Kinetics of oxygen exchange between the two isomers of bisulfite ion, disulfite ion (S2O52-), and water as studied by oxygen-17 nuclear magnetic resonance spectroscopy

Article abstract of DOI:10.1021/ic020692n

The nuclear magnetic transverse relaxation time of oxygen-17 in aqueous sodium bisulfite solutions in the pH range from 2.5 to 5 was measured over a range of temperatures, pH, and S(IV) concentrations at an ionic strength of 1.0 m. From these data the rate law for oxygen exchange between bisulfite ion and water was determined and found to be consistent with oxygen exchange occurring via the reactions SHO₃-+ H⁺ ? _k1^k_-1SO₂ + H₂O, SO₃H^- + SHO₃^- ?^k_16aSO₃^2- + SO₂ + H₂O, and SO₃H^- + SHO₃^- ?^k_16bS₂O₅^2- + H₂O, where the symbol SHO₃^- refers to both isomeric forms of bisulfite ion, one in which the hydrogen is bonded to the sulfur (denoted HSO₃^-) and another in which the hydrogen is bonded to an oxygen atom (denoted SO₃H^-). The SO₃H^- isomer exchanges oxygen atoms with water much more rapidly than does the HSO₃^- isomer. The value of k_-1 was determined and is in essential agreement with the results of a previous determination by relaxation measurements. The value of k_16a + k_16b was also found, and k_16b is at least as large as k_16a. The rate and mechanism of oxygen exchange between the two bisulfite ion environments were studied by analyzing the broadening of the HSO₃^- resonance. Oxygen exchange occurs through isomerization caused by proton transfers.

Full text of DOI:10.1021/ic020692n

Inorg. Chem. 2003, 42, 1884−1894
Kinetics of Oxygen Exchange between the Two Isomers of Bisulfite Ion,
Disulfite Ion (S2O52-), and Water As Studied by Oxygen-17 Nuclear
Magnetic Resonance Spectroscopy
David A. Horner*
Departments of Chemistry and Physics, North Central College, 30 N. Brainard St.,
NaperVille, Illinois 60540
Robert E. Connick†
Department of Chemistry, UniVersity of California, and Chemical Sciences DiVision,
Lawrence Berkeley National Laboratory, Berkeley, California 94720
Received November 30, 2002
The nuclear magnetic transverse relaxation time of oxygen-17 in aqueous sodium bisulfite solutions in the pH
range from 2.5 to 5 was measured over a range of temperatures, pH, and S(IV) concentrations at an ionic strength
of 1.0 m. From these data the rate law for oxygen exchange between bisulfite ion and water was determined and
k-1
found to be consistent with oxygen exchange occurring via the reactions SHO3- + H a SO2 + H O, SO3H- +
+
2
k1
k16a
k16b
SHO3- a SO32- + SO2 + H O, and SO3H- + SHO3- a S2O52- + H O, where the symbol SHO3- refers to both
2
2
isomeric forms of bisulfite ion, one in which the hydrogen is bonded to the sulfur (denoted HSO3-) and another in
which the hydrogen is bonded to an oxygen atom (denoted SO3H-). The SO3H- isomer exchanges oxygen atoms
with water much more rapidly than does the HSO3- isomer. The value of k-1 was determined and is in essential
agreement with the results of a previous determination by relaxation measurements. The value of k16a + k16b was
also found, and k16b is at least as large as k16a. The rate and mechanism of oxygen exchange between the two
bisulfite ion environments were studied by analyzing the broadening of the HSO3- resonance. Oxygen exchange
occurs through isomerization caused by proton transfers.
Introduction
SO3H- isomeric forms. (The hydrogen atoms in HSO3- and
SO3H- are bonded to the sulfur atom and an oxygen atom,
respectively.) Thus the rate of reaction 2, for example, is
When sulfur dioxide dissolves in water, it retains its
structure as SO2 rather than forming sulfurous acid.1 Con-
sequently, its first and second ionizations are represented as
-
the sum of the dissociation rates of the HSO3 and SO3H-
isomers. The rate constant, k2, and the equilibrium quotient,
Q2, for this overall reaction can be expressed in terms of the
total bisulfite ion concentration, which we denote as [SHO3-].
The rate of reaction 1 has been measured previously.
Eigen, Kustin, and Maass2 studied the frequency dependence
of the attenuation of sound waves in sulfur dioxide solutions
of pH < 2 and 0.1 m ionic strength. The sound absorption
SO2 + H2O { k } SHO3- + H+
(1)
1
k-1
and
k2
SHO3
{
} SO32- + H+
(2)
-
k-2
(1) (a) Gerding, H.; Nijveld, W. J. Nature 1936, 137, 1070. (b) Rao, B.
P. Proc. Indian Acad. Sci. A 1944, 20, 292. (c) Simon, A.; Waldmann,
K. Z. Anorg. Allg. Chem. 1956, 283, 359. (d) Falk, M.; Gigue`re, P.
A. Can. J. Chem. 1958, 36, 1121.
(2) Eigen, M.; Kustin, K.; Maass, G. Z. Phys. Chem. Neue Folge 1961,
30, 130.
where SHO3- represents bisulfite ion in both the HSO3- and
* To whom correspondence should be addressed. E-mail: dah@noctrl.
edu. Fax: (630) 637-5180.
† E-mail: connick@uclink4.berkeley.edu.
1884 Inorganic Chemistry, Vol. 42, No. 6, 2003
10.1021/ic020692n CCC: $25.00 © 2003 American Chemical Society
Published on Web 02/25/2003

Oxygen Exchange between Isomers of Bisulfite Ion
the free induction decays were acquired at a frequency of 67.8 MHz
using a Bruker NMR spectrometer fitted with a broad-band,
multinuclear, 10 mm probe, and the transverse relaxation time of
17O in the water site was found by the Carr-Purcell-Meiboom-
Gill method.9 The length of the 180° pulse was approximately 45
µs. Widths of the bisulfite peaks were obtained by fitting Lorentz
line shapes to spectra in which the solvent signal had been
suppressed by a two-pulse excitation sequence.7
was presumed to shift the equilibrium of reaction 1. Betts
and Voss3 studied the kinetics of oxygen exchange between
sulfite ion and water as a function of sulfite concentration
and pH in alkaline solutions (pH > 8) of ionic strength 0.9
M by using oxygen-18 as a tracer. They reported a value of
k-1 and also a value of k3, the rate constant for the
dimerization of bisulfite ion:
Each data point represents a single Lorentz line shape fitting of
a single solution. Uncertainties assigned to the line widths were
those obtained from the least-squares fitting of the peaks with
Lorentz line shapes and reflect goodness of fit rather than
reproducibility of the data. Uncertainties are reported as plus or
minus one standard deviation. Some possible errors not accounted
for by the error bars are errors in solution pH, concentration of
bisulfite ion, and magnetic field inhomogeneity correction. Such
errors would appear as systematic errors in data obtained from a
single solution.
