Molar conductivity and association constants of sodium salts of selected cinnamic acids in water at temperatures from 288.15 to 318.15?K

Article abstract of DOI:10.1016/j.molliq.2019.111370

The electrical conductivities of aqueous solutions of sodium salts of cinnamic acid, 4-hydroxycinnamic (p-coumaric) acid, 3,4-dihydroxycinnamic (caffeic) acid, 4-hydroxy-5-methoxycinnamic (ferulic) acid and 3,5-dimethoxy-4-hydroxycinnamic (sinapinic) acid

Full text of DOI:10.1016/j.molliq.2019.111370

Accepted Manuscript
Molar conductivity and association constants of sodium salts of
selected cinnamic acids in water at temperatures from 288.15 to
3
18.15K
Marta Stańczyk, Agnieszka Boruń, Małgorzata Jóźwiak
PII:
S0167-7322(19)33158-7
https://doi.org/10.1016/j.molliq.2019.111370
111370
DOI:
Article Number:
Reference:
MOLLIQ 111370
To appear in:
Journal of Molecular Liquids
Received date:
Revised date:
Accepted date:
4 June 2019
11 July 2019
13 July 2019
Please cite this article as: M. Stańczyk, A. Boruń and M. Jóźwiak, Molar conductivity and
association constants of sodium salts of selected cinnamic acids in water at temperatures
from 288.15 to 318.15K, Journal of Molecular Liquids, https://doi.org/10.1016/
j.molliq.2019.111370
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ACCEPTED MANUSCRIPT
Molar conductivity and association constants of sodium salts of selected
cinnamic acids in water at temperatures from 288.15 to 318.15 K
a
a
a
Marta Stańczyk *, Agnieszka Boruń , Małgorzata Jóźwiak
a
University of Lodz, Faculty of Chemistry, Department of Physical Chemistry, Pomorska 165,
9
0-236 Lodz, Poland
*
Corresponding author.
E-mail address: martastanczyk1@o2.pl (M.Stańczyk)
Abstract
The electrical conductivities of aqueous solutions of sodium salts of cinnamic acid, 4-
hydroxycinnamic (p-coumaric) acid, 3,4-dihydroxycinnamic (caffeic) acid, 4-hydroxy-5-
methoxycinnamic (ferulic) acid and 3,5-dimethoxy-4-hydroxycinnamic (sinapinic) acid were
measured over the temperature range (T) of 288.15 to 318.15 K at 5 K intervals. The limiting
o
m
ꢃ
molar conductivity ꢀ ꢀ and ionic association constants ꢁ ꢀꢄwere obtained using the low
ꢂ
concentration Chemical Model (lcCM). The limiting ionic conductivity and the Eyring’s
activation enthalpy of charge transport of the investigated anions were determined.
Keywords: molar conductivity, sodium salts of phenolic acid, limiting ionic conductivity,
hydrolysis
1
. Introduction
Phenolic acids are known to have a positive effect on human health due to their
antioxidant potential, which is particularly marked in the case of cinnamic acid derivatives.
They are widely distributed throughout the plant kingdom, and despite being characterized by
diverse chemical structures and pharmacological properties, they all share certain hydroxyl
and carboxylic groups [1]. However, it is possible to distinguish between simple benzoic
acids, phenylacetic acids and cinnamic acids based on the number of carbons in the side chain
(Fig 1). The most common cinnamic acid derivatives are its hydroxyl derivatives, i.e. caffeic,
ferulic, p-coumaric and synapinic acids.
1

