Thermodynamic characteristics of protolytic equilibria in aqueous solutions of glycyl peptides

Article abstract of DOI:10.1134/S0036024416110078

Protolytic equilibria in aqueous solutions of glycyl-DL-serine, glycyl-DL-threonine, and glycyl-DL-valine are investigated by means of potentiometry and calorimetry. Dissociation constants and heat effects of the above dipeptides are determined. Standard

Full text of DOI:10.1134/S0036024416110078

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2016, Vol. 90, No. 11, pp. 2170–2176. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © S.N. Gridchin, 2016, published in Zhurnal Fizicheskoi Khimii, 2016, Vol. 90, No. 11, pp. 1649–1656.
PHYSICAL CHEMISTRY
OF SOLUTIONS
Thermodynamic Characteristics of Protolytic Equilibria
in Aqueous Solutions of Glycyl Peptides
S. N. Gridchin*
Ivanovo State University of Chemical Technology, Ivanovo, 153000 Russia
*e-mail: sergei_gridchin@mail.ru
Received November 24, 2015
Abstract—Protolytic equilibria in aqueous solutions of glycyl-DL-serine, glycyl-DL-threonine, and glycyl-
DL-valine are investigated by means of potentiometry and calorimetry. Dissociation constants and heat
effects of the above dipeptides are determined. Standard thermodynamic characteristics (pK°, ΔdisG°, ΔdisH°,
Δ
disS°) of the investigated equilibria are calculated. The obtained results are compared to corresponding data
on relative compounds.
Keywords: aqueous solutions of glycyl peptides, protolytic equilibria, thermodynamic characteristics
DOI: 10.1134/S0036024416110078
INTRODUCTION
perature of the potentiometric cell was maintained
with an accuracy of 0.05 K. The potentiometric
setup was calibrated before every titration. Calibration
was performed using standard HNO3 and KOH solu-
tions that contained potassium nitrate to ensure the
required ionic strength.
Equilibria of acid–base interaction in the aqueous
solutions of L-valyl-L-valine, DL-valyl-DL-leucine,
L-leucyl-L-leucine, DL-leucyl-glycine, glycyl-DL-
leucine, DL-alanyl-DL-leucine, DL-alanyl-DL-
valine, DL-alanyl-DL-alanine, DL-alanyl-glycine,
DL-alanyl-DL-serine, DL-alanyl-DL-asparagine,
β-alanyl-β-alanine, β-alanyl-glycine, glycyl-glycine,
glycyl-β-alanine, and glycil-L-asparagine were stud-
ied earlier in our laboratory [1–12]. The effect the
ionic strength of a solution has on the values of heat
effects of the studied processes was analyzed. Standard
thermodynamic characteristics (pK°, ΔrG°, ΔrH°,
ΔrS°) of the corresponding reactions were determined.
Glycyl-DL-serine, glycyl-DL-threonine, and glycyl-
DL-valine are investigated in this work.
Calorimetric measurements were made in an
ampoule calorimeter equipped with an isothermal
jacket and KMT-14 thermistor temperature sensor.
The changes in temperature over time were recorded
automatically. The operation of calorimeter was con-
firmed using the heat of potassium chloride dissolu-
tion in water. The agreement between the experimen-
tal data and the most reliable published data [13]
showed there were no significant errors in calorimeter
operation. The heat effects of mixing 0.9484 M of
HNO3 solution with 0.0084–0.0142 М solutions of
glycyl-DL-serine, glycyl-DL-threonine and glycyl-
DL-valine were measured at 298.15 K and ionic
strengths I = 0.1, 0.5, 1.0 (KNO3) in the ranges of pH
values 4.3 → 2.5 and 8.5 → 7.4. The heats of HNO3
dilution in the solution of the supporting electrolyte
were determined at the corresponding values of the
ionic strength.
