Crystal structure and chemical thermodynamic properties of potassium d-gluconate K(d-C6H11O7)(s)

Article abstract of DOI:10.1007/s10973-017-6657-x

An important coordination compound potassium d-gluconate K[d-C₆H₁₁O₇](s) has been synthesized by liquid phase method. The chemical component and crystal structure of the important compound are characterized by chemical analysis, elemental analysis, and X-ray crystallography. Single-crystal X-ray analysis reveals that the compound exhibits the chelate property of d-gluconate anions to K⁺ cations, a six-membered chelate ring is formed by the coordination of K⁺ with O2 of carboxylate and O4 of hydroxyl in a d-gluconate, and one cation is coordinated to six d-gluconate anions. The lattice potential energy and ionic volume of the anion [d-C₆H₁₁O₇]^? are obtained from crystallographic data. In accordance with Hess’ law, a reasonable thermochemical cycle is designed according to the practical synthesis reaction of the compound and the standard molar enthalpy of formation of the compound is calculated to be ?(1754.17?±?0.19)?kJ?mol^?1 as an important physical quantity in chemical thermodynamics by an isoperibol solution–reaction calorimeter. Molar enthalpies of dissolution of the compound at various molalities are measured at T?=?298.15?K in the double-distilled water. According to Pitzer’s electrolyte solution theory, molar enthalpy of dissolution of the title compound at infinite dilution is calculated to be ΔsHm∞?=?(27.92?±?0.21)?kJ?mol^?1. In terms of the above value, the standard molar enthalpy of formation of the anion [d-C₆H₁₁O₇]^? in the aqueous solution is determined to be =??(1473.87?±?0.28)?kJ?mol^???1. The values of relative apparent molar enthalpies (^ΦL) and relative partial molar enthalpies of the solvent (Lˉ ₁) and the compound (Lˉ ₂) at different concentrations m/(mol?kg^?1) are derived from the experimental values of the enthalpies of dissolution of the compound.

Full text of DOI:10.1007/s10973-017-6657-x

J Therm Anal Calorim
DOI 10.1007/s10973-017-6657-x
Crystal structure and chemical thermodynamic properties
of potassium D-gluconate K(D-C6H11O7)(s)
You-Ying Di1,2 Yu-Han Zhang2 Yu-Pu Liu2 Yu-Xia Kong2 Chun-Sheng Zhou1
•
•
•
•
Received: 23 April 2017 / Accepted: 21 August 2017
´
´
Ó Akademiai Kiado, Budapest, Hungary 2017
Abstract An important coordination compound potassium
D-gluconate K[D-C6H11O7](s) has been synthesized by
liquid phase method. The chemical component and crystal
structure of the important compound are characterized by
chemical analysis, elemental analysis, and X-ray crystal-
lography. Single-crystal X-ray analysis reveals that the
compound exhibits the chelate property of D-gluconate
anions to K? cations, a six-membered chelate ring is
formed by the coordination of K? with O2 of carboxylate
and O4 of hydroxyl in a D-gluconate, and one cation is
coordinated to six D-gluconate anions. The lattice potential
energy and ionic volume of the anion [D-C6H11O7]- are
obtained from crystallographic data. In accordance with
Hess’ law, a reasonable thermochemical cycle is designed
according to the practical synthesis reaction of the com-
pound and the standard molar enthalpy of formation of the
compound is calculated to be -(1754.17 0.19) kJ mol-1
as an important physical quantity in chemical thermody-
namics by an isoperibol solution–reaction calorimeter.
Molar enthalpies of dissolution of the compound at various
molalities are measured at T = 298.15 K in the double-
distilled water. According to Pitzer’s electrolyte solution
theory, molar enthalpy of dissolution of the title compound
DsHm1 = (27.92 0.21) kJ mol-1. In terms of the above
value, the standard molar enthalpy of formation of the
anion [D-C6H11O7]- in the aqueous solution is determined
to be = -(1473.87 0.28) kJ mol-1. The values of rel-
ative apparent molar enthalpies (UL) and relative partial
ꢀ
ꢀ
molar enthalpies of the solvent (L1) and the compound (L2)
at different concentrations m/(mol kg-1) are derived from
the experimental values of the enthalpies of dissolution of
the compound.
Keywords Potassium D-gluconate Á Crystal structure Á
Isoperibol solution–reaction calorimeter Á Standard molar
enthalpy of formation Á Pitzer’s electrolyte solution theory Á
Molar enthalpy of dissolution at infinite dilution
Introduction
It is well known that D-glucose is one of the most important
and basic nutrients. It is often applied to supplement
nutrition and energy for some patients who lack vitamins.
More importantly, it is used as one of the carbon and
energy sources in the human body and maintains the nor-
mal physiological and biological functions for human
body. There is an aldehyde group at the end of the D-
glucose molecule, which is easily oxidized to D-gluconic
acid. The latter can be easily combined with many inor-
ganic metal ions such as K?, Na?, and Ca2?. Many
bioactive coordination compounds are produced under the
weak basicity at pH 7.4 in the body fluid, and the body fluid
acid–base balance is maintained, which have an important
influence on the growth and development of the human
body. In the past decades, D-gluconic acid series products
are widely used as nutrient additives in food, medicine and
at
infinite
dilution
is
calculated
to
be
& You-Ying Di
diyouying@126.com; myyydi@eyou.com
1
2
College of Chemical Engineering and Modern Materials,
Shangluo University/Shaanxi Key Laboratory of
Comprehensive Utilization of Tailings Resources, Shangluo,
Shaanxi 726000, People’s Republic of China
Shandong Provincial Key Laboratory of Chemical Energy
Storage and Novel Cell Technology, College of Chemistry
and Chemical Engineering, Liaocheng University,
Liaocheng 252059, People’s Republic of China
123

Y.-Y. Di et al.
pharmaceutical industry [1–3] due to the coordination
properties of D-gluconate anions to metal ions. In recent
years, as an important nutritional supplement, D-gluconate
is easily absorbed by the human body and a great attention
is paid to it by people all over the world because it is non-
toxic, fully biodegradable and can be used as new gener-
ation of biological metal supplements. For these reasons, it
is very useful to study the crystal structures and electrolyte
solution properties of D-gluconates to develop their new
application fields and to carry out relevant theoretical
research.
