Kinetics and mechanism of chromium electrodeposition from formate and oxalate solutions of Cr(III) compounds

Article abstract of DOI:10.1016/j.electacta.2009.04.072

Kinetics of multistep reaction of Cr(III) ions discharge to metal was studied on a stationary electrode and on a rotating disk electrode from the solutions containing formic acid or oxalic acid. The electroreduction of Cr(III) complex ions in aqueous solu

Full text of DOI:10.1016/j.electacta.2009.04.072

Electrochimica Acta 54 (2009) 5666–5672
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Electrochimica Acta
journal homepage: www.elsevier.com/locate/electacta
Kinetics and mechanism of chromium electrodeposition from formate and
oxalate solutions of Cr(III) compounds
V. Protsenko, F. Danilov∗,1
Department of Physical Chemistry, Ukrainian State University of Chemical Engineering, Gagarin Av. 8, Dnepropetrovsk 49005, Ukraine
a r t i c l e i n f o
a b s t r a c t
Article history:
Kinetics of multistep reaction of Cr(III) ions discharge to metal was studied on a stationary electrode and
on a rotating disk electrode from the solutions containing formic acid or oxalic acid. The electroreduction
of Cr(III) complex ions in aqueous solutions is shown to proceed via the formation of relatively stable
intermediates—Cr(II) compounds which are partially removed into bulk solution. The effect of pH, organic
ligand concentration and disk rotation velocity on the partial current density of chromium electroplating
was demonstrated. The kinetic equations of the studied process were derived and compared with the
experimental data. Kinetic parameters for the discharge of Cr(II) ions were calculated. The mechanism
of chromium electrodeposition reaction was proposed. The electrodeposition of chromium from formate
bath is suggested to proceed with the participation of hydroxocomplexes of bivalent chromium. The
oxalate complexes of bivalent chromium directly discharge in the electrolytes containing oxalic acid. The
partial polarization curves of chromium electrodeposition exhibit a current peak which may be caused
by blocking the electrode surface with poorly soluble Cr(III) hydroxide.
Received 16 February 2009
Received in revised form 31 March 2009
Accepted 30 April 2009
Available online 13 May 2009
Keywords:
Chromium
Electrodeposition
Multistep electrode process
Intermediates
Kinetics
Mechanism
© 2009 Elsevier Ltd. All rights reserved.
where E0 is the standard equilibrium potential for the correspond-
1. Introduction
ing step.
Chromium electroplating is widely used in various branches of
modern industry, the ordinary electrolytes containing extremely
toxic chromic acid. The chromium deposition is known to be possi-
ble from solutions based on much less harmful Cr(III) compounds.
Such electrolytes can be a real alternative to those containing
chromic acid [1–18]. However, the electrochemical reactions tak-
ing place by chromium electroplating from solutions of Cr(III) salts
are complicated and their comprehensive investigation is necessary
in order to improve this process.
As far back as 1929, Demassieux, Heyrovsky and Prajzler [19]
showed that the two well expressed waves were formed by the
discharge of Cr(III) ions on a dropping mercury electrode. That
means that the electrochemical process proceeds in steps with
the formation of relatively stable intermediates-bivalent chromium
compounds:
Afterwards, the step-wise character of Cr(III)-electroreduction
was confirmed in a number of publications [20–22].
The formation of Cr(II)—ions during the metal deposition from
trivalent chromium baths was emphasized to be of great impor-
tance [2,11,13].
Some reaction schemes of chromium electrodeposition were
proposed for baths containing compounds of Cr(III) [5,8,9,11,18].
For example, the electrochemical reduction of chromium(III) to
metallic chromium in the presence of formic acids was stated to
proceed via the formation of Cr(II) ions [11]. However, it is not quite
clear from this work, what kind of Cr(II) complexes takes part in the
discharge to the metal.
The electrodeposition reaction was studied from a trivalent
chromium bath containing ammonium formate and sodium acetate
[8]. The chromium electrodeposition process was suggested to
involve two consecutive reduction steps. The first step was the
reduction of a trivalent-Cr complex ion [Cr(H2O)5L]2+ to a bivalent-
Cr complex ion [Cr(H2O)5L]+ (L represents the complexing (formate
or acetate) ligand). Then the reduction of the bivalent-Cr complex
ions to metallic Cr proceeds. The rate of chromium deposition pro-
cess was controlled by the transport of the trivalent-Cr complex
ions to the cathode surface.
−
−
+e
+2e
Cr(III)
−→
Cr(II)
−→
Cr(0)
(I)
E0 = −0.41 V
E0 = −0.91 V
I step
II step
The compositions of trivalent Cr complexes in electrolytes in the
presence of formic acid and products of the electrochemical reduc-
tion process on cathode were investigated lately [17]. It was stated
∗
Corresponding author.
E-mail address: fdanilov@optima.com.ua (F. Danilov).
ISE member.
1
0013-4686/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2009.04.072

