The acidity and self-catalyzed lactonization of L-gulonic acid: Thermodynamic, kinetic and computational study

Article abstract of DOI:10.1016/j.carres.2018.07.006

Lactonization and proton dissociation of sugar acids take place simultaneously in acidic aqueous solutions. The protonation-deprotonation processes are always fast, whilst the formation and hydrolysis of γ- and δ-lactones are usually slower. Thus, both thermodynamic and kinetic information are required for the complete understanding of these reactions. The protonation constant (K_p) of L-gulonate (Gul^–) was determined from potentiometric and polarimetric measurements, while the individual lactonization constants (K_L,γ and K_L,δ) for L-gulonic acid (HGul) were obtained via ¹³C NMR experiments. The applicability of this method was proven by measuring these well-known constants for D-gluconic acid (HGluc) and by comparing them to literature data. L-gulonic acid γ-lactone (γ-HGul) has remarkable stability in contrast with δ-HGul as well as γ- and δ-HGluc. The polarimetric measurement implies that the main factor responsible for the enhanced stability of γ-HGul is that its hydrolysis is much slower than that of δ-HGul. This higher stability of the γ-HGul ring over its δ-isomer was also confirmed by quantum chemical calculations. A new confirmed feature of the reaction is that in parallel to H₃O⁺, HGul also catalyzes the formation and reverse hydrolytic processes of γ-HGul, similarly to other general acid catalysts.

Full text of DOI:10.1016/j.carres.2018.07.006

CarbohydrateResearch467(2018)14–22
Contents lists available at ScienceDirect
Carbohydrate Research
journal homepage: www.elsevier.com/locate/carres
The acidity and self-catalyzed lactonization of L-gulonic acid:
Thermodynamic, kinetic and computational study
Bence Kutusa,∗, Gábor Peintlerb, Ákos Buckób, Zsolt Ballaa, Alexandru Lupanc, Amr A.A. Attiac,
István Pálinkód, Pál Siposa
a
Department of Inorganic and Analytical Chemistry, University of Szeged, 7 Dóm tér, H-6720, Szeged, Hungary
Department of Physical Chemistry and Material Science, University of Szeged, 1 Rerrich Béla tér, H–6720, Szeged, Hungary
Department of Chemistry, Babeş-Bolyai University, 11 Arany János Street, RO-400028, Cluj-Napoca, Romania
Department of Organic Chemistry, University of Szeged, 8 Dóm tér, H-6728, Szeged, Hungary
b
c
d
A R T I C L E I N F O
A B S T R A C T
Keywords:
Gulonic acid
Gluconic acid
Lactonization constant
Lactonization kinetics
Self-catalysis
Lactonization and proton dissociation of sugar acids take place simultaneously in acidic aqueous solutions. The
protonation-deprotonation processes are always fast, whilst the formation and hydrolysis of γ- and δ-lactones are
usually slower. Thus, both thermodynamic and kinetic information are required for the complete understanding
of these reactions. The protonation constant (Kp) of L-gulonate (Gul–) was determined from potentiometric and
polarimetric measurements, while the individual lactonization constants (KL,γ and KL,δ) for L-gulonic acid (HGul)
were obtained via 13C NMR experiments. The applicability of this method was proven by measuring these well-
known constants for D-gluconic acid (HGluc) and by comparing them to literature data. L-gulonic acid γ-lactone
(γ-HGul) has remarkable stability in contrast with δ-HGul as well as γ- and δ-HGluc. The polarimetric mea-
surement implies that the main factor responsible for the enhanced stability of γ-HGul is that its hydrolysis is
much slower than that of δ-HGul. This higher stability of the γ-HGul ring over its δ-isomer was also confirmed by
quantum chemical calculations. A new confirmed feature of the reaction is that in parallel to H3O+, HGul also
catalyzes the formation and reverse hydrolytic processes of γ-HGul, similarly to other general acid catalysts.
1. Introduction
mechanism of the Fischer-Speier esterification [12]. A pioneering work
related to the lactonization of HGul and other aldonic acids was carried
Lactones are intramolecular esters of hydroxycarboxylic acids oc-
curring in nature usually as five- (γ) and six-membered (δ) cyclic
compounds. They serve as components of various aromas and odors,
hence, they are utilized in the cosmetic and food industries.
Additionally, important synthetic applications are also known (e.g., ε-
caprolactone).
L-gulonic acid and its γ-lactone (HGul and γ-HGul, Scheme 1) are
intermediates in the biosynthesis of L-ascorbic acid in mammals [1].
The enzymatic reactions involve the formation of gulonic acid from D-
glucuronic acid as discussed in detail in Refs. [2–8]. Nowadays, the
industrial production of ascorbic acid is based on the Reichstein process
applying the readily available D-glucose instead of D-glucuronic acid
[9]. Attempts were also made to obtain ascorbic acid directly from γ-
HGul or its 3,5-O-benzylidene derivative [10]. Furthermore, the diol
and diisocyanate derivatives of γ-HGul were employed to synthetize
polyurethanes [11].
out by Levene and Simms [13,14]. The five- and six-membered lactones
were found to be formed for D-gulonic, D-heptagluconic, D-galactonic,
D-gluconic and D-mannonic acids. The authors observed that the δ-
lactone was more dextrorotatory, while the γ-lactone was more levor-
otatory for the first three aldonic acids. On the other hand, gluconic and
mannonic acids could only be converted into dextrototatory lactones.
These observations are formulated in Hudson's lactone rule [15],
which stipulates that when the OH group involved in the ring closure
lies on the right side on the Fischer projection of the acid, the lactone
will be more dextrorotatory, otherwise it will be more levorotatory.
