Stabilities and partitioning of arenonium ions in aqueous media

Article abstract of DOI:10.1021/ja806899d

The phenathrenonium ion is formed as a reactive intermediate in the solvolysis of 9-dichloro-acetoxy-9,10-dihydrophenanthrene in aqueous acetonitrile and undergoes competing reactions with water acting as a base and nucleophile. Measurements of product ratios in the presence of azide ion as a trap and 'clock' yield rate constants k_p ) 3.7 × 10 ¹⁰ and k_H2O ) 1.5 × 10⁸ s^-1, respectively. Combining these with rate constants for the reverse reactions (protonation of phenanthrene and acid-catalyzed aromatization of its water adduct) gives equilibrium constants pKa ) -20.9 and pKR ) -11.6. For a series of arenonium and benzylic cations, correlation of log k_p with pK _a, taking account of the limit to k_p set by the relaxation of water (10¹¹ s^-1), leads to extrapolation of k _p ) 9.0 × 10¹⁰ s^-1 and pK_a ) -24.5 for the benzenonium ion and k_p ) 6.5 × 10¹⁰ s^-1 and pK_a ) -22.5 for the 1-naphthalenonium ion. Combining these pK_a's with estimates of equilibrium constants pK _H2O for the hydration of benzene and naphthalene, and the relationship pK_R ) pK_a + pK_H2O based on Hess's law, gives pK_R ) -2.3 and -8.0 respectively, and highlights the inherent stability of the benzenonium ion. A correlation exists between the partitioning ratio, k_p/k_H2O, for carbocations reacting in water and K_H2O the equilibrium constant between the respective reaction products, i.e., log(k_p/k_H2O) ) 0.46pK _H2O - 3.7. It implies that k_p exceeds k_H2O only when K_H2O > 10⁸. This is consistent with the proton transfer (a) possessing a lower intrinsic reactivity than reaction of the carbocation with water as a nucleophile and (b) being rate-determining in the hydration of alkenes (and dehydration of alcohols) except when the double bond of the alkene is unusually stabilized, as in the case of aromatic molecules.

Full text of DOI:10.1021/ja806899d

Published on Web 12/08/2008
Stabilities and Partitioning of Arenonium Ions in Aqueous
Media
D. A. Lawlor, R. A. More O’Ferrall,* and S. N. Rao
Contribution from the Department of Chemistry and Centre for Synthesis and Chemical Biology,
UniVersity College Dublin, Belfield, Dublin 4, Ireland
Received September 1, 2008; E-mail: rmof@ucd.ie
Abstract: The phenathrenonium ion is formed as a reactive intermediate in the solvolysis of 9-dichloro-
acetoxy-9,10-dihydrophenanthrene in aqueous acetonitrile and undergoes competing reactions with
water acting as a base and nucleophile. Measurements of product ratios in the presence of azide ion as
a trap and ‘clock’ yield rate constants kp ) 3.7 × 1010 and kH2O ) 1.5 × 108 s-1, respectively. Combining
these with rate constants for the reverse reactions (protonation of phenanthrene and acid-catalyzed
aromatization of its water adduct) gives equilibrium constants pKa ) -20.9 and pKR ) -11.6. For a series
of arenonium and benzylic cations, correlation of log kp with pKa, taking account of the limit to kp set by the
relaxation of water (1011 s-1), leads to extrapolation of kp ) 9.0 × 1010 s-1 and pKa ) -24.5 for the
benzenonium ion and kp ) 6.5 × 1010 s-1 and pKa ) -22.5 for the 1-naphthalenonium ion. Combining
these pKa’s with estimates of equilibrium constants pKH2O for the hydration of benzene and naphthalene,
and the relationship pKR ) pKa + pKH2O based on Hess’s law, gives pKR ) -2.3 and -8.0 respectively,
and highlights the inherent stability of the benzenonium ion. A correlation exists between the partitioning
ratio, kp/kH2O, for carbocations reacting in water and KH2O the equilibrium constant between the respective
reaction products, i.e., log(kp/kH2O) ) 0.46pKH2O - 3.7. It implies that kp exceeds kH2O only when KH2O
>
108. This is consistent with the proton transfer (a) possessing a lower intrinsic reactivity than reaction of
the carbocation with water as a nucleophile and (b) being rate-determining in the hydration of alkenes
(and dehydration of alcohols) except when the double bond of the alkene is unusually stabilized, as in the
case of aromatic molecules.
Introduction
carbocation stoichiometrically by flash photolysis and monitor-
ing its further reaction3 and (ii) measurement of product ratios
from trapping of the carbocation by solvent in competition with
a diffusion controlled reaction with azide ion, the so-called azide
clock method.7,8
Carbocations1 have been prominent in efforts over the past
20 years to establish the stabilities of high-energy intermediates
of organic reactions in aqueous solution.2 Equilibrium constants
for hydrolysis (pKR) or acid dissociation (pKa) have been
measured by combining rate constants for formation of the
carbocations with the less easily accessible values for their
reverse reactions, usually with solvent.3-11 The latter have been
determined by two principal methods: (i) generating the
There is a third method applied by Richard to strongly basic
carbanions,4,12 and also to the t-butyl carbocation.9 That is to
measure the rate of formation of the carbocation under condi-
tions for which its back reaction has reached the limit set by
relaxation of the aqueous solvent molecules, namely, 1011 s-1
.
This is applicable to highly unstable carbocations or to car-
bocations reacting to form unusually stable products. In this
paper we report measurements for protonated aromatic mol-
ecules (arenonium ions), for which stabilization of the product
from loss of a proton is so great that the relaxation limit is
achieved even for relatively stable carbocations.
There have been a number of previous studies of arenonium
ion equilibria. Values of pKa and pKR have been reported for
1-protonated naphthalene,10 9-protonated anthracene and 3-pro-
tonated benzofuran;11 pKa’s have also been measured for
protonation of relatively stable substituted benzenes13-15 and
(1) Laali, K. K. Recent DeVelopments in Carbocation and Onium Ion
Chemistry; American Chemical Society, Washington, DC, 2007.
(2) ReactiVe Intermediate Chemistry; Moss R. A.; Platz, M. S.; Jones,
M., Eds.; Wiley-Interscience; Hoboken, NJ, 2004.
(3) McClelland, R. A.,in ref 2, pp 3-40. McClelland, R. A. Tetrahedron
1996, 52, 6823–6858.
(4) Richard, J. P.; Amyes, T. L.; Toteva, M. M. Acc. Chem. Res. 2001,
34, 981–988.
(5) Richard, J. P.; Amyes, T L.; Lin, S.-S.; O’Donoghue, A. C.; Toteva,
M. M.; Tsuji, Y.; Williams, K. B. AdV. Phys. Org. Chem. 2000, 35,
67–115.
(6) MacCormack, A.; McDonnell, C. M.; O’Donoghue, A. C.; More
O’Ferrall, R. A. In Modern Problems in Organic Chemistry; St.
Petersburg Press: St. Petersburg, 2003, vol 14.
(7) Richard, J. P.; Rothenburg, M. E.; Jencks, W. P. J. Am. Chem. Soc.
1984, 106, 1361–1372.
(8) McClelland, R. A.; Kanagasabapathy, V. M.; Banait, N. S.; Steenken,
S. J. Am. Chem. Soc. 1989, 111, 3966–3972.
(11) MacCormack, A. C.; McDonnell, C. M.; O’Donoghue, A. C.; More
O’Ferrall, R. A. J. Am. Chem. Soc. 2002, 124, 8575–8583.
(12) Richard, J. P.; Williams, G.; O’Donoghue, A. C.; Amyes, T. L. J. Am.
Chem. Soc. 2002, 124, 2957–2968.
(9) Toteva, M. M.; Richard, J. P. J. Am. Chem. Soc. 1996, 118, 11434–
11445.
(10) Pirinccioglu, N.; Thibblin, A. J. Am. Chem. Soc. 1998, 120, 6512–
6517.
(13) Kresge, A. J.; Chen, H. J.; Hakka, L. E.; Kouba, J. E. J. Am. Chem.