EXPERIMENTAL
The electromotive force of a galvanic cell consist-
ing of an ESL-43-07 glass electrode and a saturated
EVL-1MZ silver chloride electrode was measured to
determine the equilibrium concentration of hydrogen
ions. The potential of the glass electrode was measured
with an R-363/3 potentiometer. A рН-340 pH-meter
(millivoltmeter) was used as the null detector. The
accuracy of measuring the potential was 0.1 mV.
Titration was performed using standard solutions of
nitric acid and potassium hydroxide that contained a
supporting electrolyte to avoid changes in the ionic
strength during the titration caused by dilution. A pre-
cise volume of a dipeptide solution with a given value
of ionic strength I = 0.1 (KNO3) was placed into the
RESULTS AND DISCUSSION
Potentiometric data were processed using the
PHMETR program to calculate constants for the
equilibrium of an arbitrary number of reactions
according to the measured equilibrium concentration
of one of the particles [14]. The program’s operation is
based on the principle of searching for the minimum
temperature-controlled potentiometric cell. The tem- of criterion function F by varying the constant values
2170

THERMODYNAMIC CHARACTERISTICS OF PROTOLYTIC EQUILIBRIA
2171
Table 1. Heat effects (J/mol) of dissociation reactions at
The values of ΔdisН obtained at a fixed ionic
strength allow calculating standard thermodynamic
characteristics of the investigated equilibria. The con-
centration heat effects for the reactions were extrapo-
lated to zero ionic strength using an equation with a
single individual parameter [18]:
298.15 K
I = 0.1 (KNO3) I = 0.5 (KNO3) I = 1.0 (KNO3)
Process
Glycyl-D,L-serine
(2)
(3)
886 130
44789 249
1541 114
45369 243
2002 117
46184 243
ΔdisН – Δz2Ψ(I) = ΔdisН° + bI,
(5)
Glycyl-DL-threonine
where ΔdisН and ΔdisН° are the enthalpies of the reac-
tion at finite and zero ionic strengths, respectively; b is
an empirical coefficient; Δz2 is the difference between
the squared charges of reaction products and reacting
particles; and Ψ(I) is the ionic strength function cal-
culated theoretically [18]. Corresponding values of
thermodynamic dissociation constants of dipeptides
were calculated using the equation introduced by
V.P. Vasil’ev in [18]:
(2)
(3)
849 181
4 4929 235
1470 162
45623 236
1600 156
46 493 244
Glycyl-DL-valine
(2)
(3)
–2069 113
45048 176
–1496 108
45702 183
–981 112
46076 145
that must be determined in every iteration using a
modified Hooke–Jeeves algorithm [15]. The criterion
function can be written as
pK° = pK + АγΔz2(I 1/2 /(1 + 1.6I 1/2
− 0.05I) + 0.05I,
)
(6)
F = Σ(log[H+]exp – log[H+]calc)2 → min,
(1)
where pK and pK° are the negative decimal logarithms
of the dissociation constants at finite and zero ion
strengths; Δz2 is the difference between the squared
charges of reaction products and reacting particles; Аγ
is the Debye–Huckel constant. Standard thermody-
namic characteristics of peptides dissociation are
given in Table 2 along with the results from similar
studies on dipeptides (α-amino acids derivatives),
obtained earlier in our laboratory [1–12].
The results obtained in this work are in good agree-
ment with the assumptions in [2, 4, 8] on the character
of the dependence of the changes in the thermody-
namic parameters of protolytic equilibria in solutions
of dipeptides on the structure of the lateral aliphatic
substituents in the corresponding N- and C-terminus
fragments. The reactions of betainic group dissocia-
tion are characterized by similar values of heat effects.
