Lactonization and protonation of gluconic acid: A thermodynamic and kinetic study by potentiometry, NMR and ESI-MS

Article abstract of DOI:10.1007/s10953-007-9182-x

In acidic aqueous solutions, the protonation of gluconate is coupled with the lactonization of gluconic acid. With a decrease of pC _H, two lactones (δ- and γ-) are sequentially formed. The δ-lactone forms more readily than the γ-lactone. In 0.1 mol L^-1 gluconate solutions, if pC _H>2.5 then only the δ-lactone is generated. When the pC _H is decreased below 2.0, formation of the γ-lactone is observed although the δ-lactone still predominates. In solutions with I=0.1 mol L^-1 NaClO₄ and room temperature, the deprotonation constant of the carboxylic group was determined to be log∈₁₀ K _a=3.30±0.02 using the NMR technique, and the δ-lactonization constant obtained by batch potentiometric titrations was log∈₁₀ K _L=-(0.54±0.04). Using ESI-MS, the rate constants for the δ-lactonization and the reverse hydrolysis reaction at pC _H≈5.0 were estimated to be k ₁=3.2×10^-5 s^-1 and k _-1=1. 1×10^-4 s^-1, respectively.

Full text of DOI:10.1007/s10953-007-9182-x

J Solution Chem (2007) 36: 1187–1200
DOI 10.1007/s10953-007-9182-x
ORIGINAL PAPER
Lactonization and Protonation of Gluconic Acid: A
Thermodynamic and Kinetic Study by Potentiometry,
NMR and ESI-MS
Zhicheng Zhang · Paul Gibson · Sue B. Clark ·
Guoxin Tian · Pier Luigi Zanonato · Linfeng Rao
Received: 3 November 2006 / Accepted: 15 April 2007 / Published online: 18 August 2007
© Springer Science+Business Media, LLC 2007
Abstract In acidic aqueous solutions, the protonation of gluconate is coupled with the lac-
tonization of gluconic acid. With a decrease of pCH, two lactones (δ- and γ -) are sequen-
tially formed. The δ-lactone forms more readily than the γ -lactone. In 0.1 mol·L−1 gluconate
solutions, if pCH > 2.5 then only the δ-lactone is generated. When the pCH is decreased be-
low 2.0, formation of the γ -lactone is observed although the δ-lactone still predominates.
In solutions with I = 0.1 mol·L−1 NaClO4 and room temperature, the deprotonation con-
stant of the carboxylic group was determined to be log10 Ka = 3.30 0.02 using the NMR
technique, and the δ-lactonization constant obtained by batch potentiometric titrations was
log10 KL = −(0.54 0.04). Using ESI-MS, the rate constants for the δ-lactonization and
the reverse hydrolysis reaction at pCH ≈ 5.0 were estimated to be k1 = 3.2 × 10−5 s−1 and
k
−1 = 1.1 × 10−4
s
−1, respectively.
Keywords Gluconic acid · Protonation · Lactonization · NMR · ESI-MS
1 Introduction
Gluconic acid, a polyhydroxyl carboxylic ligand, has been investigated for many years,
mainly due to its importance in a variety of industrial, pharmaceutical and biological
processes [1, 2]. Many studies dealt with solutions of high pH because gluconate forms
strong complexes with metal cations in neutral to basic solutions [3–7]. Fewer studies have
Z. Zhang · P. Gibson · S.B. Clark (
)
ꢀ
Washington State University, Pullman, WA 99164, USA
e-mail: s_clark@wsu.edu
Z. Zhang · G. Tian · P.L. Zanonato · L. Rao
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
L. Rao
e-mail: LRao@lbl.gov
P.L. Zanonato
Dipartimento di Scienze Chimiche, Università di Padova, via Marzolo 1, 35131, Padova, Italy