Experimental
Preparation of the title compound
The provenances and purities of the chemicals used in the
synthesis and calorimetric experiments are shown in
Table 1. The compound is prepared by concentrating
aqueous solution of D-gluconolactone and potassium
hydroxide (molar ratio 1: 1) in water for 2 h. When the
final solution is cool, excessive ethanol is added to the
solution. And the colorless single crystals suitable for
X-ray diffraction are obtained 5 days later by slow evap-
oration. The sample is placed in a vacuum desiccator at
T = 303.15 K to dry in vacuum for 24 h, and the final
product is placed in weighing bottles and preserved in the
desiccator. The chemical composition of the compound is
analyzed by element analyzer (model: PE-2400 II, Perk-
inElmer, USA) under ‘‘C–H–N mode’’ and ‘‘O mode.’’ The
element analyzer used in our research has three kinds of
analytical modes: ‘‘C–H–N mode’’, ‘‘C–H–N–S mode’’ and
‘‘O mode.’’ The content of the oxygen element is analyzed
exactly under the ‘‘O mode.’’ The contents of the carbon
and hydrogen elements are obtained by the H–C–N mode.
At last, the mass fraction purity of the C, H, and O is
determined by elemental analyzer. The percentage of
potassium K can be analyzed by chemical analysis, and the
values (calculated for K[D-C6H11O7]: C 30.76, H 4.74, O
47.81, K 16.69%; found: C 30.77, H 4.75, O 47.82, K
16.66%, respectively.) show that the mass fraction purity of
the compound is [0.998.
Potassium is one of the important elements necessary for
the human body. K? cation as prosthetic group of some
enzymes can promote the activity of enzyme in cells. It can
also stabilize internal structure of cells and involve in
protein synthesis. Potassium is an essential part of most
organisms and plays a very important role in the process of
neural information transfer. Both of potassium ion and
sodium ion form a ‘‘Na–K pump.’’ It can adjust the balance
of potassium and sodium in the body. ‘‘Limit sodium,
supplement potassium’’ is the basis to prevention and
treatment of high blood pressure. When too much potas-
sium is lost from body, it will lead listless, agitated mood
and even death [4]. Potassium D-gluconate can serve as a
good potassium supplement agent, it is soluble in the body
liquid, and it is easily absorbed by human body.
Thermodynamic properties of the substances are one of
the most important physical quantities in science and
technology [5–12]. In this paper, we report the crystal
structure of an important coordination compound potas-
sium D-gluconate K[D-C6H11O7](s). And the lattice poten-
tial energy and ionic volume of the common anion are
obtained from crystallographic data. The molar enthalpies
of dissolution of reactants and product in the designed
reaction are determined by an isoperibol solution–reaction
calorimeter. The standard molar enthalpy of formation of
potassium D-gluconate K[D-C6H11O7](s) is determined
based on these calorimetric experimental results. Molar
enthalpies of dissolution of potassium D-gluconate K[D-
C6H11O7](s) at various molalities are measured at
T = 298.15 K in the double-distilled water. According to
Pitzer’s theory, the molar enthalpy of dissolution of the
title compound at infinite dilution is obtained. The values
of relative apparent molar enthalpies (UL), relative partial
Crystallographic data collection and refinement
Single-crystal structure analysis of the compound is per-
formed on a Bruker Smart 1000 diffractometer with a CCD
detector with Mo-Ka radiation (k = 0.071073 nm). The
intensity data are collected in the u–x scan mode at
T = (298 2) K. The empirical absorption corrections are
based on multi-scan. The structure is solved by direct
method using SHELXTL and difference Fourier syntheses,
and all non-hydrogen atoms are refined anisotropically on
F2 by full-matrix least-squares technique using the
SHELXTL-97 program package. The hydrogen atoms are
added theoretically, riding on the concerned atoms, and not
refined. The final full-matrix least-squares refinement on F2
is applied for all observed reflections [I [ 2r(I)]. All cal-
culations are made with the program package SHELXTL
[5, 6]. We have applied for a CCDC 888208 for potassium
D-gluconate K[D-C6H11O7](s).
ꢀ
molar enthalpies (L2) of the compound and relative partial
ꢀ
molar enthalpies (L1) of the solvent (water) at different
concentrations m/(mol kg-1) are derived from the experi-
mental values of the enthalpies of dissolution of the
compound.
123

Crystal structure and chemical thermodynamic properties of potassium D-gluconate…
Table 1 The provenances and purities of the chemicals used in the synthesis and calorimetric experiments
Chemicals
Provenances
Purities (mass%)
D-Gluconolactone
J&K Scientific Ltd, China
99.5
99.99
99.5
Potassium hydroxide
Anhydrous ethyl alcohol
Potassium D-gluconate
J&K Scientific Ltd, China
Tianjin No.3 Chemical Reagent Factory, China
Prepared by our laboratory
[99
Isoperibol solution–reaction calorimeter
K1
The isoperibol solution–reaction calorimeter consists pri-
marily 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 measur-
ing system, and a data acquisition and processing system.
