Crystal structure and thermodynamic properties of the coordination compound calcium D-gluconate Ca[D-C6H11O7]2(s)

Article abstract of DOI:10.1016/j.molstruc.2020.128818

The coordination compound calcium D-gluconate, Ca[D-C₆H₁₁O₇]₂(s), was synthesized and characterized by chemical analysis, elemental analysis, and X-ray crystallography. Single crystal X-ray diffraction technique revealed that the compound was formed by two D-gluconate anions and one calcium (II) cation. And the D-gluconate anion had a curved chain configuration with an intramolecular bond. The compound exhibited an outstanding chelate property of D-gluconate anions to calcium (II) cations, and the calcium (II) cation was eight-coordinated and chelated by four D-gluconate anions. The lattice potential energy and ionic volume of the anion were calculated to be 1434.05 kJ?mol^?1 and 0.4211 nm3 from crystallographic data. In accordance with famous Hess law, a reasonable thermochemical cycle was designed and the standard molar enthalpy of formation of Ca[D-C₆H₁₁O₇]₂(s) was calculated as Δ_sH_m[Ca[D-C₆H₁₁O₇]₂, s] = -(3545.19 ± 1.07) kJ?mol^?1 by use of an isoperibol solution-reaction calorimeter. Furthermore, molar heat capacities of the compound were measured using a Quantum Design Physical Properties Measurement System (PPMS) with specific heat option within the temperature range from (1.9–300) K. The heat capacities of the compound increased with the temperature and no thermal anomaly was found in the whole temperature region. The experimental data was fitted to a function of the absolute temperature T with a series of theoretical and empirical models for the proper temperature ranges. The values of standard thermodynamic function, C_p,m^o/J?K^?1?mol^?1, Δ₀^TH_m^o/kJ?mol^?1, Δ₀^TS_m^o/J?K^?1?mol^?1, and Δ_o^TG_m^o/T/J?K^?1?mol^?1 (=Δ₀^TS_m^o-Δ₀^TH_m^o/T) from T = (0–300) K was calculated based on the fitting results. The standard molar heat capacity, entropy and enthalpy of the compound at T = 298.15 K and 0.1 MPa was determined to be C_p,m^o= (493.20 ± 2.70) J·K^?1 mol^?1, H_m^o= (75934 ± 805) J·mol^?1, S_m^o= (471.55 ± 2.78) J·K^?1 mol^?1, and G_m^o/T = - (64658 ± 808) J·K^?1?mol^?1, respectively.

Full text of DOI:10.1016/j.molstruc.2020.128818

Journal of Molecular Structure 1225 (2021) 128818
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: http://www.elsevier.com/locate/molstruc
Crystal structure and thermodynamic properties of the coordination
compound calcium D-gluconate Ca[D-C6H11O7]2(s)
,
You-Ying Di a *, Guo-Chun Zhang a, Yu-Pu Liu b, Yu-Xia Kong b, Chun-Sheng Zhou a
a College of Chemical Engineering and Modern Materials, Shangluo University / Shaanxi Key Laboratory of Comprehensive Utilization of Tailings Resources,
Shangluo, Shaanxi, 726000, PR China
b Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, College of Chemistry and Chemical Engineering, Liaocheng
University, Liaocheng, 252059, PR China
a r t i c l e i n f o
a b s t r a c t
Article history:
The coordination compound calcium D-gluconate, Ca[D-C6H11O7]2(s), was synthesized and characterized
by chemical analysis, elemental analysis, and X-ray crystallography. Single crystal X-ray diffraction
technique revealed that the compound was formed by two D-gluconate anions and one calcium (II)
cation. And the D-gluconate anion had a curved chain configuration with an intramolecular bond. The
compound exhibited an outstanding chelate property of D-gluconate anions to calcium (II) cations, and
the calcium (II) cation was eight-coordinated and chelated by four D-gluconate anions. The lattice po-
tential energy and ionic volume of the anion were calculated to be 1434.05 kJ,molꢀ1 and 0.4211 nm3
from crystallographic data. In accordance with famous Hess law, a reasonable thermochemical cycle was
designed and the standard molar enthalpy of formation of Ca[D-C6H11O7]2(s) was calculated as DsHm[Ca
Received 20 January 2020
Received in revised form
28 June 2020
Accepted 2 July 2020
Available online 26 August 2020
Keywords:
Calcium D-gluconate
X-ray crystallography
Standard molar enthalpy of formation
Physical properties measurement system
Heat capacity
[D-C6H11O7]2, s] ¼ -(3545.19
1.07) kJ,molꢀ1 by use of an isoperibol solution-reaction calorimeter.
Furthermore, molar heat capacities of the compound were measured using a Quantum Design Physical
Properties Measurement System (PPMS) with specific heat option within the temperature range from
(1.9e300) K. The heat capacities of the compound increased with the temperature and no thermal
anomaly was found in the whole temperature region. The experimental data was fitted to a function of
the absolute temperature T with a series of theoretical and empirical models for the proper temperature
Thermodynamic function
ranges. The values of standard thermodynamic function, Cpo;m/J,Kꢀ1,molꢀ1
,
DT0Hmo /kJ,molꢀ1
,
DT0Som/J,Kꢀ1,molꢀ1, and DToGmo =T/J,Kꢀ1,molꢀ1 (¼D0T Smo
-
DT0Hmo /T) from T ¼ (0e300) K was calculated based
on the fitting results. The standard molar heat capacity, entropy and enthalpy of the compound at
T ¼ 298.15 K and 0.1 MPa was determined to be Cpo;m¼ (493.20 2.70) J$Kꢀ1 molꢀ1, Hmo ¼ (75934 805)
J$molꢀ1, Smo ¼ (471.55 2.78) J$Kꢀ1 molꢀ1, and Gmo =T ¼ - (64658 808) J$Kꢀ1,molꢀ1, respectively.
© 2020 Elsevier B.V. All rights reserved.
1. Introduction
bonds in their molecular structures. Those CeH and CeC chemical
bonds are broken, a lot of CO2 and H2O are generated, and the
It is well known that the sugar is the energy and carbon sources
of the organism. In organisms, the polysaccharides are first con-
verted to the monosaccharides through a series of hydrolysis.
Simple sugar is the smallest unit of sugar. For nearly a century,
people have found up to 600 kinds of simple sugars. These are the
energy substances needed for the metabolism of organisms, and
the kind of rich chemical energy is stored in CeH and CeC chemical
energy is released when oxidation of these simple sugars is
happened in biological bodies. Since the monosaccharide in nature
has an aldehyde group, it is easily oxidized to the monosaccharide
acid. A lot of monosaccharide acids in organism are now known,
such as gluconic acid, succinic acid, malic acid, pyruvic acid, lactic
acid and so on, they have their own characteristic physiological
functions and nutritional values in organisms. However, it is found
through experimental studies and clinical applications that the
some complexes formed by these monosaccharide acids with some
life metal elements have more significant physiological and nutri-
tional values to the organism.
* Corresponding author. College of Chemical Engineering and Modern Materials,
Shangluo University, Shangluo, 726000, Shaanxi Province, PR China.
E-mail addresses: diyouying@126.com, myyydi@eyou.com (Y.-Y. Di).
D-Gluconic acid and its derivatives have become important
https://doi.org/10.1016/j.molstruc.2020.128818
0022-2860/© 2020 Elsevier B.V. All rights reserved.

