as k1Hk2/(2kϪ1H ϩ k2) and the ratio of rate constants for proton-
ation (k1H) and hydrolysis in H2O as 1 ϩ 2kϪ1H/k2. The factor 2
multiplying kϪ1 arises because of the possibility of losing one
isotope effect apparently corresponds closely to that for the
initial rate of reaction (kH O/kH, eqn. (20)).
In practice, however, it 2is clear that the experimental isotope
effect cannot correspond to the initial rate of reaction in D2O.
Assignment of a relatively large ratio of exchange to hydrolysis
rate constants (kx/kD = 7) and a large isotope effect for proton
transfer from the anthracenium ion intermediate (kϪ1H/kϪ1D = 8)
H
of two equivalent hydrogens from the methoxyanthracenonium
D
D
ion (SH2ϩ). By combining y = kϪ1H/kϪ1 = 8 and x = k2/kϪ1
=
0.28 we obtain = y/x = 28.5 and the ratio of protonation to
hydrolysis rates (1 ϩ 2y/x) as 58.
In these calculations it is assumed that the ratio kϪ1/k2 is
independent of the nature of the isotopic solvent since kϪ1 and
k2 involve attack of H2O as base and nucleophile respectively on
the same substrate and thus should be subject to similar solvent
isotope effects. However, k1 and kϪ1 will be sensitive to second-
ary isotope effects and if secondary isotope effects of 0.9 and
1.1 respectively are applied to the two rate constants the ratio
of protonation to hydrolysis rate constants is increased from 58
to 67.
are quite incompatible with kH O/kD O > 1. Although eqn. (18)
indeed represents series first 2 order kinetics, the exchange
reaction implicit in the second exponential is apparent only as a
relatively minor perturbation of the initial part of the reaction,
even when exchange is relatively slow (e.g. kx/kD = 2). Moreover,
for a slow reaction, which is monitored spectrophotometrically
and where the limiting absorbance at long reaction times is
iterated with the assumption that the kinetics are first order,
departures from first order kinetics are concealed by compen-
sating adjustments in the intial and limiting absorbances, as
becomes clear from analysis of model data. The derived rate
constant is therefore somewhat smaller than the limiting (true)
2
These calculations are also sensitive to the assumed value for
kϪ1H/kϪ1D. If this is increased from 8 to 10 the ratios of rates of
protonation to hydrolysis in H2O are increased to 80 and 70
depending on whether or not the secondary isotope effects
implicit in kϪ1H/k are taken into account. Importantly, a change
value of kD O at long reaction times, tending to increase kH O
/
2
2
kD O, but the discrepancy, even if exchange is quite slow
rel2ative to hydrolysis, does not exceed 20–30%. In other words
kH O/kD O could not be greater than ∼0.5.
D
in kϪ1H/kϪ1 has practically no effect upon q, so that kx ϩ kH
and kD can be evaluated from the exchange data independently
of the choice of isotope effects. This is because kH makes only a
small contribution to q.
2
2
Careful inspection of our experimental data revealed a barely
detectable induction period at the beginning of the reactions
of protio substrate in D2O. The difficulty we experienced of
detecting departure from first order behavior is consistent with
the exchange being relatively fast, and confirms that the derived
first order rate constants provide a good approximation to
Solvent isotope effect
Finally, it is necessary to establish whether or not the isotope
exchange measurements are consistent with the measured
solvent isotope effect for the hydrolysis of 9-methoxyanthra-
cene, kH O/kD O = 1.8. In the first place it should be noted that
kD O. It seems clear therefore that it is not possible to explain
2
the measured value of kH O/kD O = 1.8 in terms of partially rate
2
2
2
2
determining proton transfer to the 9-methoxyanthracene.
the value of kD O is based on a measurement for the reaction of
the protio subs2trate in D2O. To obtain this rate constant kD O it
2
was assumed that the reaction obeyed first order kinetics.
Strictly speaking, the reaction is series first order, and is
described by eqn. (18), as may be seen from combining
eqns. (12) and (13).
Acknowledgements
We thank Ms Geraldine Fitzpatrick and Dr AnnMarie
O’Donoghue for assistance with the NMR measurements and
a referee for suggestions and criticisms.
[SH] ϩ [SD] = A0eϪk t ϩ (1 Ϫ q)A0eϪ(k
(18)
ϩ kH)t
D
x
References
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Likewise the initial rate constant for a reaction of protio
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of the measured solvent isotope effect kH O/kD O must be given
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2
2
yield the numerical values shown based on kH/kD = 7, kϪ1H/kϪ1
D
D
= 8 and k1H/k1 = 3.5, with corrections made, as before, for
secondary isotope effects (the values shown in brackets are
uncorrected). Again it is assumed that there is no solvent
isotope effect upon the ratio kϪ1/k2.
It can be seen that limiting solvent isotope effects at complete
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reaction in D2O with kH O/kD O = 1.8. Thus the measured
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2
2
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