Effect of unlimited self-association of a component of a chemical reaction on the equilibrium states of the copper dialkyldithiophosphate systems

Article abstract of DOI:10.1016/j.molliq.2019.112128

In this paper, the redox and self-association processes of Cu(II) and Cu(I) dithiophosphates in the organic solutions were investigated by electronic absorption spectroscopy. It was shown that, over a wide concentration range of all components, the system under consideration is well described by the reduction of Cu(II) dithiophosphate with the formation of Cu(I) dithiophosphate and disulfide, followed by the unlimited self-association of the Cu(I) dithiophosphate. The results of this study also showed that the theory of ideal associated solutions can be efficiently applied for the description of this system. Considering that the self-association process is unlimited, we revealed the fundamentally new properties of highly associated compounds that simplify the description of such systems. The data obtained in this study can be useful for analyzing flotation and extraction processes with participation of Cu(II) and thiosubstituted organophosphorus acids, in particular, the commercial reagent CYANEX 301. The constants of the redox and self-association reactions were found to be as follows: К_redox = (7.5 ± 0.2) × 10^?4, β = 348.3 ± 0.7.

Full text of DOI:10.1016/j.molliq.2019.112128

MOLLIQ-112128; No of Pages 7
Journal of Molecular Liquids xxx (xxxx) xxx
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Effect of unlimited self-association of a component of a chemical reaction
on the equilibrium states of the copper dialkyldithiophosphate systems
a
b,
V.I. Kuzmin , O.A. Logutenko ⁎
a
Institute of Chemistry and Chemical Technology SB RAS, Federal Research Center “Krasnoyarsk Science Center SB RAS”, Academgorodok, 50/24, 660036 Krasnoyarsk, Russia
Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch of the Russian Academy of Sciences, Kutateladze, 18, 630128 Novosibirsk, Russia
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 4 June 2019
Received in revised form 30 October 2019
Accepted 11 November 2019
Available online xxxx
In this paper, the redox and self-association processes of Cu(II) and Cu(I) dithiophosphates in the organic solu-
tions were investigated by electronic absorption spectroscopy. It was shown that, over a wide concentration
range of all components, the system under consideration is well described by the reduction of Cu(II)
dithiophosphate with the formation of Cu(I) dithiophosphate and disulfide, followed by the unlimited self-
association of the Cu(I) dithiophosphate. The results of this study also showed that the theory of ideal associated
solutions can be efficiently applied for the description of this system. Considering that the self-association process
is unlimited, we revealed the fundamentally new properties of highly associated compounds that simplify the de-
scription of such systems. The data obtained in this study can be useful for analyzing flotation and extraction pro-
cesses with participation of Cu(II) and thiosubstituted organophosphorus acids, in particular, the commercial
Keywords:
Copper dithiophosphates
Disulfide
Redox reaction
Unlimited self-association
reagent CYANEX 301. The constants of the redox and self-association reactions were found to be as follows: Кredox
=
(7.5 ± 0.2) × 10− , β = 348.3 ± 0.7.
4
©
2018 Elsevier B.V. All rights reserved.
1
. Introduction
The organo-thiophosphorus reagents have attracted great interest
2
copper(I) while the extractant itself is oxidized to the disulfide (R )
(
Eqs. (1), (2)):
Cu2 ðaqÞ þ 2HRðoÞ ⇄ CuR2ðoÞ þ 2H ðaqÞ
þ
þ
ð1Þ
ð2Þ
for the recovery of nonferrous metals because of their high selectivity
and several reviews on their extraction properties are available in the
literature [1–4]. Van Zyl and Woollins [5] have recently reviewed the co-
ordination chemistry of the dithiophosphato, dithiophosphonato, and
dithiophosphinato ligands and their metal complexes in detail. Alkyl
substituted derivatives of dithiophosphoric acid are commonly used as
collectors in the flotation of copper sulfide ores and as reagents for sep-
aration and determination of metal ions by various methods [6]. The
commercially available dithiophosphinic acid CYANEX 301 is a very se-
lective extractant for copper and Sole and Hiskey [7] have studied the
solvent extraction of copper by this reagent in detail. However, pro-
cesses using these extractants are complicated by the redox reactions
that take place in the organic phase, thus leading to changes in the ki-
netic and thermodynamic parameters of the extraction and the irrevers-
ible decomposition of the extractant.