Longitudinal relaxation times of 17O were measured using the
inversion recovery method10 and the pulse phase-shifting technique
of Cutnell et al.11 The value of T1 of the water site was determined
by fitting the amplitude of the water peak at 10 different values of
τ to the expression
k3
{
-
2SHO3
} S2O52- + H2O
(3)
More recently k-1 has been measured by polarographic and
voltammetric methods. Reynolds and Yuan4 as well as
Tolmachev and Scherson5 measured the limiting current
during the reduction of bisulfite solutions. In both studies
the rate of SO2 reduction was assumed to be limited by the
rate of its formation from bisulfite ion. Values of k-1 reported
by these four groups are in poor agreement, differing by more
than a factor of 30. We undertook the present work to
redetermine the rate of reaction 1, gain information about
the kinetics of reaction 3, and explore the individual kinetic
roles of the two bisulfite isomers.
A(τ) ) A(∞){1 - (1 + W) exp(-τ/T1)}, where τ is the time
between 180° and sampling pulses, A(τ) is the amplitude of the
water peak at time τ, and W is a parameter that compensates for
incomplete inversion of the magnetization by the 180° pulse.12
On our chemical shift scale the water peak was always assigned
a shift of zero and downfield shifts were positive.
We have studied the kinetics of reactions 1-3 using
oxygen-17 NMR methods.6 Line-broadening analysis was
employed in the region between pH 3 and 5, in which the
S(IV) and water resonances are distinct but exchange-
broadened. In the SO2-SHO3 -SO3 system the analysis
is complicated by exchange between the two isomers of
bisulfite ion.7 We investigated the rate and mechanism of
the isomerization reaction
-
2-
Solution Composition. Total concentrations of S(IV) are
reported in units of molality, which is defined in this work as moles
of S(IV)/55.5 mol of water. Concentrations of the various species
in the bisulfite solutions were calculated from the equilibrium
quotients of reactions 1-4 and the water dissociation reaction using
values at 298 K of Q1 ) 10-1.37 m,13,14 Q2 ) 10-6.34 m,13,14 pQw )
k4
-
HSO3
{
} SO3H-
(4)
k-4
13.79,13 Q3 ) 0.082 M-1 15 and Q4 ) 4.9.7 Q3 was determined at
,
-
by studying the broadening of the 17O resonance of HSO3 .
an ionic strength of 1.0 M, while Q1, Q2, and Q4 were measured at
1.0 m ionic strength. In calculating solute molalities, we ignored
the small difference between molarity and molality in our solutions.
At 298 K and 1.0 m ionic strength the equilibrium quotients for
the acid dissociation of SO3H- and HSO3- are 5.5 × 10-7 and 2.7
× 10-6 m, respectively.
Experimental Section
NMR Measurements. Details of the NMR spectrometer, sample
temperature control, and the preparation of oxygen-free sodium
bisulfite solutions have been reported elsewhere.7 The 17O and 1H
resonance frequencies were 27.4 and 200 MHz, respectively. A
broad-band, multinuclear, 10 mm probe was used in the 17O
Using a pH meter calibrated against standard buffers, hydrogen
ion molalities were calculated from the pH meter readings, assumed
1
experiments, while H NMR spectra were acquired using a 5 mm
+
to be equal to -log(aH ), and an activity coefficient of 0.754. Here
the mean activity coefficient of 0.01 M HCl in 1 m NaCl16 was
substituted for the unknown activity coefficient of H+ in the bisulfite
solutions. The pH meter reading will be referred to by the term
“pH”.
proton probe.
The transverse relaxation time of 17O in the water of each bisulfite
solution was found by fitting a Lorentz line shape to the water
peak in a spectrum obtained by Fourier transformation of the sum
of between 200 and 6000 free induction decays produced by single
pulses. Preacquisition delay times were selected according to the
method of Canet et al.8 The measured transverse relaxation time
was corrected for an extra broadening of 2.9 ( 0.8 s-1 arising from
magnetic field inhomogeneity, the magnitude of which was
estimated from the difference between the measured line width
(half-width at half-height) and the 1/T1 of 17O in the water of a 1.0
m NaCl solution. For one solution ([S(IV)] ) 0.45 m, pH ) 4.98)
Concentrations at temperatures other than 298 K were calculated
after first correcting the equilibrium quotients for changes in
(9) (a) Carr, H. Y.; Purcell, E. M. Phys. ReV. 1954, 94, 630. (b) Meiboom,
S.; Gill, D. ReV. Sci. Instrum. 1958, 29, 688.
(10) Farrar, T. C.; Becker, E. D. Pulse and Fourier Transform NMR;
Academic Press: New York, 1971; p 20.
(11) Cutnell, J. D.; Bleich, H. E.; Glasel, J. A. J. Magn. Reson. 1976, 21,
43.
(12) Levy, G. C.; Peat, I. R. J. Magn. Reson. 1975, 18, 500.
(13) Smith, R. M.; Martell, A. E. Critical Stability Constants; Plenum: New
York, 1976; Vol. 4.
(14) Frydman, M.; Nilsson, G.; Rengemo, T.; Sille´n, L. G. Acta Chem.
Scand. 1958, 12, 878.
(15) Connick, R. E.; Tam, T. M.; von Deuster, E. Inorg. Chem. 1982, 21,
103.
(16) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic
Solutions; Reinhold: New York, 1943; p 575.
(3) Betts, R. H.; Voss, R. H. Can. J. Chem. 1970, 48, 2035.
(4) Reynolds, W. L.; Yuan, Y. Polyhedron 1986, 5, 1467.
(5) Tolmachev, Y. V.; Scherson, D. A. J. Phys. Chem. A 1999, 103, 1572.
(6) Jackson, J. A.; Taube, H. J. Phys. Chem. 1965, 69, 1844.
(7) Horner, D. A.; Connick, R. E. Inorg. Chem. 1986, 25, 2414.
(8) Canet, D.; Goulon-Ginet, C.; Marchal, J. P. J. Magn. Reson. 1976,
22, 537.
Inorganic Chemistry, Vol. 42, No. 6, 2003 1885

Horner and Connick
temperature using the van’t Hoff equation. Q1 and Q2 were corrected
for changes in temperature using 298 K values of ∆H at 1.0 m
ionic strength, ∆Cp°, and d∆Cp°/dT,17 while Qw was calculated using
298 K values of ∆H at 1.0 m ionic strength and ∆Cp°.18 Values of
∆H1, ∆H2, and ∆Hw at ionic strength 1.0 m employed in this
calculation were -3.99, -0.12, and 13.71 kcal/mol, respectively.
They were calculated19 from the reaction enthalpies at ionic strength
0 17 or 0.5 m 13 and relative partial molal enthalpies of solutes at
ionic strength 0.5 and 1.0 m,20 with the relative partial molal
enthalpy of NaHCO3(aq) substituting for the unknown relative
partial molal enthalpy of NaHSO3(aq). Q4 was calculated at
temperatures other than 298 K using ∆H4 ) -2.9 kcal/mol, which
was determined at 298 K and ionic strength 1.0 m.7 Q3 was
calculated using the 298 K, ionic strength 2.1 m reaction enthalpy
∆H3 ) -1.1 kcal/mol,15 because the relative apparent molal
enthalpies needed to correct ∆H3 to ionic strength 1.0 m were not
available.