Soc. 1971, 93, 6174–6181.
9
10.1021/ja806899d CCC: $40.75
2008 American Chemical Society
J. AM. CHEM. SOC. 2008, 130, 17997–18007 17997

A R T I C L E S
Lawlor et al.
Scheme 1
Scheme 2
azulenes.16 Here, we describe application of the azide clock to
measurements of pKR and pKa for 9-protonated phenanthrene
and extrapolate tight limits ((0.5 log units) for pKa’s of
protonated benzene and 2-protonated naphthalene.
Scheme 3
In contrast to other carbocations, in water, arenonium ions,
such as benzenonium or naphthalenonium, undergo loss of a
proton rather than nucleophilic attack by solvent. This can be
attributed to aromatic stabilization of the carbon-carbon double
bond of the deprotonated product.5,17,18 However, in the case
of phenanthrene, this stabilization is reduced and products from
both reaction paths can be detected. As a result, trapping by
azide ions yields rate constants for both reactions, and thence
equilibrium constants pKR and pKa. The difference pKR - pKa
then gives the further constant pKH2O for hydration of the
relevant carbon-carbon double bond based on the thermody-
namic cycle illustrated for the benzenonium ion 1 in Scheme 1
(taking the single arrows to denote equilibria).
reactivity of the carbocation toward reaction with water as a
base and nucleophile, are discussed briefly.4,5,21
Results
Phenanthrenonium Ion. The 9,10-hydrate of phenanthrene,
9-hydroxy-9,10-dihydrophenanthrene, 3, may be prepared by
reduction of the corresponding 9,10-epoxide.22 Reaction of the
hydrate in dilute acid leads to dehydration to form phenanthrene
Cycles similar to Scheme 1 provide useful summaries of
carbocation equilibria in aqueous solution.5,11 Where pKR cannot
be determined directly, as in the case of protonated benzene or
naphthalene, pKH2O can be evaluated from the difference in free
energies of formation of the aromatic molecule and hydrated
17
with a rate constant kde ) 3.4 × 10-3 M-1 s-1
.
By analogy
with other arene hydrates the reaction proceeds via 9-protonated
phenanthrene 4 as an intermediate, as shown in the reaction at
the top of Scheme 2. Expressed in terms of the rate constants
in Scheme 3, kde ) kHkp/(kp + kH2O), where kH refers to formation
of the carbocation and kp and kH2O to its forward and backward
reactions.
product,19 and pKR is obtained as pKa + pKH2O 11 The value of
.
pKR is important because the pKa of arenonium ions strongly
reflects the stability of the carbon-carbon double bond formed
by loss of the proton. Measurements of pKR represent more
closely the inherent stability of the carbocation.
Reaction of 3 with dichloroacetyl chloride yields the dichlo-
roacetate 5, which solvolyzes in aqueous acetonitrile in the
absence of acid to form a mixture of phenanthrene and the
hydrate (3), conditions under which the hydrate does not react
further. Measurements in a series of acetonitrile-water mixtures
yield product ratios of phenanthrene/hydrate which are weakly
dependent on solvent composition8 and give a ratio of rate
constants for deprotonation and nucleophilic reaction of the
carbocation with water kp/kH2O ) 25.
In this paper we compare values of pKR and pKa of arenonium
and other carbocations and explore partitioning of the cations
in water between the formation of hydrate or alcohol and arene
or alkene products. This partitioning is expressed by a ratio of
the rate constants kp for deprotonation and kH2O for nucleophilic
attack by water (Scheme 1). We show that a correlation exists
between logs of ratios of these rate constants [log(kp/kH2O)] and
Solvolysis of 5 in the presence of varying concentrations of
sodium azide leads to formation of an azido product presumed
to be 9-azido-9,10-dihydrophenanthrene, 6. Attempts to isolate
this product were unsuccessful, probably because of its low
concentration in comparison with other products, but it could
be identified by its HPLC retention time in relation to phenan-
threne and hydrate products, the dependence of the intensity of
its peak upon azide concentration and the growth of this intensity
with a rate constant equal to that of the solvolysis reaction.7,8,11
Figure 1 shows a plot of the ratio of concentrations of azide
adduct to phenanthrene in the products based on the relationship
of eq 1 (in which Phen denotes phenanthrene and RN3 the azide-
trapped product) and the usual assumption that the extinction
the relative stabilities of the products as expressed by pKH2O
.
The practical implications of this relationship, e.g., for the rate-
determining step in the dehydration of alcohols (to form alkene)
and the partitioning of the Fe(CO)3 coordinated benzenonium
ion in water between nucleophilic attack and deprotonation,20
as well as its more fundamental implication for the intrinsic
(14) Kresge, A. J.; Mylonakis, S. G.; Sato, Y.; Vitullo, V. P. J. Am. Chem.
Soc. 1971, 93, 6181–6188.
(15) Marziano, N.; Tortato, C.; Bertani, R. J. Chem. Soc. Perkin Trans. 2
1992, 955–957.
(16) Long, F. A.; Schulze, J. J. Am. Chem. Soc. 1964, 86, 322–327, and
327-332.
(17) Rao, S. N.; More O’Ferrall, R. A.; Kelly, S. C.; Boyd, D. R.; Agarawal,
R. J. Am. Chem. Soc. 1993, 115, 5438–5465.
(18) Pirinccioglu, N.; Jia, Z. S.; Thibblin, A. J. Chem. Soc. Perkin Trans.
2 2001, 2271–2275.
(21) Richard, J. P.; Williams, K. B.; Amyes, T. L. J. Am. Chem. Soc. 1999,
121, 8403–8404.
(19) Dey, J.; O’Donoghue, A. C.; More O’Ferrall, R. A. J. Am. Chem.
Soc. 2002, 124, 8561–8574.
(22) Krishnan, S.; Kuhn, D. G.; Hamilton, G. A. J. Am. Chem. Soc. 1977,
99, 8121–8123.
(20) Galvin, M.; Guthrie, J. P.; McDonnell, C. M.; More O’Ferrall, R. A.
J. Am. Chem. Soc. In press.
(23) Amyes, T. C.; Richard, J. P.; Novak, M. J. Am. Chem. Soc. 1992,
114, 8032–8041.
9
17998 J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008

Arenonium Ions in Aqueous Media
A R T I C L E S
Figure 1. Ratios of concentrations of trapped 9-azido-9,10-dihydrophenanthrene and phenanthrene plotted against concentrations of azide ion in 50%
aqueous MeCN at 25 °C.
coefficients of the azide and hydrate are the same.23 From
extrapolation of the slope of this and other plots for different
solvent mixtures the ratio of rate constants for formation of the
two products in water is kAz/kp ) 0.135. Making the usual
assumption of the azide clock method7,8 that trapping of the
carbocation by azide ion is diffusion controlled with rate
constant kaz ) 5 × 109 M-1 s-1 leads to kp ) 3.7 × 1010 s-1
Taking kAz ) 5 × 109 s-1 and kreorg ) 1011 s-1, the ratio
kAz/kreorg ) 0.05, and except at the highest concentrations of
azide ion eq 2 is well approximated by eq 3.
[R-N3]
[Phen]
1
1
) kAz
+
[N3]
(3)
{
}
kreorg kp
This equation implies that when the rate constant for deproto-
nation is large the limiting product ratio ) [RN3]/[Phen] ) kAz/
kreorg ) 0.05. Taking account of this limit leads to a minor
modification of the value of kp based on eq 1 from 3.7 to 5.9 ×
and, by combination of this value with kp/kH2O ) 25, to kH2O
)
1.5 × 109 s-1. Correction of the rate constant for dehydration
of phenanthrene hydrate for the small degree of reversibility
implied by the value of kp/kH2O gives kH ) 3.5 × 10-3 M-1 s-1
,
1010 s-1
.
whence KR ) kH2O/kH ) 4.3 × 1011 and pKR ) -11.6 in aqueous
solution at 25 °C.
It should be noted that it is also possible that reaction within
the ion pair involves the dichloroacetate counterion rather than
water acting as base. However, the rate of deprotonation is
sufficiently close to the relaxation limit that it seems unlikely
that kp will be much affected by replacement of a water molecule
in the solvation shell of the carbocation by a carboxylate anion.