2
Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
chemicals in the pharmaceutical, food and general chemical engi-
neering fields so that it became available in commercial quantities
[1e3]. Calcium is an essential inorganic metal ion for human. Cal-
cium D-gluconate, as one of the most important derivatives of D-
Gluconic acid, is called as “calcium with great energy”, and widely
applied in the treatment of hypocalcemia. And it was used to
counteract the overdose of magnesium sulfate [4], which was often
administered to pregnant women in order to prophylactically
prevent seizures (as inpatient experiencing preeclampsia). Calcium
D-gluconate was also used as a cardioprotective agent in hyper-
kalemia. In recent years, as a mineral supplement and nutrient
additive, calcium D-gluconate was largely applied in medicine,
pharmaceutical, food, feed, and chemical industries because it was
non-toxic and fully biodegradable [5,6]. For these reasons we
studied crystal structure and thermodynamic properties of calcium
D-gluconate, which were needed to develop its new application
fields and to carry out some relevant theoretical research.
The thermodynamic property data reported in this paper were
the most basic data that must be used in the process of industrial,
agricultural and chemical production. Through these data, impor-
tant chemical production data such as enthalpy change, equilib-
rium constant and theoretical yield of the chemical reaction in
which this compound was involved can be accurately determined.
In addition, in order to illustrate the scientific nature of the re-
ported data, we compared the thermodynamic data reported in this
paper with the property data of another compound cesium D-
gluconate published in this journal [7], and obtain the relation of
thermodynamic properties with the change of material structure.
Crystal structure was not only important for deeply studying and
discussing some thermodynamic properties of the substance, but
also it can be used to clarify the nature of relationship between the
structure and thermochemical property of the material. The lattice
potential energy was a vital measurement to weigh the bonding
ability of the molecules or ions in crystal structure, and in relation
with many significant physicochemical properties of the
substances.
vacuum desiccator at T ¼ 303.15 K to dry in vacuum for 12 h, the
final product was placed in a weighing bottle and preserved in a
desiccator. The mass fraction purity of the compound was deter-
mined by chemical analysis and element analysis (model: PE-2400,
PerkinElmer, USA), and these values (analysis, calculated for
C12H22O14Ca: C 33.49, H 5.15, O 52.05, Ca 9.31%; found: C 33.47, H
5.14, O 52.03, Ca 9.35%) have shown that the mass fraction purity of
the compound is > 0.995.
2.2. X-ray crystallography
A crystal with dimensions of 0.35 mm ꢁ 0.07 mm ꢁ 0.04 mm
was glued to the fine glass fiber and then mounted on the Bruker
Smart-1000 CCD diffractometer with Mo-K
a
radiation,
scan
l
¼ 0.071073 nm. The intensity data was collected in the
feu
mode at T ¼ (298 2) K. The empirical absorption corrections were
based on multi-scan. The structure was solved by direct method
and difference Fourier synthesis, and all non-hydrogen atoms were
refined anisotropically on F2 by full-matrix least-squares method.
All calculations were performed with the program package
SHELXTL [7,8].
A summary of crystallographic data and refinement parameters
was listed in Table 2. We have applied for a CCDC 2014305 for the
new synthesized compound Ca[D-C6H11O7]2(s).
2.3. Isoperibol solution-reaction calorimetry
The isoperibol solution-reaction calorimeter used in the work
consisted primarily of a precision temperature controlling system,
an electric energy calibration system, a calorimetric body, an
electric stirring system, a thermostatic bath made from transparent
silicate glass, a precision temperature measuring system, and a data
acquisition and processing system. During whole experiments, the
water thermostat was automatically maintained at T ¼ 298.15 K
and the maximum variation was found to be 1$10ꢀ3 K. The ther-
mometer used in the temperature measurement of the reaction
chamber was a thermistor. The temperature measurement accu-
racy of the thermometer was 0.0001 K. Experiments demon-
strated that the precision of measuring the temperature can reach
1$10ꢀ4 K. The principle and structure of the calorimeter were
described in detail elsewhere [8].
As part of a program of investigations of the crystal structures
and thermochemical properties of D-gluconates, we synthesized
the title compound Ca[D-C6H11O7]2(s). Elemental analysis, chemi-
cal analysis and X-ray crystallography were applied to characterize
the compound. The lattice potential energy and ionic volume of the
anion were obtained from crystallographic data. The standard
molar enthalpies of dissolution of reactants and products of the
designed reaction were determined by an isoperibol solution re-
action calorimeter. The standard molar enthalpy of formation of Ca
[D-C6H11O7]2(s) was determined based on these experimental re-
sults. More importantly, the heat capacities of the compound were
measured by PPMS and some important thermodynamic functions
were derived by the experimental heat capacity results.
The reliability of the calorimeter was verified previously by
measuring the enthalpy of dissolution of KCl (calorimetrically pri-
mary standard) in the double-distilled water. According to the
molar ratio of KCl to waternKCl : nH Oz1 : 1110, a certain amount of
2
KCl was dissolved in 100 cm3 of double-distilled water at T ¼
(298.150 0.001) K. The average enthalpy of dissolution of KCl was
determined to be (17547
corresponding published data (17536
13) J,molꢀ1, which compared with
3.4) J,molꢀ1 under the
same experimental conditions. Experiments demonstrated that the
uncertainty between the measuring value and the literature value
was within 0.30% [9].
2. Experimental section
2.1. Preparation of the title compound
2.4. Heat capacity measurements
The provenances and purities of the chemicals used in the
synthesis and calorimetric experiments were shown in Table 1.
In the paper, calcium D-gluconate was prepared by concen-
trating aqueous solution of D-gluconolactone with a slight excess of
calcium carbonate for 2 h, filtering off the excessive calcium car-
bonate, and adding a certain amount of anhydrous ethyl alcohol.
Colorless single crystals suitable for X-ray diffraction were obtained
one week later by slow natural evaporation. The product was
recrystallized for three times with anhydrous ethyl alcohol and
colorless crystal was gained. Finally, the sample was placed in a
The heat capacity measurements were performed using a
commercially designed calorimeter (heat capacity option of the
Physical Properties Measurement System, abbreviated as PPMS)
constructed by Quantum Design, which was recently set up at
Thermochemistry Laboratory, Dalian Institute of Chemical Physics,
Chinese Academy of Sciences. In order to verify the PPMS calo-
rimeter’s performance, we measured the heat capacities of a copper
pellet and a
a-Al2O3 crystal cylinder in the temperature range from
T ¼ (1.9e300) K and a powdered benzoic acid in the temperature

Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
3
Table 1
Information on the provenances and purities of the chemicals used in the synthesis and calorimetric experiments.
Chemicals
Provenances
Purities
D-gluconolactone
J&K Scientific Ltd. China
99.5 mass %
calcium carbonate
anhydrous ethyl alcohol
sodium D-gluconate
sodium chloride
J&K Scientific Ltd. China
Tianjin No.3 Chemical Reagent Factory. China
Prepared by our laboratory [21]
J&K Scientific Ltd. China
99.99 mass %
99.5 mass %
> 99.6 mass %, by chemical and elemental analysis.
99.99 mass %
a
calcium dichloride
calcium D-gluconate
J&K Scientific Ltd. China
Prepared by the method in the paper
99.99 mass %
99.5 mass %, by chemical and elemental analysis
a
cited as reference [21].
Table 2
Summary of crystallographic data and refinement parameters for Ca[D-C6H11O7]2(s)a.