Results
Introduction. The 17O NMR spectra of sodium bisulfite
solutions having S(IV) concentrations in the range from 0.1
to 0.5 m and with pH between 2.5 and 5 exhibit resonances
-
at ca. 195, ca. 175, and 0 ppm arising from SO3H-, HSO3 ,
and H2O, respectively.7,21 Spectral changes resulting from
variation of the pH of the solution are illustrated in Figure
1 of ref 7. The SO3H- peak at 195 ppm broadened with
increasing temperature and decreasing pH and below pH 3.6
was too broad to observe. The water peak also broadened
as the pH decreased from 5 to 3.5 and then narrowed as the
Figure 1. Temperature dependence of the difference between the measured
1/T2 and 1/T1 of the 17O in the water (site A) of sodium bisulfite solutions
of [S(IV)] ) 0.1-0.8 m and various concentrations of H+. (1/T2)A is the
measured half-width at half-height of the water peak. The term “pH” refers
to the pH meter reading at room temperature. The curves show values
calculated from eqs 13 and 17 using rate constants deduced in this work.
Data acquired at other [S(IV)] and pH values are not shown but gave similar
results (see Supporting Information).
-
pH was decreased below 3.5. The HSO3 peak at 175 ppm
broadened with increases in temperature, pH, and S(IV)
concentration. At and above pH 5 we did not observe sep-
arate 195 or 175 ppm resonances; the pH 5 spectra contained
a single solute resonance at approximately 192 ppm that
broadened with increasing temperature and whose area
corresponded to the total concentration of bisulfite ion.
The difference between 1/T2 and 1/T1 of 17O in the water
site, shown in Figure 1, along with the pH and temperature
dependence of their difference, provides evidence for an
oxygen exchange process involving water. The ratio of the
additional broadening (1/T2 - 1/T1) of the water peak to that
of the SO3H- peak is about equal to the inverse of the ratio
of peak areas, as would be expected if chemical exchange
occurs between these two species.22
These spectral features are consistent with the oxygen
exchange scheme ABC, where A ) H2O (0 ppm), B )
SO3H- (195 ppm), and C ) HSO3- (175 ppm). The rate of
oxygen exchange between A and B increases with decreasing
pH, producing the coalescence of SO3H- and water reso-
nances below pH 3.5. The rate of B-C exchange increases
with pH, causing the two bisulfite resonances to be coalesced
at and above pH 5. We interpret the observed decrease of
1/T2 - 1/T1 of the water with increasing temperature at low
pH as the exchange narrowing of the coalesced SO3H- and
water resonances.
Oxygen Exchange between HSO3- and SO3H-. The rate
-
law for oxygen exchange out of the HSO3 site was found
-
by examining the broadening of the HSO3 peak as a
(17) Goldberg, R. N.; Parker, V. B. J. Res. Natl. Bur. Stand. 1985, 90,
341.
(18) Rock, P. A. Chemical Thermodynamics; University Science: Mill
Valley, CA, 1983; p 530.
function of pH, temperature, and S(IV) concentration. The
-
broadening of the HSO3 peak at and below pH 3.5 was
analyzed using the slow-exchange limit for two site chemical
exchange22 between site C and the combined A-B site. At
these acidities exchange between SO3H- and H2O was fast
on the NMR time scale while exchange between either of
these sites and HSO3- met slow-exchange conditions. Under
(19) (a) Vanderzee, C. E. J. Chem. Thermodyn. 1981, 13, 947. (b)
Vanderzee, C. E.; Noll, L. A. J. Chem. Thermodyn. 1987, 19, 417.
(20) (a) Berg, R. L.; Vanderzee, C. E. J. Chem. Thermodyn. 1978, 10, 1049.
(b) Vanderzee, C. E.; Noll, L. A. J. Chem. Thermodyn. 1983, 15, 1015.
(c) Parker, V. B. Thermal Properties of Aqueous Uni-uniValent
Electrolytes; National Standard Reference Data Series NBS 2; U.S.
Department of Commerce, National Bureau of Standards, U.S.
Government Printing Office: Washington, DC, 1965.
(21) (a) Littlejohn, D.; Walton, S. A.; Chang, S. Appl. Spectrosc. 1992,
46, 848. (b) D. Littlejohn (private communication) has performed
additional Raman measurements that confirm the identification of the
two bisulfite isomers.
-
these conditions the half-width at half-height of the HSO3
peak, (1/T2)C, is given by22 (1/T2)C ) 1/T2C + 1/τC, where
1/T2C is the half-width at half-height due to relaxation
processes other than chemical exchange and 1/τC is the
pseudo-first-order rate constant for oxygen exchange out of
site C. Figure 2 shows the line width of the HSO3- peak at
(22) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High-Resolution
Nuclear Magnetic Resonance; McGraw-Hill: New York, 1959;
Chapter 10.
1886 Inorganic Chemistry, Vol. 42, No. 6, 2003

Oxygen Exchange between Isomers of Bisulfite Ion
about 1050 s-1, so the [S(IV)] independent term in 1/τC must
be greater than 600 s-1 at 341 K. Near this temperature the
line width increase produced by changing the pH of 0.1 m
solutions from pH 2.58 to pH 3.01 was only 50-100 s-1,
some of which is due to the term in 1/τC that is first order in
S(IV). Hence, the [S(IV)]-independent term must be between
0 and -0.2 power in the hydrogen ion concentration.
To determine the exact hydrogen ion dependence of 1/τC
we prepared plots of (1/T2)C vs [S(IV)]/{(aH )298K}p for
+
several values of p. If 1/τC ) N + L[S(IV)]/[H+]n, with N
and L constant, then the plot should be a straight line when
p ) n, provided the activity coefficients have the same values
in all the solutions at any given temperature. Graphs of
(1/T2)C data from solutions having S(IV) concentrations
ranging from 0.10 to 0.46 m and pH values ranging from
2.58 to 3.52 were most linear when p ) 1, suggesting that
the L[S(IV)]/[H+]n term in 1/τC can be written as L′[SO32-].
However, all the graphs showed systematic deviations from
linearity. The data were fitted better when a third term, first
-
order in SHO3 , was added to 1/τC to give
-
1/τC ) N + L′[SO32-] + R[SHO3 ]
(5)
In Figure 3, both the experimental values of (1/T2)C and those
determined from preliminary weighted linear least-squares
fits at each temperature to the slow exchange expression,
with 1/τC given by eq 5, are plotted against [SO32-]. The
quantity 1/T2C + N was treated as an adjustable parameter
in the least-squares analyses.
Figure 2. Dependence of the half-width at half-height of the HSO3- peak
(site C) upon the concentration of S(IV). Data at each temperature were
obtained from the same set of four sodium bisulfite solutions. At 25 °C the
ionic strength of every solution was 1.0 m, and the H+ activity as measured
by a pH meter ranged from 9.6 × 10-4 to 1.00 × 10-3. Weighted least-
squares fittings of the data at each temperature are shown as solid lines.
Data acquired at 274, 287, 303, 318, and 333 K gave similar results (see
Supporting Information).
