azide ion adduct is determined by the
magnitude of the association constant Kas (M-1) for formation
10.4% 1-N3 under these conditions. This suggests that, at most,
only ca. 50% of the azide ion adduct can be formed by the
diffusion-controlled trapping of the liberated carbocation 1+
(kT[N3-], Scheme 7). In fact, if Kas is larger than 0.20 M-1
,
-
and/or if N3 provides a small amount of assistance to the
ionization of 1-Cl within the complex N3-‚1-Cl, so that k1′ >
k1 (Scheme 7), then the preassociation mechanism could account
for the formation of all of the observed azide ion adduct. In
any event, the conclusion that no more than 50% of the observed
azide ion adduct 1-N3 can result from trapping of the free
carbocation 1+ requires that the diffusional separation of the
ion pair 1+‚Cl- to give the free carbocation 1+ be no faster
that its direct reaction with solvent, so that ks′ g k-d′ (Scheme
7). The estimated rate constant for diffusional separation of a
carbocation-anion ion pair, k-d ≈ 2 × 1010 s-1 52,58
,
then gives
ks′ g 2 × 1010 s-1. This lower limit is consistent with the value
estimated above of ks′ ≈ ks ) kreorg ≈ 1 × 1011 s-1 for the
reaction of 1+ with solvent.
-
of the preassociation complex between N3 and the substrate
(N3-‚1-Cl).
Alkene-Forming Elimination. The yield of 13% of the
disubstituted alkene 2 from the elimination of HCl across the
methyl groups of 1-Cl in 50:50 (v/v) TFE/H2O (Table 2) is
similar to the yield of 14% methylpropene from the reaction of
tert-butyl chloride under similar reaction conditions.34 However,
the total yield of the alkenes 2 and 3 from the reaction of 1-Cl
is somewhat larger than this, because the yield of the thermo-
dynamically favored alkene 3 is two-fold greater than the yield
of 2 (Table 2). The large increases in the rate constant ratios
k2/kROH and k3/kROH for partitioning of 1-X between elimination
and solvolysis as the leaving group is changed from water to
chloride to pentafluorobenzoate (Table 3) show that the leaving
group must be present in the transition state for the product
determining step for the reactions of 1-Cl and 1-O2CC6F5. The
possibility that solvent acts as a Brønsted base to promote a
concerted E2 elimination reaction59,60 of the tertiary chloride
1-Cl can be excluded, because the much stronger base lyoxide
ion does not promote this reaction (Figure 2). We therefore
conclude that the leaving group acts as the proton acceptor for
the elimination reactions of 1-Cl, and probably for the reactions
of 1-O2CC6F5.
(2) The dimensionless selectivities kMeOH/kTFE for partitioning
of 1-arylethyl carbocations between reaction with methanol and
trifluorethanol in 5:45:50 (v/v/v) MeOH/TFE/H2O exhibit a
large dependence on the stability of the carbocation when the
carbocations are solvent-equilibrated species, but they decrease
sharply to a limiting value of kMeOH/kTFE e 3.0 when the
carbocation is so unstable that it reacts directly with the
surrounding solvent pool.42,52 Therefore, the small values of
kMeOH/kTFE e 2.0 for the reactions of 1-Cl in 5:45:50 (v/v/v)
and 2:18:80 (v/v/v) MeOH/TFE/H2O (Table 3) are consistent
with the partitioning of a short-lived ion pair intermediate
between reaction with methanol and trifluoroethanol within the
small pool of surrounding solvent molecules.42,52
The rate constant for reaction of the free carbocation 1+ with
a solvent of 50:50 (v/v) TFE/H2O cannot be calculated directly
from the product azide ion selectivity kaz/ks ) 0.38 M-1 for the
reaction of 1-Cl by using the diffusion-limited trapping of 1+
-
by N3 (kT[N3-], Scheme 7) as a “clock” for the reaction of
solvent,20,21 because very little of the observed 1-N3 is formed
by trapping of the free carbocation 1+. However, this observed
azide ion selectivity can be used to estimate a lower limit on
ks′ for the direct reaction of solvent with the ion pair 1+‚Cl-,
provided it is possible to estimate the relative yields of 1-N3
obtained from the trapping and preassociation reaction path-
The alkene-forming elimination reactions of tertiary halides
and benzoate esters in polar solvents are generally assumed to