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J Solution Chem (2007) 36: 1187–1200
been conducted in solutions of low pH, and thermodynamic data that describe solution be-
havior under acidic conditions are scarce and in disagreement. Two reasons likely contribute
to this situation: (1) under acidic conditions the ability of gluconic acid to bind metal ions
is weak or moderate [8, 9], making the studies less attractive for applications; and (2) the
studies at low pH are complicated by the lactonization of gluconic acid [10, 11], a slow
reaction that is coupled to fast chemical processes such as protonation/deprotonation and
complexation. The published literature [12] shows that such lactonization also occurs with
a similar polyhydroxycarboxylic ligand, isosaccharinic acid. Although the formation of a
lactone is catalyzed by the hydrogen ion, lactonization as well as its reverse reaction (lac-
tone hydrolysis) does not alter the acidity of the solution. These complicating factors make a
direct determination of the protonation and complexation constants difficult by conventional
techniques such as acid/base potentiometry under acidic conditions.
Recently, the complexation of gluconate with lanthanides and actinides has been a subject
of study because gluconate is present in some high-level radioactive wastes and its presence
affects the f-electron element speciation in the waste processing solutions. The development
of strategies for the treatment of these waste streams requires thermodynamic data con-
cerning the f-electron element complexation under a wide range of proton concentrations
ranging from acidic to basic. For this purpose, a description of protonation and lactonization
of gluconic acid in acidic solutions is necessary.
Gluconic acid refers to D-gluconic acid derived from natural D-glucose. To be consistent
with the notations in the literature, gluconate, gluconic acid, and δ- and γ -lactone, as shown
in Scheme 1, are denoted here as GH−4 , HGH4, and δ- and γ -L, respectively, where the first
H of HGH4 refers to the proton on the carboxylate group and H4 refers to the four hydrogen
atoms on the secondary alcohols [3, 13]. The six carbon atoms are numbered starting from
the top in the order as C1 to C6.
In this paper, we report thermodynamic and kinetic data on the deprotonation and lac-
tonization of gluconic acid. Our results were obtained by multiple techniques including 13C
Scheme 1

J Solution Chem (2007) 36: 1187–1200
1189
NMR spectroscopy, specially-designed potentiometric titrations, and electrospray ioniza-
tion coupled with mass spectrometry (ESI-MS). This work aids in defining the conditions
under which lactonization is important, the form of the lactones that are produced, their rate
of production, and the corrected protonation constant of the gluconate ligand under acidic
conditions.
2 Experimental
Unless specifically described differently, all the experiments were conducted in I =
0.1 mol·L−1 NaClO4 solutions and at room temperature. Deionized and boiled water was
used in the preparation of all solutions except those used for the NMR experiments. All
chemicals were reagent grade or higher. Sodium gluconate (Acros) was used as received
without further purification.
All experiments, except the NMR data collection, were conducted under an inert at-
mosphere, involving either bubbling argon through the solutions or by using a glove box
filled with argon.
2.1 NMR
NMR experiments were conducted to understand the deprotonation and lactonization of
gluconic acid, and further to determine the deprotonation constants. The stock solution of
gluconate was prepared by dissolving sodium gluconate (NaGH4) in 99.96% D2O (Cam-
bridge Isotope Laboratories). Working solutions of gluconic acid were prepared by mixing
appropriate amounts of the stock solution, DNO3 (70% w/w in D2O, Cambridge Isotope
Laboratories) or NaOD (40% w/w in D2O, Cambridge Isotope Laboratories), and D2O. The
final concentration of gluconate in the working solutions was 0.1 mol·L−1 and the acidity
(pCD or −log10[D+]) ranged from 1.0 to 13.4. The prepared solutions were stored for three
days before the 13C NMR spectra were recorded on a Varian 300 Spectrometer at the Center
of NMR Spectroscopy at Washington State University. Separate experiments had demon-
strated that this time was sufficient for the lactonization reaction to achieve equilibrium.
In the NMR measurements, the magnetic field was stabilized by locking it to the D
signal of the solvent. The sample temperatures were regulated to be 22.0 °C during all
acquisitions. For individual samples, 5,000 to 10,000 scans were taken (with the proton
decoupler turned on) and were averaged to obtain the 13C spectra. Sodium 2,2-dimethyl-
2-silapentane-sulfonate (DSS) was used to reference all 13C NMR spectra, following the
procedures reported elsewhere [14, 15]. The pCD of the solutions, except for the two “end”
solutions, was measured by a potentiometric procedure similar to that described in the next
section. In this case, the electrode was calibrated by a standard acid/base titration in D2O.
The values of pCD in D2O were subsequently converted to pCH in H2O by the relationship:
pCD = pCH + 0.40 [16]. The acidities of the two “end” solutions (pCD = 1.0 and 13.4)
were directly calculated from the amounts of D+ and OD− added during preparation of the
working solutions because these values are outside the working range of the pH electrode.
2.2 “Batch” Potentiometric Titrations
Because the gluconate protonation reaction is coupled with the formation of lactone, and the
latter is a much slower reaction, a batch titration approach was designed to determine the
lactonization constant in conjunction with the protonation constant obtained from the NMR
experiments.