V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
5667
that the trivalent chromium exists in the form of [Cr(H2O)6]3+ in the
solution. [Cr(H2O)6]3+ exhibits regular-octahedron structure which
is a compact structure that does not make possible for the central
Cr3+ ion to be involved in an electron transfer from the cathode. In
the presence of formic acid, formate ions promote the formation
of the reactive intermediate, [Cr(H2O)4CHOO]2+, which possesses
irregular-octahedron structure with Cr3+ ion as a vertex. Therefore,
Cr3+ complex ion can immediately contact with the cathode and
then obtain electrons easily.
A comprehensive analysis of literature data on the Cr-deposition
process from trivalent baths was carried out recently [18]. It was
emphasized that some oxide–hydroxide chromium compounds
participate in the multistep electrochemical reaction of Cr(III) elec-
troreduction.
Thus, even such a brief survey shows that there is no consensus
on the mechanism of the electrochemical process concerned. The
nature of the electroactive particles taking part in the electrodepo-
sition reaction still needs to be determined.
We chose formate and oxalate trivalent chromium baths
[5,7–9,11–13] for our study.
3. Results and discussion
3.1. Cathodic polarization curves
The standard potential of chromium is highly negative (see
above); therefore, the electrodeposition reaction in aqueous solu-
tion is always accompanied by hydrogen evolution. Hence, the
following three reactions proceed at the cathode during the elec-
troplating of chromium from aqueous solutions of its trivalent
compounds:
Cr(III) + e− → Cr(II)
Cr(II) + 2e− → Cr(0)
2H+ + 2e− → H2
It should be mentioned that the chromium deposits prepared from
electrolytes containing formic acid, oxalic acid as well as and some
other organic compounds are known to contain carbon (mainly
in the form of chromium carbides) [13,15,24–26]. The electrore-
duction of organic substances are realized at the cathode together
with the metal deposition. As a first approximation, let us assume
that the multi-electron process of chromium(III) electroreduction
takes place at the cathode independently of reduction of the organic
compounds. Such an assumption simplifies analysis of the problem
concerned.
(1)
(2)
(3)
The stability constants for oxalate complexes of Cr(II) and Cr(III)
are known to be substantially higher than those for formate com-
plexes [2]. It is of interest to compare the kinetics and mechanism of
electrochemical reactions which proceed in electrolytes containing
formate or oxalate complexes of Cr(III).
The purpose of this investigation is to obtain and analyze the
quantitative data on chromium electrodeposition from formate and
oxalate baths as well as to propose the mechanism of electroreduc-
tion of Cr(III)–Cr(0).
In view of a substantial difference between the standard poten-
tials of individual stages in the reaction scheme (I), the deposition
of chromium should begin upon reaching the limiting current of
Cr(III) electroreduction to Cr(II), which is confirmed by the partial
polarization curves shown in Fig. 1 for oxalate bath. The results
obtained for formate bath look very much alike.
2. Experimental
By plotting of the above-mentioned partial voltammetric curves,
the current density corresponding to reaction (1) i1 was calculated
as the difference:
For the chromium deposition the following stock solutions
were used: 0.2 M KCr(SO4)2, 1.0 M Na2SO4, 0.5 M H3BO3, and 0.4 M
HCOOH or 0.4 M H2C2O4 as complexing agents. The pH of these
solutions was adjusted to a required value by addition of H2SO4 or
NaOH.
i1 = i˙ − iH − i2
(4)
2
were i˙ is the total current density through the electrochemical cell,
iH is the partial current density of hydrogen evolution reaction, i2
is2the partial current density of metal electrodeposition.
As one can see, the partial polarization curve of chromium depo-
sition i2 vs. E looks like wave with a current peak.
With an increase in the concentration of formic or oxalic acid in
the electrolyte, the initial (ascending) segment of the i2 vs. E curve
shifts towards more negative potentials (Fig. 2), which points to the
decrease in the metal deposition rate.
Chromium electrodeposition was carried out in
a three-
electrode cell in a potentiostatic mode (PI-50-1.1 potentiostat).
The solutions were deaerated by blowing with electrolytic hydro-
gen.
A a
stationary copper-foil plate (S = 1 cm2) as well as
gold disk (Ø 5 mm) served as the working electrodes. In some
cases, the same gold disk pressed into Teflon was used as a
rotating electrode. Prior to each experiment, the working elec-
trode was polished with magnesium oxide and then washed
with bidistillate water. The counter electrode was made of
titanium–manganese dioxide [23] and separated by a glass porous
diaphragm. A saturated Ag/AgCl electrode was used as a refer-
ence electrode. The potentials were recalculated to a standard
hydrogen electrode scale. The ohmic potential drop was mea-
sured using the potential decay curves in a pulsed electrolysis
and automatically compensated by means of the IR-compensator
of the potentiostat. The electrochemical cell was thermostated at
25 0.1 ◦C.
The total current density through the electrochemical cell was
determined by a copper coulometer. The partial current density
of chromium deposition was calculated from the cathode’s gain
in weight for deposition time 20 min. The weight of chromium
deposits obtained on a gold disk electrode (deposition time 5 s)
was determined from the charge consumed in their electrochemi-
cal dissolving in 1.0 M NaOH. Preliminary experiments showed that
chromium dissolved in 1.0 M NaOH on the gold electrode via reac-
tion Cr(0) → Cr(VI) + 6e−, with a virtually 100% current efficiency.
The partial current density of hydrogen evolution was found from
the hydrogen volume evolved.
Fig. 1. Partial polarization curves for reactions (1)–(3) obtained on a stationary elec-
trode in the electrolyte containing 0.2 M KCr(SO4)2, 0.4 M H2C2O4, 0.5 M H3BO3, 1.0 M
Na2SO4. pH 2.5; deposition time 20 min.