Kredox
2
CuR2ðoÞ ⇄ 2CuRðoÞ þ R2ðoÞ
where (aq) and (o) denote species in the aqueous and organic phases,
respectively.
A redox reaction proceeding during copper extraction with dithioic
acids and the transformation of the complex CuR
fide, followed by the formation of multinuclear oligomeric complexes
Eq. (3)), in which the ligands bridge between metal centers, have
2
into CuR and disul-
(
been reported by several authors [7–14] and are, apparently, a common
occurrence.
nCuR⇄ðCuRÞn
ð3Þ
Copper extraction with both the dialkyldithiophosphoric and
dithiophosphinic acids (HR) has been shown to be accompanied by a
redox reaction in the organic phase, wherein copper(II) is reduced to
However, while all these facts are well known, both the chemistry of
the interaction between copper(II) and dithioic acids and the equilib-
rium states involving different species formed in the solution for this
system are still not well understood.
In this work, we studied a specific feature of the interaction between
the dialkyldithiophosphate type reagents with copper cations in a two-
phase extraction system. In order to avoid the formation of precipitates
in the organic phase, octyl (2-ethylhexanol) derivatives of the reagent
⁎
Corresponding author.
E-mail address: ologutenko@solid.nsc.ru (O.A. Logutenko).
https://doi.org/10.1016/j.molliq.2019.112128
167-7322/© 2018 Elsevier B.V. All rights reserved.
0
Please cite this article as: V.I. Kuzmin and O.A. Logutenko, Effect of unlimited self-association of a component of a chemical reaction on the
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2
V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
were used in the work. A system of this type is highly interesting for a
better understanding of the chemistry of the processes occurring during
the flotation of sulfide minerals in the presence of
dialkyldithiophosphates and copper(II) ions commonly used as activa-
tors. In addition, the data obtained in this study can be useful when
studying and describing the processes of copper extraction with
dithiosubstituted phosphines of other classes, in particular, the com-
mercial reagent CYANEX 301 used in practice.
2.2. Procedure
The reaction between di(2-ethylhexyl)dithiophosphoric acid and
copper(II) was carried out in a two-phase system by contacting an
aqueous solution of copper(II) sulfate with a solution of DTPA in tolu-
ene. The process proceeds almost quantitatively in an excess of copper
in the aqueous solution and at low acidity (up to 1 mol·L ). If it was
necessary to prepare the copper(II) dithiophosphate as quickly as possi-
ble, the aqueous solution with an excess of copper sulfate was contacted
with a solution of the potassium dithiophosphate in toluene.
−1
2
. Experimental
The processes of copper oxidation and reduction in the organic
phase were studied using electronic absorption spectroscopy (EAS) at
a temperature of (25 ± 1) °С. The validity of applying this method for
the study of redox processes was supported by the identity of the elec-
tronic spectra of the copper(II) di(2-ethylhexyl)dithiophosphate solu-
tions of different compositions within a wide concentration range and
their compliance with Bouguer's law. To reach complete equilibrium
in the system, the solutions were kept for 7 days.
2
.1. Reagents
All reagents used in this work were of chemical or analytical grade.
Di(2-ethylhexyl)dithiophosphoric acid (HA, DTPA) was synthesized at
the Institute of Organic Chemistry SB RAS by the interaction of phospho-
rus pentasulfide with 2-ethylhexanol. The product obtained was puri-
fied from impurities by the oxidation of its sodium salt with iodine
resulting in the formation of the disulfide (A
2
) (Eq. (4)) which was
The electronic spectra of the organic phases were recorded with an
AvaSpec-2048L spectrophotometer. The concentration of di(2-
ethylhexyl)dithiophosphoric acid in the organic phase was determined
by potentiometric titration with sodium hydroxide in a water–acetone
solution (1:4), while the concentration of copper(II) dithiophosphate
was determined using a KFK-2 photocolorimeter.
then washed with ethanol and reduced back with hydrazine (Eq. (5))
to produce the hydrazine salt of dithiophosphoric acid which was sub-
sequently converted to the acidic form (Eq. (6)). Chemical structures
of DTPA and A
2
are illustrated in Fig. 1.