The slight increase in ΔdisH° of betainic group dissoci-
ation upon substituting N-terminus residue for ala-
nine, valine or leucine residue could be due to the pos-
itive inductive effect of the corresponding aliphatic
groups. However, the electron donor effect of these
groups is apparently not the only factor that affects the
value ΔdisH°. It is determined by the more complicated
intramolecular distribution of electron density caused
by the mutual influence of the betainic and carboxylic
fragments of the dipeptide.
where [H+]exp and [H+]calc are the equilibrium concen-
trations of H+ ions measured experimentally and cal-
culated at the current values of the equilibrium con-
stants. The equilibrium concentrations were calcu-
lated according to the Brinkley method [16]. The
estimated values of the dissociation constants of the
carboxylic and betainic groups of the dipeptides were
pK1 = 2.98 0.03, pK2 = 8.16 0.03 for glycyl-DL-
serine and pK1 = 3.01 0.04, pK2 = 8.17 0.03 for gly-
cyl-DL-threonine at 298.15 K and I = 0.1 (the corre-
sponding values of the dissociation constant values for
glycyl-DL-valine were taken from [17]: pK1 = 3.12
0.02, pK2 = 8.26 0.02 at 298.15 K and I = 0.12).
The considerable differences between the values of
the stepwise dissociation constants of the dipeptides
allows an independent calorimetric determination of
the heat effects:
H2L+ = H+ + HL,
(2)
HL = H+ + L–.
(3)
The heat effects of H2L+ and HL particle dissociation
can be calculated as the differences between the corre-
sponding heats of mixing and dilution:
ΔdisH = – (ΔmixH – ΔdilH)/α,
(4)
where ΔmixH is the heat of mixing the HNO3 solution
The presence of the alkyl group in the N-terminus
with the solution of the dipeptide in presence of the fragment of the dipeptide does not appreciably affect
supporting electrolyte in the corresponding рН range; the value of the heat of dissociation of the carboxylic
ΔdilH is the heat of dilution of HNO3 solution in the group. At the same time, introducing the aliphatic
supporting electrolyte at the same value of the ionic substituent into the C-terminus fragment of the dipep-
strength; and α is the completeness of HL and L– pro- tide determines the exothermicity of the dissociation
tonation. The values obtained for the heat effects of processes of carboxylic groups of glycyl-DL-valine,
the dissociation of glycyl-DL-serine, glycyl-DL-thre- glycyl-DL-leucine, L-leucyl-L-leucine, DL-valyl-
onine and glycyl-DL-valine at 298.15 K and ionic DL-leucine, DL-alanyl-DL-leucine, L-valyl-L-
strength values equal to 0.1, 0.5, 1.0 (KNO3) are given valine, DL-alanyl-DL-valine, and DL-alanyl-DL-
in Table 1.
alanine. The hydrophobic alkyl groups of the above