Reactions consistent with the rate law of eq 5 are
k6
{
-
-
-
(HSO3 )* + SHO3
} (SO3H-)* + SHO3
(6)
(7)
k7
-
(HSO3 )* { } (SO32-)* + H+
k-7
pH 3 and various temperatures as a function of the S(IV)
concentration. The plots are essentially linear and have
nonzero y-intercepts that increase with temperature. Since
1/T2C of a quadrupolar nucleus should decrease as temper-
ature increases,23 1/τC must be the sum of terms that are zero
and first order in S(IV).
k8
-
2-
-
(HSO3 )* + SO3
{
} (SO32-)* + SHO3
(8)
k-8
k9
\
-
(HSO3 )* + SO3H- {
} (SO32-)* + SO2 + H2O (9)
At least one term in 1/τC must be of negative order in
[H+] to account for the broadening of the HSO3- peak with
increasing pH. A given pH change had a much greater effect
upon the line width of the peak in spectra of 0.2 m solutions
than in those of 0.1 m solutions, suggesting that the term
that is first order in S(IV) is also a function of [H+]. The
following comparison of the data of Figure 2 to the change
in line width resulting from a pH change of about 0.4 unit
in 0.10 m S(IV) solutions shows the [S(IV)]-independent
term in 1/τC to be essentially independent of [H+]. By
extrapolation of 274 K data24 to [S(IV)] ) 0, an upper limit
to 1/T2C of about 450 s-1 is obtained. Because 1/T2C decreases
as the temperature is raised, it must be less than 450 s-1 at
341 K. The total line width at 341 K and [S(IV)] ) 0 is
(SO32-)* + H+ {k-10} (SO3H-)*
(10)
(11)
k-11
{
(SO32-)* + SHO3
} (SO3H-)* + SO3
-
2-
The asterisk is used to tag the oxygen atoms. Reactions 6,
8, and 11 are not elementary reactions because they contain
SHO3 . Other reactions that exchange oxygens out of the
HSO3- site were omitted from the above mechanism either
because they are slow compared with reactions 6-11 or are
mechanistically improbable.25 In particular, the mechanism
includes no reactions that exchange oxygen atoms between
sites C and A. We expect the fastest reaction of this type to
be HSO3- + H+ ) SO2 + H2O, but the rate law contains no
term that is first order in H+.
-
(23) Abragam, A. The Principles of Nuclear Magnetism; Oxford: New
York, 1961; Chapter VIII.
(24) (1/T2)C vs [S(IV)] data at 274 K may be found in the Supporting
Information.
(25) Horner, D. A. Ph.D. Dissertation, University of California, Berkeley,
CA, 1984; pp 54-67.
Inorganic Chemistry, Vol. 42, No. 6, 2003 1887

Horner and Connick
) k8, and R ) k6 + k9(1 + 1/Q4)-1. By assuming Arrhenius
behavior for k7, k8, and R and that 1/T2C is proportional to
1/T1 of water,28 we found k7, k8, and R as functions of
temperature by a single, 7-parameter weighted-least-squares
-
fitting of the (1/T2)C data, with (1/T1)A, [SO32-], [SHO3 ],
and T as the independent variables. We obtained
1/T2C ) (0.364 ( 0.052)(1/T1)A,
ln k7/s-1 ) (11.89 ( 0.23) + (-1658 ( 74)/T (covariance
) -17.29),
ln k8/(m-1 s-1) ) (19.41 ( 0.54) + (-1622 ( 166)/T,
(covariance ) -88.51), and
ln R/(m-1 s-1) ) (26.0 ( 2.6) + (-6452 ( 856)/T
(covariance ) -2205), where T is in kelvin.
Combination of k7 and Q7 yielded ln k-7/(m-1 s-1) )
29
(29.59 ( 0.23) + (-3098 ( 69)/T, with a covariance of
-15.8.
It should be possible to observe the proton resonance of
-
HSO3 if the only mechanisms for exchange of the sulfur-
bound proton are those that also produce the slow oxygen
-
exchange with SO3H- (including HSO3 dissociation). For
0.2 m S(IV) at pH 3.0 and 25 °C the value of 1/τC is about
650 s-1. Proton exchange at this rate would yield a broad
but distinct proton NMR peak if the resonance is no less
than 1600 s-1 (1.3 ppm on our instrument) from the water
resonance. However, we were unable to detect any solute
peak in proton NMR spectra of a 0.2 m sodium bisulfite
solution of pH 3 nor in spectra of 0.2, 0.4, and 1 m solutions
of pH 2, in which 1/τC is small. Suppression of the water
peak using the two pulse sequence, lowering the temperature
to nearly 0 °C, and shifting the water peak by adding DyCl3
up to 0.02 m all failed to produce an observable solute
resonance. The 500 MHz proton NMR spectra of 1 m sodium
bisulfite solutions of pH 2 and pH 4.6 also exhibited no solute
peak.30
Figure 3. Dependence of the half-width at half-height of the HSO3- peak
(site C) upon the concentration of SO32-. At each temperature the data
were obtained from the same set of six sodium bisulfite solutions. At 25
°C the ionic strength of each solution was 1.0 m, and in order of increasing
[SO32-] the pH meter reading was 2.58, 3.01, 3.00, 3.01, 3.02, and 3.52.
The solid symbols and error bars represent the experimental data. The open
symbols are points obtained from the weighted linear least-squares fitting
of the data at each temperature with the function (1/T2)C ) 1/T2C + N +
L′[SO32-] + R[SHO3-]. The quantity 1/T2C + N was treated as a single,
adjustable parameter. Data acquired at 274, 287, 303, 318, and 333 K gave
similar results (see Supporting Information).
Oxygen Exchange between SO3H- and H2O. We
investigated oxygen exchange between SO3H- and H2O by
studying the broadening of the water peak in the 17O spectra.
Because the population of oxygen in water greatly exceeded
its populations in either isomer of bisulfite ion, the treatment
of Swift and Connick31 is applicable. Neglect of direct
One obtains 1/τC from reactions 6-11 by writing the
-
expression for d[(HSO3 )*]/dt, from which [(SO32-)*] is
eliminated by the steady-state approximation. An expression
consistent with the empirical rate law is obtained if it is
assumed that k-10 . k-7 and k-11 . k-8.26 Since reaction
10 belongs to the class of rapid reactions involving proton
addition to an oxygen of the conjugate base of an inorganic
oxyacid, k-10 probably exceeds 5 × 1010 M-1 s-1.27 Our data
show26 that proton addition to a sulfite oxygen atom proceeds
much more rapidly than protonation of the sulfur atom, i.e.,
k-10 . k-7, as otherwise these two reactions would lead to
rapid isomerization. It is also likely that k-11 . k-8, because
reactions 8 and 11 are the general acid-base catalysis
analogues of reactions 7 and 10. With these assumptions we
obtain26
-
HSO3 -H2O exchange (vide supra) yields as a good
approximation
1
τBA
X +
pB 1
pB
1
(
2
1
1
)
+
-
(13)
2 + Y2
( )
)
T2
T2A pA τBA pA τBA
1
τBA
A
X +
(
)
where
pC
∆ωC
2
1
-
Y ) ∆ωB +
1/τC ) k7 + k8[SO32-] + {k6 + k9(1 + 1/Q4)-1}[SHO3 ]
(
)
pB τCB
1
1
+
2 + (∆ωC)2
(
)
(12)
T2C τCB
Comparison of this expression with eq 5 yields N ) k7, L′
(28) See Figure 6S in the Supporting Information for (1/T1)A data.