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J Solution Chem (2007) 36: 1187–1200
In a batch titration experiment, a number of individual solutions containing the same
quantity of gluconate were prepared. Different amounts of acid or base were added into
each solution to simulate one step in a titration, in which each solution represented a point
in a typical titration. After the solutions were stored for at least three days, the concentration
of the hydrogen ion in each solution was determined using a Metrohm pH meter (Model
713) equipped with a Ross combination pH electrode (Orion Model 8102). The electrode
had previously been calibrated by a standard acid/base titration so that the Emf reading of
the electrode could be converted to pCH. A detailed description of the electrode calibration
is provided elsewhere [17, 18]. Multiple batch titrations were conducted with solutions of
different concentrations of gluconate. Given the protonation constants obtained from NMR,
the equilibrium constant for lactonization of gluconic acid was calculated with the program
HYPERQUAD [19].
2.3 ESI-MS
ESI-MS measurements were explored as a method to examine the formation of a lactone
and were subsequently applied to estimate the rate constants of lactonization/hydrolysis.
All ESI-MS measurements were performed on an Agilent 1100 series instrument, using
an electrospray ionization method coupled with a quadrupole mass analyzer at Washington
State University. A sample was injected into the electrospray by pressure infusion (50 mbar),
and was run with the following instrumental conditions: (1) 3500 V negative tip voltage;
(2) 110 fragmentor factor; (3) 4.0 mL per minute flow rate of the sheath liquid; (4) 25 PSI
spray gas; and (5) a 150 °C drying gas. The mass spectrum of each run was averaged from
the recorded Total Ion Chromatogram (TIC) data.
A gluconate stock solution was prepared by dissolving sodium gluconate in water.
A sodium acetate solution, used as the sheath liquid for the electrospray measurements, was
prepared by dissolving an appropriate amount of sodium acetate (Aldrich) in water and then
diluting it with an equal volume of methanol (Aldrich). The final concentration of sodium
acetate was controlled at 5 mmol·L−1. The solutions were degassed with an ultrasonic water
bath (Branson) before being loaded into the instrument.
In the experiments, gluconic acid samples with varying values of pCH were prepared
by diluting the gluconate stock solution with water, and then acidifying the samples with
perchloric acid. These samples, after being allowed to equilibrate for three days, were run
under the instrumental conditions mentioned above to determine the specific mass signals
for the species present in these solutions.
For the kinetic experiments, a 50 mmol·L−1 NaGH4 sample was prepared by diluting the
gluconate stock solution with water, and then used to measure a mass spectrum to define a
starting point of the lactonization reaction. After this sample was acidified by 10%, a series
of mass spectra were recorded as a function of time under the same instrumental conditions
as described above.
In order to estimate the lactonization/hydrolysis rate constants, the measured mass spec-
tra versus time data were treated by the following procedures. We started by taking the
intensities of two ionic signals, where one is for a gluconate anion (m/z = 195) and the
other is for a lactone (m/z = 337), from the mass spectrum recorded at time t. The intensi-
ties of those two signals (I195 and I373) are assumed to be correlated linearly to [GH−4 ] and
[L], respectively. With consideration of the limitations associated with the sample injection
(pressure infusion) and the electrospray ionization for quantitative analysis [20], the follow-
ing correction was made to the lactone signal. Because under our experimental conditions
the gluconate anion was present in large excess over gluconic acid or lactone, we assumed