HGul is expected to be a stronger acid than caproic acid owing to
the presence of electron withdrawing OH functional groups along the
aliphatic backbone. The protonation constant, Kp, of Gul is defined as:
[HGul]⋅co
1
Ka
Kp =
=
[H+][Gul–]
(1)
Lactones are formed via acid catalysis as follows from the
where Ka is the acid dissocation constant of HGul and co means the
∗
Corresponding author.
E-mail address: kutusb@chem.u-szeged.hu (B. Kutus).
https://doi.org/10.1016/j.carres.2018.07.006
Received 20 March 2018; Received in revised form 22 June 2018; Accepted 14 July 2018
Availableonline17July2018
0008-6215/©2018ElsevierLtd.Allrightsreserved.

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
Scheme 1. Left side: structural formulae of L-gulonic acid (HGul) and its γ- and δ-lactones (γ-HGul, δ-HGul). Arrows indicate the OH groups whose attack on the C1
carbon atom yields the five- or six-membered lactone. Right side: the same for D-gluconic acid (HGluc) are shown for comparison.
standard molar concentration, 1 mol dm−3. At infinite dilution, log Kp
of HGul at 25 °C was determined to be 3.67 [13]. The value of log Kp
was determined to be 3.48 (I = 0.1 M NaClO4, via potentiometry) [16]
as well as 3.20 and 3.19 (I = 1 M NaCl, via 1H and 13C NMR spectro-
scopies) [17] at 25 °C. For comparison, the log Kp of the caproate ion
(same as the pKa of caproic acid) was reported to be 4.85 [18].
Contrary to gulonic acid, the industrially more important gluconic
acid (HGluc, Scheme 1) was studied in great detail previously. The log
them with literature data. Additionally, polarimetric experiments and
quantum chemical calculations were carried out to characterize the
lactonization kinetics and the possible structures of the lactones of HGul
present in acidic solutions.
0
2. Experimental
2.1. Reagents and solutions
0
Kp of HGluc was reported to be 3.77–3.92 [19–21] at 25 °C. At 1 M
ionic strength, log Kp was determined to be 3.30–3.63 [21–24] via
potentiometry and 3.24 [25] via 13C NMR spectroscopy, respectively.
The work of Levene and Simms is the only one concerning the
lactonization of HGul. The initial rate of δ-HGul formation was eight
times higher compared to that of γ-HGul at 25 °C [13].
By Baldwin's rules [26], both the reactions resulting the γ- or the δ-
lactone (i.e., the 5-exo-trig and the 6-exo-trig types of ring closure) are
favoured. The larger stability of the γ-lactone corresponds to the qua-
litative finding that an exo double bond stabilizes the five-membered
ring [27].
All samples were prepared with deionized water (Merck Millipore
Milli-Q) and the ionic strength of the solutions was adjusted to 1 M with
NaCl (a. r. grade, Molar Chemicals). Stock solutions of HCl were made
by volumetric dilution of cc. HCl (a. r. grade, Scharlab), and were
standardized against KHCO3. Concentrated (≈50% w/w), carbonate-
free NaOH liquor was prepared in-house from pellets (a. r. grade,
Analar Normapur) according to the procedure reported previously [32].
The caustic then was brought to volume and the stock solution and it
was standardized against HCl solution.
L-gulonic acid γ-lactone (95%, Aldrich), D-gluconic acid δ-lactone
(≥99%, Sigma) and sodium D-gluconate (≥99%, Sigma) were used
without further purification. The purity of γ-HGul and δ-HGluc was
checked by their 1H and 13C Nuclear Magnetic Resonance (NMR)
spectra (0.2 M lactone in 100% V/V D2O, see Figures S1–S4 in the
Electronic Supporting Information). Accordingly, contaminants having
peak area larger than 1% were not detected. It has to be mentioned that
contrary to γ-HGul, large portion of δ-HGluc underwent hydrolysis even
in D2O (Figures S3 and S4). The solutions of D-gluconate were made
directly from the sodium salt, while those of L-gulonate were prepared
by neutralizing the lactone with NaOH until pH ≈ 7–8. The completion
of ring-opening reaction was confirmed by the 1H and 13C NMR spectra.
The individual lactonization constants of the two isomers are ex-
pressed as:
[γ−HGul]
KL,γ
=
[HGul]
(2)
[δ−HGul]
KL,δ
=
[HGul]
(3)
These equilibrium constants can be estimated from the initial rate
coefficients of the lacton formation and reverse hydrolysis reported in
Ref. [13]. Accordingly, log KL,γ ≈ 0.60 and log KL,δ ≈ −0.49. For
HGluc, numerous works give quantitative description of the δ-lactoni-
0
zation reaction. The thermodynamic lactonization constant, log KL,δ
,
2.2. Potentiometric titrations
was calculated to be −0.95 [20] and −0.81 [21]. Depending on the
ionic strength and experimental technique used, log KL,δ ranges from
−1.15 to −0.54 [19,21,28–31]. On the other hand, log KL,γ was re-
ported to be −0.59 [19] and −0.62 [29]. Clearly, the difference in the
stability of the gluconolactones is much smaller compared to that of the
gulonolactones.
Potentiometric measurements were carried out with a Metrohm
Titrando 888 automatic titration instrument, whilst the cell potentials
were recorded with a Jenway 3540 Bench Conductivity/pH Meter using
a SenTix 62 combined glass electrode (from WTW). All samples were
stirred and thermostated to T = (25.0
0.1) °C during the titrations.