Crystallographic data
structure refinement
Empirical formula
Formula weight
Temperature/K
Wavelength/nm
Crystal system
Space group
C12H22O14Ca
430.38
(298 2)
0.071073
Monoclinic
C2
ꢂ
Unit cell dimensions/nm or
a ¼ (1.5870 0.0015), b ¼ (0.5876 0.0003), c ¼ (0.9159 0.0005),
a
¼ 90,
b
¼ (99.55 0.22),
g
¼ 90
Volume/nm3
(0.8423 0.0001)
Z
2
Calculated density/g$cmꢀ3
1.697
0.450
452
Absorption coefficient/mmꢀ1
F(000)
Crystal size/mm3
0.35 ꢁ 0.07 ꢁ 0.04
Theta range for data collection/ꢂ
Limiting indices
3.15 to 25.01
ꢀ18 ꢃ h ꢃ 15, ꢀ6 ꢃ k ꢃ 6, ꢀ10 ꢃ l ꢃ 10
1865/1305, [R(int) ¼ 0.1140]
98.9
Semi-empirical from equivalents
0.9822 and 0.8583
Full-matrix least-squares on F2
1305/55/123
Reflections collected/unique
Completeness to theta ¼ 25.00/%
Absorption correction
Max. and min. transmission
Refinement method
Data/restraints/parameters
Goodness-of-fit on F2
1.136
Final R indices [I > 2 sigma (I)]
R indices (all data)
R1 ¼ 0.1313, wR2 ¼ 0.2838
R1 ¼ 0.1997, wR2 ¼ 0.3286
755 and ꢀ1200
Largest diff. peak and hole/e$nmꢀ3
a
Uncertainty is standard uncertainty.
range from (1.9e300) K. Consequently, the sample of the title
compound calcium D-gluconate was measured in the temperature
range from T ¼ (1.9e300) K. Different temperature intervals used in
the measurements while heating from (1.9e100) K were logarith-
mic spacing below T ¼ 100 K and 10 K above T ¼ 100 K. The
powdered benzoic acid and calcium D-gluconate samples were
prepared for the heat capacity measurement according to the
technique developed by Shi et al. [10,11], in which the powdered
sample was pressed into a pellet with a number of copper stripes in
a copper cup and subsequently was loaded into the PPMS calo-
rimeter. The detailed sample preparation process can be found in
the corresponding literature [11]. The heat capacity measurement
was generally performed in two steps: (1) an ‘addenda run’, the
addenda measurement with Apiezon grease (plus Apiezon N grease
to strengthen thermal conductivity between the platform and the
sample) for the sample background, and (2) a’sample run’, the heat
capacity measurement of the pellet including the sample, the
copper stripes and the cup. The first measurement gained the heat
capacities of the empty sample platform. In the second measure-
ment, the sample was placed onto the platform and the heat ca-
pacity of the whole ensemble was measured. The heat capacities of
the sample can be consequently obtained by subtracting the known
heat capacity of copper from the total heat capacity of the pellet.
That is, the net heat capacity of the sample was then achieved from
the difference between both measurements. The sample masses of
the copper pellet and the a -Al2O3 cylinder used in the heat capacity
measurement were (67.81 and 48.94) mg, respectively. The masses
of copper foil and powdered sample were (14.81 and 11.10) mg for
the benzoic acid measurement, and (16.75) mg for the calcium D-
gluconate measurement, respectively.
Sample couplings in the measurements were typically >99% at
T > 100 K and in the range 90e99% at lower temperatures. The
performance of the calorimeter was tested by measurements on an
ultra-pure copper,
a-Al2O3 and powdered benzoic acid samples,
and the uncertainty was found to be 3% below 20 K and 1% above
20 K [11e14].
3. Results and discussion
3.1. Description of crystal structure
Ca[D-C6H11O7]2(s) was crystallized in the monoclinic crystal
system with the space group C2 and Z ¼ 2, and the unit cell di-
mensions were a ¼ (1.5870 0.0015) nm, b ¼ (0.5876 0.0003)
nm, c ¼ (0.9159 0.0005) nm,
b
¼ (99.55 0.22), as described in
Table 2. And the D-gluconate anion had a curved chain conforma-
tion with an intramolecular bond. The binding diagrams of the D-
gluconate ligand bonding to Ca2þ were shown in Fig. 1 and Fig. 2.
The unit cell figure was shown in Fig. 3.
Single crystal X-ray analysis revealed that in the molecule of Ca

4
Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
Fig. 1. Molecular structure of calcium D-gluconate Ca[D-C6H11O7]2(s).
C6H11O7]2$5H2O), sodium D-gluconate, potassium D-gluconate,
rubidium D-gluconate, and lead(ІІ) D-gluconate. And the straight
chain conformation had a six-member zigzag carbon chain which
was nearly planar. In this study, we have found that the D-gluco-
nate anion in Ca[D-C6H11O7]2(s) had a bent chain conformation
(Figs. 1 and 2). In the bent chain conformation, C2eC6 lay in a five-
member zigzag carbon chain, and C1 deviated significantly from
the carbon chain, see Figs. 1 and 2.
The environments of the Ca2þ cation and D-gluconate anion
were depicted in Fig. 2. In the title compound, each D-gluconate
anion coordinated to two cations through one hydroxyl oxygen
(O3) and one carboxylate oxygen (O1) to the first cation, and two
hydroxyl oxygen (O6 and O7) to the second cation. The cation Ca2þ
was coordinated to four D-gluconate anions, by a carboxylate ox-
ygen (O1) and hydroxyl oxygen (O3) forming a five-membered ring
to the first anion, by a carboxylate oxygen (O1B) and hydroxyl ox-
ygen (O3B) forming a five-membered ring to the second anion, by
two hydroxyl oxygen (O6A and O7A) forming a five-membered ring
to the third anion, and by two hydroxyl oxygen (O6C and O7C)
forming a five-membered ring to the fourth anion. Thus each cation
(Ca2þ) was only coordinated to two D-gluconate anion, and the
coordination compound consisted of one crystallographically in-
dependent Ca(П) centre and two D-gluconate anions.
Fig. 2. The crystal cell structure of calcium D-gluconate Ca[D-C6H11O7]2(s).
The CaeO distances of hydroxyl oxygen for Ca2þ were nearly
equal lying in the range (0.2418 0.0008) ~ (0.2485 0.0007) nm
(Table 3), and the differences from the mean were not significant.
These results were in good agreement with those of the crystal
structures in the normal alditol series [17,18]. The two CeO bonds in
the carboxyl group were found to have lengths (0.1264 0.0013)
[D-C6H11O7]2(s), the conformation of the D-gluconate anion was
very different from that in the literature [15e17]. The crystal
structure studied earlier showed that the D-gluconate anion had a
straight chain conformation as calcium D-gluconate hydrate (Ca[D-
Fig. 3. The coordination environment of the Ca2þ with D-C6H11O7ꢀ.

Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
5
Table 3
potential energy of the compound was calculated to be
UPOT ¼ 1434.05 kJ,molꢀ1, which showed that the structure of Ca[D-
C6H11O]2(s) was stable.
Selected bond lengths (nm) and bond angles (deg) for Ca[D-C6H11O7]2(s)a.