KA þ I2→2KI þ A2
A2 þ 5N2H4→4N2H4 ꢀ HA þ N2 þ 5H2O
2
2
ð4Þ
ð5Þ
ð6Þ
3. Results and discussion
The redox processes taking place in the extracts of copper(II)
dithiophosphate were studied using electronic absorption spectroscopy
since the initial copper(II) complex exhibits strong absorption in the
visible and ultraviolet regions, whereas the reduction reaction products
N2H4 ꢀ HA þ HCl→HA þ N2H4 ꢀ HCl
The purification method is based on the preferential oxidation of the
dithiophosphate ion with iodine compared to the monothiophosphate
ion and the poor solubility of the liquid disulfide in ethanol. This allows
removal of the impurities of the alkyl phosphates and potassium
monothiophosphate by washing with ethyl alcohol. According to the re-
sults of elemental analysis, potentiometric and iodimetric titration, this
procedure produced a refined product containing 95–97% of DTPA. The
acid is quite easily hydrolyzed and oxidized, so, prior to storage, it was
2
(CuA and A ) do not absorb in this spectral region. Furthermore, the
slow rate of the redox reactions allows the use of this method. Thus,
in the range of low copper concentrations (0.001–0.005 mol·L− ),
many hours are required for the system to reach equilibrium. It has
been shown that, after fast saturation (for 1–2 min) of a toluene solution
of DTPA or its potassium salt with copper(II), the optical density of the
extract gradually reduces over time to a constant value. On the other
hand, on mixing a stoichiometric amount of colorless copper(I) di(2-
ethylhexyl)dithiophosphate with a disulfide, re-formation of copper
(II) di(2-ethylhexyl)dithiophosphate, accompanying by an increase in
the optical density of the organic solution, is observed. Eventually,
when equilibrium of the forward and backward reactions is achieved,
the spectra of the solutions coincide (Fig. 2), which confirms that the re-
action proceeds in accordance with Eq. (2). This suggests that, for
Eq. (2), in the absence of additional interactions in the organic phase,
the maximum of the copper(II) concentration on an isomolar curve
1
+
+
converted to the K or Na form.
The disulfide of di(2-ethylhexyl)dithiophosphoric acid [(RO)
S(S)P(RO) ] was prepared according to the published procedure [15] by
oxidizing potassium dithiophosphate in ethanol with an iodine solution
Eq. 4). After washing with ethanol, the disulfide was extracted with
2
P(S)S-
2
(
hexane, dried over sodium sulfate, following which the hexane was
evaporated. The resulting disulfide was identified by an IR spectroscopy
method.
Copper(I) dithiophosphate was prepared by contacting a potassium
dithiophosphate solution in benzene with an aqueous solution of cop-
per(I) sulfite complexes obtained by mixing aqueous solutions of cop-
per sulfate and sodium sulfite. The organic phase was contacted with
fresh portions of the copper(I) sulfite solutions several times until an al-
most colorless extract was obtained. After removing benzene by distilla-
tion, the isolated product contained 90% of copper(I) dithiophosphate
according to elemental analysis.
2
should correspond to a CuА to A ratio of 2:1. In practice this ratio
was found to be approximately equal to 2:3 which could be
explained by the formation of tetrameric self-associates of copper
(I) dithiophosphate (Eq. (7)) as reported in earlier studies [14].
4
CuA2⇄ðCuAÞ þ 2А2
ð7Þ
4
8 17
Fig. 1. Chemical structures of the disulfide of DTPA (a) and DTPA (b). R = C H .
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V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
3
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
120
Time, h
Fig. 2. Absorbance of the organic solutions vs. time: 1 – reduction of copper(II) di(2-
−
1
ethylhexyl)dithiophosphate, [CuA
2
]
initial = 0.001 mol·L ; 2 – oxidation of copper(I) di
+
−1
(
2-ethylhexyl)dithiophosphate with disulfide, [Cu
]
t initial = 0.001 mol·L , [A
]
2 initial
=
1
0
.0005 mol·L−
.
Fig. 4. Variation of the concentration of copper(II) in the organic phase with time after
copper(II) extraction with 0.01 mol·L− DTPA in the presence of 0.1 mol·L disulfide
1
−1
(1) and copper(I) dithiophosphate (2).
The fact that the copper(I) dithio-ligand compounds are often tetra-
nuclear is well-known [7–14]. However, a deeper study of this system
revealed another unique property. Thus, it was shown that, starting
from a certain level of CuA concentration (above 0.05–0.1 М), the equi-
librium position of the redox reaction (Eq. (2)) becomes independent of
the total analytical concentration of copper(I) in the solution, just as if a
new solid phase of copper(I) dithiophosphate was formed in the sys-
tem. Fig. 3 shows the change in the extent of the copper(II)
dithiophosphate formation upon the concentration of one of the reac-
tion components, either disulfide or copper(I) dithiophosphate, while
the initial concentration of another component in the solution is fixed.