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Table 2. Standard thermodynamic characteristics of the dissociation reactions of certain dipeptides (α-amino acid derivatives)
disG°, kJ/mol disН°, kJ/mol –ΔdisS°, J/(mol K)
Glycyl-L-asparagine [1], H3N+–CH2–CO–NH–CH(CH2CONH2)–COO– (0.0, –1.21)
GRIDCHIN
Δ
Δ
Dipeptide
pK°
(2)
(3)
3.06 0.02
8.69 0.03
17.48 0.11
49.60 0.17
0.65 0.21
45.21 0.52
56.4 0.8
14.7 1.2
Glycyl-DL-serine, H3N+–CH2–CO–NH–CH(CH2OH)–COO– (0.0, –0.66)
(2)
(3)
2.98 0.03
8.36 0.03
17.01 0.17
47.72 0.17
0.82 0.13
44.22 0.25
54.3 0.7
11.7 1.0
Glycyl-DL-threonine, H3N+–CH2–CO–NH–CH(CH(CH3)OH)–COO– (0.0, –0.36)
(2)
(3)
3.01 0.04
8.37 0.03
17.18 0.23
47.78 0.17
0.87 0.24
44.35 0.24
54.7 1.1
11.5 1.0
Glycyl-DL-valine, H3N+–CH2–CO–NH–CH(CH(CH3)2)–COO– (0.0, 1.3)
(2)
(3)
3.11 0.02
8.48 0.02
17.75 0.11
48.40 0.11
–2.16 0.11
44.60 0.18
66.8 0.5
12.7 0.7
Glycyl-DL-leucine [2], H3N+–CH2–CO–NH–CH(CH2CH(CH3)2)–COO– (0.0, 1.8)
(2)
(3)
3.17 0.02
8.49 0.01
18.09 0.11
48.46 0.06
–2.60 0.13
45.18 0.20
69.4 0.6
11.0 0.8
L-Leucyl-L-leucine [2], H3N+–CH(CH2CH(CH3)2)–CO–NH–CH(CH2CH(CH3)2)–COO– (1.8, 1.8)
(2)
(3)
3.45 0.01
8.12 0.01
19.69 0.06
46.35 0.06
–1.97 0.22
45.01 0.30
72.7 0.8
4.5 1.0
DL-Leucyl-glycine [2], H3N+–CH(CH2CH(CH3)2)–CO–NH–CH2–COO– (1.8, 0.0)
(2)
(3)
3.34 0.05
8.29 0.05
19.06 0.29
47.32 0.29
0.59 0.12
45.34 0.24
62.0 1.0
6.6 1.2
DL-Valyl-DL-leucine [2], H3N+–CH(CH(CH3)2)–CO–NH–CH(CH2CH(CH3)2)–COO– (1.3, 1.8)
(2)
(3)
3.19 0.01
8.33 0.01
18.21 0.06
47.55 0.06
–2.31 0.15
45.82 0.28
68.8 0.5
5.8 0.9
DL-Alanyl-DL-leucine [3], H3N+–CH(CH3)–CO–NH–CH(CH2CH(CH3)2)–COO– (0.5, 1.8)
(2)
(3)
3.24 0.01
8.48 0.03
18.49 0.06
48.40 0.17
–1.54 0.17
45.97 0.23
67.2 0.6
8.2 1.0
L-Valyl-L-valine [4], H3N+–CH(CH(CH3)2)–CO–NH–CH(CH(CH3)2)–COO– (1.3, 1.3)
(2)
(3)
3.38 0.01
8.18 0.03
19.29 0.06
46.69 0.17
–1.89 0.26
46.04 0.40
71.0 0.9
2.2 1.5
DL-Alanyl-DL-valine [5], H3N+–CH(CH3)–CO–NH–CH(CH(CH3)2)–COO– (0.5, 1.3)
(2)
(3)
3.10 0.02
8.43 0.02
17.69 0.11
48.12 0.11
–2.23 0.24
46.22 0.40
66.8 1.0
6.4 1.4
DL-Alanyl-DL-alanine [6], H3N+–CH(CH3)–CO–NH–CH(CH3)–COO– (0.5, 0.5)
(2)
(3)
3.12 0.01
8.54 0.01
17.81 0.06
48.75 0.06
–1.72 0.11
45.89 0.56
65.5 0.5
9.6 1.9
DL-Alanyl-glycine [7], H3N+–CH(CH3)–CO–NH–CH2–COO– (0.5, 0.0)
(2)
(3)
3.18 0.03
8.35 0.03
18.15 0.17
47.66 0.17
0.74 0.11
45.14 0.22
58.4 0.7
8.5 0.9
DL-Alanyl-D,L-serine [8], H3N+–CH(CH3)–CO–NH–CH(CH2OH)–COO– (0.5, –0.66)
(2)
(3)
2.98 0.04
8.44 0.04
17.01 0.23
48.18 0.23
0.95 0.16
45.06 0.21
53.9 0.9
10.4 1.0
The values of the Hansch indices are given in parentheses. These indices characterize the hydrophobicity of the lateral substituents in
the corresponding betainic and carboxylate fragments of the dipeptides [19].