During whole experiment, the water thermostat is auto-
matically maintained at T = 298.15 K and the maximum
variation is found to be 1 9 10-3 K. Experiments have
demonstrated that the precision of measuring the temper-
ature can reach 1 9 10-4 K. The principle and structure
of the calorimeter are described in detail elsewhere [5, 6].
The reliability of the calorimeter is verified previously
by measuring the molar enthalpy of dissolution of KCl
(calorimetrically primary standard) in the double-distilled
water. According to the molar ratio of KCl to water,
O6
C5
O1
O4
C2
C6
C4
C3
O2
C1
O5
O7
K
O
H
O3
C
Fig. 1 Molecular structure in crystallographic independent unit of
potassium D-gluconate K[D-C6H11O7](s)
essentially as same as what found in the studies [14, 15]
about the crystal structures of potassium D-gluconate,
rubidium D-gluconate and lead(II) D-gluconate, where the
gluconate ion is almost fully extended and its six carbon
atoms lie approximately in a common plane.
nKCl : nH O ꢀ 1 : 1110, a certain amount of KCl is dis-
2
solved in 100 cm3 of double-distilled water at
T = (298.15 0.001) K. The average enthalpy of disso-
lution of KCl is (17,547 13) J mol-1, which compares
with corresponding published data (17,536 3.4) J mol-1
under the same experimental conditions [13]. Experiments
demonstrate that the uncertainty between the measuring
value and the literature value is within 0.30% [5, 6].
A six-membered chelate ring is formed by the coordi-
nation of K? with O2 of carboxylate and O4 of hydroxyl in
a D-gluconate. The environment of the D-gluconate ligand
bonding to the alkali metal ion (K? cation) and the ion-
numbering scheme is shown in Fig. 2. In the title com-
pound, each cation coordinates with six anions through
hydroxyl oxygen and carboxylate oxygen, and each D-
gluconate anion coordinates with six cations through
hydroxyl oxygen and carboxylate oxygen (see Fig. 2).
Thus, each alkali metal cation (K? cation) is coordinated to
only one D-gluconate anion, and the coordination com-
pound consists of one crystallographic independent alkali
metal cation and one D-gluconate anion. And each cation is
surrounded by a shell composed of oxygen atoms. The
framework diagrams illustrating the coordination polyhe-
dron of the title compound is given in Fig. 3.
Results and discussion
Description of crystal structure
The molecular structure of the compound is plotted in Fig. 1. A
summary of crystallographic data and refinement parameter is
listed in Table 2. The selected bond lengths and angles of the
title compound are listed in Table 3. From Table 2, it is found
that the crystal system of K[D-C6H11O7](s) is orthorhombic, the
space group is P2(1)2(1)2(1), unit cell dimensions are
a = 0.50350(6) nm, b = 0.74224(8) nm, c = 2.3517(2) nm,
a = b = c = 90° and Z = 4.
Single-crystal X-ray analysis reveals that in each one
molecule of K[D-C6H11O7](s), the conformation of the D-
gluconate anion is a six-member zigzag carbon chain
which is nearly planar (see Fig. 1). The conformation is
The distances of carboxylate oxygens to the metal cation
are very close (see Table 3), lying in the range 0.2660(2)–
0.2913(2) nm for K[D-C6H11O7]. The distances of hydroxyl
oxygen to K? cation are lying in the range 0.2748(2)–
0.3024(2) nm. The C–C bond lengths range from 0.1507(4)
to 0.1534(4) nm for K[D-C6H11O7], the C–OH bonds from
123

Y.-Y. Di et al.