Contrary to HGluc, quantitative studies for the lactonization reac-
tions of HGul are sporadic. Thus, the available data need to be extended
to provide better understanding of the protonation, lactonization
equilibria and the lactonization kinetics of this aldonic acid. In this
study, we report on the protonation and individual lactonization con-
stants obtained from potentiometric and 13C NMR measurements. The
accuracy of the protonation and lactonization constants of HGul were
checked by determining these constants also for HGluc and comparing
To minimize the incidental dissolution of CO2, N2 atmosphere was
applied.
The calibration of the electrode was performed by titrating 70 cm3
solution of 0.02 M NaOH with 0.2 M malonic acid (at 1 M ionic
strength). The intercept and slope of the electrode were calculated
utilizing the pHCali program [33], and the calibration curve was found
to be Nernstian.
To avoid problems associated with the lactonization of HGul and
15

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
HGluc in acidic medium, measurements for determining Kp were started
in the alkaline region. In all cases, 70 cm3 of solutions containing
[NaGluc]T,0 = 0.10–0.30 M NaGluc or NaGul were titrated with
[HCl]T,0 = 0.25–1.0 M, and the data were evaluated with the PSEQUAD
program [34]. (For the component X, hereafter the total concentration
is denoted as [X]T,0 (titrations) or [X]T (polarimetric and NMR mea-
surements), while [X] represents the equilibrium concentration.)
It should be emphasized again that the aim of all experiments
concerning Gluc– was to validate the methods used to determine the
equilibrium constants for Gul–.
2.5. Quantum chemical calculations
Geometry optimizations for γ-HGul and δ-HGul were carried out
using the M11 range-separated hybrid meta-GGA DFT functional [39]
coupled with the def2-TZVP [40] basis set. The recently developed M11
DFT functional was shown to provide excellent performance for main-
group energies, proton and electron affinities, barrier heights, bond
dissociation and noncovalent interaction energies.
Calculations were performed first in vacuum, then in the framework
of implicit water molecules. Solvent effects were taken into account by
applying the Conductor-like Polarizable Continuum Model (CPCM)
[41] using the default set of radii from the Universal Force Field (UFF)
[42]. To find the respective conformers, optimizations were augmented
with conformational analysis, that is, the dihedral angle was system-
atically changed by 60° along the freely-rotating C–C bonds. All cal-
culations were carried out using the Gaussian 09 software package
[43].
2.3. NMR measurements
1H and 13C NMR spectra were recorded on a Bruker Avance DRX
500 MHz NMR spectrometer equipped with a 5 mm inverse broadband
probe head furnished with z oriented magnetic field gradient capability.
The magnetic field was stabilized by locking it to D2O prior to mea-
surements. The temperature was kept at T = (25
1) °C during all
spectra acquisitions. 64–128 as well as 256–8192 interferograms were
collected to obtain 1H and 13C spectra, respectively.
The geminal (2JH,H) or vicinal (3JH,H) coupling constants for γ-HGul
obtained in D2O are presented in Table S1. These parameters were
previously reported for the spectroscopically equivalent D-gulonic acid
3
γ-lactone [35]. The agreement is within 0.5 Hz except for J4,5, being
the deviation as much as 3.1 Hz.
The lactonization reactions were performed in excess HCl. Time
dependence of the 13C NMR spectra were followed in a solution con-
taining [NaGul]T = 0.34 M, [HCl]T = 0.37 M and 20% V/V D2O. The
equilibrium measurements were undertaken for solutions with
[Gul–]T = 0.40–0.42 M and [HCl]T = 0.44–0.50 M as well as
[Gluc–]T = 0.40 M and [HCl]T = 0.46–0.59 M. The completion of the
reaction was checked periodically by polarimetry.
For HGluc, the lactone formation was found to be reversible
[19–21,28–31]. In order to check the reversibility of lactonization of
HGul, a solution containing 0.42 M NaGul was acidified with 0.63 M
HCl, and the equilibrium solution was re-neutralized with 0.63 M
NaOH. By the 1H and 13C NMR spectra (Figures S5 and S6), no irre-
versible side reactions were observed.
3. Results and discussion
3.1. Protonation of L-gulonate
The potentiometric measurements for the gulonate-containing so-
lutions are shown in Fig. 1. The four independent titrations were fitted
simultaneously, and the ionic product of water, pKw, was taken as 13.76
[44]. To characterize the goodness of the fit, the so-called fitting
parameter (FP) was used, which can be defined as:
n
2
∑
(Y
− Y
)
i,calc
i,meas
i=1
FP =
(4)
n − k
where Yi,calc and Yi,meas are the ith calculated and measured data (cell
potential or optical rotation), n means the number of measured points,
and k denotes the number of the fitted parameters. For the titrations,
the FP was 0.7 mV. The determined stability constants with their triple
Having reached the equilibrium, 20% V/V D2O was added to all
solutions prior to spectra acquisition resulting dilution ratio of 0.8 and
I = 0.8 M.
2.4. Polarimetric measurements
The optical rotation of the samples was recorded with an Optech
PL1 polarimeter equipped with a sodium lamp and having an accuracy
of 0.05°. The length of the light path was 200 mm. All experiments
were performed at T = (25
2) °C.
The specific rotations of L-Gul–, γ-L-HGul and D-Gluc– were de-
termined by calibration at 1 M ionic strength. These values with their
triple standard errors (SE, given in parentheses) are as follows:
−13.5(3)°, 57.8(3)° and 13.0(3)°. Previously, specific rotation of
−12.8° was reported for L-Gul– [17], while −55.0° was obtained for γ-
D-HGul [13]. For D-Gluc–, values ranging between 12.0° and 15.6°
[19,20,28,36] were reported.