J Solution Chem (2007) 36: 1187–1200
1191
that any change in [GH−4 ] by lactonization was negligible throughout the kinetic course. As
a result, an averaged intensity of the gluconate signal (Iave) could be referred to as an ex-
pected value for the gluconate anion, and therefore the intensity of the lactone signal at the
time t was corrected to It by the following equation:
It = I373(I195/Iave
)
(1)
This corrected intensity (It) was used in the correlation with the lactone concentration.
3 Results and Discussion
3.1 Assignment of 13C NMR Peaks
Within the pCH range studied, we observed six primary peaks for the six carbons of the
gluconate molecule, and each of these six primary peaks sometimes had two smaller peaks
associated with them depended on chemical conditions. This is shown in Fig. 1. Due to
the rapid exchange of the proton ion involved in protonation reactions, chemical shifts of
13
Fig. 1
C NMR spectra of gluconic acid and its related lactones. A Varian 300 Spectrometer operated at
75.5 MHz was used for recording the spectra: 5000–10000 scans for individual spectra, 0.6 Hz line broad-
0
−1
DNO3
13
ening, C
= 0.1 mol·L in D O, and t = 22 °C (room temperature). Acid/base concentrations used
NaGH4
2
for pC adjustment are: C
= 70% w/w in D O and C
= 40% w/w in D O. The peak identifica-
H
2
NaOD
2
tion is relative to the standard C NMR spectrum of gluconate [Aldrich 18,633-3] and δ-lactone [Aldrich
G2000-1]. (a) pC = 6.66; (b) pC = 2.54; (c) pC = 1.99; (d) pC = 1.42
H
H
H
H

1192
J Solution Chem (2007) 36: 1187–1200
individual carbons in the conjugate acid and base cannot be separated [21]. As a result, one
group with six sharp intensive peaks, existing over the entire pCH range and shifting with
the pCH, is attributed to the conjugate species (HGH4 and GH−4 ). These peaks are assigned
to C1 (C=O), C2, C4, C5, C3 and C6, in the order of increasing field (Fig. 1), as previously
published [11].
As the pCH value approaches the acidic range, two additional groups appeared sequen-
tially in the spectra with slight intensities (Fig. 1). The first group to appear represents the δ-
lactone, and thus the second peak is assigned to the γ -lactone. The intensities of the lactone
peaks increase with decrease of the pCH, but the chemical shifts of these peaks remain con-
stant, implying that lactonization and hydrolysis have no effect on the NMR measurement
for these two lactones. This observation is in agreement with the earlier work by Sawyer
et al. [10] and Combes et al. [11], where they have confirmed the slow kinetics of lac-
tonization/hydrolysis. For example, in the work by Combes et al., the rate constants for lac-
tonization and hydrolysis were determined to be around 10−5 s−1 at pCH = 2.4 [11]. These
reaction rates are quite low in terms of the 13C NMR time scale. Therefore, the recorded 13
C
NMR spectra for the lactones, as indicated in Fig. 1, are independent of those reactions [21].
The sequential appearance of the two groups of lactone peaks also suggests that for-
mation of the two lactones occurs differently. The δ-lactone is formed more readily than
the γ -lactone. As indicated from Fig. 1a–b, if the pCH is >2.5, then only the δ-lactone is
formed. When the pCH is decreased to <2.0, the γ -lactone starts to form in measurable
amounts (Fig. 1c–d) although the δ-lactone form still predominates.
3.2 Protonation constants by NMR
In acidic aqueous solutions, gluconic acid (e.g., protonated gluconate) undergoes lactoniza-
tion into δ- and γ -lactone, and the two lactones interconvert with each other as shown in
Scheme 2 [10]:
Scheme 2
Scheme 3
As discussed in the previous section, only the δ-lactone is formed when pCH > 2.5. Fur-
thermore, the pCH is always > 2.5 under the experimental conditions for the batch potentio-
metric titrations and ESI-MS that were used for evaluating the thermodynamic and kinetic
properties of lactonization. We, therefore, made the following simplifications in this study,
i.e., we ignored the interconversion of the two lactones and considered only the δ-lactone
(designated as L) formation (Scheme 3). The equilibrium constants of protonation (Ka) and
δ-lactonization (KL) were defined as Eqs. 2 and 3, respectively:
[HGH4]
Ka =
KL =
(2)
(3)
[GH−4 ][H+]
[L]
[HGH4]
where [HGH4], [GH−4 ], [H+] and [L] denote the molar concentrations of HGH4, GH−4 , H+
and L, respectively.