ACCEPTED MANUSCRIPT
Phenolic acids are commonly found in food and dietary supplements as bioactive
components. However, the salts of phenolic acids, especially those formed with alkali metals,
are much more water soluble then the acids themselves, and hence are better suited for use as
potential disinfectants or preservatives. Recent studies describing the activities of a range of
structurally-varied phenolic acid salts against food-borne pathogens indicate that both
phenolic acids and their salts can be used as natural chemical agents to preserve food [2, 3].
The objects of such studies are most often o-, m- and p-coumaric acids, caffeic and cinnamic
acid [2, 4, 5].
One well-known sodium salt of a cinnamic acid derivative containing both hydroxyl
and methoxy groups is sodium ferulate (SF). It is easily synthesized and offers greater
stability and water solubility than ferulic acid; as such, it is widely used in scientific research
and clinical medicine, as well as in the food and cosmetics industries. For example, SF is used
in foods to mask the aftertaste of acesulfame potassium, an artificial sweetener patented by
Kraft Foods [6]. It is also an active agent in Chinese medicinal herbs such as Angelica
sinensis, Cimicifuga heracleifolia and Lignsticum chuangxiong, and has been approved by the
State Office of Drugs in China for treating cardiovascular and cerebrovascular diseases and
for use as a prophylactic against thrombosis. In addition, clinical trials have found it to exhibit
low toxicity [7], and it is regarded as safe for use in humans.
The present paper presents precise measurements of the electrical conductivity of the
aqueous solutions of the sodium salts of cinnamic acid and its selected derivatives: cinnamic
acid (NaCin), 4-hydroxycinnamic acid (p-NaCou), 3,4-dihydroxycinnamic acid (NaCaf), 4-
hydroxy-5-methoxycinnamic acid (NaFer) and 3, 5-dimethoxy-4-hydroxycinnamic acid
(NaSyn). All conductivities were measured at temperatures (T) from 288.15 K to 318.15 K in
-4
-2
-3
a concentration range (c) ranging from ~ 1·10 to ~ 1.5·10 mol·dm at atmospheric
pressure. The structures of all investigated salts are presented in Fig. 2. The salts were chosen
to demonstrate the influence of changes in their structure, i.e. location and number of
hydroxyl or methoxy groups, on their conductometric properties. The effect of hydrolysis on
the limiting molar conductivity for the investigated salts was also evaluated.
o
m
The obtained data allowed the limiting molar conductivity ꢀ ꢀ and the association
ꢆ
constants ꢁ ꢀ for the investigated salts to be determined using the low concentration
ꢅ
Chemical Model (lcCM). The limiting ionic conductivity, hydrodynamic radius of the anions
and the values for Eyring activating enthalpy of charge transport of the anions were also
calculated.
2

ACCEPTED MANUSCRIPT
2
. Materials and methods
Sodium cinnamate (AK Scientific, Inc, USA, 98%) was dried under vacuum at T =
73.15 K to constant mass. The sodium salts of p-coumaric, caffeic, ferulic and synapinic acid
3
were prepared using trans-p-coumaric acid (TCI, Tokyo, Japan, >98.0%), 3,4-
dihydroxycinnamic acid, predominantly trans isomer (ACROS ORGANICS, USA, 99+%),
trans-ferulic acid (Sigma Aldrich, China, 99%), 3,5-dimethoxy-4-hydroxycinnamic acid,
predominantly trans isomer (ACROS ORGANIC, USA, 98%), and sodium hydroxide
(micropills pure, P.A., Avantor Performance Material Poland S.A.).
The appropriate amounts of acid and aqueous sodium hydroxide were mixed in a
stoichiometric ratio 1:1; the mixture was then heated and stirred to dissolve the acid and
evaporate the solvent. The procedure is described in more detail elsewhere [2, 9]. The
obtained salts were washed with acetone and dried at T = 373.15 K to constant mass. The
1
synthesized salts were tested by H NMR spectra to confirm that significant amounts of
impurities were absent. The spectra for the synthesized salts were consistent with those given
in the literature [10-13]. The purity of the salt obtained was 98 %.
All the solutions were prepared gravimetrically using an analytical balance (Sartorius RC
-5
2
10D) with a precision of ±1·10 g. Densities were measured with an Anton Paar DMA 5000
M oscillating U-tube densimeter equipped with a thermostat with temperature stability within
0.001 K. The densimeter was calibrated with dry air and ultrasonically-degassed extra-pure
±
-4
-3
water. The estimated expanded uncertainty of the density is ± 1.5·10 g·cm . The density (ρ)
of the sodium salts as a function of sodium salt molality (m – moles of electrolyte per
kilogram of solution) and temperature are presented in Table A1 in the Supporting
Information.
Conductivity measurements were performed with a three-electrode cell and a 6430 B
Precision Component Analyzer (Wayne-Kerr Electronics, UK) under an inert gas atmosphere
and at frequencies (ν) of 0.2, 0.5, 1, 1.5, 2, 3, 5, 10 and 20 kHz. The temperature was
controlled within 0.001 K by an ultrathermostat with a PD controller (Performance Digital,
LABO PLUS, USA). The measurement procedure was based on the method described by
Bešter-Rogač et al. [14, 15] and used in our previous study [8]. Considering the sources of
error (calibration, purity of samples, measurements), the uncertainty of the conductivity
measurements was estimated to be ± 0.5 %.
3