A more serious limitation is that the analysis fails to take
account of reaction by a preassociation mechanism. For sol-
volytic reactions of different charge types Richard has measured
contributions from preassociation to values of [RN3]/[solvolysis
product] in the range 0.2-0.7.25 The value of [RN3]/[Phen] )
0.135, which we find is below that range even before correction
for a limiting value of 0.05.
In so far as the aim of this paper is to establish equilibrium
constants we will not pursue these issues but simply note that
by neglecting preassociation and trapping by azide of an
unrelaxed ion (pair) the kp determined represents a minimum
value. Because the maximum value of kp, kreorg ) 1011 s-1, is
less than three times greater than the value of 3.7 × 1010 derived
from the simple partitioning based in Scheme 2, the maximum
error in log kp and the derived value of pKR () -11.6) is log
2.7 or 0.4 log units, while the difference of log kp from the
value based in Scheme 3 is 0.2 units.
-
[RN3] kAz[N3
]
)
(1)
[Phen]
kp
However, this analysis is oversimplified on three counts. The
first is neglect of an explicit treatment of solvent relaxation as
a limit on the rate of deprotonation of the phenanthrenonium
ion. The influence of this limit has been considered by Richard
in relation to the protonation of highly reactive carbanions by
water12 and is adapted to the deprotonation of carbocations in
Scheme 3 below in which kreorg ) 1011 s-1 is a constant for
solvent relaxation and R-X and Phen refer to the dichloroac-
etate 5 and phenanthrene, respectively.
The second simplification is negelect of ion pairs. In Scheme
3, deprotonation and attack of azide ion on the phenan-
threnonium ion are shown as occurring on R+X- and X-R+,
which represent ion pairs before and after relaxation of the
solvent, respectively. Richard24 has estimated a rate constant
for dissociation of an ion pair in water as 1.6 × 1010 s-1, and
this will become significant if kp is comparable with this value.
However, if the ratio of kp to the diffusion constant for the azide
ion kAz is unaffected by the ion pairing the kinetic expression
based in Scheme 3 simplifies to that of eq 2.
A value for the pKa of the phenanthrenonium ion may be
obtained by combining kp with a rate constant kA for protonation
of phenanthrene. The latter may be derived from an isotope
[R-N3]
[Phen]
kAz
kAz
)
+
[N3] (2)
{
}
kreorg kp{1 + (kAz ⁄ kreorg)[N3]}
effect-corrected rate constant for protonation of the 1-position
26
of naphthalene (1.7 × 10-11 M-1 s-1
)
and a ratio of partial
(24) Richard, J. P.; Amyes, T. L.; Toteva, M. M.; Yukata, T. AdV. Phys.
Org. Chem. 2004, 39, 1–25.
(25) Richard, J. P. ref 2, pp 4-67.
9
J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008 17999

A R T I C L E S
Lawlor et al.
rate factors for tritium exchange at the 9-position of phenan-
threne27 and 1-position of naphthalene.28 From the derived value
of kA ) 5.0 × 10-11, we find Ka ) kp/kA ) 7.4 × 1020 and pKa
) -20.9 in aqueous solution at 25 °C, with an estimated error
of (0.5.
The consistency of these pKa and pKR values is confirmed
by the relationship pKa - pKR ) pKH2O implied in Scheme 1,
in which pKH2O is the (negative log of) the equilibrium constant
for hydration of the 9,10-double bond of phenanthrene. Com-
parison of the value pKa - pKR ) 9.3 with a value of pKH2O
)
9.2 estimated from the free energies of formation of phenan-
threne and phenanthrene hydrate19 shows good agreement.
Comparably good agreement is found between experimental and
estimated values of pKH2O for hydration of the 1,2-double bond
of naphthalene (13.7 and 14.2) and 9,10-hydration of anthracene
(7.5 and 7.4).
In so far as the rate constant kH can be measured with a
precision of a few percent the uncertainty in pKR should be
controlled by uncertainty in the magnitude of the rate constant
for azide trapping (ca. (0.2 log units) and kp/kH2O ((0.1 log
units). In principle pKa is subject to greater uncertainty because
of extrapolation and interpolation involved in determining kA.
However, this is mitigated in some degree by good agreement
between experimental and estimated values of pKH2O. This
suggests (0.4 log units as the likely error for pKa.
Figure 2. Plot of logs of rate constants for deprotonation of carbocations
against pKa in aqueous solution at 25 °C: filled circles, arenonium ions;
open circles, secondary benzylic cations; squares, tertiary cations. The
correlation line has a slope of -0.41, changing to zero as relaxation of the
solvent becomes rate-determining. The dashed line intersects the correlation
line at the pKa of the benzenonium ion (see text).
listed in Tables 1-3. The carbocations include arenonium
ions10,11,13-17 and cyclic and noncyclic secondary5,30 and
tertiary,5,9,31 usually benzylic, carbocations. The line drawn in
the figure is based only on the arenonium ions, which are shown
as filled circles. Measurements for the latter come from azide
trapping of cations derived from protonation of naphthalene,10,11
1-methylnaphthalene,32 anthracene,11 phenanthrene, or benzo-
furan11 and direct measurements of rate and equilibrium
constants for more stable multiply substituted methyl-,15,33
methoxy-, or hydroxy-benzenonium ions13,14,34 and protonated
azulenes.16,35-37 The line has slope -0.41 except at strongly
negative pKa values where the relaxation of water becomes rate
controlling.
Benzenonium and 1-Naphthalenonium Ions. Attempts to trap
the benzenonium ion with azide ion following the procedure
used by Pirinccioglu and Thibblin for the naphthalenonium ion10
were unsuccessful. This must be partly because deprotonation
of the ion is sufficiently fast that only a small amount of trapping
occurs even at high azide concentrations. Thus if the rate
constant of 9 × 1010 M-1 s-1 derived below is correct and the
azide trapping is diffusion controlled with rate constant 5 ×
109 M-1 s-1 (which indeed is probably not the case), only 7%
trapping would be observed at a 1 M concentration of NaN3.
Moreover, McClelland has shown that the azide-trapped product
from the structurally related dimethyl derivative of the 3-phenyl
substituted benzenonium ion 7 solvolyzes with a half-life of 5
min.29 If our estimate below that 1 is 10 times more stable than
7 is correct the half-life of the trapped azide (8, X ) N3) would
be significantly less than this and would not be detectable by
an HPLC method which at best takes several minutes per sample
for analysis. Trapping of 7 was possible because the dimethy-
lation precludes deprotonation as a reaction path and although
solvolysis of the azide derivative is rapid the hydrate formed
as the product of solvolysis (8, X ) OH) exists in equilibrium
with the azide.29 The possibility of monitoring trapping of the
benzenonium ion by UV under kinetic control, as proved
effective in the case of the anthracenonium ion,11 is precluded
by the high absorption of azide ions and the much higher
concentrations required for trapping in the case of benzenonium
than anthracenonium ions.
Measurements for carbocations other than arenonium ions
are based on azide trapping.5,7,25,30 However, because reaction
of the carbocation normally yields exclusively an alcohol as
product the trapping leads to values of kH2O for nucleophilic
reaction with water but not kp for deprotonation. Combination
of kH2O with measurement of the rate constant kH for acid-
catalyzed conversion of the alcohol to the carbocation then yields
a value of pKR. The value of kH is obtained from racemisation
or oxygen isotope exchange of the alcohol or by Richard’s
method7 of combining rate constants measured in water-tri-
fluoroethanol (TFE) mixtures with a measurement of the
partitioning of the carbocation between alcohol and trifluoroethyl
(26) Cox, R. A. J. Phys. Org. Chem. 1991, 4, 233–241.
(27) Bancroft, K. C. C.; Bott, R. W.; Eaborn, C. J. Chem. Soc. Perkin
Trans. 2 1972, 95–97.
(28) Eaborn, C.; Golborn, P.; Spillett, R. E.; Taylor, R. J. Chem. Soc. B
1968, 1112–1123.