As seen, an increase in the concentration of disulfide in the solution
rapid extraction of copper(II) from an aqueous solution with DTPA in
the presence of an excess of disulfide or copper(I) dithiophosphate in
the initial organic solution (Eq. (1)). The concentration of 0.1 mol·L−
of the added reagents was sufficient to achieve the limiting values of
copper(II) dithiophosphate concentrations in the equilibrium state of
the system. As seen from Fig. 4, in full accordance with the above data,
in the excess of disulfide (curve 1), after the formation of copper(II)
dithiophosphate, no copper(II) reduction in the extract occurs over
time. In another case (curve 2), the introduction of an excess of cop-
per(I) dithiophosphate in the organic phase does not prevent the reduc-
tion of copper(II) due to which its concentration in the extract
significantly decreases over time reaching the residual content which
is equal to that in the previous experiment.
1
−1
above 0.05 mol·L (curves 1a and 1b) leads to a 100% shift in the equi-
librium position of the oxidation reaction of copper(I) dithiophosphate.
In the second case (curves 2a and 2b), when adding copper
(
I) dithiophosphate to an organic solution at a fixed initial disulfide con-
Thus, the data obtained convincingly shows that the equilibrium po-
sition of the redox reaction (Eq. (2)), starting from a certain level of CuA
concentration (above 0.05–0.1 M), becomes almost independent of the
analytical concentration of copper(I) in solution. At the same time, the
influence of the second component of the reaction, the disulfide, is con-
sistent with this redox reaction over a wide concentration range. In
centration, only 40–50% of this reaction component is converted to cop-
per(II) and any further increase in the CuA concentration does not
change the equilibrium state of the system.
The reliability of this conclusion was confirmed by other data given
in Fig. 4. In this case, copper(II) dithiophosphate was prepared by
Fig. 3. The degree of chemical conversion of copper(I) di(2-ethylhexyl)dithiophosphate
(
curves 1a and 1b) and disulfide (curves 2a and 2b) to copper(II) di(2-ethylhexyl)
dithiophosphate as function of disulfide and copper(I) di(2-ethylhexyl)
dithiophosphate concentration in the organic phase respectively. The initial CuA and A
a
2
2
Fig. 5. Dependence of the equilibrium СuA concentration on the concentration of the
+
concentrations are 0.002 (1a, 2a) and 0.005 (1b, 2b) mol·L−
1
.
disulfide in the solution. [Cu
]
t
= 0.1 (1, □) and 0.2 (2, ) mol·L
−1
.
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4
V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
particular, Fig. 5 shows the dependency of the СuA
2
concentration on
Accordingly, we find
the concentration of the disulfide at two fixed initial concentrations of
copper(I) dithiophosphate. It is seen from the resulting data that an in-
crease in the disulfide concentration leads to an increase in the equilib-
rium copper(II) concentration in solution, in full agreement with the
reaction described by Eq. (2). These dependences for various CuA con-
centrations coincide (within the limits of experimental error) and can
be quantitatively described by Eq. (8). This equation formally lacks
one of the reaction components, such as CuA.
Xꢀ
ꢁ
∞
ðCuAÞ ðlÞ ¼ ½CuAꢂ=ð1−β½CuAꢂÞ
ð11Þ
1
n
Then the average degree of polymerization of the linear associates
can be found from Eq. (12):
ꢀ
ꢁ
Xꢀ
ꢁ
þ
∞
1
nðlÞ ¼ Cu ðlÞ =
ðCuAÞ ðlÞ ¼ 1=ð1−β½CuAꢂÞ
ð12Þ
t
n
2
On analysis of Eq. (10) we can see that, an increase in the copper
К ꢁ ½СuА2ꢂ =½A2ꢂ
ð8Þ
+
(
I) concentration ([Cu (l)]
t
) in solution results in an increase in the
[
CuA] monomer concentration. However, the value of the [CuA] concen-
Analysis of various possible processes involving the interaction of
the components which could explain this result showed that this is
caused by unlimited self-association of one of the components of the re-
action, copper(I) dithiophosphate. The self-association of copper
+
tration is limited because, when [Cu (l)]
when implementing the above assumption, with increasing copper
I) concentration in solution, the concentration of the monomer and
t
→ ∞, then β[CuA] → 1. Thus,
(
any other polymeric linear forms will tend to 1/β. Accordingly, on sub-
stitution of the monomer concentration in the equilibrium constant ex-
pression (Eq. (13)) for the redox reaction (Eq. (2)), we obtain an
expression (14) from which it follows that the copper(II) concentration
in a high copper(I) concentration solution depends only on the disulfide
concentration and does not depend on the copper(I) concentration.