(29) Q7 ) Q2(1 + Q4).
(30) McKenna, S. T. Private communication, 2002.
(31) Swift, T. J.; Connick. R. E. J. Chem. Phys. 1962, 37, 307.
(26) Details may be found in the Supporting Information.
(27) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1.
1888 Inorganic Chemistry, Vol. 42, No. 6, 2003

Oxygen Exchange between Isomers of Bisulfite Ion
Betts and Voss3 measured the rate of oxygen exchange
between S(IV) species and water in basic solutions and found
a rate law consistent with the existence of three single-step
oxygen exchange reactions:
2
1
1
1
+
+
+ (∆ωC)2
(
)
pC 1 T2C
T2C τCB
1
T2B
X )
+
2 + (∆ωC)2
pB τCB
1
1
(
)
T2C τCB
SO3H- + H+ {k-15} SO2 + H2O,
(15)
and the symbols have the following meanings:
k15
(1/T2)A ) the half-width at half-height (line width) of the
A (water) peak;
k16a
(SO3H-)* + SHO3
and
{
} (SO2)* + (H2O)* + SO3 (16a)
-
2-
1/T2i ) the natural line width of site i, i.e., the line width
the peak would have in the absence of chemical exchange;
1/τij ) the pseudo-first-order rate constant for oxygen
exchange from site i to site j;
k16b
(SO3H-)* + SHO3
{
} S2(O2)*O32- + (H2O)* (16b)
-
pi ) the fraction of 17O nuclei that are in site i;
∆ωi ) the precession frequency of the 17O nuclei in site
i in the absence of chemical exchange minus the spectral
frequency at which the water peak has its maximum height.32
The pseudo-first-order rate constant for oxygen exchange
between the SO3H- site and H2O, 1/τBA, was evaluated from
eq 13. The value of 1/T2A was assumed to equal (1/T1)A. We
set 1/T2C equal to the value obtained from the fitting of the
HSO3- line width data (vide supra) and estimated that 1/T2B
was equal to (1/T1)A ( 100%, but 1/τBA was relatively
insensitive to these values.33 Equation 5 was used to calculate
In acidic solutions, the pseudo-first-order rate constant, 1/τBA,
for oxygen exchange between sites B and A due to the above
reactions has the form
pB
1
1
3
)
(k-15[H+] + k16[SHO3 ])
(17)
-
(
)
τBA pSO H-
3
-
where pSO H is the fraction of oxygen nuclei present in
3
SO3H- and k16 ) k16a + k16b. To compare our data with this
rate law, we examined the dependence of 1/τBA upon [H+]
-
-
1/τCB. In calculating the population ratios pC/pB and pB/pA,
and [SHO3 ]. The dependence of (1/τBA)(pB/pSO H ) upon
hydrogen ion concentration for six solutions having [SHO3 ]
3
2-
-
we assumed that resonances of the minor species S2O5
,
SO2, and SO32- were coalesced with that of SO3H-, so that
the B site comprised these species.34 (In solutions with S(IV)
concentrations greater than 4 m the S2O5 did contribute
) 0.19 m is shown in Figure 4. The variation of the ordinate
with [H+] is due almost entirely to changes in 1/τBA, because
2-
-
the values of (pB/pSO H ) all fall between 1.04 and 1.07. At
3
2-
high acidity 1/τBA approaches first order in [H+] but shifts
to a smaller order at lower acidities. At each temperature
the data are fitted well (dashed curves) by the expression
significantly to peak areas and the S2O5 and bisulfite
resonances were coalesced.) The values of ∆ωB and ∆ωC
were approximately 33 500 and 30 200 s-1, respectively, and
were corrected for small changes resulting from the coales-
cence of the A and B resonances at low pH.35
pB
1
τBA
) G[H+] + F
(18)
(
)
p
SO3H-
For any (1/T2)A two values of 1/τBA are obtained upon
solving eq 13. When both were real and positive, we chose
the correct value by examining Figure 1 to see whether the
water peak broadened (smaller value) or narrowed (larger
value) as the temperature increased. In spectra of pH 5
where F and G are temperature-dependent parameters. The
data in Table 1 show that 1/τBA is independent of [S(IV)] at
pH 3, where F is insignificant, and therefore, G must be
zero order in S(IV), in agreement with eq 17.
-
solutions the HSO3 and SO3H- peaks were coalesced; in
Above pH 3 the F term is nonnegligible, and 1/τBA
increases with increasing [S(IV)]. Figure 5 shows plots of
these cases we calculated a second value of 1/τBA from the
width of the S(IV) peak. Because the exchange between
bisulfite ion and water was in the slow-exchange limit at
pH 5, the half-width at half-height of the S(IV) peak is (1/
T2)S ) 1/T2S + 1/τSA, where the combined S(IV) site is
labeled with the letter S. To obtain 1/τBA we replaced 1/τSA
with [pB/(pB + pC)](1/τBA) and calculated 1/T2S, the line width
of the S(IV) peak in the absence of oxygen exchange with
water, using the two-site exchange expression
+
-
-
the function (1/τBA)(pB/p
) - G[H ] vs [SHO3 ] at each
SO3H
temperature for solutions having a pH of 5, all at 1.0 m ionic
-
strength except for the solution having [SHO3 ] ) 0.69 m,
which had an ionic strength of 0.9 m. The data are not highly
precise because the H2O peak is only slightly broadened at
pH 5. Nevertheless, the data in Figure 5 do suggest that F is
-
proportional to [SHO3 ]. Although the points from the 0.19
m solution lie above lines drawn through the origin, a
pB
pC
nonzero y-intercept in Figure 5 would correspond to a term
1
T2S
1
1
)
+
+
-
(
)
(
)
in F that contains [SHO3 ] to zero or a negative power. Such
pB + pC T2B
pB + pC T2C
a term could be explained by adding the reaction SO3H- f
2
2
pB pC
(∆ωB - ∆ωC)2(τBC + τCB) (14)
(pB + pC)4
(32) This is not Swift and Connick’s definition of ∆ωi, but it is a good
approximation because the chemical shifts of the S(IV) peaks relative
to water were large in comparison to changes in the position of the
water peak.
for the width of the exchange narrowed S(IV) peak.22 Values
of 1/τBA determined in this manner agreed well with those
obtained from the water peak line width data.
(33) Reference 25, pp 93-96.
(34) Reference 25, pp 75-77.
(35) Reference 25, pp 98-103.
Inorganic Chemistry, Vol. 42, No. 6, 2003 1889

Horner and Connick
and ln k16/(m-1 s-1) ) (19.52 ( 0.37) + (-3141 ( 120)/T,
with a covariance of -44.34, where T is in kelvin. Results
of this fitting are shown as the solid curves in Figures 4 and
5. To confirm the rate law of eq 17, the line broadenings
predicted by these values of k-15 and k16 were calculated.
The results, shown as the solid curves of Figure 1, compare
favorably with the experimental line broadenings.