Ca(1)eO(1)#1
Ca(1)eO(1)
Ca(1)eO(6)#2
Ca(1)eO(6)#3
Ca(1)eO(3)#1
Ca(1)eO(3)
Ca(1)eO(7)#3
Ca(1)eO(7)#2
O(1)eC(1)
(0.2396 0.0008)
(0.2396 0.0008)
(0.2418 0.0008)
(0.2418 0.0008)
(0.2425 0.0007)
(0.2425 0.0007)
(0.2485 0.0007)
(0.2485 0.0007)
(0.1264 0.0013)
(0.1272 0.0015)
(0.1446 0.0013)
(0.1461 0.0013)
O(5)eC(4)
O(6)eC(5)
O(7)eC(6)
C(1)eC(2)
C(2)eC(3)
C(3)eC(4)
C(4)eC(5)
C(5)eC(6)
(0.1445 0.0012)
(0.1474 0.0012)
(0.1424 0.0014)
(0.1527 0.0016)
(0.1474 0.0014)
(0.1499 0.0014)
(0.1533 0.0014)
(01480 0.0016)
(125.4 1.1)
In addition, for a salt of molecular formula MpXq,
ꢀ
ꢁ
Vm MpXq ¼ pVþ þ qV
(2)
ꢀ
where V- and V were the volumes of the anion and cation, p ¼ 1,
þ
and q ¼ 2 for Ca[D-C6H11O]2(s). VCa2þ was reported to be 0.0201 nm3
[20]. The V- (the volume of the anion D-C6H11Oꢀ7 ) was calculated to
be 0.2005 nm3.
O(1)-C(1)-O(2)
O(1)-C(1)-C(2)
O(2)-C(1)-C(2)
O(2)eC(1)
O(3)eC(2)
O(4)eC(3)
(117.9 1.1)
(116.6 1.0)
Symmetry code: #1 -xþ1, y, -zþ1; #2 -xþ1/2, y-1/2, -zþ1; #3 xþ1/2, y-1/2, z.
3.3. The standard molar enthalpy of formation of Ca[D-C6H11O7]2(s)
The designed reaction was shown as follows:
a
Uncertainty is standard uncertainty.
nm and (0.1272 0.0015) nm, respectively. The angles O1eC1eC2
and O2eC1eC2 were (117.9 1.1)ꢂ and (116.6 1.0)ꢂ, respectively.
The carboxyl groups were symmetrical within experimental errors
2Na[D-C6H11O7](s) þ CaCl2(s) ¼ Ca[D-C6H11O7]2(s) þ 2NaCl(s) (3)
with an angle of (125.4
1.1)ꢂ between the two CeO bonds
The standard molar enthalpies of dissolution of the reactants
and products of the reaction (3) in the selected solvent (100 cm3 of
double-distilled water) were measured by an isoperibol solution-
reaction calorimeter, respectively. The enthalpy change of the re-
action (3) was calculated from the data of above standard molar
enthalpies of dissolution.
(Table 4). The differences were probably due to inaccuracy in the
structure analysis and the different crystal forces for the two oxy-
gen atoms [15,17].
The information on hydrogen bonds was listed in Table 4. In the
structure, there were five different OeO distances shorter than
0.30 nm, of which O(5)eH(5)$$$O(2) was the only intramolecular
hydrogen bond. All oxygen atoms of hydroxyl groups and carboxyl
group of the title compound participated in intermolecular
hydrogen bonds. The shortest hydrogen bond of length
(0.2725 0.0008) nm was from hydroxyl oxygen (O3) (as donor) to
carboxyl oxygen (O2) (as acceptor). The longest hydrogen bond of
length (0.2952 0.0011) nm in crystal was associated with a hy-
droxyl oxygen O4 (as acceptor). Of the five hydroxyl groups, O4 and
O5 both donated and accepted hydrogen bonds; O3, O6, and O7
each donates, but did not accept hydrogen bond.
About 1.0 ꢁ 10ꢀ3 mol of Na[D-C6H11O7](s) in the reaction (3) was
dissolved in 100 cm3 of double-distilled water at T ¼ 298.15 K. The
experimental results of the process were shown in the reference
[21], the average value was determined as DsHmo ;1¼ (18.936 0.180)
kJ$molꢀ1. If “s” represented 100 cm3 of double-distilled water, the
dissolution process may be expressed as:
{Na[D-C6H11O7](s)} þ “s” ¼ Solution A1
(4)
The stoichiometric number of CaCl2(s) {n(Na[D-C6H11O7](s)):
n(CaCl2(s)) ¼ 2 : 1} in the reaction (3) was regarded as a norm for
sample weighing, about 5.0 ꢁ 10ꢀ4 mol of CaCl2(s) was dissolved in
the solution A1 at T ¼ 298.15 K. The experimental results of the
process were shown in Table 5 and the dissolution process may be
expressed as follows:
3.2. Lattice potential energy and ionic volume of D-C6H11Oꢀ7 anion
The equation (1) was used to estimate lattice potential energy
for the generalized type of the salts of MpXq [19]:
h
.
i
X
ꢀ
ꢁ
ꢀ
ꢁ
niz2i
a’
Vm1=3 MpXq
þ
b
’
(1)
{CaCl2(s)} þ Solution A1 ¼ Solution A2
(5)
UPOT MpXq
¼
In the measurement of the enthalpy of dissolution, the hydro-
scopicity of anhydrous calcium dichloride will cause large errors,
making the measurement results unreliable. However, this problem
has been taken into account in the measurement of enthalpy of
dissolution. Before the enthalpy of dissolution was formally
measured, we have tested repeatedly and found that the mea-
surement was reliable when the calcium dichloride sample was
heated up to 400 K, kept at high temperature for 12 h and dehy-
drated by use of a vacuum dryer, and the calcium chloride sample
where a0 and b0 were appropriate fitted coefficients chosen ac-
cording to the stoichiometry of the salt, ni was the number of ions
with a charge zi in the formula unit, Vmwas the molecular volume in
units of nm3 [19]. In the case of the salts of formula MpXq with
charge ratio (2 : 1) like Ca[D-C6H11O7]2(s), z ¼ 2, z ¼ 1, p ¼ 1,
þ
ꢀ
q ¼ 2,
a
’ ¼ 133.5 kJ molꢀ1 nm,
b
’ ¼ 60.9 kJ,molꢀ1 [19], and the
Vmwas calculated to be 0.4211 nm3 according to Vmðnm3Þ ¼ Mm
=
rNA
¼
1:66045 ꢁ 10ꢀ3Mm
=r(Table 2), consequently, lattice
Table 4
Hydrogen bond lengths (nm) and bond angles (ꢂ)a.
D-H … A
d(D-H)/nm
d(H … A)/nm
d(D … A)/nm
<(DHA)/ꢂ
O(7)eH(7) … O(4)#5
O(6)eH(6) … O(1)#2
O(4)eH(4) … O(5)#6
O(3)-H(3B)∙∙∙O(2)#7
O(5)eH(5) … O(2)
0.082
0.082
0.085
0.082
0.082
0.213
0.197
0.207
0.191
0.209
(0.2952 0.0011)
(0.2759 0.0011)
(0.2866 0.0012)
(0.2725 0.0008)
(0.2739 0.0012)
117.8
159.9
163.2
156.2
135.9
Symmetry code: #2 -xþ1/2, y-1/2, -zþ1; #5 x, yþ1, z; #6 -xþ1/2, y-1/2, -zþ2; #7 x, y-1, z.
a
Uncertainty is standard uncertainty.