proceed by a stepwise mechanism through the carbocation-
leaving group ion pair intermediates of the solvolysis reaction
(kp′, Scheme 7),51,53-55,61-63 and the possibility of concerted
unimolecular elimination through a cyclic transition state such
as 6 and 7 is not considered in the interpretation of experimental
-
ways.52 The yield of 1-N3 from the reaction of 1-Cl with N3
by a preassociation mechanism depends on the stability of the
preassociation complex (Kas, Scheme 7) and on the relative rates
of ionization of 1-Cl within this complex (k1′) and of free 1-Cl
(k1). In the limit that all of the azide ion adduct is formed by
a preassociation mechanism in which N3- provides no assistance
to ionization of the substrate (k1′ ) k1, Scheme 7), then kaz/ks
) Kas, so that the value of Kas for formation of the preassociation
-
complex between N3 and the substrate can be determined
directly from the yield of the azide ion adduct. Such a value
of Kas ) kaz/ks ) 0.20 M-1 has been estimated for the reaction
of (3,5-bis(trifluoromethyl)phenyl)diazomethane in 50:50 (v/
v) TFE/H2O, for which the putative 3,5-bis(trifluoromethyl)-
benzyl carbocation intermediate of the stepwise reaction of this
substrate is too unstable to undergo diffusion-limited trapping
by azide ion.58 The total yield of 39% of the alkenes 2 and 3
from the reaction of 1-Cl in 50:50 (v/v) TFE/H2O (Table 2) is
unaffected by the addition of 0.50 M N3- (Results). Therefore,
at [N3-] ) 0.50 M, the yield of 1-N3 from the reaction of 1-Cl
by a preassociation mechanism with Kas ) 0.20 M-1 is expected
to be 5.5%, which is only ca. 50% of the observed yield of
data for these reactions.6 However, the mechanism for the
elimination reactions of tertiary alkyl derivatives such as 1-Cl
and 1-O2CC6F5 in aqueous solutions deserves very close
scrutiny for the following reasons:
(1) It is not clear why the partitioning of the 1+‚Cl- ion pair
should lead to the formation of significant amounts of an alkene
(59) Bunnett, J. F.; Sridharan, S. J. Org. Chem. 1979, 44, 1458-1471.
(60) Bunnett, J. F.; Migdal, C. A. J. Org. Chem. 1989, 54, 3037-3041.
(61) Frisone, G. J.; Thornton, E. R. J. Am. Chem. Soc. 1968, 90, 1211-
1215.
(62) Thibblin, A.; Sidhu, H. J. Chem. Soc., Perkin Trans. 2 1994, 1423-
1428.
(58) Finnemann, J. I.; Fishbein, J. C. J. Am. Chem. Soc. 1995, 117, 4228-
4239.
(63) Jansen, M. P.; Koshy, K. M.; Mangru, N. N.; Tidwell, T. T. J. Am.
Chem. Soc. 1981, 103, 3863-3867.

11444 J. Am. Chem. Soc., Vol. 118, No. 46, 1996
ToteVa and Richard
product. The reason for this is two-fold: (a) Cl- is a very weak
Brønsted base (pKa ) -7 in water);64 and (b) the alkene
products are thermodynamically less stable than the adducts of
the carbocation to solvent (falk ) 0.011, Table 4).29
(2) Increasing concentrations of N3- lead to different changes
in the yields of the solvolysis and elimination reaction products
(Figure 3). The constant total yield of the alkenes 2 and 3 from
the reactions of 1-Cl and 1-O2CC6F5 in the presence of
increasing concentrations of N3- in 50:50 (v/v) MeOH/H2O and
TFE/H2O (Figure 3 and Results) is inconsistent with the
formation of an ionic reaction intermediate which partitions
between addition of solvent (ks′, Scheme 7) and loss of a proton
(kp′, Scheme 7). These results are consistent with the following
mechanistic interpretation: (a) As discussed above, the solvent
adducts 1-Solv are formed primarily from reaction of the free
substrate (1-Cl) and the azide ion adduct 1-N3 is formed from
-
reaction of the preassociation complex of the substrate with N3
(N3-‚1-Cl, Scheme 7). (b) The conversion of 1-Cl to the
preassociation complex N3-‚1-Cl leads to the formation of 1-N3
at the expense of only 1-Solv. (c) The yield of the alkenes 2
and 3 is insensitive to the conversion of 1-Cl into the
preassociation complex N3-‚1-Cl, because these products are
formed by concerted elimination reactions of both free 1-Cl
and 1-Cl within the preassociation complex N3‚1-Cl, with the
same first-order rate constant (ke, Scheme 7).6
(3) The rate constant for the collapse of 1+‚Cl- to 1-Cl was
estimated above to lie close to the vibrational limit of 1013 s-1