To determine the specific rotations of L-HGul and D-HGluc, solution
series with [Gul–]T = 0.31 M and [HCl]T = 0.03–0.35 M as well as with
[Gluc–]T = 0.40 M and [HCl]T = 0.03–0.49 M were prepared. Batch pH
measurements were also carried out with a glass electrode (SenTix,
calibrated against commercial buffers in the pH range of 1–10). Both
optical rotation and pH readings were undertaken simultaneously and
right after the sample preparation. The Kp was calculated with the aid of
the OriginLab software [37].
Of the four samples used for the equilibrium studies (see the pre-
vious section), the one containing [Gul–]T = 0.42 M and
[HCl]T = 0.46 M was used to follow the lactonization kinetics of HGul.
The optical rotation of this solution was determined in regular time
intervals, and the experimental data were evaluated by means of the
ChemMech program [38].
Fig. 1. Potentiometric titration curves for Na-L-gulonate (Gul–). Experimental
conditions: T = (25.0
0.1) °C, I = 1 M (NaCl), V0 = 70 cm3. Analytical
concentrations of Gul– and of the titrant: [Gul–]T,0 = 0.097 M and
[HCl]T,0 = 0.972 M (black); 0.294 M and 0.972 M (magenta); 0.196 M and
0.496 M (blue); 0.097 M and 0.243 M (red). The titrations started in the alkaline
region with [OH−
]T,0 = 0.01–0.02 M. Symbols and solid lines represent the
measured and calculated data, respectively. (For interpretation of the refer-
ences to colour in this figure legend, the reader is referred to the Web version of
this article.)
16

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
Table 1
Protonation (log Kp), γ- and δ-lactonization constants ((log KL,γ, log KL,δ) for L-gulonate (Gul–) and D-gluconate (Gluc–). Data correspond to T = 25 °C unless indicated
differently. Additionally, the 3 SE values are given in parentheses.
Reaction
Background el.
Stability constant
Methoda
Ref.
H3O+ + Gul– = HGul + H2O
I → 0
0.1 M NaClO4
1 M NaCl
1 M NaCl
1 M NaCl
1 M NaCl
0.8 M NaCl
1 M NaCl
not indicated
0.8 M NaCl
not indicated
I → 0
log Kp = 3.67
3.48(6)
POT
POT
POT
POT
13
16
3.325(4)b
3.33(3)d
p. w.c
p. w.
17
3.14(9)
3.19(9)
POL
13C NMR
13C NMR
POL
HGul = γ-HGul + H2O
log KL,γ = 0.79(3)
0.73(3)
p. w.
p. w.
13
p. w.
13
0.60e
POL
HGul = δ-HGul + H2O
log KL,δ = −0.91(6)
13C NMR
POL
−0.49e
H3O+ + Gluc– = HGluc + H2O
log Kp = 3.85
3.77(6)
POL
POL
19
20
I → 0
I → 0
1 M NaCl
1 M NaCl
1 M NaCl
1 M NaCl
1 M NaCl
1 M NaClO4
1 M NaClO4
1 M NaClO4
0.8 M NaCl
not indicated
not indicated
I → 0
3.92(10)
POT
POT
POT
POL
21
3.371(5)b
3.37(3)d
p. w.
p. w.
p. w.
24
25
21
22
23
p. w.
19
29
20
21
28
21
31
21
p. w.
21
19
3.26(6)
3.35(3)
3.24(3)
3.63(1)
3.48(18)
3.30(10)
log KL,γ = −0.68(2)
−0.59(6)
−0.62
log KL,δ = −0.95
−0.81(9)
−0.89
POT
13C NMR
POT
POT
POT
NMR
POL
GC
POL
POT
POL
HGluc = γ-HGluc + H2O
HGluc = δ-HGluc + H2O
I → 0
≈0.004 Mf
0.1 M NaClO4
0.1 M NaClO4
0.5 M NaClO4
0.8 M NaCl
1 M NaClO4
not indicated
not indicated
not indicated
−0.91(6)
−0.54(12)g
−0.93(10)
−0.65(1)
−1.15(6)
−0.73(3)
−0.67
POT
13C NMR
POT
13C NMR
POT
POL
GC
POL
29
30
−0.66g
a
POT = potentiometry, POL = polarimetry, NMR = nuclear magnetic resonance spectroscopy, GC = gas chromatography using flame ionization detector.
Protonation constant calculated by simultaneous curve fitting.
Present work.
Suggested protonation constant by individual curve fitting.
Calculated from the rate coefficients determined at pH ≈ 2.
b
c
d
e
f
Corresponds to pH = 2.36 reported by the authors; no additional background electrolyte was used.
Data correspond to T = 20 [30] and 22 °C [31], respectively.
g
standard error ( 3 SE) as well as the literature data are presented in
the log Kp of Gluc– is in good agreement with literature data [22–25]
obtained under the same experimental conditions, only the equilibrium
constant given in Ref. [21] seems to be out to some extent.
Polarimetric measurements were also carried out with samples
containing [Gul–]T = 0.31 M; the corresponding optical rotation values
are depicted in Fig. 2. Upon increasing [HCl]T, the optical rotation of
Gul– markedly increases allowing the calculation of Kp. The observed
rotation (α) depends on the concentrations of Gul– and HGul by eq. (6):
Table 1. For comparison, the same data for HGluc are also indicated.
By the rate law, one would expect higher reaction rate for lactoni-
zation with increasing aldonate concentration. To decide whether this
reaction proceeded in the gulonate-containing systems or not, the
curves were fitted individually as well. If the lactonization goes to
completion, the apparent protonation constant (Kp,app) of the anion can
be expressed as:
–
–
α = αGul [Gul ] + αHGul [HGul]
(6)
([HGul] + [γ−HGul] + [δ−HGul])⋅c
Kp,app
=
= Kp (1 + KL,γ + KL,δ
)
[H+][Gul–]
where [Gul–] and [HGul] are the corresponding actual concentrations
(in mol·dm−3) while αHGul and αGul– are referred to as the products of
the specific rotation and the path length (in °·dm3·mol−1).