J Solution Chem (2007) 36: 1187–1200
1193
Owing to the slow kinetics of the lactonization/hydrolysis reactions [10, 11], the glu-
conate protonation reaction can be monitored separately from the lactonization/hydrolysis
reaction by observing the NMR chemical shifts as a function of pCH [21] so that a pro-
tonation constant can be independently determined. Taking a simple protonation reaction
(Eq. 4) as an example, we can describe the principle behind this determination method. The
protonation constant (KH) is defined by Eq. 5:
A + H ꢀ HA
(4)
(5)
[HA]
KH
=
[A][H]
where [A], [HA], and [H] are the molar concentrations of A, HA, and H, respectively.
Because the two conjugate species (A and AH) undergo interconversion through the rapid
exchange of a proton, an observed chemical shift (δobs) for each nucleus is a mole-fraction
weighted average of the two resonances δA and δHA, as described by Eq. 6 [21]:
[A]δA + [HA]δHA
δobs
=
(6)
[A] + [HA]
Manipulation of Eq. 5 yields [HA] = KH[A][H], and substitution of this relation into
Eq. 6 gives the relationship between the observed chemical shift (δobs) and the proton ion
concentration ([H]), as described by Eq. 7:
KH[H]δA + δHA
δobs
=
(7)
1 + KH[H]
where KH, δA, and δHA are constant. The program HYPNMR2000, having the approach
described above, was used to fit the experimental data of δobs versus pCH to obtain the value
of KH.
The results of fitting the gluconate chemical shifts as a function of pCH using the pro-
gram HYPNMR2000 [22] are depicted in Fig. 2, and the calculated protonation constants
are summarized in Table 2. As the pCH changes from 2.0 to 6.0, the largest displacement
of the chemical shift occurs for the C1 (C=O) atom (Fig. 2), which suggests that the car-
boxylic group is deprotonated. The displacement magnitude (≈3.0 ppm) and direction (e.g.,
towards higher frequency with increasing values of pCH) are consistent with previous work
[23], confirming that the carboxylic group is the most acidic site of the HGH4 molecule. Fig-
ure 2 also reveals that the C2 and C4 atoms exhibit the next largest displacements. In view
of the pCH range under consideration and the expected dissociation constants of aliphatic
alcohols [26], it is unlikely that these displacements are attributable to the deprotonation
of a gluconate hydroxyl group. A more plausible explanation is that deprotonation of the
carboxylic group initiates a modification of the conformation of the gluconate molecule,
resulting in alterations in the hydrogen-bonding environment of the C2 and C4 hydroxyl
groups, but not of the C3, C5 and C6 groups. Similar behavior has been described by Cho
et al. [24] for isosaccharinic acid (ISA).
The calculated protonation constant of the carboxylic group is log10 Ka = 3.30 0.02
(Table 2). This value indicates that gluconic acid is a slightly stronger acid than the simple
monocarboxylic acids (e.g., log10 Ka ≈ 4.6 for acetic, butanoic and hexanoic acids [25]),
but it is similar to that of other α-hydroxycarboxylic acids (e.g., log10 Ka ≈ 3.6 for hy-
droxyacetic, 2-hydroxybutanoic and 2-hydroxyhexanoic acids [25]) and isosaccharinic acid

1194
J Solution Chem (2007) 36: 1187–1200
Fig. 2 HYPNMR2000 fitting results for the chemical shifts of the individual gluconate carbons as a function
0
−1
◦
of the pC : C
= 0.1 mol·L
and t = 22 C (room temperature). Acid/base concentrations used
H
NaGH4
for the pC adjustments are: C
experimental data; solid line, calculated values
= 70% w/w in D O, C
= 40% w/w in D O. Symbols: (ꢁ),
H
DNO3
2
NaOD
2
(log10 Ka ≈ 3.2 to 3.3 [24]). This slight increase in acidity might be attributed to the forma-
tion of hydrogen bonding between the carboxylate group and the C2/C4 hydroxyl groups,
which could stabilize the deprotonated form and result in a lower value for log10 Ka.
In the near neutral to basic range of pCH = 6.0 to 13.0, it was observed that the chemical
shifts simply show an inflection point near the high pCH edge. Due to the limited data in
this region, the exact reason for this inflection point is not clear, but two different mecha-
nisms could explain this observation. One is that deprotonation occurs on a hydroxyl group.
Although it is difficult to determine uniquely which group undergoes deprotonation, the C4
hydroxyl group appears to be a logical choice due to its largest displacement. The corre-
ꢀ
sponding equilibrium and protonation constant (Ka ) are described as follows:
GH23− + H+ ꢀ GH−4
(8)
(9)
[HGH−4 ]
ꢀ
Ka
=
[GH23−][H+]
ꢀ
The HYPNMR2000 [22] fitting program yielded log10 Ka = 12.9 0.6. Taking into
consideration the high uncertainty introduced by the limited number of data points available
for the fitting at high values of pCH, we decided to increase the uncertainty of this value
ꢀ
and express this constant as log10 Ka = 13 1, which is close to the pKa (log10 Ka) range
observed for aliphatic alcohols (pKa = 15 to 20) [26].
Another possible reason for this inflection point is the occurrence of an interaction be-
tween the sodium (Na+) and gluconate (GH−4 ) ions. Such complexation has been discussed