6
Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
Table 5
Dissolution enthalpies of reactants and products of the reaction (3) in the selected solvent. In which DsHmο ¼ Qs/n ¼ e(
D
Es/
D
Ee) $ I2Rte (M/W), DsHmο is standard molar
Ee is
at
enthalpy of dissolution of the sample, Qs is heat effect of sample dissolution, n is the mole number of the sample, DEs is the voltage change during the sample dissolution, D
the voltage change during the electrical calibration, I is the electric current through the heater (I ¼ 20.00 mA), R is the electrical resistance of the heater (R ¼ 1216.9
U
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
n
T ¼ 298.15 K), te is the heating duration of electrical calibration, M is the molar mass of the sample, and W is mass of sample. sa
¼
i¼1ðx ꢀ xÞ2=nðn ꢀ 1Þ, where sa is standard
uncertainties, x is the mean value of a set of measurement results, n is the experimental number, xi is a single value in a set of measurements. "s": 5.56 mol of double-distilled
water. Solution A1: 1.0 ꢁ 10ꢀ3 mol of {Na[D-C6H11O7](s)} þ 5.56 mol of double-distilled water. Solution B1: 1.0 ꢁ 10ꢀ3 mol of {NaCl(s)} þ 5.56 mol of double-distilled water.
System
CaCl2(s)
Solvent
No.
W/(g)
D
Es/
D
Ee
te/(s)
Qs/(J)
DsHmo /(kJ,molꢀ1
)
Solution A1
1
2
3
4
5
0.05539
0.05542
0.05545
0.05547
0.05545
0.9181
0.9214
0.9599
0.9536
0.9941
61.437
60.921
59.546
59.609
56.562
ꢀ27.370
ꢀ27.239
ꢀ27.736
ꢀ27.582
ꢀ27.283
ꢀ54.843
ꢀ54.551
ꢀ55.517
ꢀ55.188
ꢀ54.610
Avg. DsHmo ;2 ¼ - (54.942 0.182) kJ$molꢀ1
Ca[D-C6H11O7]2(s)
Solution B1
1
2
3
4
5
0.21500
0.21508
0.21507
0.21510
0.21520
0.8526
0.8566
0.8708
0.8607
0.8605
34.594
33.328
34.218
34.140
16.687
14.311
13.880
14.458
14.258
14.243
28.648
27.774
28.933
28.528
28.485
Avg. DsHo ¼ (28.474 0.192) kJ,molꢀ1
m;4
The uncertainty of temperature T is 0.001 K with a water bath thermostat; The uncertainty of pressure P is 1 kPa; The uncertainty of the mass W is 0.00001 g; The
uncertainty of voltage change is 0.0002 V with a high precision voltage stability; The uncertainty of the heating duration te is 0.001 s.
were weighed under the atmosphere of the high purity nitrogen in
a glove box. These practices ensured the reliability of measurement
of enthalpy of dissolution.
We have corrected the equation (3) in the reference [21], it
should be revised to “D-C6H10O6(s)þNaOH(s) / Na[D-C6H11O7(s)
(3)” because D-C6H10O6(s) was molecular formula of D-glucono-
lactone rather than gluconic acid, the water H2O(l) has been deleted
from the products of original chemical equation. Standard molar
enthalpy of formation of sodium D-gluconate has been recalculated
The enthalpies of dissolution of the products of the reaction in
100 cm3 of double-distilled water were measured under the same
condition as the above. The experimental results of dissolution of
{NaCl(s)} in the solvent “s” were shown in the reference [21,22], the
average value of the enthalpy of dissolution was determined as
to be Df Hmo ðC6H11O7Na; sÞ ¼ - (1758.51 0.48) kJ$molꢀ1
.
One reaction scheme applied to derive the standard molar
enthalpy of formation of the title compound was given in Table 6.
The enthalpy change of the reaction (3) was combined with some
DsHo ¼ (4.539 0.059) kJ$molꢀ1. The experimental results of the
m;3
process were listed in Table 5 and the dissolution process may be
expressed as:
auxiliary
thermodynamic
-(1758.51
data,
Df Hmo ðC6H11O7Na; sÞ
¼
0.48) kJ$molꢀ1 [21],
Df Hmo ðCaCl2 ; sÞ ¼ ꢀ795.80 kJ molꢀ1 [23], and Df Hmo ðNaCl; sÞ ¼ -
411.12 kJ molꢀ1 [23], the standard molar enthalpy of formation of Ca
[D-C6H11O7]2(s) was calculated to be:
{NaCl(s)} þ “s” ¼ Solution B1
(6)
(7)
{Ca[D-C6H11O7]2(s)} þ Solution B1 ¼ Solution B2
Then the enthalpy change of the reaction (3) can be calculated in
accordance with the experimental results as follows:
Df Hmo ½ðC6H11O7Þ2Ca;sꢄ¼
D
H8¼2
H5þ
D
H1þ
D
H2ꢀð2
D
H3þ H4Þ
D
þ2
D
DH6ꢀ2
D
H7 ¼DrHmo
X
X
DrHmo
¼
DsHmo ðreactantsÞ ꢀ
DsHmo ðproductsÞ
þ2Df Ho
O Þ Na;sꢄþ
D
fHmo ðCaCl ;sꢄ
ꢂ
ꢃ
mðC6H11
7
2
2
¼ 2DsHmo :1 þ DsHmo :2 ꢀ 2DsHmo ;3 þ DsHmo ;4
ꢀ2
D
fHmo ðNaCl;sꢄ ¼ꢀ54:622
¼ 2
DH1 þ
DH2 ꢀ ð2
DH3 þ
DH4Þ ¼ 2 ꢁ 18:936
þ2ꢁðꢀ1758:51Þꢀ795:80
ꢀ 54:942 ꢀ ð2 ꢁ 4:539 þ 28:474Þ
þ2ꢁ411:12¼ꢀð3545:19 1:07Þkjmolꢀ1
ꢂ
ꢃ
¼ ꢀ 54:622 0:462 Κj molꢀ1
The results of refractive indexes were important information
Table 6
Reaction scheme used to determine the standard molar enthalpy of formation of the compound Ca[D-C H11O7]2(s). In whichDf Hmo is standard molar enthalpy of formation,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
6
P
n
DsHmo is molar enthalpy of dissolution, sa
experimental number, xi is a single value in a set of measurements.
¼
i¼1ðx ꢀ xÞ2=nðn ꢀ 1Þ, where sa is standard uncertainties, x is the mean value of a set of measurement results, n is the
fHmo orðDsHmo sa
Þ
No.
Reactions
Formed Solution
D
/(kJ , molꢀ1
)
1
2
3
4
5
6
7
8
{Na[D-C6H11O7](s)} þ “s” ¼
A1
A2
B1
B2
(18.936 0.180) [21],
- (54.942 0.182)a,
H2
(4.539 0.059) [21], H3
(28.474 0.192)a,
H4
- (1758.51 0.48)a,
DH1
{CaCl2(s)} þ Solution A1
{NaCl(s)} þ “s” ¼
¼
D
D
{Ca[D-C6H11O7]2(s)} þ Solution B1
¼
D
Na(s) þ 6C(s) þ 11/2H2(g) þ 7/2O2(g) ¼ Na[D-C6H11O7](s)
Ca(s) þCl2(g) ¼ CaCl2(s)
D
H5
ꢀ795.80 [23],
D
H6
Na(s) þ Cl2(g) ¼ NaCl(s)
- 411.12 [23], D
H7
12C(s) þ 11H2(g) þ 7O2(g) ¼ Ca[D-C6H11O7]2(s)
- (2973.54 1.07)a,
DH8
a
Obtained from the paper.

Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
7
used to detect whether the difference of the structure and
composition between two kinds of solutions existed. In this paper,
the measured values of the refractive indexes of solution A2 and
solution B2 were (1.3310 0.0002) and (1.3312 0.0001), respec-
tively. The results indicated that solution A2 was consistent with
solution B2, and there was no difference in the structure, chemical
components, and physicochemical properties between the two
solutions. Therefore, the designed thermochemical cycle was
reasonable and reliable, and can be used to calculate the standard
molar enthalpy of formation of Ca[D-C6H11O7]2(s).
3.4. Heat capacities
The heat capacities of the compound were measured by the
PPMS. The low temperature experimental molar heat capacities of
the compound from T ¼ (1.9e300) K were listed in Table 7 and
shown in Fig. 4. It can be seen from Fig. 4 that heat capacities of the
crystal compound increased with the increase of the temperature
in a smooth and continuous manner in the whole temperature
region. In order to obtain a quantitative knowledge of the thermal
properties of the crystalline material, the fundamental thermody-
namic functions, such as heat capacity Cp, enthalpy H, and entropy S
should be measured, calculated and interpreted with molecular
motion models. The experimental low temperature heat capacity
was linked to the vibrational molecular motion of the compound, it
was a function of the temperature, and it was necessary to fit the
experimental heat capacities to a function. The first fitting was
carried out for the temperature range (0e10) K, the second in the
range of (10e50) K and the third in the range of (50e300).
Each heat capacity contribution can be expressed using an
appropriate temperature dependent equation. For data of sufficient
quality in the low temperature range (T＜10 K), the heat capacities
of the compound were given in the form of an acceptable alternate
equation
Fig. 4. Plot of the experimental and fitted heat capacities of the compound as a
function of temperature from 1.9 K to 300 K.
For the middle temperature range (10 K＜T＜50 K), the heat
capacities were fitted to an orthogonal polynomial function as
follows,
Cpo;m ¼ A0 þ A1T þ A2T2 þ A3T3 þ A4T4 þ A5T5 þ A6T6
þ A7T7
(10)
And in the high temperature range above 50 K, the heat capacities
were fitted to a combination of Debye and Einstein functions as
follows,
Cpo;m ¼ nDDðqDÞ þ nEEðqEÞ þ aT þ bT2
(11)
Cpo;m
¼
g
T þ B3T3 þ B5T5 þ B7T7
(9)
where nD and nE were Debye and Einstein parameters, D(qD) and
E(qE) were Debye and Einstein functions, qD and qE were Debye and
Einstein temperatures. The term of (aT þ bT2) was related to a
where the odd-power terms represented the vibration frequency.
Table 7
Molar heat capacities at constant pressure for the compound from (2e300) K. The
estimate standard uncertainties in the pressure
p
and temperature
T
are
Table 8
u(p) ¼ 0.10 mPa, and u(T) ¼ 0.01 K (2 < T/K < 20), u(T) ¼ 0.02 K (20 < T/K < 100), and
u(T) ¼ 0.05 K (100 < T/K < 300). The standard uncertainties of the heat capacity
measurements are 0.03CPo;mfrom T ¼ (1.9e20) K and 0.025CPo;mfrom T ¼ (20e300) K
for the compound Ca[D-C6H11O7]2(s).
Summary of the fitting parameters of heat capacity data of the compound
comprising the entire temperature region (1.9e300) K. Fits are segmented into three
overlapping ranges. The most valid range and %RMS for each fit are given along with
the fitting parameters.
CPo;m
CPo;m
/J,Kꢀ1,molꢀ1
Temperature range/K
Parameters
Coefficients
T/K
CPo;m /J,Kꢀ1,molꢀ1 T/K
T/K
/J,Kꢀ1,molꢀ1
Low temperature fits,
Range 1.9e10 K
g
/(J$molꢀ1$Kꢀ2
)
1.5268E-03
1.3014E-03
1.0875E-05
ꢀ6.8900E-08
1.742
ꢀ4.3979E-01
2.6186E-01
ꢀ5.9808E-02
7.9451E-03
ꢀ2.8857E-04
5.2663E-06
ꢀ4.8952E-08
1.8319E-10
0.286
7.641
220.461
7.327
471.109
ꢀ3.3484E-01
2.9078E-03
0.274
B3/(J$molꢀ1$Kꢀ4
B5/(J$molꢀ1$Kꢀ6
B7/(J$molꢀ1$Kꢀ8
RMS%
)
)
)
1.92
2.12
2.35
2.61
2.90
3.21
3.56
3.95
4.38
4.86
5.40
5.99
6.64
7.37
8.18
9.08
0.0126
0.0167
0.0205
0.0277
0.0375
0.0512
0.0704
0.0962
0.134
0.186
0.257
0.357
0.492
15.38
6.126
8.118
10.70
13.87
17.78
22.50
28.14
34.78
42.37
51.63
61.81
72.92
85.78
99.34
114.10
130.26
147.33
166.49
120.81 223.44
130.84 240.83
140.96 257.48
150.99 273.56
161.09 288.58
171.17 304.40
181.26 319.29
191.34 333.94
201.47 347.51
211.63 361.83
221.70 378.37
231.80 392.10
241.88 407.98
251.91 421.13
262.02 436.14
272.10 451.52
282.09 466.96
292.21 482.93
302.33 499.01
17.06
18.95
21.04
23.37
25.94
28.80
31.99
35.51
39.37
43.70
48.50
53.82
59.74
66.31
73.62
81.70
90.67
Middle temperature fits,
Range 10e50 K
A0/(J$molꢀ1$Kꢀ1
A1/(J$molꢀ1$Kꢀ2
A2/(J$molꢀ1$Kꢀ3
A3/(J$molꢀ1$Kꢀ4
A4/(J$molꢀ1$Kꢀ5
A5/(J$molꢀ1$Kꢀ6
A6/(J$molꢀ1$Kꢀ7
A7/(J$molꢀ1$Kꢀ8
RMS%
)
)
)
)
)
)
)
)
High temperature fits,
Range 50e305 K
nD/mol
QD/K
nE/mol
QE/K
0.681
0.941
1.293
10.14 1.804
11.23 2.456
12.46 3.352
13.84 4.545
a/(J$molꢀ1$Kꢀ2
b/(J$molꢀ1$Kꢀ3
%RMS
)
)
100.62 183.32
110.79 204.67

8
Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
Table 9
Standard thermodynamic functions of the compound as a function of the temperature T and at the standard pressure Po ¼ 0.1 MPa. All calculated thermodynamic values have a
estimated standard uncertainties of about 0.025,X below 300 K, where X represents the thermodynamic property. CPo;m/J,Kꢀ1,molꢀ1 is molar heat capacity at constant
pressure, DT0Hmo /J,molꢀ1 is standard molar enthalpy, DT0Som/J,Kꢀ1,molꢀ1 is standard molar entropy, DoT Gom=T/J,Kꢀ1,molꢀ1
¼
DT0Som DT0Hmo /T.