(29) McClelland, R. A.; Ren, D.; Ghobrial, D.; Gadosy, T. A. J. Chem.
Soc. Perkin Trans. 2 1997, 451–456.
(30) Fujio, M.; Keeffe, J. R.; More O’Ferrall, R. A.; O’Donoghue, A. C.
J. Am. Chem. Soc. 2004, 126, 9982–9992.
(31) Gold, V.; Gruen, L. C. J. Chem. Soc. B 1966, 600–603.
(32) Jia, Z. S.; Thibblin, A. J. Chem. Soc. Perkin Trans. 2 2001, 247–251.
(33) Adsetts, J. R.; Gold, V. J. Chem. Soc. B 1969, 950–956.
(34) Kresge, A. J.; Chiang, Y.; Sato, Y. J. Am. Chem. Soc. 1967, 89, 4411–
4424.
The pKa of the benzenoniumion, nevertheless, can be inferred
from a correlation of rate constants (kp) for deprotonation of
carbocations with their pKa values shown in Figure 2. Rate
constants and equilibrium constants included in the figure are
9
18000 J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008

Arenonium Ions in Aqueous Media
A R T I C L E S
Table 1. Rate Constants and Equilibrium Constants for Formation and Reaction of Carbocations in Aqueous Solution at 25 °C
a Rate constant for H3O+-catalyzed conversion of alcohol or aromatic hydrate to carbocation. b Rate constant for reaction of the carbocation with
c
water. Rate constant for protonation of a π-bond by H3O+ to give indicated carbocation. d Rate constant for deprotonation of carbocation by water.
e KR ) [ROH][H+]/[R+]. f Equilibrium constant for addition of H2O to the carbon-carbon double bond of conjugate base of carbocation. g Mea-
surements in 50:50 (v/v) TFE-H2O mixtures.
Table 2. Rate and Equilibrium Constants for Formation and Reaction of Carbocations in Water or 50:50 Trifluoroethanol Water Mixtures at
25 °Ca
a The t-butyl cation is in water, refs 5 and 30. The measurements for all other cations refer to 50% v/v TFE-H2O mixtures, ref 5. b Rate constant for
H3O+-catalyzed conversion of alcohol or aromatic hydrate to carbocation. c Rate constant for reaction of the carbocation with water. d Rate constant for
protonation of a <116>-bond by H3O+ to give indicated carbocation. e Rate constant for deprotonation of carbocation by water. f KR ) [ROH][H+]/
[R+]. g Equilibrium constant for addition of H2O to the carbon-carbon double bond of conjugate base of carbocation.
ether. If necessary kH may be extrapolated from the mixed
solvent to water,30 or azide trapping may be carried out in the
mixed solvent. The results for the cations in Tables 1 and 2
refer to water, whereas those for the tertiary cations in Table 3
are mainly for TFE-water mixtures.
The value of pKR ) log(kH/kH2O) so determined may be
5,11
combined with a measured or estimated value of pKH2O
for
the alkene corresponding to the conjugate base of the car-
bocation to provide pKa.5 This in turn can be combined with
a rate constant kA for hydration of the alkene, for which
9
J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008 18001

A R T I C L E S
Lawlor et al.
Table 3. Rate and Equilibrium Constants for Protonation of Methyl-, Methoxy-, and Hydroxy-Substituted Benzenes and Azulenes in Aqueous
Solution at 25 °C
a Rate constant for H3O+-catalyzed exchange of tritium from tritium-labelled substrate, except as indicated. b Rate constant for incorporation from
tritiated acid solutions, TH2O+/THO. c Isotope effect for partitioning arenonium intermediate. d Based on estimated value of kH/kD ) 4.8 (see text).
protonation of the alkene is normally the rate-determining
step. Finally the rate constant kp is obtained from the
relationship pKa ) log(kA/kp).
and kreorg are the rate constants for deprotonation and relaxation,
respectively. The rate expression based on this scheme is shown
in eq 5 and the line drawn through the points in Figure 2
represents a best fit to this expression with kreorg ) 1011 s-1 and
an optimized linear dependence of log kp upon pKa (log kp )
-0.41pKa + 1.51).
For the correlation in Figure 2, rate and equilibrium constants
have been corrected for statistical factors. Because kp most
commonly refers to proton abstraction from a methylene group
no correction is made for the symmetry number 2 but rate
constants for proton transfer from a CH3 group are divided by
1.5 and from (CH3)3C+ by 4.5. The rate constants kA (and hence
the equilibrium constants Ka) are corrected for the number of
equivalent positions for protonation, but without correction for
the two faces of a double bond. Thus the symmetry correction
for protonation of benzene is 1/6 and for protonation of a
symmetrical alkene 1/2.
As indicated above, the correlation line in Figure 2 refers
only to arenonium ions. Inclusion of a wider range of structures
leads to significant scatter. However, this scatter appears to be
systematic rather than random in character. Thus, negative
deviations from the plot are associated with delocalization of
carbocationic charge to an oxygen atom; positive deviations
occur for tertiary cations, shown as squares. Further structures
lead to similar systematic deviations (e.g., positive for vinyl
ethers,38 negative for enols or enolate anions39,40) but there is
no obvious increase in scatter or change in average slope.
Within the precision of the data, the correlation of arenonium
ions is linear, except at the most negative pKa values. At high
reactivities and negative pKa values, however, a best fit is
expected to show curvature as a consequence of the deproto-
nation rate approaching a limit of 1011 s-1 for the rotational
relaxation rate of water.24,41 The calculated correlation line is
based on Richard’s analysis of the protonation of enolate and
related carbanions.12 Applied to the deprotonation of arenonium
ions it leads to the reaction scheme shown in eq 4 in which kp
kreorg
kp
ROH + H+ f R+·H2O y z H2O·R+ 98 Arene
(4)
kreorg
kobs)kreorgkp⁄(kp+kreorg)
(5)
A pKa for protonated benzene may be obtained from Figure
2 by combining the measured rate constant for protonation of
benzene by H3O+, based on measurements of hydrogen isotope
exchange (kA ) 2.6 × 10-14 M-1 s-1),26 with the simple
relationship between rate and equilibrium constants, Ka ) kp/
kA. Substituting for kA and taking logs gives pKa ) -log kp -
14.36. This expression is represented in Figure 2 by the dashed
line of slope -1, which intercepts the log kp - pKa correlation
line at kp ) 9 × 1010 and pKa ) -24.5 (after statistical correction
of kA by 1/6). These are the values for protonated benzene.
A similar analysis may be used to obtain a pKa for 2-proto-
nated naphthalene, for which log kA ) -12.38 ( 0.33.26 This
leads to kp ) 6.5 × 1010 and pKa ) -22.5 (after statistical
correction of kA by 1/4). It may be noted that these high values
of kp imply a near absence of a primary isotope effect on isotope
exchange reactions. The fact that in practice the reactions do
show moderate isotope effects26 is a consequence of the mea-
surements being made in concentrated acid solutions in which
the effective basicity of water, and hence the rate of proton
transfer, is significantly less than in pure aqueous or dilute acid
solutions.
Nucleophilic Reactions of Cations with Water. As described
below, values of pKa for benzenonium and naphthalenonium
ions may be combined with pKH2O, the equilibrium constant
for 1,2 addition of water across a double bond of the aromatic
molecule,19 to obtain values of pKR ) pKH2O - pKa for
hydrolysis of the ions. From pKR we may then derive a rate
constant kH2O for nucleophilic reaction of the ion with water.
Rate constants for the acid-catalyzed dehydration of the
products of hydrolysis, namely the hydrates of benzene and
naphthalene, 2 and 9, have been reported previously.17 These
correspond to the rate constants for rate-determining conversion
of the hydrates to carbocations because the exceptional stability
(35) Thomas, R. J.; Long, F. A. J. Am. Chem. Soc. 1964, 86, 4770–4773.
(36) Schulze, J.; Long, F. A. J. Am. Chem. Soc. 1964, 86, 331–335.
(37) Longridge, J. L.; Long, F. A. J. Am. Chem. Soc. 1966, 88, 1293–
1297.