ACCEPTED MANUSCRIPT
3
. Results and discussion
The densities, viscosities and relative permittivity values of water have been described
previously [8].
To convert molonity ꢇꢈ into molar concentration (c), the values of density gradients (b)
were determined independently and used in the following equation ꢉꢊ ꢇꢈ ꢋ ꢌ ꢋ ꢌ ꢎꢏ ꢇꢈ ꢐ
ꢍ
where ρ is the density of the solution. Molar concentration was needed for the conductivity
equation. The density gradients and the molar conductivity of the sodium salts ꢀ ꢀ are
m
presented in Table A2 (Supporting Information) as a function of sodium salt molality (m –
moles of electrolyte per kilogram of solvent) and temperature. The relationship between m,
ꢇꢈ ꢄand c is as follows ꢇꢈ ꢋ ꢉꢊꢌ ꢋ ꢇꢊ ꢑꢎꢇꢒꢀꢐwhere M is the molar mass of electrolyte.
The conductivity data was analyzed by the low concentration Chemical Model (lcCM)
[
16] using the following equations:
ꢀm ꢋ ꢓꢔꢀ ꢕꢖ ꢓꢉꢀ ꢎꢙ ꢓꢉꢀꢄln ꢓꢉꢀꢎꢚ ꢓꢉꢀꢕꢚꢛꢊꢘ ꢓꢉꢀꢛꢊꢘꢜ (1)
o
ꢗꢊꢘ
m
ꢃ
ꢘ
ꢘ
ꢁ
ꢋ ꢑꢕꢓꢀꢊꢝꢓ ꢉꢞ ꢠ
(2)
(3)
ꢂ
ꢟ
ꢗꢊꢘ ꢗꢊꢘ
ꢗꢊꢘ ꢗꢊꢘ
ꢡꢢꢞ ꢋ ꢕꢝꢣꢓ
ꢉ
ꢠꢊꢝꢑꢎꢤꢥꢓ
ꢉ
ꢠ
ꢟ
o
m
In these equations, ꢀ is the limiting molar conductivity; α is the dissociation degree of an
o
A
electrolyte; ꢁ ꢄis the ionic association constant; R is the distance parameter of ions; y is the
±
activity coefficient of ions on the molar scale; A and B are the Debye–Hückel equation
coefficients. The analytical form of the parameters S, E, J and J3/2 has been presented
previously [16]. The calculation was performed as described by Bešter-Rogač [17, 18]. The
description of the procedure for determining the distance parameter R for various types of
compounds is described in literature [17-22]. In the case of our study, we assumed the
distance parameter R = 0.820 nm, the same as in the papers [17, 18], in which both this
parameter and the method of its determination were described in detail.
Figure 3 shows the relationship between molar conductivity for the aqueous solution
of NaSyn as a function of temperature. The remaining salts show a similar relationship. In the
case of p-NaCou, NaFer and NaSyn, molar conductivity values decrease slightly with
increasing concentration, while more significant changes can be observed for NaCin and
NaCaf. All investigated salts demonstrated a significant increase in molar conductivity with
an increase of temperature.
4