Table 2 Summary of crystallographic data and refinement parame-
ters for potassium D-gluconate K[D-C6H11O7](s)
Table 3 Selected bond lengths (nm) and bond angles (°) for potas-
sium D-gluconate K[D-C6H11O7](s)
Properties
Crystallographic data and refinement
parameters
Selected bond lengths/nm or angles/°
K(1)–O(1)
K(1)–O(2)#1
K(1)–O(2)#2
K(1)–O(4)#2
O(1)–C(1)
0.2660(2) C(4)–O(5)–H(5)
0.2793(2) C(5)–O(6)–H(6)
0.2913(2) C(6)–O(7)–H(7)
0.3024(2) O(2)–C(1)–O(1)
0.1251(3) O(2)–C(1)–C(2)
0.1252(3) O(1)–C(1)–C(2)
0.1409(3) O(3)–C(2)–C(3)
109.5
Empirical formula
Formula weight
Temperature/K
Wavelength/nm
Crystal system
Space group
C6H11O7K
234.25
109.5
109.5
298
2
124.2(3)
119.5(3)
116.2(3)
114.9(3)
113.1(2)
108.7(2)
106.5
0.071073
Orthorhombic
P2(1)2(1)2(1)
O(2)–C(1)
O(3)–C(2)
Unit cell dimensions/nm or a = 0.50350(6)
°
O(3)–H(3)
O(4)–C(3)
0.08200
0.1429(3) C(3)–C(2)–C(1)
0.08200 O(3)–C(2)–H(2)
0.1421(4) C(3)–C(2)–H(2)
0.08200 C(1)–C(2)–H(2)
0.1416(4) O(4)–C(3)–C(4)
0.08200 O(4)–C(3)–C(2)
0.1417(4) C(4)–C(3)–C(2)
0.08200 O(4)–C(3)–H(3A)
O(3)–C(2)–C(1)
b = 0.74224(8)
c = 2.3517(2)
a = 90
O(4)–H(4)
O(5)–C(4)
106.5
b = 90
O(5)–H(5)
O(6)–C(5)
106.5
c = 90
110.5(2)
110.5(2)
114.1(2)
107.1
Volume/nm3
0.87886 (16)
O(6)–H(6)
O(7)–C(6)
Z
4
Calculated density/g cm-3
1.770
0.616
O(7)–H(7)
C(1)–C(2)
Absorption coefficient/
mm-1
0.1531(4) C(4)–C(3)–H(3A)
0.1531(4) C(2)–C(3)–H(3A)
107.1
C(2)–C(3)
107.1
F(000)
Crystal size/mm3
488
C(2)–H(2)
0.09800
0.1517(4) O(5)–C(4)–C(5)
0.09800 C(3)–C(4)–C(5)
0.1534(4) O(5)–C(4)–H(4A)
0.09800 C(3)–C(4)–H(4A)
0.1507(4) C(5)–C(4)–H(4A)
O(5)–C(4)–C(3)
113.3(2)
105.3(3)
112.6(2)
108.5
0.38 9 0.10 9 0.08
2.88 to 25.02
C(3)–C(4)
Theta range for data
collection/°
Limiting indices
C(3)–H(3A)
C(4)–C(5)
-5 B h B 5, -8 B k B 8,
-27 B l B 8
C(4)–H(4A)
C(5)–C(6)
108.5
108.5
Reflections collected/unique 3969/1542 [R(int) = 0.0467]
C(5)–H(5A)
C(6)–H(6A)
C(6)–H(6B)
O(1)–K(1)–O(2)#1
O(1)–K(1)–O(2)#2
0.09800
0.09700
0.09700
83.21(6)
68.43(6)
O(6)–C(5)–C(6)
O(6)–C(5)–C(4)
C(6)–C(5)–C(4)
O(6)–C(5)–H(5A)
C(6)–C(5)–H(5A)
C(4)–C(5)–H(5A)
O(7)–C(6)–C(5)
O(7)–C(6)–H(6A)
C(5)–C(6)–H(6A)
O(7)–C(6)–H(6B)
C(5)–C(6)–H(6B)
111.7(3)
112.2(3)
111.6(3)
107.0
Completeness to
theta = 25.02/%
99.9
Absorption correction
Semi-empirical from equivalents
Max. and min. transmission 0.9524 and 0.7996
Refinement method
Full-matrix least-squares on F2
107.0
Data/restraints/parameters
Goodness-of-fit on F2
1542/1/132
0.920
O(2)#1–K(1)–O(2)#2 145.63(3)
107.0
O(1)–K(1)–O(4)#2
O(2)#1–K(1)–O(4)#2
O(2)#2–K(1)–O(4)#2
C(1)–O(1)–K(1)
79.04(6)
87.33(6)
69.03(6)
130.08(18)
109.5
108.8(3)
109.9
Final R indices [I [ 2 sigma R1 = 0.0357, wR2 = 0.0775
(I)]
109.9
R indices (all data)
R1 = 0.0450, wR2 = 0.0832
109.9
Largest diff. peak and hole/ 290 and -258
e nm-3
C(2)–O(3)–H(3)
109.9
C(3)–O(4)–H(4)
109.5
H(6A)–C(6)–H(6B) 108.3
Symmetry codes: #1 -x ? 1, y - 1/2, -z ? 1/2; #2 x ? 1, y, z
0.1409(3) to 0.1429(3) nm for K[D-C6H11O7], and the
differences from the means in lengths are within the limits
of the experimental error. These results are in good
agreement with those of the crystal structures in the normal
D-gluconate salts. The differences are probably due to
inaccuracy in the structure analysis and the different crystal
surrounding for every atoms. The two C–O bonds in the
carboxyl group are found to have lengths 0.1251(3) and
0.1252(3) nm for K[D-C6H11O7]. The angles (see Table 3)
O1–C1–C2 and O2–C1–C2 are 116.2(3)° and 119.5(3)° for
K[D-C6H11O7], respectively. The carboxyl groups are
symmetrical within experimental errors with an angle of
124.2(3)° between the two C–O bonds for K[D-C6H11O7].
The differences are not significant. Similar differences are
observed in many other determinations, but these always
involve the different crystal forces for carboxylate oxygen.