J Solution Chem (2007) 36: 1187–1200
1195
Table 1 Experimental data and corrections for the kinetics of the lactonization reaction as determined with
0
−1
the ESI-MS method. Starting solutions: C
−1
= 50 mmol·L , V = 10 mL, pC ≈ 6.2; added acid,
H
NaGH4
0
C
= 0.99 mol·L , V
= 0.05 mL, and pC ≈ 5.0
H
HClO4
HClO4
Time, t
Intensity (I
)
Calibrated I
Extent of equilibrium
m/z
373
(hr)
I
I
(I )
t
(I − I )/(I − I ), %
e
t
e
195
373
0
0.00
0.13
0.30
0.47
0.63
0.80
0.97
1.13
1.56
2.15
3.15
4.15
36.00
72.00
65101
60110
62802
63010
63790
62900
56806
58910
58205
59606
57250
55500
55803
55010
56
318
56
100.0
97.0
89.0
79.6
71.3
67.4
59.9
56.3
46.2
32.9
19.2
11.8
0.1
315
1035
1873
2622
2967
3642
3960
4866
6057
7286
7945
8995
9002
1090
1979
2805
3130
3470
3912
4750
6055
7001
7412
8395
8305
0.0
Table 2 Thermodynamic and kinetic properties of the protonation and lactonization of gluconic acid
Reaction
Stability/kinetic constants
Note
Protonation:
2−
−
+
−1
−1
H
H
+ GH ꢀ GH
log
log
K
K
= 13
1
NMR: I = 0.1 mol·L , room temp.
ꢀ
10
10
a
3
4
−
+
+ GH ꢀ HGH
= 3.30 0.02
NMR: I = 0.1 mol·L , room temp.
a
4
4
Lactonization:
−1
HGH ꢀ L + H O
log
K
= −(0.54 0.04)
−5 −1
Batch titration: I = 0.1 mol·L , room temp.
L
4
2
10
k
1
HGH ꢂ L
k = 3.2 × 10
1
s
ESI-MS: pC ≈ 5.0, room temp.
H
4
k
−1
−4 −1
k
−1
= 1.1 × 10
s
in Cho et al.’s work [24] for ISA. It is expected that the GH−4 complexation reaction with
Na+ is weak, but its effect can be appreciable only when the concentration of Na+ is suffi-
ciently high, which is the case when pCH approaches 13. This complexation reaction may
break the inner-molecular hydrogen bonding of gluconate, causing a conformational change
and thereby producing the chemical shift displacement seen at pCH near 13 as shown in
Fig. 2.
3.3 Lactonization constant by potentiometry
The batch titrations were made in both directions as is shown in Fig. 3. The titration process
was performed in the basic-to-acidic direction first and then in the acidic-to-basic direc-
tion. As discussed in the last section, only the carboxylic group deprotonates in this pCH
range (2.5 to 6.0). Given the value of log10 Ka = 3.30 obtained from the NMR study, the