(
I) dibutyl dithiophosphate is well known. In the 1970's, when studies
were made of the crystal structures of the dialkyl dithioic acid com-
plexes with some metals, the copper(I) complexes were believed to
be mostly tetramers [16,17]. The process of self-association is due to
the presence of two active centers in the copper(I) dithiophosphate
molecule: on the one hand, coordinatively unsaturated copper
(
I) cations as the electron acceptor, and on the other hand, the sulfur
2
:
2
Kredox ¼ ½CuAꢂ ½A2ꢂ=½CuA2ꢂ
ð13Þ
ð14Þ
atom of the reagent as the electron donor (Fig. 6). It is obvious that
some other forms of associations may exist in these solutions. Without
dwelling on the possible structures of the associates, it should be
noted that the intermolecular interactions can lead to the formation of
various linear and cyclic polymers. For a quantitative estimation of the
formation of linear polymers, we used the theory of ideal associated so-
lutions [18]. In this case, the formation process of the associates is de-
scribed by the following Eq. (9):
2
:
2
Kredox ≈ 1=β ½A2ꢂ=½CuA2ꢂ
Here we assume that there are no other interactions in the system,
except for those considered above, i.e. no self-association or solvation
of both the disulfide and CuA and, therefore, their total and monomeric
2
concentrations are almost equal ([A
Eq. (14) can be rewritten as follows:
2 t 2 2 t 2
] ≈ [A ] and [CuA ] ≈ [CuA ]).
9
β2
>
>
CuA þ CuA ⇄ ðCuAÞ
>
2
2
>
2
>
=
½A ꢂ ≈ β K
ꢀ ½CuA2ꢂ
ð15Þ
β3
2
redox
ðCuAÞ þ CuA ⇄ ðCuAÞ
ð9Þ
2
3
>
⋯
⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯
>
2
>
2 2
In accordance with Eq. (15), the dependence of [A ] on [CuA ] is lin-
ear over a wide concentration range of the components of the system.
The slope of the straight line is equal to β Kredox. The β Kredox value
was found to be:
βn
ðCuAÞn−1 þ CuA ⇄ ðCuAÞn;
>
;
2
2
where β
n
is the equilibrium constant for the formation of a self-
2
associate consisting of n molecules of CuA.
β K
redox
= 91.3 ± 8.
It is accepted, as a first approximation, that the energy of the addi-
tion of each successive СuА molecule to a polymeric molecule does
not depend on the length of the polymer chain. In this case, the associ-
The redox reaction can be used to study the coupled processes of
self-association of copper (I) dithiophosphate and, in this regard, this
system is unique. The monomer concentration in Eq. 10, describing
the process of unlimited self-association with the formation of linear
polymers, is the most important indicator for the analysis of self-
association processes. The monomer concentration, more precisely the
[CuA]/√Кredox value, was calculated from spectrophotometric data
using an expression for the equilibrium constant of the redox reaction
(Eqs. (13), (16)):
ation constants for the formation of linear polymers are equal: β ≈ β
≈ … ≈ β ≈ … Thus for the total analytical concentration of copper
I) in the linear polymers in solution we find:
2
≈
β
3
n
(
+
[
Cu (l)]
t
= [CuA] + 2[(CuA)
[CuA] + 2β[CuA] + …. + nβ [CuA] = ....,
2
] + 3[(CuA)
3
n
] + …. + n[(CuA) ] + …
2
n-1
n
=
For this sequence with unlimited n we have
ꢀ
ꢁ
þ
2
2
Cu ðlÞ ¼ ½CuAꢂ=ð1−β½CuAꢂÞ
ð10Þ
½CuAꢂ=√ Кredox ¼ √ ½CuA ꢂ =½А ꢂ ¼ ½СuA ꢂꢂ=√ ½A ꢂ
ð16Þ
t
2
2
2
2
The total concentration of the linear polymers can be expressed as
The dependence of this value on the CuA concentration in
∞
1
∑[(CuA)
n
2 3 n
(l)] = [CuA] + [(CuA) ] + [(CuA) ] + …. + [(CuA) ] +
dilogarithmic coordinates is shown in Fig. 7. As can be seen from these
+
…
data, at high copper(I) concentration (N0.1 М), the [Cu ]
t
value is prac-
tically constant and the slope of the line is close to zero thus testifying to
the formation of very high molecular weight associates. For this concen-
tration range, the [CuA] value approaches 1/β and, accordingly, [CuA]/
2
√К
redox → 1/β√Kredox = 1/√β Kredox. At low Cu(I) concentrations, over
a wide range of values, the slope of the dependence varies from 0.24
to 0.3, which might lead to the wrong conclusion about the formation
of stable tri- and tetramers in solution. However, an analysis of the de-
+
t
2
pendence of [Cu ] on β[CuA]/(1-β[CuA]) showed a fairly good agree-
ment with Eq. (10) which describes the formation of linear polymers.