Hydrogen bonds distances and angles are listed in
Table 4. In the structure, there are six different O–O
123

Crystal structure and chemical thermodynamic properties of potassium D-gluconate…
K3
K2
K1
O4
O5
O3
O2
O4
O2
O1
K1
O1
O6
K
O
C
O1
O2
O4
O6
O7
K6
K5
K4
Fig. 2 The environment of the cations and anions for potassium D-gluconate K[D-C6H11O7](s)
O2
Table 4 Hydrogen bond lengths (nm) and bond angles (°) for
potassium D-gluconate K[D-C6H11O7](s)
D-HÁÁÁA
d(D-H)/
nm
d(HÁÁÁA)/
d(DÁÁÁA)/
\(DHA)/
°
nm
nm
O1A
O(3)–
0.082
0.082
0.082
0.082
0.082
0.082
0.193
0.196
0.245
0.203
0.199
0.197
0.2726(3)
0.2779(3)
0.2991(3)
0.2718(3)
0.2759(3)
0.2684(3)
164.3
175.8
124.9
140.9
156.6
145.0
H(3)ÁÁÁO(1)#3
O(4)–
H(4)ÁÁÁO(2)#1
O(4)–
H(4)ÁÁÁO(1)#1
O(5)–
H(5)ÁÁÁO(7)#4
O(6)–
K
O6E
O4C
O1D
O4
H(6)ÁÁÁO(5)#2
O(7)–
K
H(7)ÁÁÁO(3)#5
O
H
C
Symmetry codes: #1 -x ? 1, y - 0.5, -z ? 0.5; #2 x ? 1, y, z; #3
x - 1, y, z; #4 x - 0.5, -y ? 1.5, -z; #5 x ? 0.5, -y ? 1.5, -z
O2B
Fig. 3 Framework diagram of the coordination polyhedron for
potassium D-gluconate K[D-C6H11O7](s)
For the salts MX (1:1), MX2 (1:2), and M2X (2:1),
Eq. (1) is changed to:
distances shorter than 0.3 nm for K[D-C6H11O7]. All the
oxygen atoms of hydroxyl groups of the title compound
participate in intermolecular hydrogen bonds utilizing all
oxygen-bonded hydrogen atoms.
ꢀ
ꢁ
UPOT ¼ jzþjjzÀjm a0=Vm1=3 þ b0
ð2Þ
where z? and z- are the respective charges on the cation
and anion of the compound, v is the number of ions per
molecule and equals (p ? q). In the case of the salt of
formula MX with charge ratio (1:1) like K[D-C6H11O7],
Lattice potential energy and ionic volume of D-
C6H11O27 anion
z? = 1,
z- = 1,
p = 1,
q = 1,
v = 2,
a0 = 117.3 kJ mol-1 nm, b0 = 51.9 kJ mol-1 [16], and
Equation (1) used to estimate lattice potential energy of
generalized type of salt MpXq is obtained from the literature
[16]:
Vm is in unit of nm3 and expressed as follows:
À
Á
Vm= nm3 ¼ Mm=qNA ¼ 1:66045 Â 10À3Mm=q
ð3Þ
ꢀ
ꢁ
X
UPOT
¼
niz2i a0=Vm1=3 þ b0
ð1Þ
where NA is Avogadro’s constant, 6.02245 9 1023
molecule mol-1, Mm is molar weight of the molecule, q is
the density of the substance, and Vm(MX) is calculated to
be 0.2198 nm3 for K[D-C6H11O7] from Eq. (3). Thus,
Eq. (2) is changed to [16]:
where a0 and b0 are appropriate fitted coefficients chosen
according to the stoichiometry of the salt, ni is the number
of ions with a charge zi in the formula unit, and Vm is the
molecular volume.
123

Y.-Y. Di et al.
Table 5 Enthalpies of dissolution of reactants and product of reaction (6) in the selected solvents (T = 298.15 0.001 K and
P = 101.22 0.01 kPa)
System
Solvent
s
No.
W/g
DEs/DEe
te/s
Qs/J
DsHmo /kJ mol-1
D-C6H10O6(s)
1
2
3
4
5
0.17833
0.17826
0.17840
0.17823
0.17847
-1.0046
-0.9081
-0.9776
-0.9906
-0.8678
37.437
18.249
18.230
18.100
18.221
18.653
18.698
41.078
38.468
38.827
44.484
18.100
18.247
18.663
18.733
Avg. DsHmo ;1 = (18.380 0.123) kJ mol-1
KOH(s) Solution A1
1
2
3
4
5
0.05700
0.05670
0.05691
0.05670
0.05673
1.3950
1.0295
1.3412
0.8750
1.5691
102.422
138.390
106.593
162.859
90.531
-69.328
-69.131
-69.371
-69.218
-68.927
-68.246
-68.412
-68.407
-68.498
-68.174
Avg. DsHmo ;2 = -(68.347 0.059) kJ mol-1
K[D-C6H11O7](s)
s
1
2
3
4
5
0.23405
0.23425
0.23430
0.23443
0.23435
-1.2379
-0.8759
-1.1480
-0.8795
-1.4125
39.172
46.016
40.922
54.250
33.390
23.530
23.058
22.795
23.152
22.886
23.551
23.040
22.790
23.134
22.876
Avg. DsHmo ;3 = (23.078 0.133) kJ mol-1
In which DsHmo = Qs/n = -(DEs/DEe)ÁI2Rte (M/W), DsHmo is standard molar 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, DEe is the voltage change during the
electrical calibration, I is the electric current through the heater (I = 20.00 mA), R is the electrical resistance of the heater (R = 1216.9 X at
T = 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.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
n
2
ra ¼
i¼1 ðx À xÞ =nðn À 1Þ, where 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’’: double-distilled water. For potassium D-gluconate K[D-C6H11O7](s): Solution A1: {D-C6H10O6(s)} ? ‘‘s’’. Solution A:
{KOH(s)} ? Solution A1. Solution B: {K[D-C6H11O7](s)} ? ‘‘s’’. After the reaction is complete, the final molalities of K[D-C6H11O7](s) in
solution A and solution B are the same, 1.0 9 10-2 mol kg-1
1=3
UPOT ¼ cðq=MmÞ þd
D-C6H10O6ðsÞ þ KOHðsÞ ¼ K½D-C6H11O7ŠðsÞ
ð6Þ
ð4Þ
The standard molar enthalpies of dissolution of the
reactants and product of the reaction (6) in the selected
solvent (100 cm3 of double-distilled water) are measured
by an isoperibol solution–reaction calorimeter, respec-
tively. The enthalpy change of the reaction is calculated
from the data of above standard molar enthalpies of
dissolution.
where the values of the constants for MX (1:1) are:
c = 1981.2 kJ mol-1 cm and d = 103.8 kJ mol-1. Lattice
potential energy of the compound is determined to be
U
POT{K[D-C6H11O7]} = 492.56 kJ mol-1, which reveals
that the structure of K[D-C6H11O7] is stable.