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J Solution Chem (2007) 36: 1187–1200
−1
Fig. 3 Batch titrations for the lactonization of gluconic acid at I = 0.1 mol·L
and room temperature.
0
0
−1
−1
Cup solution: V = 20 mL and C
= 50 mmol·L . Titrant: C
= 0.9893 mol·L
for the
NaGH4
HClO4
−1
base-to-acid direction (a) and C
experimental pC ; solid line, fitted pC
= 1.0015 mol·L for the acid-to-base direction (b). Symbols: (ꢀ),
NaOH
H
H
δ-lactonization constant was calculated to be log10 KL = −(0.54 0.04) by fitting these
titration data with the program HYPERQUAD [19].
Sawyer et al. [10] used pH measurements and the optical rotation method to investi-
gate the deprotonation and lactonization of gluconic acid within the pH range 2.0 to 5.0, and
obtained log10 KL = −0.86. Careful inspection of their work suggests that the difference be-
tween their result and ours is caused by use of the different protonation constants determined
in these two studies. Due to the limitations of the methods and the techniques available
forty-five years ago, the protonation constant that they determined likely has a large uncer-
tainty. If their determined protonation constant (log10 Ka = 3.70) is substituted by our value
(log10 Ka = 3.30), then re-evaluation of the lactonization constant yields log10 KL = −0.51,
which is the same as ours considering our uncertainty limits. Also, Combes et al. employed
an optical rotation method in combination with high-performance liquid chromatography,
to investigate the kinetics of the lactonization of gluconic acid and the hydrolysis of the
δ-lactone at pCH = 2.4 [11]. From their kinetic results, the stability constant of the lac-
tonization reaction was calculated to be log10 KL = −0.65, which is close to our value.
Assuming that the hydroxyl group deprotonates at high pCH values, and using our de-
termined protonation and lactonization constants, the speciation of gluconic acid in the pH
region from 2 to 14 was calculated and is shown in Fig. 4. For solutions with pCH < 5, the
two equilibria, protonation and lactonization, are coupled and the ratio of the lactone and

J Solution Chem (2007) 36: 1187–1200
1197
Fig. 4 A speciation diagram for
gluconic acid at the constant
gluconate concentration
−1
(0.1 mol·L ). Species fraction
−
lines: solid—GH
,
4
dash—HGH , dash-dot-dot—L,
4
2−
dot—GH
3
Scheme 4
k
1
HGH4 ꢂ L
k −1
1
acid concentrations remains constant as the pCH changes. When pCH > 11.0, the hydroxyl
group starts to deprotonate.
3.4 Rate Constants of Lactonization and Hydrolysis
The rate constants of δ-lactonization and hydrolysis are defined as k1 and k−1, respectively
(Scheme 4).
As an essential step for estimating these constants with the ESI-MS method, the mecha-
nism of lactone ionization during the electrospray process needs to be discussed first. Under
the negative operation mode of ESI, a lactone could accordingly be ionized in two ways.
One mechanism is by the deprotonation of a hydroxyl group of the lactone [27], in which
the lactone is directly ionized. The other mechanism is by the adduction of an anion to the
lactone [20]. The gluconate ion, a main anion in the sample, could be a good candidate for
this adduct. The experimental results (Fig. 5) verify both possibilities. Two types of lactone
anions are formed and detected with the ESI-MS method: m/z = 175 (deprotonation of hy-
droxyl group) and m/z = 373 (lactone adducted by gluconate). Since the pCH values of the
samples are within the range of 3.0 to 6.5, the detected lactone is likely to be the δ-lactone.
Figure 5 also indicates that without acidification, no lactone signals are observed (Fig. 5a),
but with the decrease of pCH, the lactone signals appear (Fig. 5b–c). This observation is
in agreement with our potentiometric results, i.e., that the amount of the lactone formed is
inversely related to the pCH of the gluconate solutions. It is therefore suggested that ESI-MS
measurements can be used to follow the formation of a lactone. Between these two signals,
the one at m/z = 373 is more sensitive with a well-defined ionization mechanism, and hence
it was chosen to be an indicating signal for the lactone in the kinetics studies.
Using m/z = 373 as an indicator for the lactone, we employed the ESI-MS results to
estimate the rate constants for lactonization and hydrolysis, taking advantage of this quick
measurement method compared to the slow kinetics of the lactonization/hydrolysis, and