(38) Richard, J. P.; Williams, K. B. J. Am. Chem. Soc. 2007, 129, 6952–
6961.
(39) Chiang, Y., Jr.; Kresge, A. J. J. Am. Chem. Soc. 1994, 116, 8358–
8359. Chiang, Y.; Kresge, A. J.; Santaballa, J. A.; Wirz, J. J. Am.
Chem. Soc. 1988, 110, 5506–5510.
(40) Keeffe, J. R.; Kresge, A. J.; Schepp, N. P. J. Am. Chem. Soc. 1990,
112, 4862–4868.
(41) Kaatze, U.; Pottel, R.; Schumacher, A. J. Phys. Chem. 1992, 96, 6017–
6020.
9
18002 J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008

Arenonium Ions in Aqueous Media
A R T I C L E S
Scheme 4
Aside from these deviations, the linearity of the correlation
line in Figure 2 outside the high reactivity limit is at first
surprising. It can be attributed to modification of the ‘normal’
Marcus curvature, associated with a decrease in barrier to
reaction arising from increased thermodynamic driving force,
by a compensating effect of an increase in intrinsic barrier (i.e.,
barrier to a thermoneutral reaction).42 This compensation has
been discussed by Richard for the formation of enolate anions.43
The increase (in intrinsic barrier) arises from a decrease in
resonance stabilization of a reactant or increase in resonance
stabilization of a product.44,45 In the present instance both
possibilities are likely43 because the carbocation reactant and
aromatic product are subject to extensive π-delocalization. It
should be noted that, in addition to the compensation for Marcus
curvature, the deviations from the correlation in Figure 2 can
be attributed to variations in intrinsic barrier.
of the aromatic product renders deprotonation of the carboca-
tions extremely fast as shown above. The rate constants kH2O
for nucleophilic attack of water on the benzenonium ion and
naphthalenonium ion to form the hydrates 2 or 9 can neverthe-
less be derived from the relationship KR ) kH2O/kH.
An objective of this paper is to examine relative reactivities
of carbocations toward deprotonation and nucleophilic attack
by water. It is for this reason that values of kH2O are listed
together with kp in Tables 1 and 2. As discussed below,
partitioning of the carbocations may be expressed as log(kp/
kH2O), and is then well correlated by the equilibrium constant
for hydration of the arene or alkene product arising from
The rate constant kp ) 3.7 × 1010 for the phenanthrenonium
ion determimned in this work represents an important point on
the correlation because of its close approach to the limit for
rotational relaxation of water. It slightly exceeds the value of
1.6 × 1010 measured by Pirinccioglu and Thibblin for naph-
thalene protonated at the 1-position.10 A limiting rate constant
(1011 s-1) has been incorporated into the plot reflecting a change
in rate-limiting step from deprotonation to solvent relaxation,
and this leads to curvature of the plot, and eventually a lack of
dependence of kp on pKa for sufficiently acidic arenonium ions.
Although kp for the benzenonium ion cannot be measured
experimentally its value appears to be so close to the relaxation
limit as to be accurately determinable. Because the rate constant
available for benzene is that for protonation (kA ) 4.4 × 10-15
for a single carbon)26 we make use of the relationship Ka )
kp/kA to derive a value of kp ) 9 × 1010 s-1 and pKa ) -24
from the intersection of the line log kp ) log kA - pKa (shown
as the dashed line) with the correlation line in the figure.
A value of pKa ) -24 for the benzenonium ion agrees
surprisingly well with pKa ) -23.5 estimated by Kresge from
oxygen substitutent effects on the stabilities of protonated
benzenes based on the pKa values in Table 2 and similar
measurements.13 It also agrees with that inferred by Marziano
(reading from her graph) from a correlation of rate constants
for hydrogen isotope exchange of aromatic molecules with pKa
values.15 Marziano’s method is similar to our own, but the most
acidic cation available to her was protonated mesitylene (pKa
) -12.7). Figure 2 contains measurements for a number of
more acidic cations including the phenanthrenonium ion (pKa
) -20.9) and takes account of the limit on the rate constant
represented by the relaxation of water. Moreover because of
this limit, extrapolations of kp, as in Figure 2, involve much
smaller changes in rate constant than extrapolations based on
rate constants for isotope exchange or protonation of the
aromatic molecules (kA) considered by Marziano. With respect
to the last point, we previously estimated kp ) 5 × 1010 s-1 for
the benzenonium ion on grounds that it must lie between 1.6 ×
19
deprotonation, pKH2O. Values of pKH2O are also included in
the table therefore and, for completion, rate constants kA and
kH and equilibrium constants pKR. The combined data provide
a comprehensive summary of rate and equilibrium constants
for a wide range of structures of carbocations reacting in aqueous
solution.
Discussion
The equilibrium constants pKa, pKR, and pKH2O for phenan-
threne protonated at the 9-carbon atom (4) are summarized in
the cycle of Scheme 4. The equilibria are represented by single
arrows to emphasize the relationship between equilibrium
constants implied by Hess’s law, i.e., pKH2O ) pKR - pKa. As
described above, generation of the phenanthrenonium ion by
solvolysis of the dichloroacetate precursor 5 in aqueous media
leads to competing deprotonation to form phenanthrene and
nucleophilic reaction to give the phenathrene hydrate 3. Ap-
plication of the azide clock method7,8 leads to rate constants
for both reactions and, by combination with values for the acid-
catalyzed reverse processes, to evaluation of all the equilibrium
constants shown in Scheme 4.
For protonated benzene trapping by azide ions is precluded
by the high rate of proton loss to form benzene and probable
rapid solvolysis of any small amounts of cyclohexadienyl azide
formed. Nevertheless, a deprotonation rate constant can be de-
rived from a correlation of logs of rate constants with pKa values
for deprotonation of other carbocations, especially arenonium
ions, combined with the assumption that these rate constants
are limited for highly acidic cations by the rate constant 1011
s-1 for rotational relaxation of water.5,9,41 This correlation is
shown in Figure 2. It includes a wide range of structures of
carbocations leading to a considerable scatter of points. How-
ever, the correlation is based on the filled circles representing
arenonium ions, which are secondary cyclic allylic or benzylic
cations. There are systematic deviations for tertiary carbocations,
shown as squares, which appear to yield a separate correlation
line and fall mainly above the line for the arenonium ions.
Secondary carbocations containing oxygen or other electroneg-
ative substituents conjugated with the charge center, fall below
the line.
1010 s-1 for the 1-protonated naphthalenonium ion and 1011s-1
.
This gave pKa ) -24.3. The correlation of Figure 2 suggests
that kp is significantly closer to its limiting value. However, the
revised pKa ) -24.5, differs from the earlier value by less than
the error of (0.26 log units estimated for the log of the rate
(42) Richard, J. P. Tetrahedron 1995, 51, 1535–1573.
(43) Amyes, T. L.; Richard, J. P. J. Am. Chem. Soc. 1996, 118, 3129–
3141.
(44) Bernasconi, C. F. AdV. Phys. Org. Chem. 1992, 27, 119–238.
(45) Kresge, A. J. Can. J. Chem. 1974, 52, 1897–1903.
9
J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008 18003

A R T I C L E S
Lawlor et al.
Chart 1. pKR Values of Carbocations
constant for the protonation of benzene kA.26 Since kp is so close
to 1011, the uncertainty in pKa corresponds to the combined
errors in log kA and the log of the relaxation limit.
Following the same procedure as for the benzenonium a pKa
) -22.5 may be estimated for the 2-protonated naphthale-
nonium ion. Again this is based on the rate constant kA for
protonation extrapolated by Cox from measurements of hydro-
gen isotope exchange.26
These pKa’s for the benzenonium and naphthalenonium ions
may be converted to hydrolysis constants pKR by calling upon
values of pKH2O ) 22.2 and 14.6, respectively, for the hydration
of benzene and naphthalene.19 From the relationship pKR ) pKa
+ pKH2O we then obtain pKR ) -2.3 for the benzenonium ion
and -8.0 for the 1-naphthalenonium ion.