ACCEPTED MANUSCRIPT
Figure 4 shows the molar conductivity of all salts tested at 298.15 K. The highest
molar conductivity for the investigated salts were observed for the NaCin and the lowest for
NaFer.
o
m
ꢃ
Table 1 presents the ꢀ and ꢁ values for the investigated salts. The association
ꢂ
ꢃ
constants ꢁ are very low, with the maximum value obtained in the present study being only
ꢂ
3
-1
9
.8 dm ·mol . This finding indicates that all of the investigated salts are nearly fully
dissociated in water; similar results were also obtained previously for sodium salts of benzoic
acid derivatives [8].
The limiting molar conductivity of all investigated salts was found to increase with
temperature, which is caused by a decrease in solvent viscosity. Of all the salts, the most
significant increase in limiting molar conductivity, together with the highest values, were
observed for NaCin. An increase in the number of substituents, as well as their type,
significantly reduced the limiting molar conductivity of studied salts. Much smaller
differences in limiting molar conductivity were observed between NaBen and the salts o-
NaSal, m-NaSal, p-NaSal, NaPro, NaVal and NaSyr [8]. In the case of NaCin salts, such a
significant difference may be due to the elongation of the carbon chain at the carboxyl group,
as well as the presence of a double bond in this chain.
The limiting molar conductivity of the salts investigated in the present study follows
the sequence NaCin > NaSyn > p-NaCou > NaCaf > NaFer at temperatures of 288.15 K and
2
93.15 K; however, at the other tested temperatures, the sequence becomes NaCin > NaSyn >
NaCaf > p-NaCou > NaFer, with p-NaCou and NaCaf changing places. These two salts, both
of which contain one or two hydroxyl groups with the maximum difference between them
being two units, were found to have similar values; hence, in this case, an increase in the
number of hydroxyl groups in the molecule does not appear to significantly affect the limiting
molar conductivity value.
This finding contradicts those observed for the sodium salts of certain benzoic acid
derivatives (p-NaSal and NaPro): for these, the presence of higher numbers of hydroxyl
groups was found to be associated with a significant decrease in conductivity [8]. The
difference between the limiting molar conductivity for those salts increased linearly with
increasing temperature, with the greatest difference observed at 318.15 K [8]. However, in the
present study, the greatest difference between the cinnamic acid salts p-NaCou and NaCaf
was observed at 298.15 K. Much greater differences in limiting molar conductivity were
5

ACCEPTED MANUSCRIPT
observed for the salts containing methoxy groups (i.e. NaFer and NaSyn), but this difference
was found to decrease with increasing temperature; surprisingly, the limiting molar
conductivity of each salt increases with the number of methoxy groups in the molecule.
The next stage of our study examined the limiting molar conductivity values of the
ꢃ
ꢂ-
anions ꢦ in water using the appropriate literature value for the sodium cation [23].
ꢃ
ꢂ-
ꢧꢀ ꢋ ꢨꢃ
ꢧꢀꢕꢦꢃ
ꢦ
ꢎ
ꢧꢀ
(4)
ꢩꢐꢄꢄꢪꢫꢂ
ꢪꢫ
The results for all investigated anions are presented in Table 2.
Using Walden's rule, the Stokes (hydrodynamic) radii r was calculated for the
s
investigated anions
ꢃ
ꢂ-
ꢬꢦ ꢋ ꢭꢮꢯꢰꢱꢲ ꢊꢴ
(5)
ꢳ
ꢵ
where z is the charge number of the ion, η is the dynamic viscosity of water.
i
The results of these calculations were collected in Table 3.
-
The hydrodynamic radius of the studied anions increases in the following order: Cin <
-
-
-
-
Syn < p-Cou < Caf < Fer for the two lowest studied temperatures (288.15 K and 293.15 K)
-
-
-
-
-
and Cin < Syn < Caf < p-Cou < Fer for the remaining temperatures (from 298.15 K to
-
3
18.15 K). The hydrodynamic radius for Cin changes slightly with increasing temperature.
-
For the Fer anion, the hydrodynamic radius was found to decrease as the temperature
increased, with an exception being observed at 313.15 K. Interestingly, while very little
-
-
change in hydrodynamic radius was observed for both p-Cou and Syn below 298.15 K, the
radius of the former was found to decrease slightly above this temperature while that of the
-
latter only increased slightly. For the Caf anion, the hydrodynamic radius did not change
between 288.15 K and 293.15 K. If we know van der Waals radii we can compare them with
the hydrodynamic radii to obtain information about the hydration of the ions. However, as the
-
van der Waals radius for the above ions are unknown, we can only assume that the Cin anion
is subject to slight hydration, resulting in a greater effect on mobility and ionic conductivity
-
than for the other studied anions. Of the studied anions, Fer probably possesses the largest
hydration shell.
ꢹ
ꢸ
The Eyring activation enthalpy of charge transport ꢶꢷ for the investigated anions
was obtained using the dependence:
ꢃ
ꢂ-
ꢹ
ꢸ
ꢡꢢꢦ ꢎꢯꢊꢺꢡꢢꢌ ꢋ ꢕꢶꢷ ꢊꢥꢧꢎꢻ
(6)
ꢍ
6