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V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
Fig. 3. Partial polarization curves of chromium electrodeposition from (a) formate
bath and (b) oxalate bath on the gold electrode at different pH: (1) 2.5; (2) 3.0; (3)
3.6. Deposition time 5 s.
Fig. 2. Partial polarization curves of chromium electrodeposition from (a) formate
bath and (b) oxalate bath on the gold electrode at different concentrations of organic
acid, mol/dm3: (1) 0.2 HCOOH; (2) 0.4 HCOOH; (3) 0.2 H2C2O4; (4) 0.4 H2C2O4; (5)
0.8 H2C2O4. pH 2.5; deposition time 5 s.
In all cases, the increase in the electrode rotation rate results in
the increase in the maximum values of electrodeposition current
density i2,max
.
In the initial segment of polarization curve, the rate of electro-
chemical reaction of metal deposition increases with an increase
in pH for formate bath (Fig. 3). On the contrary, with increasing
pH for oxalate bath, the metal deposition rate slightly dimin-
ishes.
3.2. Theoretical model
Turning back to the above-mentioned question about the mul-
tistep mechanism of chromium deposition process, it should be
emphasized that the possibility of the simultaneous transfer of
three electrons by the discharge of Cr(III) ions was examined in
literature along with the stepwise mechanism of chromium(III)
ions reduction. For example, the direct transfer of three electrons
was discussed for the process of chromium electrodeposition from
acetate complexes of Cr(III) without formation of intermediates
[27].
However, similar assertions are relatively not numerous and
there is no convincing theoretical argumentation of the assumption
about the simultaneous transfer of three electrons in the reaction
of chromium deposition. It is necessary also to take into account
that the extraordinarily small probability of simultaneous transfer
of several electrons in an elementary act is generally accepted in
modern electrochemistry [28,29]. Therefore, there is good reason
to believe that multistep reaction scheme of Cr(III) electroreduction
is generally accepted among most researchers of this process.
As indicated above, the rate of chromium deposition reaction
depends on the concentration of reactants which do not partici-
pate immediately in the total reaction (2); then one can suppose
that the electrochemical process concerned is complicated and
involves some different chemical and electrochemical steps. Thus,
The value of the maximum current density (i2,max) was found
to rise with increasing HCOOH concentration. Quite the opposite,
at higher concentration of H2C2O4, the current density of the peak
decreases.
When pH being diminished, the maximum achievable
chromium deposition rate i2,max grows both for oxalate electrolyte
and for formate one.
All other factors being equal, the maximum current density of
the chromium electrodeposition in the formate bath is achieved at
much higher values than in oxalate electrolyte (the corresponding
values differ approximately by an order of magnitude).
Presumably, some difference between the values of i2 in
Figs. 1–3, respectively, results from the diversity of experimental
conditions (different nature of copper and gold substrates and dif-
ferent deposition time).
In accordance with experimental data (Fig. 4), an increase in
the electrode rotation rate decelerates the chromium electrode-
position process in the ascending section of polarization curve
for formate bath. In solutions containing H2C2O4, the rate of the
chromium electrodeposition reaction remains virtually unchanged
with increasing the disk rotation velocity (in ascending section of
i2 vs. E curve).