Oxygen Exchange between Bisulfite Ion and Disulfite
2-
Ion (S2O52-). No separate S2O5 resonance was observed
in the 17O NMR spectra of any of our solutions. In particular,
2-
-
in spectra of a solution in which both S2O5 and SHO3
made an appreciable contribution to peak areas ([S(IV)] )
2-
-
4.7 M), the S2O5 and SHO3 resonances were apparently
coalesced with each other but not with the water peak. By
what mechanism is oxygen exchanged between bisulfite ion
and disulfite ion? The mechanism proposed earlier for
-
exchange between SHO3 and S2O52-, reaction 16b, also
produces oxygen exchange between bisulfite ion and water.
We attempted to determine whether an exchange process
such as (16b) can account for the simultaneous existence of
a coalesced S(IV) peak and a separate water peak due to the
large chemical shift of water relative to the S(IV) species or
whether the peak pattern requires the existence of an
-
2-
additional SHO3 -S2O5 oxygen exchange pathway that
does not produce oxygen exchange between these species
-
2-
and water, such as SO2 + SHO3 a S2O5 + H+.
We acquired spectra of a solution in which [S(IV)] ) 4.7
M and pH ) 4.5 at several temperatures between 258 and
323 K, conditions for which the populations of oxygen atoms
in the SHO3- and S2O52- environments were approximately
equal.36 Analysis of the line width and chemical shift data
Figure 4. Product of the pseudo-first-order rate constant for exchange of
17O from site B to H2O (site A) and the population ratio of all oxygens in
site B to oxygens in SO3H-, plotted as a function of -log [H+] for six
different sodium bisulfite solutions of [S(IV)] ) 0.20 m and ionic strength
1.0 m. Solid and open symbols denote values obtained from analysis of the
broadening of the water peak in the 17O NMR spectra of the solutions,
while the × symbols denote values obtained through analysis of the
broadening of the coalesced S(IV) peak (located at ca. 192 ppm) in the
spectrum of the solution of highest pH. Uncertainties on the S(IV) data are
not shown but are smaller than the uncertainties in the corresponding water
peak data. Each dotted curve represents the weighted linear least-squares
fitting of the expression F + G[H+] to the displayed water peak data at a
single temperature, while the solid curves show the values of (k-15[H+] +
k16[SHO3-])/3 obtained by a single fitting of the water peak 1/τBA data at
all temperatures, pH values, and S(IV) concentrations with the function
given in eq 17. Data acquired at 282, 295, 310, 325, and 341 K gave similar
results (see Supporting Information).
2-
revealed that the chemical shift of S2O5 is roughly 164
ppm and that the psuedo-first-order rate constant for oxygen
-
2-
exchange from SHO3 to S2O5 exceeds 1500 s-1 at 263
K. The spectral features described above do not require a
-
2-
SHO3 -S2O5 oxygen exchange mechanism other than
reaction 16b yet do not exclude such reactions. Moreover,
k16b is likely greater than or equal to k16a. Details may be
found in the Supporting Information.
SO2 + OH- to the proposed oxygen exchange mechanism
but is ruled out by Betts and Voss’ data.3 They found no
evidence for a term of this sort, although it would necessarily
have been the dominant term in their basic solutions. Even
if their largest oxygen exchange rate were attributed to such
a term, it is easily shown that this term would be negligible
at pH 5. It is thus likely that the points in Figure 5
Discussion
Several possible explanations exist for our inability to
observe the HSO3 peak in proton NMR spectra. First, our
assignment of the 175 and 195 ppm resonances to HSO3
-
-
and SO3H-, respectively, may be incorrect, in which case
both HSO3- and SO3H- would exchange protons rapidly with
water, the former via reaction 1 and the latter via reaction
10. This possibility seems ruled out by the results of
Littlejohn et al., who showed that the temperature depen-
dence of the intensity of the Raman H-S stretch of bisulfite
solutions matched qualitatively that of the 17O NMR
resonance at 175 ppm.21 A second, more likely reason is
that the HSO3- and H2O peaks in the proton spectrum were
-
corresponding to [SHO3 ] ) 0.19 m contain a systematic
error. The data from this solution are also graphed as the
pH 5 data in Figure 4, where the likely systematic error
appears as 1/τBA values that seem too large.
Having tentatively established that the rate law of eq 17
accounts for our data, the 1/τBA data at every temperature,
pH, and bisulfite ion concentration were fitted with the form
of eq 17 in which the Arrhenius parameters of k-15 and k16
served as regression parameters. Weighted nonlinear least-
squares fitting of the data yielded ln k-15/(m-1 s-1) ) (30.54
( 0.11) + (-3511 ( 36)/T, with a covariance of -4.12,
(36) The spectrometer on which the spectra of the 4.7 M and 0.800 m
solutions were acquired was similar to the spectrometer described in
the Experimental Section but had a magnetic field strength of 4.2 T,
corresponding to an 17O Larmor frequency of 24.4 MHz. It accepted
20 mm (outside diameter) sample tubes.
1890 Inorganic Chemistry, Vol. 42, No. 6, 2003

Oxygen Exchange between Isomers of Bisulfite Ion
Table 1. Effect of S(IV) Concentration upon (1/τBA)(pB/pSO H ) at pH 3 and Various Temperatures
-
3
-1
10-3(1/τBA)(pB/pSO H ) (s
)
-
3
-a
-log [H+]a
[S(IV)] (m)
pB/pSO H
288 K
295 K
310 K
318 K
333 K
340 K
3
2.89
2.88
2.89
2.90
0.101
0.199
0.326
0.456
1.04
1.06
1.07
1.09
47 ( 12
51 ( 6
51 ( 5
50 ( 3
52 ( 10
60 ( 5
62 ( 4
54 ( 4
71 ( 7
79 ( 4
76 ( 3
75 ( 3
80 ( 6
87 ( 3
82 ( 2
80 ( 2
81 ( 4
96 ( 3
92 ( 3
85 ( 3
83 ( 5
93 ( 3
94 ( 3
87 ( 3
a At 298 K.
q
coalesced or fortuitously superimposed. Third, if there exists
activation for the dissociation of the HSO3- isomer, ∆S7
)
any mechanism, such as H*SO3- + H+ a HSO3- + (H+)*
-38 cal/(mol K), seems unusually negative, but the net
entropy change for this reaction is -45 cal/(K mol).7,39 In
an acid dissociation reaction most of the overall entropy
change should appear in ∆Sq because the activated complex
will have the proton already well separated from the anion.
-
-
or H*SO3 + H2O a HSO3 + H*HO, that exchanges
protons between HSO3- and H2O without leading to oxygen
exchange between HSO3 and other species, then our
-
estimate of 1/τ for proton exchange would be too low.