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Table 3. Standard thermodynamic characteristics of the dissociation reactions of dipeptides (glycine and β-alanine derivatives)
Δ
disG°, kJ/mol
Δ
disН°, kJ/mol
–ΔdisS°, J/(mol K)
Dipeptide
pK°
Glycyl-glycine [9], H3N+–CH2–CO–NH–CH2–COO–
(2)
(3)
3.16 0.01
8.31 0.01
18.04 0.06
47.43 0.06
0.61 0.14
44.19 0.33
58.5 0.5
10.9 1.1
Glycyl-β-alanine [10], H3N+–CH2–CO–NH–CH2CH2–COO–
(2)
(3)
4.04 0.05
8.37 0.06
23.06 0.29
47.78 0.34
1.36 0.18
42.97 0.28
72.8 1.1
16.1 1.5
β-Alanyl-glycine [11], H3N+–CH2CH2–CO–NH–CH2–COO–
(2)
(3)
3.24 0.03
9.62 0.08
18.49 0.15
54.91 0.46
1.24 0.15
47.83 0.21
57.9 0.7
23.7 1.7
β-Alanyl-β-alanine [12], H3N+–CH2CH2–CO–NH–CH2CH2–COO–
(2)
(3)
4.02 0.02
9.59 0.03
22.93 0.11
54.74 0.15
2.42 0.28
46.70 0.28
68.8 1.0
27.0 1.3
Table 4. ΔdisS° (J/(mol K)) values of the overall dissociation reactions of certain dipeptides and functional groups of the
corresponding amino acids
–ΣΔdisS°
°
°
°
–Δ
–Δ
disSΣ
–ΔdisScarb
disSbet
Dipeptide
Glycyl-glycine
(2) + (3)
(2) + (3)
(2)
(3)
69.4 1.2 [9]
66.0 1.2
69.1 1.2
66.9 1.6
67.3 1.6
67.0 1.4
78.6 1.6
89.7 1.2
69.5 1.5
90.1 1.5
70.5 1.3
68.3 1.7
68.4 1.4
80.0 1.7
75.6 1.5
70.2 2.2
79.7 2.5
30.1 0.4 [20]
27.9 1.2 [21]
28.3 1.1 [22]
28.0 0.8 [23]
39.6 1.2 [24]
50.7 0.5 [25]
30.1 0.4 [20]
50.7 0.5 [25]
30.1 0.4 [20]
27.9 1.2 [21]
28.0 0.8 [23]
39.6 1.2 [24]
35.2 0.9 [25]
30.1 0.4 [20]
39.6 1.2 [24]
39.0 1.1 [20]
39.0 1.1 [20]
39.0 1.1 [20]
39.0 1.1 [20]
39.0 1.1 [20]
39.0 1.1 [20]
39.4 1.4 [25]
39.4 1.4 [25]
40.4 1.2 [25]
40.4 1.2 [25]
40.4 1.2 [25]
40.4 1.2 [25]
40.4 1.2 [25]
40.1 2.2 [24]
40.1 2.2 [24]
Glycyl-DL-serine
Glycyl-DL-threonine
Glycyl-L-asparagine
Glycyl-DL-leucine
Glycyl-β-alanine
66.2 1.5
71.1 1.4 [1]
80.4 1.0 [2]
88.9 1.9 [10]
81.6 1.8 [11]
95.8 1.5 [12]
66.9 1.1 [7]
64.3 1.3 [8]
69.8 1.5 [6]
75.4 1.2 [3]
75.1 2.0 [6]
68.6 1.6 [2]
77.2 1.3 [2]
β-Alanyl-glycine
β-Alanyl-β-alanine
DL-Alanyl-glycine
DL-Alanyl-DL-serine
DL-Alanyl-DL-asparagine
DL-Alanyl-DL-leucine
DL-Alanyl-DL-alanine
DL-Leucyl-glycine
L-Leucyl-L-leucine
°
is the change in the entropy of the overall dissociation reactions of carboxylic and betinic groups of the dipeptide; ΣΔ S° =
Δ
Δ
disSΣ
dis
°
°
°
°
are the changes in the entropy of the stepwise reactions of the dissociation of the carboxylic
dis
+ Δ
(
and Δ
Sbet
disScarb
Sbet
Δ
disScarb
dis
and betainic groups of the corresponding amino acids).
dipeptides apparently form a medium with low dielec- effect is related to the bonding of a substantial number
of water molecules by corresponding zwitterions. At
the same time, a change in the reaction’s entropy gen-
erally conforms to an increase in the lateral substituent
hydrophobicity (Figs. 1 and 2).