The β[CuA] value was found from spectrophotometric data using
Fig. 6. Electron donor and electron acceptor centers in the copper(I) dithiophosphate
molecule.
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V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
5
From the relation (19), the value of the self-association constant β
was determined:
β ¼ 348:3 ꢃ 0:7
ð20Þ
Thus, the self-association of CuA, to a first approximation, can be de-
scribed by the formation of only linear polymers, therefore, the total an-
alytical concentration of copper (I) in solution is:
ꢀ
þꢁ
2
Cu
¼ ½CuAꢂ=ð1–348:3 ꢄ ½CuAꢂÞ
ð21Þ
t
Taking into account the β2Kredox and β values, the constant for the
redox reaction (Kredox) has been estimated to be:
ꢂ
ꢃ
β2K
ꢀ β ¼ 91:3 ꢄ ð348:3Þ
−2
−2
Kredox
¼
¼
redox
−
4
ð7:5 ꢃ 0:2Þ ꢄ 10
ð22Þ
Eqs. (13) and (21) describe reasonably well the interactions in the
organic phase for the extraction of copper(II) with DTPA. In Fig. 9, the
calculated curves of an isomolar series of the copper(I) di(2-
ethylhexyl)dithiophosphate and disulfide interaction, and the corre-
sponding experimental points are shown. As seen, the data obtained al-
most coincide, thus showing that the “abnormal” position of the
maximum of the curve is caused by the unlimited self-association of
Fig. 7. Dependence of the copper(I) di(2-ethylhexyl)dithiophosphate monomer
concentration on the total analytical copper(I) concentration in the solution.
Eq. (17):
the product of the reaction
dithiophosphate.
–
copper(I) di(2-ethylhexyl)
2
β½CuAꢂ ¼ √ β Kredox∙½CuA2ꢂ=√ ½А2ꢂ
ð17Þ
The data to allow assessment of the fraction of copper(II) in the or-
ganic phase (αCuA2) on the total copper concentration are given in
Fig. 10 and Table 1. The figure also shows the calculated dependence
of the fraction of copper (II) in the solution. In this case, as previously,
the experimental and calculated values coincide. This dependence also
has an “abnormal” character. Indeed, when taking into account only
The total analytical concentrations of Cu(I) used in this analysis were
−
1
b0.05 mol·L , since when it is higher, β[CuA] becomes close to 1 and,
2
accordingly, the error in determining the (1-β[CuA]) value sharply in-
creases. The data obtained are shown in Fig. 8. From the value of the
slope of the obtained dependence, we can find the β value. For that,
Eq. 10 has to be transformed as follows:
2
the redox reaction (Eq. (2)), an increase in the CuA concentration
should result in an increase in the fraction of copper(II) in the organic
phase due to the shift of equilibrium of the redox reaction (Eq. (2)) to
the left, i.e. to the side that produces the fewer number of species. In
fact, the opposite phenomenon is observed and the fraction of copper
ꢀ
ꢁ
þ
2
2
Cu ðlÞ ¼ ½CuAꢂ=ð1−β½CuAꢂÞ ¼ ð1=βÞ∙ðβ∙½CuAꢂÞ=ð1−β½CuAꢂÞ
ð18Þ
t
(
II) in the organic phase decreases rapidly with increasing total copper
while Eq. (18) has to be rewritten as Eq. (19):
concentration which is due to significant self-association of the reaction
product – copper (I) dithiophosphate. According to our estimation, the
average degree of self-association of CuA, at a copper (I) concentration
ꢀ
ꢁ
2
þ
F ¼ ðβ∙½CuAꢂÞ=ð1−β½CuAꢂÞ ¼ ðβÞ∙ Cu ðlÞ
ð19Þ
t
−1
of about 0.004 mol·L , is already N16 (Table 1).