Isomerization of HSO3- to SO3H- proceeds primarily via
2-
In their study of oxygen exchange between SO3 and
-
water, Betts and Voss3 found evidence for an exchange
process that is second order in S(IV), which they attributed
to the dimerization of bisulfite ion (reaction 3). We also
detected an exchange process that is second order in S(IV),
but ascribe it to two reactions: 16a and 16b. Although neither
our data nor those of Betts and Voss distinguish between
reactions 16a and 16b, we think it likely that reaction 16a,
the general acid-base catalysis analogue of reaction 15,
contributes appreciably to oxygen exchange with water. Not
only would general acid-base catalysis be expected for
reaction 15, but the ratio k-15/k16 is consistent with the
Brønsted relation for acid-base catalysis.37 The experimental
value of this ratio is reproduced when Brønsted’s exponent
R is about 0.5. Tolmachev and Scherson5 also found evidence
for general acid catalysis of the formation of SO2 from
bisulfite ion. Nevertheless, this reasoning in no way rules
out reaction 16b. Reaction 9, one of the two elementary
reactions that contribute to reaction 16a, is unimportant
because the upper limit to k9 is about 90 m-1 s-1 at 298 K,
compared with a value of k16 of about 8000 m-1 s-1. Because
isomerization of HSO3- is slow, the reactions of SO3H- with
proton removal from HSO3 . In our solutions, proton transfer
2-
to SO3 (reaction 8) was more rapid above pH 3.5 than
proton transfer to a water molecule (reaction 7), while
isomerization via reactions 6 and 9 was a minor contributor
under all conditions. From the ratio k8/k7 one calculates the
exponent â in Brønsted’s equation37 for base catalysis of
-
HSO3 dissociation to be 0.6 at 298 K, a value typical of
general base catalysis. General acid-base catalysis is of
course expected when the rate-determining step involves
proton transfer. The rate of addition of H+ to SO32- to form
-
HSO3 is well below the diffusion limit, in contrast to the
rate of association expected for the same two ions to form
the oxyacid. The rate constant for acid dissociation of SO3H-
is about 50 times greater than that for the dissociation of
HSO3- at room temperature. Dissociation and recombination
of SO3H- are sufficiently fast to make all three SO3H-
oxygens equivalent on the NMR time scale provided the
S-O and S-O-H resonances are separated by no more than
a few thousand hertz.
Agreement between the experimental data and the pre-
dicted curves in Figures 1, 4, and 5 is quite good considering
that only four adjustable parameters were used to fit data
covering a wide range of temperature, [SHO3-], and pH. The
poorer quality of fit at high and low temperatures suggests
some inaccuracy in the temperature measurements, but the
directions of the deviations are incompatible with a consistent
systematic error. In some parts of Figure 1 the predicted
water peak broadenings are systematically too small. Most
likely these deviations arose from an underestimate of the
inhomogeneity correction. The deviations of experimental
data from the predicted curves of Figure 5 were discussed
earlier. No significant improvement in fitting the data was
obtained by adding other reasonable oxygen exchange
mechanisms.
-
HSO3 must not contribute significantly to k16.
In Table 3 our rate constants for reactions that exchange
oxygen between bisulfite ion and water are compared with
those obtained by other workers. The distinction between
molar and molal units is probably unimportant compared to
uncertainties in the rate constant values. The existence of
two isomers of bisulfite ion necessitated a reinterpretation
of the data of Eigen et al.2 Reaction 15 is much more rapid
than both reaction 16 and the isomerization reaction at the
acidities at which Eigen et al. worked, so their measured
relaxation time, τII, may be attributed to reaction 15 only,
i.e., τII ) {k-15([H+] + [SO3H-] + Q15)} -1. Their relaxation
time data then yielded a value of k-15, from which we
calculated k-1 at 0.1 m ionic strength. This value was also
Table 2 lists the rate constants evaluated in this work and
the corresponding enthalpies and entropies of activation. The
uncertainties assigned to our values are unusually small be-
cause they are standard deviations of least squares parameters
and, therefore, may underestimate the actual uncertainties
significantly.
(37) (a) Bell, R. P. Acid-Base Catalysis; Clarendon: Oxford, U.K., 1941;
Chapter V. (b) The Proton in Chemistry, 2nd ed.; Cornell: Ithaca,
NY, 1973; Chapter 10.
(38) Frost, A. A.; Pearson, R. G. Kinetics and Mechanism; Wiley: New
York, 1953; Chapter 7.
(39) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow,
I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref.
Data 1982, 11, Suppl. 2.
The activation entropies in Table 2 are reasonable for
reactions of ions in aqueous solution.38 The entropy of
Inorganic Chemistry, Vol. 42, No. 6, 2003 1891

Horner and Connick
estimate the activity coefficients of the reactants and activated
complex of reaction 15 for a solution composition of 0.2 m
NaHSO3 and 0.8 m NaCl.42
Our experimental value of k-1 agrees well with that of
Eigen et al. (compare the fifth and sixth entries of Table 3)
but is less than one-third of Reynolds and Yuan’s value4
and is 1 order of magnitude smaller than the value reported
by Tolmachev and Scherson.5 Although our rate law agrees
with that of Betts and Voss,3 our rate constants differ
substantially from theirs. Betts and Voss’ reported value of
k-1 exceeds ours by about a factor of 20 but really differs
by a factor of 60 because their reported rate constants are
inexplicably smaller, by a factor of 3, than those we
calculated from their data. Betts and Voss’ value of k-1 is
nearly equal to that of a diffusion-controlled reaction,
surprisingly large for a reaction that involves the breaking
of a sulfur-oxygen bond.
Reynolds and Yuan’s value of k-1 is presumably less
precise than the others in Table 3 because it was determined
from measurements at just two pH values. Rate constants
determined by their polarographic method contain a system-
atic error if, as seems likely, the conversion of bisulfite ion
to SO2 is catalyzed by the buffer. Tolmachev and Scherson’s
data are not fitted well by their general acid catalysis model.
In particular, the slope of the pH dependence of their Figure
3 does not match the expected value, and the precision of
the fitting of their rate data as a function of H+ and acetic
acid concentrations decreased markedly when the data set
was enlarged to include more than one pH. Furthermore,
although both groups worked at high ionic strengths, neither
made activity coefficient corrections in analyzing their data.
Consequently the rate constants found by these groups can
only be taken as quite approximate.
We were especially uneasy with discrepancies between
our results and those of Betts and Voss because of the
simplicity of their method. Surprisingly, oxygen exchange
rates calculated26 from our rate constants agree with Betts
and Voss’ rate vs pH data at a fixed [S(IV)] of 0.30 M (their
Figure 1). For example, at pH 9.80 and [SO32-] ) 0.30 M
we calculate -log[rate/(m-1 s-1)] ) 3.89, while Betts and
Voss’ Figure 1 gives -log[rate/(M-1 s-1)] ) 3.85. Betts and
Voss’ plot of -log(rate) vs 1/T at [S(IV)] ) 0.30 M (their
Figure 3) also agrees well with one calculated from our rate
constants. We also carried out an oxygen exchange experi-
ment43 to verify Betts and Voss’ rate data: we prepared a
0.30 m sodium sulfite solution by dissolving sodium sulfite
in 17O-enriched water, adjusted the pH to 10.0 with HCl,
+
-
Figure 5. Graph of (1/τBA)(pB/pSO H ) - G[H ] vs the calculated
3
concentration of bisulfite ion for five different sodium bisulfite solutions
having room-temperature pH values ranging from 4.97 to 5.13. The most
concentrated solution ([SHO3-] ) 0.69 m) had an ionic strength of 0.90
m, while the other four had ionic strengths of 1.0 m. Each dashed line
represents the weighted least-squares fitting of the data at a single
temperature, while the solid lines represent the values of k16[SHO3-]/3
obtained by a single fitting of the data at all temperatures, pH values, and
S(IV) concentrations with the function given in eq 17. Data acquired at
282, 295, 310, 325, and 341 K gave similar results (see Supporting
Information).
and then measured the areas of the SO3 and H2O peaks44
2-
in the 17O NMR spectrum at 14 different times between 0
and 105 h. Analysis45 of these data yielded -log[rate/(m-1
s-1)] ) 4.50 at 21.3 °C, compared with Betts and Voss’ value
of -log[rate/(M-1 s-1)] ) 4.22 at 24.7 °C. Although the
corrected to ionic strength 1.0 m using Pitzer’s equations40
and the ionic interaction parameters of Rosenblatt41 to
(42) Reference 25, pp 129-131.