In addition, for a salt of molecular formula MpXq,
À
Á
Vm MpXq ¼ pVþ þ qVÀ
ð5Þ
The samples KOH(s) and D-C6H10O6(s) used in the
solution calorimetry are of analytical grade and newly
bought from J&K Scientific Ltd, China. Purity of D-C6
H10O6(s) is analyzed to be [99.5% by elemental analysis
and HPLC. The labeled purity of the KOH(s) is more than
99.99% in mass percentage, when bought and delivered to
our laboratory it is sealed in good condition in a small glass
bottle. Weighing the sample KOH(s) used in the solution–
reaction calorimetric experiments is carried out in the clean
glove box containing the high-purity nitrogen, and a suit-
able cap made from polytetrafluoroethylene (PTFE) is
where V- and V? are the volumes of the anion and cation,
p = 1 and q = 1 for K[D-C6H11O7]. V?(K?) is 0.0277 nm3
according to the literature [17], The V- (the volume of the
anion D-C6H11O7-) is estimated to be 0.1921 nm3.
Standard molar enthalpy of formation
of the compound K[D-C6H11O7](s)
The title compound is supposed to be the product in the
following chemical reaction. The designed reaction is
shown in the following:
123

Crystal structure and chemical thermodynamic properties of potassium D-gluconate…
26
25
24
23
0
2
4
6
8
10
103m/(mol kg–1)
Fig. 4 Plot of the measured DsHm against molality for potassium D-
gluconate K[D-C6H11O7](s) at T = 298.15 K
covered to the sample cell because KOH(s) is a kind of the
air sensitive and hygroscopic compound.
About 1.0 9 10-3 mol of D-C6H10O6(s) in the reaction
(6) is dissolved in 100 cm3 of double-distilled water at
T = 298.15 K. The experimental results of the process are
shown in Table 5. If ‘‘s’’ represented 100 cm3 of double-
distilled water, the dissolution process may be expressed as:
fD-C6H10O6ðsÞg þ ‘‘s’’ ¼ Solution A1
ð7Þ
The stoichiometric number of KOH(s) {n(D-C6H10O6
(s)):n(KOH(s)) = 1:1} in the reaction (6) is regarded as a
norm for sample weighing, about 1.0 9 10-3 mol of
KOH(s) is dissolved in the solution A1 at T = 298.15 K.
The experimental results of the process are shown in
Table 5 and the dissolution process may be expressed as:
fKOHðsÞg þ Solution A1 ¼ Solution A
ð8Þ
The enthalpies of dissolution of the product in 100 cm3
of double-distilled water are measured under the same
condition as the above. The experimental results of the
process are listed in Table 5, and the dissolution process
may be expressed as:
fK½D-C6H11O7ŠðsÞg þ ‘‘s’’ ¼ Solution B
ð9Þ
Then the enthalpy change of the reaction (6) can be
calculated in accordance with the experimental results as
follows:
X
X
DrHmo
¼
DsHmo ðreactantsÞ À
DsHmo ðproductsÞ
¼ DsHmo :1 þ DsHmo :2 À DsHmo :3
¼ 18:380 À 68:347 À 23:078
¼ Àð73:045 Æ 0:191Þ kJ molÀ1
The enthalpy change of the reaction (6) is combined
:
with
some
auxiliary
thermodynamic
data,
123

Y.-Y. Di et al.
UL
DfHmo ðC6H10O6; sÞ = -1256.4 kJ mol-1
[18]
and
P
ð0ÞL
where I is ionic strength ( miz2=2), b , bMð1XÞL, and CMX
i
MX
DfHmo ðKOH; sÞ = -424.72 kJ mol-1 [19], the standard
molar enthalpy of formation of K[D-C6H11O7](s) is deter-
mined to be:
ð0ÞL
are Pitzer’s parameters for enthalpy, the coefficients b
MX
ð1ÞL
and b account for various types of short-range interac-
tions between M and X, and for indirect forces arising from
MX
DfHmo ðC6H11O7K; sÞ ¼ DrHmo þ DfHmo ðC6H10O6; sÞ
UL
the solvent, the third coefficient CMX represents for triple
þ DfHmo ðKOH; sÞ
ion interactions and is important only at high concentra-
tions or with strong triple ion interaction [20]. In this paper,
¼ À73:045 À 1256:4 À 424:72
UL
¼ Àð1754:17 Æ 0:19Þ kJ molÀ1
:
CMX may not be overlooked for the aqueous solution of
K[D-C6H11O7](s) because formation and breaking of the
-
six-membered chelate ring of the D-C6H11O7 anion with
The results of refractive indexes are the important
information used to detect whether the difference of the
structure and chemical composition between two solutions
exists. We have measured the refractive indexes of the two
solutions by Abbe refractometer. Uncertainty of the
instrument is 0.0003. The experimental temperature in
the room is (20.0 0.1) °C. In this paper, the measured
values of the refractive indexes of solution A and solution
B are (1.3309 0.0002) and (1.3308 0.0003) for the
aqueous solution of K[D-C6H11O7](s), respectively. The
results indicate that solution A is consistent with solution
B, and there is no difference in the structure, chemical
components and physicochemical properties between the
two solutions. Therefore, the designed thermochemical
cycle is reasonable and reliable and can be used to calcu-
late the standard molar enthalpy of formation of K[D-
C6H11O7](s).