Using the definition of Kp (eq. (1)) and the mass balance equation
for Gul–:
(5)
It follows from eq. (5) that Kp,app ≥ Kp and only Kp,app can be de-
termined by potentiometry, since this method is not able to distinguish
whether the pH change is the result of protonation or lactonization. The
apparent constant would also be higher if the lactonization processes
took place only partially (in this case KL should to be replaced by the
reaction quotient, QL). Each curve, however, yielded the same log Kp,app
values within 0.01 unit of uncertainty. Hence, Kp is independent from
[Gul–]T,0 (i.e., Kp,app = Kp), which means that our constants truly cor-
respond to the protonation process.
[Gul–]T = [Gul–] + [HGul]
(7)
the rotation can−bpeH expressed as:
–
Kp10 αHGul + αGul
α = [Gul–]T
1 + Kp10–pH
(8)
The log Kp of Gul– agrees fairly with the one obtained from NMR
measurements at the same temperature and ionic strength [17], while
where [Gul–]T is the total concentration of the anion. During calcula-
tions, the molar rotations of the two anions were held constant at the
17

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
Fig. 2. Optical rotation of Na-L-gulonate (Gul–) as
Experimental conditions: T = (25
a function of pH.
2) °C, I = 1 M (NaCl); [Gul–]T = 0.306 M
Fig. 3. 13C NMR spectrum of L-gulonic acid (HGul) and its γ- and δ-lactones (γ-
HGul and δ-HGul). Inset: region of carboxylate and carbonyl resonances.
and [HCl]T = 0.031–0.311 M. Symbols and solid lines represent the measured
and calculated data, respectively.
Experimental conditions: T = (25
1) °C, I = 0.8 M (NaCl), 20% V/V D2O;
[Gul–]T = 0.336 M, [HCl]T = 0.368 M. Peaks of HGul are labeled as C1–C6,
while the γ and δ symbols correspond to the respective lactones.
value determined from calibrations. As a result, the FP was found to be
0.03°. The protonation constants obtained for the two aldonic acids are
shown in Table 1.
Given that potentiometry is a more accurate method and is used
more widely for the determination of protonation constants, the value
of log Kp is suggested to be 3.33 for Gul– as well as 3.37 for Gluc–
(determined via titrations).
method was successfully employed to determine the KL of xylonic acid
[47].
Based on these assumptions, KLγ and KL,δ can be estimated by eqs.
(9) and (10):
The main aim of these measurements was to determine the specific
rotation of HGul. The calculated rotation was converted to traditional
units yielding [αHGul] = 5.7(8)°. For comparison, these measurements
were undertaken for HGluc as well and [αHGluc] was determined to be
−5.7(8)°.
The specific rotation of HGluc at T = 20–25 °C was reported to be
between −6.9° and 5.80° [19,20,28,30,45,46] pointing to the un-
certainty of the experimental data. Nevertheless, −6.7° [45] and −6.9°
[46] were determined from freshly prepared HGluc, which is close to
our value and to those reported previously [19,30]. Based on this
agreement, the specific rotation found for HGul seems to be reliable.
Aγ−HGul
[γ−HGul]
≈
≈
= KL,γ
= KL,δ
AHGul
[HGul]
(9)
[δ−HGul]
Aδ−HGul
AHGul
[HGul]
(10)
where A is the respective total integrated area belonging to the acid or
the lactones. It is seen in Fig. 3 that δ-HGul is formed to a very low
extent. Thus, a reliable estimate for its concentration required long
spectral acquisition (8192 scans), which was also applied for Gluc–. The
C1 (carbonyl) peak of δ-HGul did not appear even after such long ac-
cumulation time due to its long relaxation time.
The lactonization constants calculated this way are presented in
Table 1, whilst the corresponding speciation diagrams are depicted in
Fig. 4. The log KL,γ of HGul is in fair agreement with the one calculated
3.2. Lactonization equilibria for L-gulonic acid
Applying excess HCl, remarkable conversions of HGul and HGluc to
their lactones were observed both in the 13C and the 1H NMR spectra.
The latter spectra, however, were not well-resolved preventing their use
from further quantitative analysis. The 13C peaks of δ-HGul and γ-
HGluc were assigned by comparing the spectra of the equilibrium so-
lutions to those of γ-HGul and δ-HGluc (Figures S2 and S4) and to those
of the anions [17,25]. A 13C NMR spectrum for the equlibrium solution
of HGul and its lactones is shown in Fig. 3.
It is clearly shown in Fig. 3 that γ-HGul is formed in the largest
amount. The extreme stability of γ-HGul over δ-HGul reflects the qua-
litative rule that an exo double bond stabilizes the five-membered rings
[27].
Although the actual structures of the acids and their lactones are
rather different, the number of the O and H nuclei attached to the same
carbon atom remains unaltered leading to similar relaxation times and
hence, similar peak areas. Consequently, the sum of the integrals of
C1–C6 may be applied for estimating the ratio of the actual con-
centrations within a certain spectrum. In addition to the well-separated
peaks of the 13C nuclei, (i) the position of the lactone signals is in-
dependent of the pH, (ii) the concentration of the free anion is negli-
gible in excess of HCl, and (iii) this method does not require the exact
value of pH (contrary to the determination of Kp). Moreover, this
Fig. 4. Speciation diagram of the gulonate-related (Gul–) species as a function
of pH. The calculations correspond to T = 25 °C, I = 0.8–1.0 M and
[Gul–]T = 0.300 M.