Thus, a model, taking into account both the redox process and un-
limited self-association of the product of the redox reaction copper
(
I) dithiophosphate using only two equilibrium constants, Kredox and
β, well describes the behavior of the complex system under
Fig. 9. Determination of the ratio between the reacting components by the isomolar series
2
Fig. 8. Dependence of the β∙[CuA]/(1-β∙[CuA]) (F) value on the total analytical
concentration of copper (I) in the solution.
method for the CuA – A
2
system. Points are experimental data and lines were calculated
using the model. [Cu+
]
t
−1
.
2
+ [A ] = 0.01 (1), 0.02 (2) and 0.05 (3) mol·L
Please cite this article as: V.I. Kuzmin and O.A. Logutenko, Effect of unlimited self-association of a component of a chemical reaction on the
equilibrium states..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.112128

6
V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
at small copper (I) concentrations. However, it is not as large as it
could be in the case of di(2-ethylhexyl)phosphoric acid or carboxylic
acids, which also form self-associates due to intermolecular hydrogen
bonds. For these organic acids, the cyclic dimer structures predominate
(
Fig. 11).
In the system under study, two main types of self-associates can be
formed (Fig. 12) with the coordination numbers of copper equal to 2
I) and 4 (II). Self-associates of the first type (Fig. 12, I) have many op-
(
tions for spatial arrangements resulting in the formation of various dif-
ferent complexes. They have relatively mobile terminal atoms of Cu and
S, similar to that of O and H in di(2-ethylxyl)phosphoric acid, which can
form coordinate bonds to produce cyclic unreactive structures. The sec-
ond type of self-associates (Fig. 12, II) has a rigid linear structure which
makes the formation of cyclic compounds impossible. Most likely, the
low fraction of cyclic associates is due to the predominant formation
of self-associates of the second type.
Fig. 10. Influence of the total copper concentration in the organic phase on the amount of
copper (II) in solution on extraction by DTPA in toluene. Points are experimental data and
lines were calculated using the model.
4. Conclusions
This study has shown that the processes of chemical transformations
of copper(II) dithiophosphates in organic solutions, over a wide concen-
tration range of all components, are well described by the redox reac-
tion resulting in the formation of copper(I) dithiophosphate and
disulfide followed by the self-association of the copper
(I) dithiophosphate. Despite the low value of the equilibrium constant
for the redox reaction of copper(II) dithiophosphate (Kredox = (7.5 ±
consideration over a wide range of the component concentrations.
However, a fairly good description of the system by the proposed
model seems unusual since it does not take into account the formation
of stable cyclic structure associates which could take place in solution in
the range of low copper (I) concentrations described by the following
Eq. (23):
−
4
0
.2) × 10 ), at a total copper concentration in the solution of
9
>
;
−1
ðCuAÞ ðlÞ⇄ðCuAÞ ðcÞ >
0.01 mol·L , the fraction of copper(I) dithiophosphate is about 70%
and it further increases as the copper concentration increases. This
shift in the position of equilibrium of the redox reaction to the right, to-
wards copper(I), is caused by the formation of stable CuA self-associates
occurring due to the formation of the intermolecular bonds S → Cu (the
value of the self-association constant is about 348). Obviously, the
strong electron-accepting properties of the copper(I) dithiophosphate
molecules should be taken into account when analyzing the adsorption
mechanism of the dithiophosphate collector on the surface of the sulfide
minerals in the presence of a copper salt added to the aqueous solution
for activation of the flotation process.
2
2
>
=
ðCuAÞ ðlÞ⇄ðCuAÞ ðcÞ
3
3
ð23Þ
ðCuAÞ ðlÞ⇄ðCuAÞ ðcÞ >
4
4
⋯
⋯⋯⋯⋯⋯
The fraction of copper (I) in the cyclic polymers is determined by
Eq. (24) and depends on the equilibrium constants of the cyclization re-
actions (Eq. (23)):
ꢀ
ꢀ
ꢀ
ꢁ
9
2
ðCuAÞ ðcÞ ¼ 2К2ðcÞβ½CuAꢂ
>
2
>
>=
ꢁ
2
3
ðCuAÞ ðcÞ ¼ 3К3ðcÞβ ½CuAꢂ
3
ꢁ
ð24Þ
3
4 >
ðCuAÞ ðcÞ ¼ 4К4ðcÞβ ½CuAꢂ >
The self-association reaction of copper(I) dithiophosphate is directly
related to the redox reaction which makes it possible to follow the pro-
cess quite accurately using a spectrophotometric method, which is often
a problem when studying intermolecular interactions in other cases.