Stabilities of Carbocations. For protonated benzene, naph-
thalene and phenathrene it is evident that pKR has a much
smaller negative value than pKa. This is because pKR is
influenced primarily by the stability of the carbocation, with
only limited interaction between the reacting OH group of the
alcohol (aromatic hydrate) and structural changes in the rest of
the molecule, whereas the pKa strongly reflects stabilization of
the double bond in the aromatic molecule. This is particularly
striking in the case of benzene for which pKa ) -24.5 and
pKR ) -2.3. The reasonableness of the value for pKR is
confirmed by comparison with pKR ) -3.5 for the 2,2-dimethyl-
4-phenyl benzenonium ion 7 measured by McClelland.46
The more negative pKa than pKR for the benzenonium ion is
also consistent with its reacting more readily with water as a
base than a nucleophile. The rate constant for nucleophilic
reaction with water can be estimated as kH2O ) 4.5 × 104 by
combining pKR with the rate constant for the reverse acid-
catalyzed formation of the carbocation from benzene hydrate,
kH ) 180.17 This is more than 106 times less than the rate
constant for deprototonation.
decreases pKR and hence the stability of the cations, whereas
for simple solvolysis reactions benzylic substrates are usually
more reactive than allylic.17 However, we defer discussion of
this question to a later paper.
Further comparisons of pKR values are shown in Chart 1.
Apart from the influence of benzoannellation they illustrate the
stabilizing effects of an endocyclic oxygen47 or π-bond, as well
as coordination by an Fe(CO)3 group.20 The low stability of
the fluorenyl cation48 is also apparent and, by contrast, the
stability conferred by addition of a methylene bridge11 to the
benzhydryl cation.23 The value of pKR ) -16.4 for the t-butyl
cation9 is included as a point of comparison. The pKR values
of -12.5 for the benzhydryl cation and -16.7 for the fluorenyl
cation are shown in brackets because they have been been
adjusted by subtracting 0.8 from the measured values in 50:50
TFE-H2O mixtures23 to allow a better comparison with the
other values in water.
Product Partitioning. The equilibrium constants pKa and pKR
offer a guide to relative rates of reaction of a carbocation with
water as a base and a nucleophile. This is indicated in Figure 3
in which the logs of ratios of rate constants for deprotonation
and nucleophilic attack kp/kH2O are plotted against pKR - pKa
) pKH2O. For the arenonium ions and other secondary carboca-
tions, which are shown as circles, a linear relationship is found
with slope 0.42. Positive deviations from the correlation occur
for tertiary carbocations shown as squares and are discussed
below.
It is noteworthy that the line in Figure 3 does not pass through
the origin. When pKa and pKR for a cation are equal (pKH2O
)
0) the reaction with water as a nucleophile is favored by 1500-
fold. This reflects a lower intrinsic barrier to the nucleophilic
reaction, previously noted by Richard.4,5,21 The lower barrier
probably arises because nucleophilic attack involves making of
a single (O-C) bond, whereas deprotonation involves making
and breaking of several bonds (O-H and C-H and a CdC
π-bond).44,49
It is noteworthy that while pKR varies significantly between
the benzenonium, naphthalenonium and phenanthrenonium ions,
from -2.3 to - 8.0 to -11.6, the pKa’s of these ion are rather
similar, -24.5, -22.5, and -20.9. This similarity is consistent
with the uniformly large rate constants for deprotonation which
fall in the range 1010-1011 s-1. However, in the light of the
very different stabilities of the aromatic products it is a first
The dashed line in the figure corresponds to log kp/kH2O ) 0
and thus kp ) kH2O. From the point of intersection of the plot
with this line, it is apparent that the pKa of a carbocation should
be seven or more units more negative than pKR for elimination
to be preferred over substitution. Since relative rates of de-
protonation and nucleophilic attack control the rate determining
step in the acid-catalyzed dehydration of alcohols (and reverse
hydration of alkenes) it is not surprising that proton transfer is
normally rate determining in these reactions. Only when the
surprising. That stability is reflected in the values of pKH2O
)
22.2, 14.6, and 9.3 for benzene, naphthalene and phenanthrene,
respectively. The reason for the uniformity of the pKa’s and
deprotonation rate constants is that it reflects compensation
between the stability of the product and the stability of the
carbocation as expressed in the relationship pKa ) pKR - pKH2O.
A question remains: why do the stabilities of the arenonium
cations vary as they do? It is clear that benzoannelation sharply
(47) Katritzky, A. R.; De Rosa, M.; Grzeskowiak, N. E. J. Chem. Soc.
Perkin Trans. 2 1984, 841–847.
(48) (a) Courtney, M. C.; MacCormack, A. C.; More O’Ferrall, R. A. J.
Phys. Org. Chem. 2002, 15, 529–539. (b) Jiao, H.; Schleyer, P. von
R.; McAllister, M. A.; Tidwell, T. T. J. Am. Chem. Soc. 1997, 119,
7075–7083. (c) Herndon, W. C.; Mills, N. S. J. Org. Chem. 2005, 70,
8492–8496.
(46) McClelland, R. A. Personal communication. The value of-3.5 from
direct measurement corrects a value of-5.3 based on the azide clock
reported earlier (ref 29).
(49) Dewar, M. J. S. J. Am. Chem. Soc. 1984, 106, 1361–1372.
9
18004 J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008

Arenonium Ions in Aqueous Media
A R T I C L E S
line corresponding to log kp/kH2O ) 0. It is noteworthy that there
is no pronounced negative deviation at the right-hand side of
the plot where the rate of deprotonation of the benzenonium
ion has reached its limit. However, this may be partly because
the line drawn through the points masks a tendency to curvature
for the more acidic protonated aromatic substrates.
Where nucleophilic and basic reactions of carbocations are
not limited by water relaxation the correlation of Figure 3
implies that their relative rates simply depend on the equilibrium
constant for hydration of the double bond, i.e., the relative
stabilities of the alkene or arene and alcohol or hydrate products.
In so far as an equilibrium constant for hydration is readily
estimated even when pKa and pKR are unknown,11 it is generally
easy to predict which will be the faster reaction or rate-
determining step. In an earlier paper20 the fact that the ben-
zenonium ion undergoes preferential deprotonation whereas its
Fe(CO)3 complex is subject to substitution finds a straightfor-
ward explanation. An MP2 calculation of an equilibrium
constant for hydration of the Fe(CO)3 coordinated benzene
formed by deprotonation of the coordinated benzenonium ion
yields a value of pKH2O ≈ -4.50 This value compares with pKH2O
) 22.2 for benzene. Not only does it imply that the coordinated
hydrate is thermodynamically more stable than coordinated
benzene but that nucleophilic attack of water is much faster
Figure 3. Plot of logs of kp/kH2O for secondary (O) and tertiary (0)
carbocations against pKH2O for hydration of the alkene conjugate base
correlated by a best straight line log(kp/kH2O) ) 0.46pKH2O - 3.7.
double bond of the product is unusually stabilized, e.g., by
forming part of an aromatic system is carbocation formation
rate-determining.
The simplest interpretation of the linearity of the correlation
is that it represents a combination of free energy relationships
between log kp and pKa on the one hand and log kH2O and pKR
on the other, as represented in eqs 6 and 7.
than deprotonation. According to Figure 3 we can expect kH2O
/
kp ≈ 104.
Summary. Measurements of rate and equilibrium constants
give kp ) 3.7 × 1010 s-1 and pKa ) - 20.9 for deprotonation
of the phenanthrenonium ion in water at 25 °C. They help anchor
a correlation between log kp and pKa for a range of protonated
aromatic molecules, taking account of the limit for kp set by
the rotational relaxation of the solvent (1011 s-1). From this
correlation, pKa’s for protonated benzene and naphthalene are
inferred. Combining these with equilibrium constants pKH2O for
addition of water to a double bond of the aromatic molecule
furnishes hydrolysis constants pKR. In contrast to pKa, pKR
measures the stability of the arenonium ion independently of
that of the aromatic molecule. In particular, pKR ) -2.3 for
protonated benzene shows that it is a relatively stable carboca-
tion. Values of pKH2O are also useful in predicting (a) ratios of
rate constants kp/kH2O for partitioning of carbocations between
reactions with water as a base and a nucleophile and (b) the
rate-determing step in a dehydration reaction.
log kp)-mapKa+ca
(6)
(7)
log kH2O)-mRpKR+cR
The correlation of log kp with pKa is illustrated in Figure 2
of this paper. That between log kH2O and pKR has been
considered by McClelland who found linear correlations with
only limited scatter for structurally homogeneous families of
carbocations, such as diarylmethyl, triarylmethyl or aryldi-
methoxy.3 Equations 6 and 7 can be combined as log(kp/kH2O
)
) m(pKR - pKa) + c, provided that the slopes of the individual
plots ma and mR are equal. This indeed seems to be the case.