K? cation are similar to the three-ion interaction and fur-
-
ther hydrolyzation of the D-C6H11O7 anion takes place at
low concentrations because the D-gluconic acid is a weak
acid similar to acetic acid. The hydrolyzation reaction of
the D-C6H11O7- anion will produce the hydroxide ion, and
a model of the triple ion interaction will be formed by K?,
D-C6H11O7 anion and OH-. v is the total number of ions
-
formed from the salt (v = vM ? vX). zM and zX are the
respective charges on the cation and anion of the com-
pound. b is a parameter with the value 1.2 kg1/2 mol-1/2 for
all solutions. y0 = 2[1 - (1 ? aI1/2)exp(-aI1/2)]/a2I and
a = 2.0 kg1/2 mol-1/2. m/(mol kg-1) is the molality of the
compound. R is molar gas constant, 8.3145 J mol-1 K-1
.
AH is Debye–Huckel parameter for enthalpy [20, 21],
AH = 1986 J mol-1 at T = 298.150 K.
For the case of salt of formula MX with charge ratio (1:
1) such as K[D-C6H11O7](s), the apparent relative molar
enthalpy UL for K[D-C6H11O7](s) may be expressed as:
Molar enthalpy of dissolution at infinite dilution
and Pitzer’s parameters
ꢀ
ꢁ
UL ¼ 2ðAH=2:4Þ ln 1 þ 1:2I1=2
h ꢀ
ꢁ
i
The title compound is soluble in the double-distilled water.
The experimental values of molar enthalpies of dissolution
(DsHm) of the title compound in the double-distilled water
are given in Table 6, and the curvilinear relationship of
DsHm/(kJ mol-1) with molalities m/(mol kg-1) is shown in
Fig. 4.
UL
ð0ÞL
ð1ÞL
À 2RT2 m b
þ y0bMX þ m2CMX=2
ð12Þ
MX
The molar enthalpy of dissolution of the compound
(DsHm) in the double-distilled water is expressed as
[20, 21]:
0.0175
0.0170
/
DsHm ¼ DsHm1 þ L
ð10Þ
0.0165
0.0160
0.0155
in which DsHm1 is the molar enthalpy of dissolution at
infinite dilution, UL is the apparent relative molar enthalpy.
For the salt of MX (1:1), the apparent relative molar
enthalpy UL may be expressed as: [22]
0.000
–0.002
–0.004
–0.006
ꢀ
ꢁ
UL¼vjzMzXjAH ln 1þbI1=2 =2b
0.000
–0.002
–0.004
–0.006
h
i
UL
ð0ÞL
ð1ÞL
1=2
À2vMvXRT2 mbMX þmy0bMX þðvMvXÞ m2CMX=2
–0.008
–0.008
–0.010
ð11Þ
Fig. 5 The 3D chart of Y against -m and -my0 for potassium D-
gluconate K[D-C6H11O7](s)
123

Crystal structure and chemical thermodynamic properties of potassium D-gluconate…
From Eqs. (10) and (12), the working equation to
determine Pitzer’s parameters is shown as:
endothermic process, and an entropy-driven process
instead of enthalpy-driven process. It mainly ascribes to the
breaking of ionic bonds, chelate bonds and van der Waals
interaction forces existing in the compound needing to
absorb large amount of heat energy.
h
ꢀ
ꢁ
i
À
Á
Y ¼ DsHm À AH ln 1 þ 1:2I1=2 =1:2 = 2RT2
UL
ð1ÞL
¼ a0 À mbð0ÞL À my0bMX À m2CMX=2
ð13Þ
is the extrapolation function and
MX
where
Y
Relative partial molar enthalpies
a0 ¼ DsHm1=ð2RT2Þ. Regression of Y against -m, -my0
and -0.5 m2 is made by least squares to obtain
The relative partial molar enthalpies of solvent (L1) and
solute (L2) are important thermodynamic functions of the
electrolyte solution. Generally, there are many ways used
to determine the relative partial molar enthalpies. In this
paper, they are obtained by the apparent relative molar
enthalpy (UL) and partial derivative of UL against m.
The relative partial molar enthalpy of the double-dis-
tilled water (L1) as the solvent is expressed as:
a0 = 0.01889, bð0ÞL = -51.9832, bð1ÞL = 56.1199 and
MX
MX
UL
CMX = 639.1015 with a standard deviation of the fitting
1.45278 9 10-4 for K[D-C6H11O7](s), respectively. The
molar enthalpy of dissolution for the title compound at
infinite
DsH1
dilution
is
determined
to
be
= (27.92 0.21) kJ mol-1. The 3D
mfK½DÀC6H11O7ŠðsÞg
chart of Y against -m and -my0 is plotted in Fig. 5.
À
Á
ð0ÞL
ð1ÞL
are attributed to the short-
MX
L1 ¼ ÀMH Om2 oUL=om
ð14Þ
ꢀ
The quantities b
and b
MX
2
T;P
range interaction between the cation and anion. Generally
The formula to determine relative partial molar enthalpy
ð0ÞL
ð1ÞL
are very
MX
speaking, the absolute values of b
small for an usual electrolyte and have a tendency to
and b
MX
of the each compound (L2) is,
À
Á
U
U
ꢀ
L2 ¼ L þ m o L=om
ð15Þ
increase along with the volume and the quantity of the ion.