Given the peculiarities of the self-association process of copper
(I) dithiophosphate, when the molecule has both electron-donor and
electron-acceptor atoms, this system can be considered to be an ideal
example for studying the linear self-association of molecules in solu-
tions. The results of this study have shown the efficiency of application
of the theory of ideal associated solutions for the description of this sys-
tem using the model in which unlimited self-association of copper
4
>
;
⋯
⋯⋯⋯⋯⋯
+
where the symbol (c) denotes a cyclic polymer, [(Cu )
i
(c)] is the con-
centration of copper (I) in the cyclic polymer with a chain length of i,
and К (c) is the equilibrium constant for the formation of a cyclic poly-
i
mer from the linear associate with a chain length equal to i.
Accordingly, if the formation of cyclic polymers took place in this
system it would lead to a significant deviation from linearity for the
+
2
[
t
Cu ] = f(β∙[CuA]/(1-β∙[CuA]) ) dependency (Fig. 8). In fact, such a
discrepancy between experimental and calculated data are observed
Table 1
2
]/[Сu]
t
), the total analytical concentrations of CuA
) in the solution. All concentrations are given in molarity units (mol·L ) for the system in equilibrium.
2 2 2 2 t
([CuA ]), A ([А ) and its monomeric form ([CuA]), and the average
]), CuA ([Сu+]
The change in the fraction of copper (II) (α = [CuА
degree of self-association (n) depending on the total concentration of copper ([Cu]
−1
t
[
[
[
[
[
Cu]
CuА
t
0.001
0.0004
0.0003
0.0006
0.0028
0.440
1.33
0.002
0.0008
0.0006
0.0012
0.0034
0.400
1.46
0.003
0.0011
0.0009
0.0019
0.0036
0.357
1.49
0.004
0.0014
0.0013
0.0026
0.0040
0.347
1.58
0.005
0.0016
0.0015
0.0030
0.0044
0.354
1.68
0.006
0.0019
0.0018
0.0036
0.0047
0.344
1.74
0.006
0.0021
0.0021
0.0043
0.0048
0.331
1.78
0.008
0.0025
0.0028
0.0055
0.0049
0.309
1.81
0.01
0.02
0.03
0.04
2
]
0.0031
0.0034
0.0069
0.0056
0.314
2.05
0.0053
0.0073
0.0147
0.0065
0.267
2.47
0.0075
0.0113
0.0225
0.0073
0.248
3.03
0.0095
0.0153
0.0305
0.0080
0.237
3.76
А
2
]
Cu+]
CuA]
t
α
n
[
[
[
[
[
Cu]
CuА
t
0.05
0.06
0.07
0.08
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2
]
0.0113
0.0194
0.0387
0.0085
0.226
4.40
0.0126
0.0237
0.0474
0.0086
0.210
4.63
0.0140
0.0280
0.056
0.0088
0.200
5.05
0.0157
0.032
0.0643
0.0092
0.196
6.09
0.0182
0.0409
0.0818
0.0094
0.182
7.23
0.0287
0.0856
0.1710
0.0103
0.144
16.30
0.0396
0.130
0.260
0.0115
0.132
0.0451
0.177
0.355
0.0112
0.113
0.0502
0.225
0.450
0.0111
0.100
0.0533
0.273
0.547
0.0107
0.089
0.0596
0.320
0.640
0.0110
0.085
А
2
]
Cu+]
CuA]
t
α
n
≫16
≫16
≫16
≫16
≫16
Please cite this article as: V.I. Kuzmin and O.A. Logutenko, Effect of unlimited self-association of a component of a chemical reaction on the
equilibrium states..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.112128

V.I. Kuzmin, O.A. Logutenko / Journal of Molecular Liquids xxx (xxxx) xxx
7
Fig. 11. Dimer structures of DEHPA (a) and a carboxylic acid (b).
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.molliq.2019.112128.
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[
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Please cite this article as: V.I. Kuzmin and O.A. Logutenko, Effect of unlimited self-association of a component of a chemical reaction on the
equilibrium states..., Journal of Molecular Liquids, https://doi.org/10.1016/j.molliq.2019.112128