The slope of the plot in Figure 2 is -0.41 and that in Figure 3
is 0.46. The slopes of McClelland’s plots fall between -0.68
and -0.54. However, McClelland studied tertiary or diaryl-
methyl cations whereas our cations are secondary benzylic or
allylic. A plot of log kH2O against pKR for the secondary cations
of Figures 2 and 3 gives the lower slope of -0.44 (Figure S1).
A steeper slope for tertiary than secondary cations is also
characteristic of a correlation of log kp with pKa, as indicated
by the squares in Figure 1, for which the slope is -0.62.
It may be noted that there is a mild inconsistency between
the correlations of secondary cations in that the slope of 0.46
in Figure 3 is greater than the (negative) slopes of its ‘constitu-
ent’ correlations of log kp and log kH2O (-0.41 and -0.44). This
difference is removed by restricting all three correlations to a
common set of structures.
The simplest interpretation of the larger deviations of tertiary
carbocations (squares) from the correlation of Figure 3 is that
these represent nucleophilic reactions at or close to the limit
set by solvent relaxation. This is true of the tertiary butyl cation
for which the rate constant for deprotonation, kp ) 8 × 108 s-1
is still short of this limit. Clearly if kp continues to increase
with increasing instability of the cation while kH2O remains
constant kp/kH2O will increase. In the limit that both kp and kH2O
achieve their limiting values the point should fall on the dashed
Experimental Section
Instruments, Synthesis, Analytical Methods. 1H and 13C NMR
spectra were measured on Varian 300 and 500 (Unity) MHz NMR
spectrometers. UV-vis spectra and kinetic measurements were
recorded on a Cary 50 spectrophotometer equipped with an auto-
matic cell changer thermostatted at 25 ( 0.1 °C. HPLC measure-
ments were made with a Waters 600 HPLC system with dual
wavelength absorbance detection.
Phenanthrene hydrate (1-hydroxy-1,2-dihydrophenanthrene, 3)
was prepared by epoxidation of phenanthrene22 and reduction of
the resulting 9,10-phenanthrene oxide with LiAlH4, as described
previously.17 Its dichloracetoxy ester derivative, 9-dichloroacetoxy-
1,2-dihydrophenanthrene (5) was prepared by adding dichloroacetyl
chloride (0.90 g) to an ice-cold stirred solution of the hydrate (0.10
g) in 10 mL of anhydrous dichloromethane containing 0.10 mL of
pyridine. The solution was allowed to warm to room temperature
and after two hours was quenched with 10 mL of saturated aqueous
sodium bicarbonate. The organic layer was separated and washed
(50) Guthrie, J. P. Unpublished result.
9
J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008 18005

A R T I C L E S
Lawlor et al.
with with water (3 × 20 mL), dried over sodium sulfate and the
the rate constant for dehydration, 3.40 × 10-3 M-1 s-1, we then
solvent removed under reduced pressure. The crude product was
obtain kH ) 3.5 × 10-3 M-1 s-1
.
1
triturated with cyclohexane to give a brown oil (0.15 g, 95%); H
Trapping of the Phenanthrenonium Ion by Azide Ions. In
principle the value of kH may be combined with that of kH2O to
obtain KR ) kH2O/kH. Normally, kH2O would be obtained from
solvolysis of the dichoroacetate ester 5 in the presence of azide
ions and measurement of the ratio of azide-trapped product RN3
(9-azido-9,10-dihydrophenanthrene) and phenanthrene hydrate (ROH).
From the relationship [RN3]/[ROH] ) kAz[N3-]/kH2O, a value of
kH2O would then be obtained by assigning the value of kAz for
reaction of the carbocation with azide ion as 5 × 109 M-1 s-1, the
rate constant for diffusion controlled reaction of oppositely charged
ions in water. In practice, the ratio of azide to hydrate product,
which should depend linearly upon the concentration of azide ions,
is influenced by formation of excessive amounts of hydrate product
which leads to downward curvature of a plot of [RN3]/[ROH] at
high concentrations of azide ions. This behavior is understandable
if hydrolysis of the ester to form the hydrate without intervention
of the carbocation is catalyzed by azide ions acting as a nucleophilic
or general base catalyst.30,54
Rather than kAz/kH2O therefore the rate constant ratio kAz/kp was
determined by plotting [RN3]/[phenanthrene] against [N3-]. Mea-
surements of product ratios by HPLC are listed in Table S1 and
plots of product ratios against azide concentration similar to that
in Figure 1 gave slopes 0.150, 0.156, and 0.21 in 50%, 60%, and
74% aqueous acetonitrile, respectively. The measurements in 74%
water showed considerable scatter reflecting the insolubility of
phenanthrene and consequently low concentrations of products
analyzed. The slope in 74% H2O was disregarded therefore and
the other two values extrapolated to water on the assumption that
the slope of a plot of log kp against % acetonitrile had a slope of
0.14, as found for kH2O for the reaction of benzhydryl cations with
water by McClelland.8 This implies that the variation in kH2O with
solvent composition is opposite to that found here for 50% and
60% water. However, the discrepancy is small and again probably
a symptom of the poor solubility of phenanthrene in the more
aqueous solvent mixture. The extrapolated value of kaz/kp was 0.135
with a likely error of (0.015 (equivalent to (0.06 in derived pK’s).
From kp ) 5 × 109/0.135 ) 3.7 × 1010 and kp/kH2O ) 25 we then
obtain kH2O ) 1.5 × 109 M-1 s-1. Combining kH2O with kH ) 3.5
× 10-3 M-1 s-1 gives KR ) kH2O/kH ) 4.3 × 1011 and pKR ) -11.6.
The ionization constant Ka for the phenanthrenonium ion may
be obtained by combining kp with the rate constant kA for
protonation of phenanthrene. An approximate value for this rate
constant may be derived from the comparison of the partial rate
factor for hydrogen isotope exchange of 9-tritiated phenanthrene
at 70 °C in trifluoroacetic acid (1610)27 with that of 1-tritionaph-
thalene (1160).28 The isotope-corrected rate constant for protonation
of 1-tritionaphthalene in dilute aqueous sulfuric acid at 25 °C has
(300 MHz, CDCl3): δ 3.24 (2H, d, J9,10 ) 4.7 Hz, H10), 5.79 (1H,
s, CHCl2), 6.14 (1H, t, J9,10 ) 4.5 Hz, H9), 7.25-7.87 (8H, m).
Solvents used for kinetic measurements comprised distilled water
or water mixed with HPLC grade acetonitrile. In a typical mea-
surement 20 µL of a stock solution of substrate in acetonitrile (2
× 10-3-10-2 M) was injected into 2 mL of aqueous acid or aqueous
acetonitrile in a silica cuvette. Reactions were initially surveyed
by repetitive scans of UV-vis spectra and then monitored at a single
wavelength.
HPLC measurements were used for product analysis and moni-
toring of kinetics where products trapped by azide ions were formed.
Solvolysis of the dichloroacetate ester of phenanthrene hydrate (5)
was initiated by injecting 25-30 µL of a stock solution of substrate
into 0.25-0.5 mL of an acetonitrile-water mixture. Samples of
25 µL from the reaction were quenched in 500 µL of acetonitrile,
which inhibited further solvolysis on the time scale of the analyses.