ð1ÞL
T;P
ð0ÞL
It may be noted that the absolute values of b
are significantly greater than those of usual electrolytes
and b
MX
The partial derivative of UL against m, (qUL/qm)T,P, is
obtained under constant pressure and temperature (CMX is
MX
UL
-
mainly since the volume of the anion D-C6H11O7 is
not neglected):
À
greater than those of the usual electrolytes. This shows that
various types of strong short-range interactions exist
ꢀ
ꢁ
Á
oUL=om
¼AH= 2m1=2þ2:4m
T;P
h
ꢀ
ꢁ
i
between cation and anion in the solutions obtained from
ð0ÞL
UL
ð0ÞL
À2RT2
b
þbðM1ÞXLexp À2m1=2 þmCMX
MX
dissolution of the title compound. b
is a negative value,
MX
ꢀ
ꢁ
that is, obðM0ÞX=oT \0, which indicates that the value of
ð16Þ
p
According to the relationships shown in Eqs. (10), (14),
ð0ÞL
b drops with the rise of the temperature. This shows that
the interionic repulsive force decreases with the increase of
(15), and (16), apparent relative molar enthalpies (UL) and
relative partial molar enthalpies of the double-distilled
water (L1) as the solvent and the title compounds (L2) as
the solute are obtained. All the results calculated above are
listed in Table 6.
MX
UL
the temperature. The third coefficient CMX for triple ion
interactions has a very high value in the research, it may be
-
ascribed to the chelate behavior of the D-C6H11O7 anion
with K? cation in the aqueous solution and further
-
hydrolyzation of the D-C6H11O7 anion at low concentra-
Standard molar enthalpy of formation of the anion
[D-C6H11O7]2(aq) in the aqueous solution
tions, and the larger ionization energy of the electrovalent
compound in water is caused mainly by the formation and
destruction of the six-membered chelate ring and further
The potassium D-gluconate K[D-C6H11O7](s) is dissociated
into the anion [D-C6H11O7]- and the cation K? in the
aqueous solution according to the following ionization
equation,
-
hydrolyzation of the D-C6H11O7 anion at low concentra-
tions. The two processes need to absorb larger heat quantity
than normal process.
The degree of chaos of K[D-C6H11O7](s) is increased
when it is dissociated to K?(aq) and D-C6H11O7-(aq) in the
double-distilled water. It is concluded that the entropy
change of the dissolution reaction is greater than zero
according to the statistical explanation of the entropy in
statistical thermodynamics. From the values of molar
enthalpies of dissolution, we deduce the conclusion that the
dissolution of the title compound in the water is a typical
K½D-C6H11O7ŠðsÞ ! KþðaqÞ þ ½D-C6H11O7ŠÀðaqÞ
The standard molar enthalpy of formation of the anion
[D-C6H11O7]- in the aqueous solution is calculated
according to Eq. 18 based on Eq. 17,
ð17Þ
À
Á
DfHmo D-C6H11OÀ7 , aq ¼ DsolHm1
þ DfHmo ðK½D-C6H11O7Š,sÞ À DfHmo ðKþ,aqÞ
ð18Þ
123

Y.-Y. Di et al.
The standard molar enthalpy of formation of the anion [D-
References
C6H11O7]-(aq)
is
calculated
to
be
DfHmo
À
Á
D- C6H11OÀ7 , aq = -(1473.87 0.28) kJ mol-1 through
the molar enthalpy of dissolution at infinite dilution
DsolHm1 = (27.92 0.21) kJ moþl-1 and some auxiliary ther-
modynamic data, such as DfHmo ðK ,aqÞ = -252.38 kJ mol-1
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[20],
and
DfHmo ðK½D-C6H11O7Š,sÞ = -(1754.17
0.19) kJ mol-1, as described in the paper.
Conclusions
1. Potassium D-gluconate K[D-C6H11O7](s) is synthe-
sized, and the crystal structure is determined by X-ray
crystallography. The lattice potential energy is deter-
mined to be UPOT[K[D-C6H11O7]] = 492.56 kJ mol-1
.
-
The ionic volume of D-C6H11O7 is calculated to be
0.1921 nm3.
2. In accordance with Hess’ law, reasonable thermo-
chemical cycle is designed, and the standard molar
enthalpy of formation of potassium D-gluconate K[D-
C6H11O7](s) is calculated to be -(1754.17
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infinite
dilution
is
calculated
to
be
(27.92 0.21) kJ mol-1. The standard molar enthalpy
of formation of the anion [D-C6H11O7]-(aq) is calcu-
À
Á
lated to be DfHmo D-C6H11OÀ7 , aq = -(1473.87
ð0ÞL
ð1ÞL
0.28) kJ mol-1. The Pitzer’s parameters (b , b
MX
MX
UL
and CMX) are obtained through Pitzer’s theory.
4. The values of apparent relative molar enthalpies (UL)
and relative partial molar enthalpies of the solvent (L1)
and the compounds (L2) are derived, respectively.
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Supplementary material
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mentary 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:
(?44) 1223-336-033; or e-mail: deposit@ccdc.cam.ac.uk.
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Acknowledgements This work is financially supported by the
National Natural Science Foundations of China under the contract
NSFC No. 21273100.
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123