18

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
from the rate coefficients given in Ref. [13]. On the other hand, the
present value of log KL,δ is lower by ≈ 0.4 units. Both literature data,
however, are based on estimated initial reaction rates.
For the δ-lactonization constant of HGluc at I > 0, the deviation of
our values from literature data is not higher than 0.2 logarithmic units
(except for those given in Ref. [21]). Although our constants might be
affected by the presence of 20% V/V D2O, and the different ionic
strength (0.8 M), the difference is lower than the scattering range of the
reported values. Thus, the lactonization constants of HGluc given here
are reliable at least at the semi-quantitative level which validates the
constants of HGul, too.
The surprisingly high γ-lactonization constant of gulonic acid im-
plies that this species should be considered when complexation equi-
libria between metal ions and Gul– are studied in the acidic pH range.
This is even more important when the metal ion is inert preventing the
use fast potentiometric titrations.
Fig. 6. Optical rotations for L-gulonic acid (HGul) as a function of time.
Experimental conditions: T = (25
3.3. Lactonization kinetics of L-gulonic acid
2) °C, I = 1 M (NaCl); [Gul–]T = 0.420 M,
The applicability of 13C NMR spectroscopy to characterize the lac-
tonization reaction was utilized to find which lactone is formed faster.
In a solution containing 0.34 M NaGul and 0.37 M HCl, the integrals of
the different species were calculated, while the reaction was followed
for a sufficiently long time (11 h). The six peaks of the acid and addi-
tional signals appeared 20 min after solution preparation. These peaks
were at the same position as those of δ-HGul assigned during the
equilibrium measurements (Fig. 3).
New signals appeared in the spectra after 27 min; these peaks were
assigned as those of γ-HGul. The peak intensity of the six-membered
lactone, however, increased faster compared to its isomer.
Consequently, the formation of δ-HGul is faster in accordance with the
observations of Levene and Simms [13].
[HCl]T = 0.461 M. Full circles represent the measured points. Dashed line:
calculated points by assuming reactions 13 and 17 (model 1); solid line: cal-
culated points by assuming reactions 13, 17 and 21 (model 2). Insets: zoomed
regions where model 1 shows the largest deviation from the experimental
curve.
Q
L,δ reaches a constant value (indicated with dashed line). This limiting
value can be regarded as KL,δ obtained from the 13C spectra of the
equilibrium solutions (Table 1). In conclusion, δ-HGul reaches the
equilibrium rapidly, even when the reaction is far from the overall
equilibrium state. Additionally, the assumption that δ-HGul would be
an unstable intermediate can be ruled out.
For HGluc, the calculation of rate constants was based on the ob-
servation that the equilibrium between HGluc and δ-HGluc is estab-
lished long before the formation of γ-HGul [19]. Conversely, the present
measurements (Fig. 5) provide spectroscopic evidence that this as-
sumption is not applicable for the lactonization of HGul.
Similarly to the lactonization constants, the reaction quotient at a
given time (QL), can be estimated by the relative peak areas:
Aγ−HGul,t
[γ−HGul]t
≈
≈
= QL,γ
= QL,δ
Despite the advantage of 13C NMR in identifying the different lac-
tones, accurate rate constants cannot be deduced due to the large un-
certainty of the calculated integral ratios. Thus, polarimetry was chosen
to study the kinetics of lactonization in detail, similarly to those pub-
lished in the literature [13,14,19,20,28,30].
AHGul,t
[HGul]t
(11)
Aδ−HGul,t
[δ−HGul]t
AHGul,t
[HGul]t
(12)
These reaction quotients are plotted in Fig. 5. It is seen that after 4 h,
The optical rotation was recorded for the solution containing
[Gul–]T = 0.420 M and [HCl]T = 0.461 M; the measured points are
plotted in Fig. 6. The initial rotation is positive according to the specific
rotation of HGul. The measured values then decrease slightly due to the
formation of the δ-lactone. During 10 days, the formation of γ-lactone
exhibits a remarkable increase reaching a constant value of 7.1° im-
plying the completion of the reaction. The direction of the overall
change is the opposite but, expectedly, its shape is the same as that
measured by Levene and Simms [13] for D-gulonic acid.
If the specific rotation of δ-HGul was positive, it would be even
smaller than that of the acid, which is very unlikely for a cyclic com-
pound. Hence, [αδ-HGul] is a large negative value, contrary to [αγ-HGul].
Since the nucleophilic OH group lies on the left (δ) or right (γ) side on
the Fischer projection of HGul, δ-HGul is more levorotatory while γ-
HGul is more dextrorotatory than the acid. Accordingly, L-gulonic acid
obeys Hudson's lactone rule [15], hence, [αδ-HGul] < [αHGul] < [αγ-
HGul].
To model the experimental points, the acid-catalyzed lactonization
and lactone hydrolysis for the two lactones were taken into account
first.
Fig. 5. Reaction quotients (QL) for L-gulonic acid (HGul) γ- and δ-lactones (γ-
HGul and (δ-HGul) as a function of time. Experimental conditions: T =
HGul + H3O+ = δ−HGul + H3O+ + H2O
(13)
(25
1) °C, I = 0.8 M (NaCl), 20% V/V D2O; [Gul–]T = 0.34 M,
[HCl]T = 0.37 M. Qγ,L and Qγ,L were defined as the ratio of the total 13C peak
area of the lactone and that of HGul. The dashed line represents the δ-lacto-
nization constant, KL,δ, determined from equilibrium measurements.
r = k1 [H3O+][HGul]
(14)
(15)
1
r
−1
= k–1[H3O+][δ−HGul]
19

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
Table 2
Reaction rate coefficients for the δ- and γ -lactonization (k1, k2, k3) and the reverse hydrolysis reactions (k–1, k–2, k–3) of L-gulonic
acid (HGul) at T = (25
2) °C and I = 1 M (NaCl). The coefficients were determined via polarimetry; 3 SE is given in par-
entheses.