-
DToGom=T
T/K
CPo;m/J,Kꢀ1,molꢀ1
DT0Hmo /J,molꢀ1
D0T Som/J,Kꢀ1,molꢀ1
/J,Kꢀ1,molꢀ1
0
0
0
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
0.000926
0.002839
0.006764
0.013804
0.025172
0.042211
0.066412
0.099407
0.14296
0.19892
0.26917
0.35555
0.45972
0.57785
0.71525
0.87341
1.05362
1.2570
1.4845
1.7369
2.3189
3.0063
3.8009
4.7025
5.7099
6.8204
8.0307
9.3368
10.734
12.217
20.741
30.653
41.460
52.852
64.639
76.636
88.582
100.16
111.38
122.31
133.03
143.56
153.92
164.13
174.16
184.01
203.13
221.45
238.98
255.76
271.89
287.45
302.56
317.34
331.86
346.24
360.55
374.87
389.26
403.79
418.50
433.44
448.65
453.51
464.17
480.02
493.20
496.21
0.000211
0.001091
0.003385
0.008373
0.017910
0.034490
0.061314
0.102367
0.162480
0.247393
0.363780
0.519251
0.722302
0.980927
1.3034
1.6996
2.1805
2.7571
3.4415
4.2458
6.2650
8.9187
12.313
16.556
21.754
28.010
35.428
44.104
54.132
65.600
147.289
275.312
455.301
690.882
984.481
1337.63
1750.76
2222.79
2751.78
3336.10
3974.52
4666.05
5409.83
6205.02
7050.80
7946.29
9882.65
12006
0.000818
0.001963
0.003771
0.006592
0.010802
0.01680
0.025023
0.035937
0.050048
0.067889
0.090022
0.11702
0.14947
0.18775
0.23219
0.28328
0.34153
0.40739
0.48134
0.56380
0.75581
0.98628
1.2576
1.5716
1.9298
2.3332
2.7825
3.2780
3.8199
4.4078
8.0182
12.659
18.187
24.462
31.364
38.794
46.660
54.867
63.330
71.985
80.790
89.713
98.728
107.82
116.96
126.14
144.58
163.05
181.47
199.80
218.00
236.05
253.93
271.64
289.19
306.58
323.82
340.92
357.90
374.78
391.56
408.26
424.90
430.14
441.50
458.06
471.55
474.60
ꢀ0.00020
ꢀ0.00087
ꢀ0.00227
ꢀ0.00481
ꢀ0.00909
ꢀ0.01591
ꢀ0.02627
ꢀ0.04138
ꢀ0.06273
ꢀ0.09205
ꢀ0.13134
ꢀ0.18289
ꢀ0.24927
ꢀ0.33333
ꢀ0.43805
ꢀ0.56663
ꢀ0.72252
ꢀ0.90942
ꢀ1.1313
ꢀ1.3922
ꢀ2.0489
ꢀ2.9166
ꢀ4.0351
ꢀ5.4460
ꢀ7.1930
ꢀ9.3207
ꢀ11.875
ꢀ14.901
ꢀ18.446
ꢀ22.556
ꢀ53.165
ꢀ104.46
ꢀ181.23
ꢀ287.57
ꢀ426.89
ꢀ602.09
ꢀ815.56
ꢀ1069.3
ꢀ1364.7
ꢀ1702.9
ꢀ2084.8
ꢀ2511.0
ꢀ2982.0
ꢀ3498.4
ꢀ4060.3
ꢀ4668.0
ꢀ6021.6
ꢀ7559.8
ꢀ9282.4
ꢀ11189
ꢀ13278
ꢀ15549
ꢀ17999
ꢀ20627
ꢀ23431
ꢀ26410
ꢀ29562
ꢀ32886
ꢀ36380
ꢀ40043
ꢀ43875
ꢀ47874
ꢀ52040
ꢀ53386
ꢀ56372
ꢀ60870
ꢀ64658
ꢀ65533
8.5
9.0
9.5
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
273.15
280
290
298.15
300
14309
16783
19422
22219
25170
28269
31515
34906
38440
42117
45938
49903
54014
58274
62684
64105
67248
71968
75934
76849

Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
9
Fig. 6. Comparison of the heat capacity data reported in this paper with those of ce-
sium D-gluconate published in this journal.
Fig. 5. Plot of the relative deviations of the experimental heat capacity values from the
fitted values against the absolute temperature when the experimental temperatures
are less than 10 K.
cesium
D-gluconate
was
determined
to
be
Df Hmo ½CSC6H11O7; sꢄ ¼ -(1789.21 0:52) kJ,molꢀ1, as described in
the literature [7]. The absolute values of lattice potential energy,
standard molar enthalpy of formation, and low-temperature heat
capacities from 0 to 300 K of cesium D-gluconate were greatly less
than those of Ca[D-C6H11O]2(s), which was ascribed to the molec-
ular weight of calcium gluconate was much larger than that of
cesium gluconate. The calcium ion is a divalent positive ion, while
the cesium ion is a monovalent positive ion. The higher the number
of charges, the stronger the ionic bonds formed by the ions and the
greater the interaction force, this was resulting in greater lattice
potential energy and other thermodynamic properties. Comparison
of the heat capacity data reported in this paper with those of ce-
sium D-gluconate published in this journal [7] was plotted in Fig. 6,
it was obviously shown from the Fig. 6 that heat capacities of ce-
sium D-gluconate from 0 to 300 K were greatly less than those of Ca
[D-C6H11O]2(s). The lower the temperature, the smaller the differ-
ence in heat capacity between the two compounds, and eventually,
as the temperature approached zero K, the heat capacities of the
two compounds approached zero, which agreed with principle of
the third law of thermodynamics. In addition, ionic volumes of
anion D-C6H11Oꢀ7 reported in the paper and literature [7] were
almost same, which showed that this method about the calculation
of ionic volumes was right.
correction for the difference of (Cp - Cv). The fitting parameters, %
RMS, and ranges of validity for these fits as well as those for the
mid- and high-temperature regions were tabulated in Table 8. It
should be mentioned that the fitting parameters listed in Table 8
had no physical meaning other than low temperature fitting co-
efficients. The standard deviation for the compound was obtained
as a %RMS ¼ 1.742, %RMS ¼ 0.286, and %RMS ¼ 0.274, respectively,
from the low to high temperature for each fitting.
Using these fitting functions representing the heat capacity data
of the compound from our PPMS measurements, Thermodynamic
function
values,
Cpo;m/J,Kꢀ1,molꢀ1
,
DT0Hmo /J,molꢀ1
,
DT0Som/J,Kꢀ1,molꢀ1, and DoT Gmo =T/J,Kꢀ1,molꢀ1 were derived at the
smoothed temperatures between (0 and 300) K with the results
shown in Table 9. The heat capacity data were extrapolated from
(2e0) K. The calculated standard entropy and enthalpy at 298.15 K
and 0.1 MPa was Cpo;m
¼
(493.20
2.70) J$Kꢀ1 molꢀ1
,
Hmo ¼ (75934 805) J$molꢀ1, Smo ¼ (471.55 2.78) J$Kꢀ1 molꢀ1, and
Gom=T
¼
-(64658
808) J$Kꢀ1,molꢀ1
, respectively, for the
compound.
For the purpose of explaining the reliability of heat capacity
results, a detailed error analysis pattern from 0 to 10 K for under-
standing the accuracy of the heat capacity measurement results has
been given in Fig. 5. In the lower temperature range of 0e10 K, the
relative deviations of the experimental heat capacity values from
the fitted values were within 3.5% mainly because the experi-
mental heat capacities were very small. But when the experimental
temperatures were more than 10 K, the relative deviations were
less than 0.2% based on the big experimental heat capacities.
Therefore, we have only listed the pattern for the relative de-
viations against the absolute temperatures in the extremely low
temperature range.
5. Conclusions
(1). Crystal structure of the title compound was measured by X-
ray crystallography.
(2). The standard molar enthalpy of formation of the compound
was determined by an isoperibol solution-reaction
calorimeter.