ACCEPTED MANUSCRIPT
where D is an empirical constant.
Comparing the slope of the linear dependencies of ꢄlnꢦ ꢎꢯꢊꢺlnꢌ against the inverse of the
o
A-
ꢍ
ꢹ
ꢸ
-1
-
-1
temperature (1/T) yielded the following ꢶꢷ values: 18.33 kJ∙mol for Cin , 18.43 kJ∙mol
-
-1
-
-1
-
-1
-
for p-Cou , 21.08 kJ∙mol for Caf , 23.54 kJ∙mol for Fer and 14.97 kJ∙mol for Syn (Fig 5).
Regarding the activation enthalpy of charge transfer, greater differences were observed
between the cinnamic acid salts tested in the present study than the sodium salts of benzoic
acid derivatives studied previously [8]. Those differences were small and higher than those
ꢹ
ꢸ
-
related to the viscous flow of pure water. While the ꢶꢷ value of the Syn anion was almost
identical to that of pure water, those of the other studied anions were higher; this indicates that
the charge transport in these solutions requires ion desolvation and rearrangement of the
solvent molecule around the ion to a certain extent. These processes are slightly more
-
-
pronounced for the Caf and Fer anions, for which the difference is much larger.
The final stage of the study examined the effect of hydrolysis on molar conductivity.
The degree of hydrolysis (β) and the limiting molar conductivity were evaluated as described
previously [8]. The β values of the sodium salts of p-coumaric, caffeic, ferulic and sinapinic
acid (Table A3) were determined based on the literature values for their dissociation constant
(
K ) [24] at 298.15 K (Table A4): the obtained values were very small, ranging from
a
0
.0001442 to 0.0012803. In the case of NaCin (Table A5), K is known for a wide range of
a
temperatures [25] (Table A6) and therefore β could be assessed across the entire temperature
range: it was found to range from 0.0001464 (318.15 K) to 0.0009232 (288.15 K). The
differences between the degree of hydrolysis (β) the highest and lowest temperatures are very
small at any given concentration.
For NaCin, at each of the temperatures studied, the limiting molar conductivity value
o
m
calculated excluding the effect of hydrolysis (ꢀ ) was practically identical to that calculated
o
mꢐꢄꢼ
accounting for hydrolysis ꢀ ꢀ (Table 4). The largest differences between these values
2
-1
(
0.18 S·cm ·mol ) were observed in the case of NaSyn and NaFer (Table 5). The smallest
2
-1
o
mꢐꢄꢼ
differences were obtained for NaCaf (0.08 S·cm ·mol ). However, the values of ꢀ
are
o
m
o
m
always slightly lower than these of ꢀ because ꢀ also includes the conductivity contributed
by NaOH. As in the case of benzoic acids salts, the differences in limiting molar conductivity
of all the studied cinnamic acid salts are much smaller than the estimated uncertainty
regarding conductivity measurements (± 0.5%); as such, it appears that the hydrolysis of the
salt has no significant effect on the analysis of conductometric data. If the hydrolysis would
7

ACCEPTED MANUSCRIPT
have a greater impact, it would be visible already in the behavior presented in figures 3 and 4,
respectively (as described in Ref. 26).
4
. Conclusions
The obtained values of association constants are insignificant, which indicates that the
investigated salts are completely dissociated in aqueous solution. For the two lowest of the
studied temperatures (i.e. 288.15 K and 293.15 K), the limiting ionic conductivity of the salts
-
-
-
-
-
decreases in the following order: Cin > Syn > p-Cou > Caf > Fer , while the hydrodynamic
-
-
-
-
-
radius increases in the opposite direction: Cin < Syn < p-Cou < Caf <Fer . For the
-
remaining studied temperatures (from 298.15 K to 318.15 K), the order is as follows: Cin >
-
-
-
-
Syn > Caf > p-Cou > Fer , with the hydrodynamic radius again increasing in the opposite
-
-
-
-
-
direction: Cin < Syn < Caf < p-Cou < Fer . Although an change in the number of hydroxyl
groups in the molecules of the studied salts does not significantly affect the limiting molar
conductivity, the number of methoxy groups does. Among the investigated salts, phenomenon
of hydrolysis does not affect the analysis of conductometric data.
Acknowedgment
This work is part of the research program for young scientists “Thermodynamic studies of
selected macromolecules in terms of their application in industry, environmental protection
and medicine” with project number B1711100001600.02, is financed by the University of
Lodz.
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1
0