1198
J Solution Chem (2007) 36: 1187–1200
0
−1
Fig. 5 Mass spectra of acidified gluconate samples with C
= 50 mmol·L : (a) 0.0% acidification
NaGH4
and pC = 6.2; (b) 50% acidification and pC = 4.3; (c) 100% acidification and pC = 3.3
H
H
H
its capacity to identify the lactone. Assuming that the δ-lactonization and hydrolysis fol-
low pseudo-first-order reactions with respect to the concentrations of gluconic acid and the
δ-lactone, respectively [10, 11], the two rate constants (k1 and k−1) are thus related to the
equilibrium constant (KL) as given by Eq. 10:
k1
KL =
(10)
k
−1
and the corrected lactone signal (It ) can be described as a function of time (t) by Eq. 11:
ꢀ
ꢁ
ꢀ
ꢁ
Ie − It
Ie − I0
KL
k1
ln
=
k1 +
t
(11)
where Ie and I0 indicate the intensities of the lactone signal at equilibrium and at an initial
concentration, respectively. The details for deriving Eq. 11 can be found elsewhere [28].
Table 1 lists the measured intensities of the gluconate signal (m/z = 195) and the lactone
signal (m/z = 373) for the kinetic sample at pCH ≈ 5.0, as well as the related corrections
mentioned in Sect. 2.3. Figure 6 shows the graph of ln{(Ie −It )/(Ie −I0)} versus the time t.
The observed linear relationship confirms the assumption of pseudo-first-order reactions,
and provides a value of the rate constant, 0.523. Using this value, the δ-lactonization rate
constant (k1) is 3.2 × 10−5 s−1 according to Eq. 11, and consequently the hydrolysis rate
constant (k−1) is calculated to be 1.1 × 10−4 s−1 using KL = 0.29 as described by Eq. 10.
All obtained constants are summarized in Table 2.

J Solution Chem (2007) 36: 1187–1200
1199
Fig. 6 Kinetic results for
lactonization obtained with the
ESI-MS method. Starting
0
solutions: C
−1
= 50
NaGH4
0
mmol·L , V = 10 mL,
pC ≈ 6.2; added acid,
H
−1
C
V
= 0.99 mol·L
,
HClO4
HClO4
= 0.05 mL, and
pC ≈ 5.0. Symbol (ꢁ):
H
experimental data; solid line,
fitted values
It is interesting to note that lactonization and hydrolysis follow first-order reactions with
respect to the concentration of gluconic acid and the lactone, respectively, and the resulting
rate constants are close to those reported by Combes et al. [11] (k1 = 3.807 × 10−5 s−1 and
k
−1 = 1.730 × 10−4 s−1).
4 Conclusion
Gluconic acid undergoes two equilibria, carboxylate protonation and lactonization, in acidic
media. The variations of the amount of lactonization with the pCH were investigated using
13C NMR spectroscopy. With a decrease of the pCH, the amount of lactonization increases
but the formation of the two lactones (δ- and γ -lactone) occurs differently. The δ-lactone
is generated more readily than the γ -lactone. In 0.1 mol·L−1 gluconate solutions where
the pCH > 2.5, only the δ-lactone is formed. When the pCH < 2.0, the formation of the
γ -lactone is observable although the δ-lactone does predominate.
The thermodynamic properties of these two equilibria were determined by NMR and
batch potentiometric titrations. At I = 0.1 mol·L−1 NaClO4 and room temperature, the
carboxylate protonation and δ-lactonization constants were determined to be log10 Ka =
3.30 0.02 and log10 KL = −(0.54 0.04), respectively.
Negative-mode ESI-MS measurements were applied to examine the formation of lac-
tones within the pCH range of 3.0 to 6.5. The δ-lactone species were detected either as an
alkoxide anion (deprotonation of hydroxyl group) or as an adducted anion (adduction by
gluconate). At pCH ≈ 5.0, the ESI-MS method was used to investigate the kinetic proper-
ties of lactonization and hydrolysis. The rate constants for the δ-lactonization (k1) and the
hydrolysis (k−1) reactions were estimated to be 3.2 × 10−5 s−1 and 1.1 × 10−4
s
−1, respec-
tively.
Acknowledgements This work was supported by the U.S. DOE’s Environmental Management Science
Program at Washington State University. The work performed at Lawrence Berkeley National Laboratory
(LBNL) was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences
under Contract No. DE-AC02-05CH11231 at LBNL. The authors are thankful to the anonymous reviewers
whose comments have helped to improve this manuscript.

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J Solution Chem (2007) 36: 1187–1200
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