Introducing additional methylene units into the
glycine fragments upon moving from glycyl-glycine to
glycyl-β-alanine, β-alanyl-glycine and then to
β-alanyl-β-alanine (Table 3) lowers the acidity of cor-
tric permeability [6], reinforcing the interactions
between ammonium cations and carboxylic anions.
The stronger interactions between oppositely charged
ions could also be the reason for the changes in the dis-
tribution of the solvated molecules of the solvents
around the dipeptide molecules, which subsequently
lowers the ΔdisS° of carboxylic group dissociation (and
raises the ΔdisS° of betainic group dissociation). This
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2174
GRIDCHIN
−ΔS°
74
(a)
leu-leu
gly-leu
val-val
70
66
62
58
54
H2L+ = H+ + HL
val-leu
ala-val
gly-val
ala-leu
ala-ala
leu-gly
ala-xxx (r = 0.938)
gly-xxx (r = 0.943)
gly-gly
ala-gly
gly-asn
ala-asn
gly-thr
gly-ser
ala-ser
−1
0
1
2
πcarb
−ΔS°
(b)
ala-asn
gly-asn
14
gly-xxx (r = −0.459)
gly-val
gly-thr
gly-ser
ala-ser
gly-gly
gly-leu
ala-ala
10
6
ala-xxx (r = −0.824)
ala-gly
leu-gly
ala-leu
ala-val
val-leu
HL = H+ + L−
leu-leu
val-val
2
−1
0
1
2
πcarb
Fig. 1. Effect of C-terminus amino acid residue lateral substituent hydrophobicity on the Δ S° value for the dissociation of
dis
dipeptide functional groups (π
are the Hansch indices).
carb
responding carboxylic or betainic group due to the dipeptides, due to the increasing distance between
growing inductive effect of the hydrocarbon chain and positive and negative charge carriers. The changes in
additionally helps raise the degree of hydratation of the degree of hydration of zwitterions caused by the
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THERMODYNAMIC CHARACTERISTICS OF PROTOLYTIC EQUILIBRIA
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−ΔS°
(a)
72
68
64
60
56
52
leu-leu
val-val
val-leu
xxx-leu (r = 0.647)
gly-leu
gly-val
ala-leu
ala-val
ala-ala
xxx-val (r = 0.924)
leu-gly
H2L+ = H+ + HL
gly-gly
ala-gly
xxx-gly (r = 0.956)
gly-asn
gly-ser
ala-asn
gly-thr
ala-ser
−0.5
0
0.5
1.0
1.5
2.0
πbet
−ΔS°
(b)
ala-asn
gly-asn
14
gly-val
gly-ser
gly-thr
gly-leu
gly-gly
HL = H+ + L−
ala-ser
ala-ala
10
6
xxx-gly (r = −0.950)
ala-gly
ala-leu
leu-gly
ala-val
val-leu
leu-leu
xxx-val (r = −0.970)
xxx-leu (r = −0.986)
val-val
2
−0.5
0
0.5
1.0
1.5
2.0
πbet
Fig. 2. Effect of N-terminus amino acid residue lateral substituent hydrophobicity on the Δ S° value for the dissociation of
dis
dipeptide functional groups (π are the Hansch indices).
bet
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2176
GRIDCHIN
11. S. N. Gridchin and D. F. Pyreu, Russ. J. Gen. Chem.
varying distance between ammonium cations and car-
boxylic anions apparently explains the substantial dif-
ferences between the ΔdisS° values for the dissociation
reactions of identical functional groups of the dipep-
tides and amino acids, while the similar values of
77, 1037 (2007).
12. V. P. Vasil’ev, L. A. Kochergina, and O. N. Krutova,
Izv. Vyssh. Uchebn. Zaved., Khim. Khim. Tekhnol. 46
(6), 69 (2003).
13. W. B. Parcker, Thermal Properties of Aqueous Uni-Uni-
valent Electrolytes (NSRDS-NBS, Washington, DC,
1965), Vol. 2, p. 342.