so that this ion pair may not exist as an intermediate in a
potential energy well for the time of even one bond vibration
(≈10-13 s).23 If there is no significant chemical barrier to
collapse of 1+‚Cl- to neutral reactant, then elimination of HX
from 1-X may proceed by a concerted mechanism which is
enforced because the ion pair intermediate of the stepwise
reaction is too unstable to exist in an energy well for the time
of a bond vibration.23
Figure 4. The free energy profile for ionization of a tertiary chloride
to give the carbocation-chloride ion pair. A nucleophilic interaction
between the tertiary carbocation and solvent may increase the rate of
formation of the ion pair by either of the following mechanisms: (A)
a decrease in the intrinsic kinetic barrier to the reaction, which will
result in equal decreases in the kinetic barriers to both the formation
(k1) and collapse (k-1) of the ion pair; and (B) a decrease in the
thermodynamic barrier to the reaction, which will result in a decrease
in the kinetic barrier to formation of the ion pair through a late
carbocation-like transition state.
acidity, so that the data may also be explained by different
sensitivities of the reactions of tert-butyl and adamantyl
derivatives to changes in the acidity of the solvent, with differing
degrees of electrophilic “pull” by solvent to the ionization of
these substrates.70-72 Changes in the ground state solvation of
the substrate may also contribute to solvent effects on the rate
constants for solvolysis,73-75 and it has been suggested that some
apparent relationships between solvolysis rate and solvent
nucleophilicity in fact represent correlations of rate with the
ground state solvation of a phenyl group.76
(4) A concerted pathway for elimination of HCl from tert-
butyl chloride has been identified in a recent quantum mechan-
ical/molecular mechanical coupled potential simulation of the
ionic fragmentation of tert-butyl chloride in water.65
The small product rate constant ratios kMeOH/kTFE ) 1.4 and
2.0 determined for the reaction of 1-Cl with methanol and
trifluoroethanol in 5:45:50 and 2:18:80 (v/v/v) MeOH/TFE/H2O,
respectively, show that the replacement of trifluoroethanol by
methanol results in only a small nucleophilic stabilization of
the product-determining transition state, which is the addition
of solvent to the carbocation within the ion pair 1+‚Cl- (see
8A). There are also only small stabilizations of the transition
states for the rate- and product-determining steps of the reaction
The Question of Solvent Assistance to the Ionization of
1-Cl. The effects of changes in bulk solvent on the rate
constants for solvolysis represent the sum of many contributing
factors which are extremely difficult to separate and quantify.
The rate constants for reaction of tert-butyl halides show an
apparent larger sensitivity to changes in the nucleophilicity of
bulk solvent than those for adamantyl derivatives which react
by a limiting unassisted stepwise mechanism.66-69 These data
may correspond to nucleophilic solvent assistance to the
ionization of tert-butyl chloride to form a nucleophilically
“solvated” ion pair intermediate. There is a strong correlation
between the nucleophilicity of protic solvents and their Brønsted
-
of 1-Cl by the very good nucleophile N3 (Table 1). This
suggests that there also is no assistance to the reaction of this
substrate by the much more weakly nucleophilic solvent.77
(70) Abraham, M. H.; Taft, R. W.; Kamlet, M. J. J. Am. Chem. Soc.
1981, 46, 3053-3056. McManus, S. P.; Sedaghat-Herati, M. R.; Karaman,
R. K.; Neamati-Mazraeh, N.; Cowell, S. M.; Harris, J. M. J. Org. Chem.
1989, 54, 1911-1918.
(64) (a) Jencks, W. P.; Regenstein, J. In Handbook of Biochemistry and
Molecular Biology, Physical and Chemical Data, 3rd ed.; Fasman, G. D.,
Ed.; CRC Press: Cleveland, OH, 1976; Vol. 1; pp 305-351. (b) The
observation that hydrochloric acid is completely dissociated in methanol
and in ethanol [Bell, R. P. The Proton in Chemistry, 2nd ed.; Cornell
University Press: Ithaca, New York, 1973; p 44] requires that Cl- be a
much weaker base than 50:50 (v/v) MeOH/H2O.