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o
m
o
A
Table 1. Limiting molar conductivity ꢀ ꢐ association constants ꢁ and standard deviations σ(ꢀ) for the investigated salts in water over the
temperature range from 288.15 K to 318.15 K.
NaCin
p-NaCou
NaCaf
o
ꢃ
o
ꢃ
o
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
ꢂ
m
ꢂ
m
ꢂ
m
T/K
σ (ꢀ)
σ (ꢀ)
σ (ꢀ)
2
-1
3·
-1
2
-1
3·
-1
2
-1
3·
-1
S·cm ·mol
dm mol
S·cm ·mol
dm mol
S·cm ·mol
dm mol
2
2
2
3
3
3
3
88.15
93.15
98.15
03.15
08.15
13.15
18.15
81.57 ± 0.17
92.87 ± 0.16
104.59 ± 0.16
116.88 ± 0.15
129.78 ± 0.15
143.06 ± 0.17
156.93 ± 0.20
9.11 ± 0.01
9.77 ± 0.01
9.68 ± 0.01
9.47 ± 0.01
9.34 ± 0.01
9.13 ± 0.01
9.06 ± 0.01
0.57
0.55
0.55
0.52
0.52
0.58
0.69
59.30 ± 0.02
66.81 ± 0.03
74.95 ± 0.05
83.76 ± 0.04
92.70 ± 0.05
101.95 ± 0.05
111.78 ± 0.05
0.90 ± 0.01
0.00
0.05
0.12
0.16
0.13
0.16
0.18
0.18
57.86 ± 0.01
65.35 ± 0.02
76.86 ± 0.02
84.68 ± 0.01
94.57 ± 0.02
102.75 ± 0.02
112.86 ± 0.03
2.01 ± 0.01
1.97 ± 0.01
3.56 ± 0.01
4.08 ± 0.01
2.59 ± 0.01
3.07 ± 0.01
2.18 ± 0.01
0.05
0.06
0.06
0.05
0.09
0.06
0.10
0.00
0.00
0.00
0.00
0.05 ± 0.01
Table 1. continued
NaFer
NaSyn
o
ꢃ
o
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
ꢂ
m
ꢂ
m
T/K
σ (ꢀ)
σ (ꢀ)
2
-1
3·
-1
2
-1
3·
-1
S·cm ·mol
dm mol
S·cm ·mol
dm mol
2
2
2
3
3
3
3
88.15
93.15
98.15
03.15
08.15
13.15
18.15
55.31 ± 0.03
62.74 ± 0.04
70.49 ± 0.04
82.52 ± 0.05
91.51 ± 0.05
99.74 ± 0.04
109.34 ± 0.05
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.10
0.13
0.15
0.19
0.16
0.15
0.19
63.00 ± 0.05
71.63 ± 0.04
80.60 ± 0.05
89.22 ± 0.05
98.13 ± 0.05
105.83 ± 0.07
113.13 ± 0.11
0.00
0.00
0.16
0.15
0.18
0.18
0.19
0.27
0.39
0.05 ± 0.01
0.68 ± 0.01
1.52 ± 0.01
0.13 ± 0.01
0.00
1
1