(3). In addition, the molar heat capacities of the crystalline
compound were measured in the temperature range from
(1.9e300) K using the PPMS, and the experimental heat ca-
pacities were fitted to a series of theoretical and empirical
models.
4. Comparison of thermodynamic data of calcium D-
gluconate with cesium D-gluconate.
Lattice potential energy of cesium D-gluconate and ionic volume
of anion D-C6H11O7ꢀ were reported to be UPOT ¼ 478.25 kJ,molꢀ1
and V- ¼ 0.2039 nm3, and standard molar enthalpy of formation of
(4). Some standard thermodynamic functions of the compound
were calculated based on the heat capacity fitting curves. The

10
Y.-Y. Di et al. / Journal of Molecular Structure 1225 (2021) 128818
(2004) 1341e1345.
standard entropy at 298.15 K and 0.1 MPa was determined to
be Smo ¼ (471.55 2.78) J$Kꢀ1 molꢀ1 for the compound.
[4] A.E. Omu, J. Al-Harmi, H.L. Vedi, L. Mlechkova, A.F. Sayed, N.S. Al-Ragum,
Magnesium sulphate therapy in women with pre-eclampsia and eclampsia in
Kuwait, Med. Princ. Pract. 17 (2008) 227e232.
[5] S. Lo Presti, M. Moresi, Recovery of sodium gluconate from model solutions by
reverse osmosis, J. Food Eng. 44 (2000) 109e117.
[6] I. Mariam, S.A. Nagra, I. Haq, S. Ali, Application of 2-factorial design on the
enhanced production of calcium gluconate by a mutant strain of Aspergillus
Niger, Bioresour. Technol. 101 (2010) 4075e4080.
[7] J.P. Liu, Y.Y. Di, Y.X. Kong, Y.P. Liu, F.Y. Chen, C.S. Zhou, Crystal structure and
thermochemical properties of cesium D-gluconate Cs[D-C6H11O7](s), J. Mol.
Struct. 1199 (2020) 126977.
[8] Y.Y. Di, Y.H. Zhang, Y.X. Kong, C.S. Zhou, Crystal structure and thermochemical
properties of potassium pyruvate C3H3O3K(s), J. Therm. Anal. Calorim. 127
(2017) 1523e1532.
Supplementary material
CCDC 2014305 contains the supplementary crystallographic
data for the title compound. The data can be obtained free of charge
via http://www.ccdc.cam.ac.uk/deposit or from the Cambridge
Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ,
UK; fax: (þ44) 1223-336-033; or e-mail: deposit@ccdc.cam.ac.uk.
[9] Y.P. Liu, Y.Y. Di, D.H. He, Q. Zhou, J.M. Dou, Crystal structures, lattice potential
energies, and thermochemical properties of crystalline compounds (1-
CRediT authorship contribution statement
CnH2nþ1NH3)2ZnCl4(s)(n
10755e10764.
¼
8, 10, 12, and 13), Inorg. Chem. 50 (2011)
You-Ying Di: Conceptualization, Methodology, Software. Guo-
Chun Zhang: Data curation, Writing - original draft. Yu-Pu Liu:
Investigation. Yu-Xia Kong: Writing - review & editing. Chun-
Sheng Zhou: Software, Validation.
[10] Q. Shi, C.L. Snow, J. Boerio-Goates, B.F. Woodfield, Accurate heat capacity
measurements on powdered samples using Quantum Design physical
a
property measurement system, J. Chem. Thermodyn. 42 (2010) 1107e1115.
[11] Q. Shi, J. Boerio-Goates, B.F. Woodfield, An improved technique for accurate
heat capacity measurements on powdered samples using
a commercial
relaxation calorimeter, J. Chem. Thermodyn. 43 (2011) 1263e1269.
[12] R.X. Dai, S.H. Zhang, N. Yin, Z.C. Tan, Q. Shi, Low-temperature heat capacity
and standard thermodynamic functions of b-d-(-)-arabinose (C5H10O5),
J. Chem. Thermodyn. 92 (2016) 60e65.
[13] R. Jia, K.Y. Sun, R.C. Li, Y.Y. Zhang, W.X. Wang, H. Yin, D.W. Fang, Q. Shi,
Z.C. Tan, Heat capacities of some sugar alcohols as phase change materials for
thermal energy storage applications, J. Chem. Thermodyn. 115 (2017)
233e248.
Declaration of Competing Interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
[14] J.J. Calvin, M. Asplund, Y. Zhang, B.Y. Huang, B.F. Woodfield, Heat capacity and
Acknowledgements
thermodynamic functions of g-Al2O3, J. Chem. Thermodyn. 112 (2017) 77e85.
[15] C.D. Littleton, A structure determination of the gluconate ion, Acta Crystallogr.
6 (1953) 775e781.
[16] M.W. Wieczorek, J. Blaszczyk, B.W. Krol, Effects of cation interactions on sugar
anion conformation in complexes of lactobionate and gluconate with calcium,
sodium or potassium, Acta Crystallogr. C52 (1996) 1193e1198.
[17] T. Lis, Structure of sodium D -gluconate, Na[C6H11O7], Acta Crystallogr. C40
(1984) 376e378.
[18] T. Lis, Structure of lead(II) D -gluconate, Pb[C6H11O7]2, Acta Crystallogr. C40
(1984) 374e376.
[19] H.D.B. Jenkins, D. Tudela, L. Glasser, Lattice potential energyestimation for
complex ionic salts from density measurements, Inorg. Chem. 41 (2002)
2364e2367.
This work was financially supported by the National Natural
Science Foundations of China under the contract NSFC No.
21873063. We thanked Prof. Quan Shi at Thermochemistry Labo-
ratory, Dalian Institute of Chemical Physics, Chinese Academy of
Sciences for the heat capacity measurements using a Quantum
Design Physical Property Measurement System (PPMS).
References
[20] L. Glasser, H.D.B. Jenkins, Internally consistent ion volumes and their appli-
cation in volume-based thermodynamics, Inorg. Chem. 47 (2008) 6195e6202.
[21] Y.Y. Di, Y.H. Zhang, Y.P. Liu, Y.X. Kong, C.S. Zhou, Crystal structure and ther-
modynamic properties of sodium D-gluconate Na[D-C6H11O7](s), J. Therm.
Anal. Calorim. 127 (2017) 1835e1843.
[22] W.W. Zhong, Y.Y. Di, Y.P. Liu, J.M. Dou, Crystal structure, lattice potential
energy, and thermochemical properties of a novel compound barium d-glu-
conate tetrahydrate, J. Chem. Thermodyn. 69 (2014) 145e151.
[23] M.W. Chase, NIST-JANAF Themochemical Tables, fourth ed., J. Phys. Chem.
Ref. Data, 1998, pp. 1e1951. Monograph 9.
[1] J. Bao, K. Furumoto, K. Fukunaga, K. Nakao, A kinetic study on air oxidation of
glucose catalyzed by immobilized glucose oxidase for production of calcium
gluconate, Biochem. Eng. J. 8 (2001) 91e102.
[2] A. Sharma, V. Vivekanand, R.P. Singh, Solid-state fermentation for gluconic
acid production from sugarcane molasses by Aspergillus Niger ARNU-4
employing tea waste as the novel solid support, Bioresour. Technol. 99
(2008) 3444e3450.
[3] H. Znad, J. Markos, V. Bales, Production of gluconic acid from glucose by
Aspergillus Niger: growth and non-growth conditions, Process Biochem. 39