(65) Hartsough, D. S.; Merz, K. M., Jr. J. Phys. Chem. 1995, 99, 384-
390.
(66) Bentley, T. W.; Bowen, C. T.; Parker, W.; Watt, C. I. F. J. Am.
Chem. Soc. 1979, 101, 2486-2487. Bentley, T. W.; Bowen, C. T.; Morton,
D. H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1981, 103, 5466-5475.
(67) Bentley, T. W.; Carter, G. E. J. Am. Chem. Soc. 1982, 104, 5741-
5747.
(71) Harris, J. M.; McManus, S. P.; Sedaghat-Herati, M. R.; Neamati-
Mazraeh, N.; Kamlet, M. J.; Doherty, R. M.; Taft, R. W.; Abraham, M. H.
In AdVances in Chemistry Series; Harris, J. M., McManus, S. P., Eds.;
American Chemical Society: Washington, DC, 1987; pp 247-253.
(72) The most careful correlation of these data is consistent with the
conclusion that there is a small amount of nucleophilic assistance to the
ionization of tert-butyl derivatives [Bentley, T. W.; Roberts, K. J. Chem.
Soc., Perkin Trans. 2 1989, 1055-1060].
(73) Arnett, E. M.; Bentrude, W. G.; Burke, J. J.; Duggleby, P. M. J.
Am. Chem. Soc. 1965, 87, 1541-1553.
(74) Gajewski, J. J. J. Org. Chem. 1992, 57, 5500-5506.
(75) McLennan, D. J.; Martin, P. L. J. Chem. Soc., Perkin Trans. 2 1982,
1091-1097.
(68) Kevill, D. N.; Kamil, W. A.; Anderson, S. W. Tetrahedron Lett.
1982, 45, 4635-4638.
(69) Kevill, D. N.; Anderson, S. W. J. Am. Chem. Soc. 1986, 108, 1579-
1585.
(76) Kevill, D. N.; Ismail, N. H. J.; D’Souza, M. J. J. Org. Chem. 1994,
59, 6303-6312.

Lifetime of a Simple Tertiary Carbocation
J. Am. Chem. Soc., Vol. 118, No. 46, 1996 11445
s-1 23
.
Similarly, it is difficult to understand how there can be
a large equilibrium stabilization of the carbocation by a
nucleophilic interaction with solvent (“nucleophilic solvation”),
because once nucleophilic (i.e., bonding) interactions between
these reactants become stabilizing it is simplest that the reactants
should continue to products in a strongly exothermic reaction,
without passage over an free energy maximum. We know of
no theoretical support for the alternative coordinate for a reaction
through nucleophilically solvated carbocation reaction interme-
diate in which partial bond formation between solvent and
tertiary carbocation is first stabilizing as the solvated intermedi-
ate is formed, then destabilizing with the approach to the
transition state for nucleophilic addition of solvent, and again
stabilizing after passage over the reaction transition state.
Our results show that tertiary carbocation-chloride ion pairs
lie in a shallow potential energy well, with very small barriers
to collapse of the carbocation by the addition of solvent or Cl-
(k-1 g ks′ ≈ 1011 s-1, Scheme 7 and Figure 4). A nucleophilic
interaction with solvent might lead either to a reduction in the
“intrinsic” kinetic barrier, which would lead to equal increases
in the rate constants for both the formation and collapse of the
ion pair (Figure 4, A), or to a net thermodynamic stabilization
of the carbocation, which would be expressed primarily as a
decrease in the kinetic barrier to formation of the ion pair, which
proceeds through a late carbocation-like transition state (Figure
4, B). The former effect cannot be large, because the rate
constant for collapse of the tertiary carbocation back to reactants
(k-1, Figure 4) is already close to the vibrational limit of 1013
Acknowledgment. This work was supported by a grant from
the National Institutes of Health (Grant GM 39754).
Supporting Information Available: Details of procedures
for the synthesis of the compounds used in this work, and a
table showing the change with time in the yields of the products
of the perchloric acid-catalyzed reactions of 1-OH and 2 in 50:
50 (v/v) TFE/H2O (5 pages). See any current masthead page
for ordering and Internet access instructions.
(77) Raber, D. J.; Harris, J. M.; Hall, R. E.; Schleyer, P. v. R. J. Am.
Chem. Soc. 1971, 93, 4821-4829.
JA9617451