°
for the overall reactions of dipeptide dissocia-
ΔdisS
∑
tion and the ΣΔdisS° sum of the stepwise dissociation
reactions of carboxylic and betainic groups of the cor-
responding aminoacids remain similar (Table 4).
14. V. A. Borodin, E. V. Kozlovskii, and V. P. Vasil’ev,
Zh. Neorg. Khim. 31, 10 (1986).
15. D. Himmelblau, Applied Nonlinear Programming
(McGraw-Hill, New York, 1971).
ACKNOWLEDGMENTS
16. A. A. Bugaevskii and B. A. Dunai, Zh. Anal. Khim. 26,
This work was performed at the Research Institute
of Thermodynamics and Kinetics of Chemical Pro-
cesses, Ivanovo State University of Chemical Tech-
nology. It was supported by the Russian Foundation
for Basic Research, project no. 14-03-00360-a.
205 (1971).
17. N. V. Petrov, A. P. Borisova, I. A. Savich, and
V. I. Spitsyn, Dokl. Akad. Nauk SSSR 192, 574 (1970).
18. V. P. Vasil’ev, Thermodynamic Properties of Electrolyte
Solutions (Vysshaya Shkola, Moscow, 1982) [in Rus-
sian].
19. S. D. Varfolomeev, Chemical Enzymology (Akademiya,
REFERENCES
1. V. P. Vasil’ev, L. A. Kochergina, G. G. Gorboletova,
and O. N. Popova, Russ. J. Phys. Chem. A 73, 586
(1999).
Moscow, 2005) [in Russian].
20. V. P. Vasil’ev, L. A. Kochergina, V. Yu. Garavin, and
A. V. Grudochkin, in Theoretical Methods of Solution
Properties Description (Ivanov. Khim.-Tekhnol. Inst.,
Ivanovo, 1987), p. 87 [in Russian].
21. V. P. Vasil’ev, L. A. Kochergina, S. G. Iven’kova, and
S. Yu. Anferova, in Solvation Processes in Solutions (Iva-
nov. Khim.-Tekhnol. Inst., Ivanovo, 1985), p. 55 [in
Russian].
2. S. N. Gridchin, Russ. J. Gen. Chem. 85, 810 (2015).
3. S. N. Gridchin and G. G. Gorboletova, Russ. J. Gen.
Chem. 78, 429 (2008).
4. S. N. Gridchin, Russ. J. Gen. Chem. 83, 1315 (2013).
5. V. P. Vasil’ev, L. A. Kochergina, and O. N. Krutova,
Russ. J. Phys. Chem. A 77, 1929 (2003).
22. V. P. Vasil’ev, L. A. Kochergina, S. G. Grosheva, and
O. N. Korneva, Izv. Vyssh. Uchebn. Zaved., Khim.
Khim. Tekhnol. 34 (3), 48 (1991).
6. G. G. Gorboletova and L. A. Kochergina, J. Term.
Anal. Calorim. 87, 561 (2007).
23. S. N. Gridchin, Izv. Vyssh. Uchebn. Zaved., Khim.
7. S. N. Gridchin, G. G. Gorboletova, and D. F. Pyreu,
Khim. Tekhnol. 53 (12), 136 (2010).
Russ. J. Phys. Chem. A 81, 1941 (2007).
24. L. A. Kochergina, A. I. Lytkin, O. N. Krutova, and
8. S. N. Gridchin and D. F. Pyreu, Russ. J. Phys. Chem.
K. V. Damrina, Russ. J. Inorg. Chem. 60, 647 (2015).
A 89, 1 (2015).
25. V. P. Vasil’ev, L. A. Kochergina, and V. Yu. Garavin,
9. G. G. Gorboletova, S. N. Gridchin, and E. S. Sazon-
Zh. Obshch. Khim. 62, 213 (1992).
ova, Russ. J. Phys. Chem. A 79, 1222 (2005).
10. S. N. Gridchin, G. G. Gorboletova, and D. F. Pyreu,
Translated by P. Vlasov
J. Term. Anal. Calorim. 90, 607 (2007).
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Vol. 90
No. 11
2016