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Can. J. Chem. Vol. 78, 2000
in the normal direction (kH/kD > 1) generated by solvation of
the hydroxide ion being formed in this reaction (25). Strong
isotope effects consistent with this expectation have in fact
been observed for such reactions in other systems, e.g.,
kH/kD = 7.5 for hydron transfer from water to the β-carbon
atom of isobutyrophenone enolate ion (26), kH/kD = 6.5 to
9.1 for the corresponding reactions of a series of ynolate
ions (12), and kH/kD = 7.1 for that of the enolate dianion of
fluorene-9-carboxylic acid (16). The present isotope effects
therefore argue against an electrophilic mechanism for
uncatalyzed ketene hydration.
These isotope effects, on the other hand, are consistent
with a nucleophilic mechanism. The simplest variant of such
a mechanism would involve a single water molecule and
give a zwitterionic product, as shown in eq. [7]. Since no
bonds to isotopically substituted hydrogen are broken or
made in this process, there would be no primary component
in the isotope effect on such a process. There would, how-
ever, be two secondary components: one produced by solva-
tion of the negative charge being generated on the ketene
oxygen atom and another produced by the change from neu-
tral to positively-charged oxygen-hydrogen bonds in the at-
tacking water molecule. The maximum value of the latter
secondary component can be estimated as 1/ᐉ2, where
ᐉ(= 0.69) is the fractionation factor for a fully positively
the rate-determining reaction coordinate, and there is, there-
fore, no primary isotope effect (29). Even in situations
where proton transfer is isolated and the only heavy-atom
motion is diffusional encounter of proton donor and acceptor
or separation of proton transfer products, proton transfer is
not fully rate-determining and solvent isotope effects are
small (30). Cyclic ketene hydration mechanisms avoiding
zwitterionic products are therefore likely to show small, if
any, primary isotope effects. Neutralization of the zwitteri-
onic charge, moreover, will diminish the secondary effects
produced by charge generation as described above, and the
overall solvent isotope effects will be small, just like those
for the zwitterionic mechanism. Small isotope effects should
therefore be characteristic of uncatalyzed ketene hydration
proceeding by nucleophilic attack of water on the ketene
carbonyl carbon atom, no matter what the detailed reaction
mechanism is.
Acknowledgements
We wish to thank Professor S. D. Christian for his gener-
osity in providing us with a computer program that performs
linear least squares analysis on data with both dependent and
independent variables subject to error. We are also grateful
to the Natural Sciences and Engineering Research Council
of Canada for financial support of this work.
charged oxgyen-hydrogen bond (25b). This gives (kH/kD)max
=
2.1. It is more difficult to estimate the other one of these sec-
ondary isotope effect components because, although it is
known that a fully negatively charged oxygen atom, such as
that in the hydroxide ion, is solvated by three water mole-
cules whose solvating oxygen-hydrogen bonds have fraction-
ation factors φ 0.7 (25), the negative charge in this case is
partly delocalized into the ketene double bond and the rest
of the molecule. It is likely, however, that this secondary
component can contribute as much as another factor of two,
raising the overall maximum value to kH/kD = 4 and easily
accommodating the range of isotope effects listed in Table 1.
In addition to the reaction mechanism of [eq.] 7 giving a
zwitterionic product, other nucleophilic mechanisms may be
written in which the zwitterion is avoided by proton transfer
from the attacking water to the ketene oxygen atom through
a cyclic array of several intervening water molecules. Such
mechanisms are favored by ab initio calculations (27) and
there is evidence that the hydration of ketenes in organic sol-
vents involves more than one water molecule (28), although,
of course, in purely aqueous solution the reaction order in
water cannot be determined. At any rate, protons are trans-
ferred in such mechanisms, but it is unlikely that this will
add much of a primary component to the overall isotope ef-
fect. In a proton transfer such as this, where the transfer is
between electronegative atoms and is accompanied by
heavy-atom reorganization, protonic and heavy-atom motion
appear to be uncoupled, with proton transfer taking place in
a rapid step either before or after the heavy-atom reorganiza-
tion; protonic motion consequently does not contribute to
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