Analyses were carried out by injection of 10 µL of this solution
onto a Hichrome-5 C18 reverse phase column with aqueous
acetonitrile as the mobile phase and a flow rate of 1 mL/min. Peaks
for the ester reactant and the phenathrene and phenanthrene hydrate
(3) products were identified by comparison of their retention times
with those of known samples. When the solvolyses were carried
out in the presence of sodium azide a new peak appeared which
was identified as 9-azidophenanthrene from the dependence of its
intensity on the concentration of azide ions, the identity of its rate
of appearance with that of other products and its retention time
relative to that of the phenanthrene and phenanthrene hydrate (0.7
and 1.8) as compared with retention times for other azide-alcohol-
hydrocarbon combinations.7,11,23
Kinetic and Product Analyses. A rate constant for dehydration
of phenanthrene hydrate had been determined previously as 3.40
× 10-3M-1s-1
.
17 To derive kH for carbocation formation this must
be corrected for reversibility by measuring partitioning of the
solvolytically generated carbocation between hydration and dehy-
dration products under conditions that these are not equilibrated.
The fraction of hydrate formed from solvolysis of ester derivatives
of phenanthrene hydrates was previously estimated as ca. 15% from
UV measurements.17 However, considerably more accurate values
can be obtained by HPLC. Care must also be taken that part of the
hydrate product does not come from hydrolysis of the ester function
of the reactant, the contribution of which can be minimized by
addition of a small amount of HCl (10-3M) to the reacting solutions.
The solvolysis of 1-dichloroacetoxy-1,2-dihydronaphthalene in
aqueous acetonitrile to form predominantly phenanthrene was
monitored from an increase in absorbance at 250 nm; it gave rate
constants 1.30, 4.13, and 16.3 × 10-4 s-1 in 50%, 60%, and 74%
(v/v) aqueous acetonitrile respectively. The ratios of phenanthrene/
hydrate in the same solutions were determined as 24, 25, and 25,
respectively. In the absence of HCl the corresponding values were
20, 21, and 16. An estimate of the contribution of uncatalysed
hydrolysis based on the measured rate constant51,52 for hydrolysis
of CH3CH2COOCHCl2 and expected effect of a phenanthryl
substituent (modeled as PhCHCH2Ph with σ* ≈ 0.3)53 indicated
that this hydrolysis is very much slower than the observed rate of
solvolysis. The lack of dependence of kp/kH2O on the composition
of acetonitrile-water mixtures is consistent with a similar finding
for the anthracenonium ion.17
been extrapolated from measurements in concentrated acid solutions
26
as 1.7 × 10-11 M-1 s-1
.
If we assume that the exchange rate
constants in trifluoroacetic acid show an Arrhenius dependence on
temperature and differ only in activation energy we can derive a
ratio of partial rate factors in trifluoroacetic acid at 25 °C as 1.46.
If this ratio is unaffected by the change from trifluoroacetic acid to
water as solvent, and the isotope effects for the two substrates
(which have almost the same reactivity) are the same, then kA for
the protonation of phenanthrene is derived as 2 × 1.46 × 1.7 ×
10-11 ) 5.0 × 10-11 (where the factor of 2 takes account of
equivalence of the 9- and 10-positions). We then find Ka ) kp/kA
) 7.4 × 1020 and pKa ) -20.9.
The rate constant for dehydration of phenanthrene hydrate
corresponds to kH/(1 + kp/kH2O) as implied in Scheme 2. The ratio
kp/kH2O is given by the ratio phenanthrene to phenanthrene hydrate
products in the solvolysis reaction, which was taken as 25. From
The values of kA and kH can be combined with an equilibrium
constant KH2O for hydration of phenanthrene to give an independent
check on the value of kp/kH20. The equilibrium constant KH2O can
be written as a quotient of rate constants kAkH2O/kHkp as implied in
Scheme 2 (from which, however, kA is missing). A value for KH2O
) 6 × 10-10 can be derived from free energies of formation of
(51) Jencks, W. P.; Carriulo, J. J. Am. Chem. Soc. 1961, 83, 1743–1750.
(52) Eutranto, E. K.; Cleve, N. J. Acta Chem. ScandanaVica 1963, 17, 1584–
1594.
(53) Williams A. Free Energy Relationships in Organic and Bioorganic
Chemistry; Royal Society of Chemistry: Cambridge, 2003.
(54) Jencks, W. P.; Carriulo, J. J. Am. Chem. Soc. 1960, 82, 1778–1785.
9
18006 J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008

Arenonium Ions in Aqueous Media
A R T I C L E S
phenanthrene and phenanthrene hydrate in aqueous solution if the
latter value is estimated from the expected effect of a 9-hydroxyl
substituent on the free energy of formation of 9,10-dihydrophenan-
threne.20 From the relationship kp/kH2O ) kA/kHKH2O we then obtain
from the values of kA, kH, and KH2O, kp/kH2O ) 24. This is in
fortuitously good agreement with the value of 25 derived from
measurements of phenanthrene/hydrate product ratios.
Treatment of Literature Data. Most of the data taken from
the literature and listed in Tables 1-3 were used without modifica-
tion. However, kinetic and equilibrium measurements for the oxygen
substituted benzenonium ions in Table 3 were re-extrapolated from
strongly acidic media to dilute aqueous solutions using the
formalism of Cox and Yates.55 This led to small changes in the
values.
The kinetic measurements for all the substrates in Table 3 refer
to hydrogen exchange of a tritium-labeled aromatic molecule (Ar-
T). As shown in the reaction of eq 8 and derived kinetic expression
of eq 9, to obtain the rate constant for protonation of the substrate
(kA) the measured rate constant kxT must be corrected for an isotope
effect (kH/kT) from partitioning of the arenonium ion intermediate
(ArTH+). Moreover, as indicated by the superscript T, the derived
value of TkA must also be corrected for a secondary tritium isotope
effect.
was used. Use of a common value is justified by the relatively mild
dependence of isotope effects on reactivity and the fact that an error
of a factor of 2 would fall within the range of scatter observed for
the different substrates in the correlation of Figure 2. For mesitylene,
for which an isotope effect measurement was also lacking, a primary
isotope effect (kH/kD ) 4.8) was inferred from a rough correlation
of isotope effects with reactivity recorded by Cox.17 Derivation of
kH/kT from the measured rate constant for uptake of tritium from
the solvent required assignments of fractionation factors l ) 0.691.442
for tritium in H2TO+ and φ ) 1.11.442 for tritium in the protonated
intermediate (ArTH+), where the coefficient 1.442 is the exponent
of the Swain-Schaad relationship relating deuterium and tritium
isotope effects.56 For all substrates studied the secondary isotope
effect on kA was taken as the value measured for trimethoxybenzene,
HkA/TkA ) 1.15.57
Acknowledgment. This work was supported by The Science
Foundation Ireland (Grant No. 04/IN3/B581).
Supporting Information Available: Table S1 listing data from
product analyses based on trapping experiments following
solvolysis of ester 5 in aqueous acetonitrile-water mixtures
containing sodium azide; Figure S1 showing a plot of logkH2O
against pKR for carbocations in Tables 1 and 2. This material is
available free of charge via the Internet at http://pubs.acs.org.
JA806899D
Tk
A
kx )
(9)
1 + kH ⁄ kT
(55) (a) Cox, R. A. AdV. Phys. Org. Chem. 2000, 35, 1–66. (b) Bagno, A.;
Scorrano, G.; More O’Ferrall, R. A. ReV. Chem. Intermed. 1987, 7,
313.
(56) Kresge, A. J.; More O’Ferrall, R. A.; Powell, M. F. Isotopes in Organic
Chemistry; Elsevier: Amsterdam, 1987; Vol. 7, pp 177-272.
(57) Kresge, A. J.; Chiang, Y. J. Am. Chem. Soc. 1967, 89, 4411–4417.
Values of kH/kT are listed in Table 3. The values are quite large
because they correspond to a primary tritium isotope effect amplified
by a secondary effect. For the methoxy and hydroxybenzenes a
common value of kH/kT ) 20.3 measured for trimethoxybenzene
9
J. AM. CHEM. SOC. VOL. 130, NO. 52, 2008 18007