Reactiona
Rate coefficient
Reference
HGul + H3O+ = δ-HGul + H3O+ + H2O
k1 = 1.5(5)·10−3 M−1 s−1
p. w.
p. w.
13
k
–1 = 1.3(3)·10−2 M−1 s−1
k1 [H3O+] = 3.1·10−5 s−1c
k–1∗[H3O+] = 9.6·10−5 s−1c
k2 = 2.2(6)·10−4 M−1 s−1
∗
13
HGul + H3O+ = γ-HGul + H3O+ + H2O
p. w.b
p. w.
13
k
–2 = 4.0(1.1)·10−5 M−1 s−1
k2∗[H3O+] = 3.8·10−6 s−1c
k–2∗[H3O+] = 9.6·10−7 s−1c
k3 = 2.5(8)·10−5 M−1 s−1
13
p. w.
p. w.
HGul + HGul = γ-HGul + HGul + H2O
k
–3 = 4.7(1.5)·10−6 M−1 s−1
a
Excess H3O+ or HGul given in the reaction equation act as a catalyst.
Present work.
Data correspond to T = 25 °C. The pseudo-first order rate coefficients were determined at pH ≈ 2.
b
c
k1
(preventing direct comparison of the rate coefficients). It is worth
mentioning that the effect of self-catalysis can be observed near the
minimum and at the end of the reaction. Hence, full curve fitting is
necessary to pinpoint this process, as opposed to the method of initial
rates.
Moreover, the self-catalysis for δ-HGul was taken into account, too,
but the FP could not be lowered probably because of the low conversion
of δ-lactonization. For HGluc, the direct interconversion of δ-HGul to γ-
HGul (above pH ≈ 4) was proposed earlier [48–50]. It should be noted,
however, that our 1H and 13C NMR spectra of the partially hydrolyzed
δ-HGluc (in D2O) showed the presence of HGluc but γ-HGluc was ab-
sent. Considering such reaction for the gulonate-containing system did
not yield lower FP.
The rate coefficients obtained by assuming reactions (13), (17) and
(21) are presented in Table 2. It is seen that both the rates of formation
and hydrolysis are higher for δ-HGul. The ratio of k1 and k2 is 6.8, while
the ratio of k–1 and k–2 is 325. Hence, the remarkable difference be-
tween KL,γ and KL,δ does not arise from the rate of formation but from
the rate of hydrolysis. Since the k–1/k–2 parameter is closely related to
the relative stability of the lactone rings, our finding supports quanti-
tatively that an exo double bond stabilizes the γ-lactone ring [27].
Interestingly, the k2 rate coefficient was found to be 8.6 times larger
than k3 inferring that the initial step of lactonization, which is the
protonation of the carbonyl oxygen, proceeds much faster with H3O+
(H+) than with HGul. In general acid catalysis the rate-determining
step is the protonation of the COOH group. It follows from the me-
chanism that the stronger the acid the higher the reaction rate since H+
can be released easier. HGul is weaker acid than H3O+, hence k3 < k2.
(The same relation, k–3 < k–2 holds for the reverse hydrolysis, too.) In
conclusion, HGul is a general acid catalyst. Numerous general acid
catalysts (e.g., acetic acid, malonic acid) were studied for the hydrolysis
of δ-HGluc in the work of Pocker and Green [20]. Our observations
imply that if the aldonic acid is used in sufficiently high concentrations,
it can catalyze its own lactonization and lactone hydrolysis processes.
KL,δ
=
k
(16)
(17)
(18)
(19)
−1
HGul + H3O+ = γ−HGul + H3O+ + H2O
r2 = k2 [H3O+][HGul]
r
= k–2 [H3O+][γ−HGul]
−2
k2
KL,γ
=
k
(20)
−2
H3O+ acts as a catalyst in these reactions (model 1) and its con-
centration was nearly constant (≈0.044 M, i.e., pHc ≈ 1.35) throughout
the reaction, because of employing excess HCl. During the fitting pro-
cedure, the protonation constant (from potentiometry) and the specific
rotations (from polarimetry) were kept constant. Regarding the lacto-
nization, the low conversion of δ-lactonization results in strong corre-
lation between KL,δ and the unknown [αδ-HGul], thus, KL,δ was fixed as
well. On the other hand, KL,γ was treated as a parameter to be fitted.
The calculated rotations are depicted as dashed line in Fig. 6. The
optical rotation could be appropriately fitted for the majority of the
points, however, significant deviations remained around the minimum
(≈3000 s) and from 105 s. By this model, the FP was found to be 0.09°.
Beside H3O+, HGul may also serve as a proton source. Hence, the
decrease of its concentration would lead to the decrease of the reaction
rate when significant amount of γ-HGul was formed at the expense of
HGul. The model, therefore, was extended with the following reaction:
HGul + HGul = γ−HGul + HGul + H2O
(21)
r3 = k3 [HGul]2
(22)
r
= k–3 [HGul][γ−HGul]
(23)
−3
k3
KL,γ
=
k
(24)
−3
The model augmented with eqs. (22)–(24) (model 2) provided sa-
tisfactory fitting for the whole duration of the reaction (solid line in
Fig. 6) since the two ranges of systematic deviations disappeared. Ac-
cordingly, the FP decreased to 0.07°. The log KL,γ was found to be 0.73,
0.06 unit lower than the one obtained via 13C NMR (log KL,γ = 0.79,
Table 1). This difference is acceptable considering the different ex-
perimental methods and the overlapping uncertainty intervals of the
two constants. Moreover, the specific rotation of δ-HGul was calculated
to be −85(9)°.