(40) Pitzer, K. S. J. Phys. Chem. 1973, 77, 268.
(43) This experiment was done on the Bruker NMR spectrometer described
in the Experimental Section.
(41) Rosenblatt, G. M. In Flue Gas Desulfurization; Hudson, J. L., Rochelle,
G. T., Eds.; ACS Symposium Series 188; American Chemical
Society: Washington, DC, 1982; p 57.
2-
(44) The SO3 resonance was observed at 210 ppm.
(45) Duffield, R. B.; Calvin, M. J. Am. Chem. Soc. 1946, 68, 557.
1892 Inorganic Chemistry, Vol. 42, No. 6, 2003

Oxygen Exchange between Isomers of Bisulfite Ion
Table 2. Summary of Rate Constants Obtained in This Study
Arrhenius parameters
q
q
∆H298
∆S298
rate const
value at 298 K
ln A
Ea/R (K)
covariancea
(kcal mol-1
)
(cal K-1 mol-1
)
k7
k-7
k8
k-15
k16
(5.6 ( 0.1) × 102 s-1
11.89 ( 0.23
29.59 ( 0.23
19.41 ( 0.54
30.54 ( 0.11
19.52 ( 0.37
1653 ( 74
3098 ( 69
1622 ( 166
3511 ( 36
3141 ( 120
-17.3
-15.8
-88.5
-4.12
-44.3
2.7 ( 0.1
5.6 ( 0.1
2.6 ( 0.3
-37.9 ( 0.5
-1.7 ( 0.5
-22 ( 1
(2.08 ( 0.06) × 108 m-1 s-1
(1.17 ( 0.05) × 106 m-1 s-1
(1.40 ( 0.01) × 108 m-1 s-1
(8.0 ( 0.3) × 103 m-1 s-1
6.38 ( 0.07
5.6 ( 0.2
0.2 ( 0.2
b
-21.7 ( 0.7
a Covariance of ln A and -Ea/R. k16 ) k16a + k16b (see text). For comparison, the single oxygen-exchange experiment at pH 10.0 and 21.3 °C yielded
b
k16 ) 5 × 103 m-1 s-1
.
Table 3. Comparison of Rate Constants of Reactions That Exchange Oxygen Atoms between Bisulfite Ion and Water
a Units are Μ-1 s-1 b Units are m-1 s-1 c Value reported in ref 3. The data from ref 3 yield a value three times greater (see text). d Calculated using k-1
. .
) k-15/(1 + Q4-1). e Obtained by first calculating k-15 using data from ref 2 (see text). The value of k-1 in ref 2 was reported to only one significant figure.
f Estimated value, obtained by applying approximate activity coefficient correction to value at ionic strength 0.1 m. g Calculated using k ) k16/(1 + Q4-1).
factor of 2 discrepancy is puzzling, Betts and Voss’ rate vs
pH data at 0.3 M S(IV) are generally confirmed.
This interpretation would be consistent with our finding at
pH 10 of a rate ca. 2-fold lower than the Betts and
Voss rate. Moreover, in two experiments where they ad-
justed the pH with hydrochloric acid rather than boric acid
buffer, Betts and Voss’ rates were ca. 3-fold lower than in
their experiments with boric acid buffer. In the three ex-
periments where their pH was adjusted with ammonia, the
rates were about the same as with boric acid buffer, but
ammonium ion could have increased the rate by general acid
catalysis as its acid ionization constant is close to that of
boric acid.
The uncertainty in the S(IV) dependence along with their
extremely high value of k-1 makes Betts and Voss’ results
questionable. This uncertainty could be removed by measur-
ing the [SO32-] dependence of the oxygen exchange rate
under more carefully controlled conditions.
Our rate constants do not reproduce Betts and Voss’
oxygen exchange rates for other S(IV) concentrations (their
Figures 2 and 4). While Betts and Voss found an overall
reaction order in S(IV) of 1.15 ( 0.03, our results predict
that the observed order in S(IV) would be 2 at their pH.
Betts and Voss allowed the ionic strengths of their solutions
to range from 0.90 to 1.80 M and at 0.90 M adjusted ionic
strength by replacing the 2-1 electrolyte Na2SO3 with a 1-1
electrolyte. When Betts and Voss’ data are corrected for ionic
strength differences,26 their observed order in S(IV) increases
to about 1.5 and their rate constants come closer to ours,
but a substantial discrepancy remains.
In most of Betts and Voss’ experiments a boric acid buffer
(no concentrations given) was used to stabilize the pH.
Possibly the boric acid was providing general acid cataly-
sis so that at low sulfite concentrations the reaction was
first order in sulfite ion and boric acid while at high sulfite
ion concentrations it approached second-order sulfite ion
dependence. Boric acid is a known general acid catalyst.46
Our rate constant, k-15, is only 1000 times smaller than
that of a diffusion controlled reaction. It differs markedly
(46) Bell, R. P.; Edwards, J. O.; Jones, R. B. In The Chemistry of Boron
and its Compounds; Muetterties, E. L., Ed.; Wiley: New York, 1967;
p 218.
Inorganic Chemistry, Vol. 42, No. 6, 2003 1893

Horner and Connick
from the rate constant of the analogous reaction between
hydrogen ion and bicarbonate ion, which has a room-
temperature value of 6 × 104 M-1 s-1.47 It is known that the
Acknowledgment. This work was supported by the
Director, Office of Science, U.S. Department of Energy under
Contract No. DE-AC03-76SF00098.
-
hydrogen in HCO3 is bonded to an oxygen atom. For this
Supporting Information Available: Plots of data for solutions
and temperatures not shown in Figures 1-5, a figure showing (1/
T1)A vs T, details of the analysis of the rate law derived from
reactions 6-11, details of the analysis of oxygen exchange between
bisulfite ion and disulfite ion, and details of the comparison of our
rate constants to those of ref 3. This material is available free of
charge via the Internet at http://pubs.acs.org.
-
reason Eigen, Kustin, and Maass suggested that the HSO3
isomer is responsible for the high rate of reaction 1, but our
results show that SO3H- reacts more rapidly with H+ to
produce SO2 and H2O. The great difference in rates between
the bisulfite and bicarbonate reactions may be due to the
small amount of atomic rearrangement needed for the
O-S-O remnant of bisulfite ion to attain the bent SO2
structure compared with the amount required to transform
the O-C-O fragment to linear CO2.
IC020692N
(47) Gibbons, B. H.; Edsall, J. T. J. Biol. Chem. 1963, 238, 3502.
1894 Inorganic Chemistry, Vol. 42, No. 6, 2003