ACCEPTED MANUSCRIPT
ꢃ
ꢂ-
Table 2. Limiting ionic conductivity ꢦ of anions of investigated salts in water at different
temperatures.
-
-
-
-
-
Cin
p-Cou
Caf
Fer
Syn
T/K
ꢃ
ꢂ-
2
-1
ꢦ /S·cm ·mol
2
2
2
3
3
3
3
88.15
93.15
98.15
03.15
08.15
13.15
18.15
41.85
48.06
54.44
61.16
68.25
75.51
85.57
19.58
22.00
24.80
28.04
31.17
34.40
40.42
18.14
20.54
26.71
28.96
33.04
35.20
41.50
15.59
17.93
20.34
26.80
29.98
32.19
37.98
23.28
26.82
30.45
33.50
36.60
38.28
41.77
Table 3. Hydrodynamic radii r of the investigated anions at different temperatures.
s
-
-
-
-
-
Cin
p-Cou
Caf
Fer
Syn
T/K
rs/nm
2
2
2
3
3
3
3
88.15
93.15
98.15
03.15
08.15
13.15
18.15
0.172
0.170
0.169
0.168
0.167
0.166
0.161
0.368
0.372
0.372
0.367
0.366
0.365
0.341
0.397
0.399
0.345
0.355
0.345
0.357
0.332
0.462
0.457
0.453
0.384
0.381
0.391
0.362
0.310
0.305
0.303
0.307
0.312
0.328
0.330
Table 4. Limiting molar conductivity of sodium cinnamate in water at different temperatures
excluding and including the effect of hydrolysis.
NaCin
2
88.15 K
81.57
293.15 K
92.87
298.15 K
104.59
303.15 K
116.88
308.15 K
129.78
313.15 K
143.06
318.15 K
156.93
o
m
2
-1
ꢀ
/S·cm ·mol
o
mꢐꢄꢼ
2
-1
ꢀ
/S·cm ·mol
81.54
92.86
104.58
116.87
129.77
143.05
156.93
Table 5. Limiting molar conductivity of the investigated salts in water at 298.15 K excluding
and including the effect of hydrolysis.
p-NaCou
NaCaf
NaFer
NaSyn
2
98.15 K
o
2
-1
ꢀ
/S·cm ·mol
74.95
74.81
76.86
76.78
70.49
70.31
80.60
80.42
m
o
mꢐꢄꢼ
2
-1
ꢀ
/S·cm ·mol
1
2

ACCEPTED MANUSCRIPT
COOH
COOH
COOH
R1
R3
R1
R3
R
2
R1
R3
R
2
R
2
Fig.1. Division and structure of phenolic acids
O
O
+
Na
a)
O
O
HO
O
O
+
+
Na
Na
b) HO
c) HO
O
O
MeO
O
+
Na
MeO
O
+
Na
HO
HO
OMe
d)
e)
Fig. 2. The structures of the investigated salts; a) sodium cinnamate, b) sodium p-coumarate,
c) sodium caffeinate, d) sodium ferulate, e) sodium synapinate
1
3

ACCEPTED MANUSCRIPT
1
1
1
20
10
00
90
80
70
60
50
0
0.02
0.04
0.06
0.08
-3 1/2
0.1
0.12
1
/2
c /(mol·dm )
1
/2
Fig. 3. Molar conductivity ꢀ of aqueous solution of NaSyn versus c at experimental
m
temperatures ● 288.15 K; ■ 293.15 K; ♦ 298.15 K; ▲ 303.15 K; ● 308.15 K; ■ 313.15 K; ♦
3
18.15 K. The lines represent the lcCM calculations.
1
1
1
20
10
00
9
8
7
6
5
0
0
0
0
0
0
0.02 0.04 0.06 0.08
0.1
0.12
1
/2
-3 1/2
c /(mol·dm )
Fig. 4. Molar conductivity ꢀ of ● NaCin; ▲ p-NaCou; ♦ NaCaf; ● NaFer; ■ NaSyn versus
m
1
/2
c in water at 298.15 K. The lines represent the lcCM calculations.
1
4

ACCEPTED MANUSCRIPT
7
.5
6
6
5
4
.5
5
.5
0
.0031
0.0032
0.0033
0.0034
0.0035
(
T/K)-1
ꢃ
ꢂ-
-
-
-
-
Fig. 5. Plot of ꢡꢢꢦ ꢎꢯꢊꢺꢡꢢꢌ as a function of 1/T for ● Cin ; ▲ p-Cou ; ♦ Caf ; ● Fer and ■
ꢍ
-
Syn in water.
1
5

ACCEPTED MANUSCRIPT
Graphical abstract
Highlights


Conductivity of sodium cinnamate, sodium p-coumarate, sodium caffeinate, sodium
ferulate and sodium synapinate in water.
The sodium salts of cinnamic acid and its derivatives are completely dissociated in
aqueous solution.


The limiting molar conductivity and ionic molar conductivity were determined.
The hydrolysis of the salts has no significance in the analysis of conductometric data.
1
6