The catalytic role of HGul is unusual, but can be explained by its
high concentration (≈0.42 M). Similar concentration of HGul, 0.25 M,
was applied by Levene and Simms [13], which is in the same order of
magnitude; however, they analyzed only the initial reaction rates
3.4. The relative stability of L-gulonic acid γ- and δ-lactones
Previously, the equilibrium conformation of D-gulonic acid γ-lactone
was studied by 1H NMR spectroscopy [35]. Accordingly, γ-D-HGul fa-
vours the envelope conformation in equilibrium having the C2-OH
group quasi-equatorially oriented. Additionally, the HOCH2-CHOH side
chain prefers the arrangement in which the interaction between the C5-
OH and C3-OH groups is absent. Concerning the results of other aldo-
pentono-lactones, the authors proposed that intramolecular hydrogen
bonds play role in the stabilization of the preferred structures.
These observations are supported by the optimized structure of the
enantiomer γ-L-HGul (Fig. 7). It is worth mentioning that the C=O
20

B. Kutus et al.
CarbohydrateResearch467(2018)14–22
delocalization of the π electrons again results that the C1-O1A bond
length is shorter than the C4-O1A one (1.341 vs. 1.435 Å). The distances
between C2-OH and C3-OH (2.043 Å) as well as between C4-OH and
C3-OH (2.411 Å) indicate hydrogen bonding.
Conversely, there is no interaction between the C2-OH group and
the carbonyl oxygen (O1B). This finding may in part explain the dif-
ferences in the stability constants, but there can be other factors (e. g.,
repulsion and overlapping orbitals), which affect the structure of the
lactones. To disentangle all the interactions affecting the stability of
these molecules would require more detailed computational analysis,
which was beyond the scope of the present study.
4. Conclusions
Below pH = 5, the L-gulonate and the diastereomer D-gluconate
undergo protonation as was attested by potentiometric and polarimetric
measurements. The protonation constant was found to be very similar
for the two anions as a token of structural similarity (i.e., the number of
OH groups). The basicity of the COO− functional group, thus, is not
significantly affected by the differences in the configuration of the OH
groups. Moreover, this structural relationship yields the same absolute
specific rotations for the acids formed upon protonation.
Fig. 7. Optimized structure of L-gulonic acid γ-lactone (γ-HGul). The calcula-
tions were performed at the M11/def2-TZVP level while solvent effects were
taken into account by the CPCM model. The hydrogen bonds are visualized with
dashed lines.
On the contrary, the relative arrangement of the individual OH
groups along the carbon chain exhibits remarkable effect with regard to
the stability of the five-membered (γ-HGul, γ-HGluc) and the six-
membered lactones (δ-HGul, δ-HGluc) forming in acidic medium. The
γ- and δ-lactonization constants of HGluc (log KL,γ = −0.68, log
K
K
L,δ = −0.65) and the δ-lactonization constant of HGul (log
L,δ = −0.91) are small and similar in magnitude. Conversely, much
higher stability was observed for γ-HGul having log KL,γ of 0.73–0.79.
Concerning the lactonization kinetics of gulonic acid, δ-HGul is
formed faster, but the reverse hydrolysis of γ-HGul take place much
slower, which appears to be the main reason of the higher stability of γ-
HGul. The enhanced stability of the γ-lactone ring over its δ-isomer was
confirmed by quantum chemical calculations, too.
Surprisingly, kinetic experiments show that beside H3O+, HGul can
also act as a catalyst. In other words, HGul can catalyze its own γ-lac-
tonization and the reverse hydrolysis if applied in sufficiently high
concentrations. In this respect, gulonic acid probably behaves as a
general acid catalyst similarly to other weak acids, which were studied
previously concerning the lactonization processes of gluconic acid. The
existence of this self-catalysis implies that such reactions may take
place for other aldonic acids as well.
Fig. 8. Optimized structure of L-gulonic acid δ-lactone (δ-HGul). The calcula-
tions were performed at the M11/def2-TZVP level, while solvent effects were
taken into account by the CPCM model. The hydrogen bonds are visualized by
dashed lines.
Acknowledgements
double bond is partially delocalized through the O-C=O ester group. As
a result, the C1-O1A bond length becomes shorter (1.333 Å) than the
C4-O1A one (1.461 Å). The envelope conformation is slightly distorted
as the dihedral angle for the C2-C1-O1A-C4 moiety is 5.81° instead of
0°.
Furthermore, two weak hydrogen bonds are formed between the
O1B atom and the C2-OH group (2.373 Å) as well as between the C2-
OH and C3-OH groups (2.178 Å).
The authors are grateful for the technical assistance provided by
Ilona Halasiné-Varga. Research leading to this contribution was fi-
nanced by the GINOP-2.3.2-15-2016-00013 and the NKFIH K 124265
Grants. All these supports are highly appreciated.
Appendix A. Supplementary data
Concerning δ-HGluc, the half-chair conformation was reported to
prevail in aqueous medium [51], and it was deduced that the relative
arrangement of C2-OH and C5-OH functions has a key role. That is, if
these two groups are trans-disposed (e.g., for δ-D-HGluc and δ-D-HGul),
the half-chair, otherwise the boat conformation is favoured. This
statement is confirmed by the present calculation for δ-L-HGul (Fig. 8),
albeit its structure is somewhat distorted. That is, the dihedral angle for
the C5-O1A-C2-C3 and the O1A-C1-C2-C3 moieties are −29.72° and
24.53° instead of 0°.
Supplementary data related to this article can be found at https://
doi.org/10.1016/j.carres.2018.07.006.
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