V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
5669
fact justifies the assumption that the reaction (6) can be always in
equilibrium.
The concentration of EAC of bivalent chromium near the elec-
trode surface (CS) is related to the concentration of Cr(II)init by the
formula:
ꢁ
CXꢀ
i
i
ꢂ
i
j
ꢀ
i,j
ꢁ
CS = KeqCS,init
·
= KeqCS,init
·
Ci,j
(7)
CXꢀ
j
j
where Keq is the equilibrium constant of reaction (6); CS,init is the
concentration of Cr(II)init
ꢁ
ꢁ
ꢁ
ꢀ
;
Ci,j
=
CXꢀ
/
i
i
CXꢀ is a co-factor that
i,j
i
j
j
j
takes into account the product of equilibrium concentrations of
reactants Xi(j)
.
We assume that the activity factors of participants of reaction
(6) are included into equilibrium constant Keq
.
For reaction (2), the following equation is valid:
ꢃ
ꢄ
˛2F
RT
i2 = 2Fk2CS exp
−
E
(8)
where k2 is the rate constant of the electrode reaction (2); ˛2 is the
apparent transfer coefficient; E is the electrode potential.
From (7) and (8), we obtain the equation:
ꢃ
ꢄ
ꢂ
˛2F
RT
ꢀ
i2 = 2Fk2ꢀ CS
Ci,j exp
−
E
(9)
i,j
where k2ꢀ = k2keq is an effective rate constant.
The rate of the diffusion flow of Cr(II) ions from the electrode
surface to the electrolyte volume can be estimated from the equa-
tion:
ꢅ
ꢆ
ꢂ
D
ꢀ
i,j
v = (CS + CS,init) = kDCS,init 1 + Keq
·
Ci,j
(10)
ı
where D is the diffusion coefficient for Cr(II) complex ions, which
we assume the same for both Cr(II)init and Cr(II)EAC; ı is the effective
Fig. 4. Partial polarization curves of chromium electrodeposition from (a) formate
bath and (b) oxalate bath on the gold rotating disk electrode. pH 2.5; deposition time
5 s.
diffusion layer thickness; kD = D/ı is a diffusion mass transfer coef-
ꢁ
ꢀ
i,j
ficient. Assume now that Keq
·
Ci,j ꢁ 1, which means CS ꢁ CS,init
.
Then Eq. (10) takes the form:
the expressions described the chromium deposition process have
to be derived.
v = kDCS,init
(11)
From (5), (9), and (11), we obtain:
As it follows from Fig. 1, the current density of incomplete reduc-
tion of Cr(III) ions to Cr(II) is greater than the current density of
metal deposition. It means that only a part of the total amount of
Cr(II) ions formed at the first stage of Cr(III) discharge is reduced
further to the metal. The excess of bivalent chromium ions are accu-
mulated in the bulk electrolyte. Hence, the electroreduction of Cr(II)
compounds is the limiting stage of electrochemical transformations
in Eq. (I).
ꢇ
ꢁ
ꢀ
2i1k2ꢀ
k2ꢀ
Ci,j exp −(˛2F/RT)E
i,j
ꢇ
i2
=
(12)
ꢁ
ꢀ
i,j
Ci,j exp −(˛2F/RT)E + kD
This equation contains no CS,init, whose experimental determina-
tion is very difficult. Eq. (12) can be put in the linear form:
ꢁ
ꢀ
k2ꢀ
Ci,j
i,j
i2
˛2F
RT
ln
= ln
−
E
(13)
In accordance with the aforesaid, the rates of individual steps of
the Cr(III) electroreduction should satisfy the relationship:
2i1 − i2
kD
In accordance with Eq. (13), the lines plotted on the coordinates
ln(i2/(2i1 − i2)) vs. E can be used in order to calculate kinetic param-
eters of reaction (2). Such a method of determination of kinetic
parameters is applicable to any form of the i1 vs. E curve.
It seems reasonable to obtain an equation for an i2 vs. E curve
which does not contain i1. For mixed kinetics of reaction (1), the
formula is valid:
i1
F
i2
=
+ v
(5)
2F
where v is the rate of the convective–diffusion removal of Cr(II) ions
into bulk solution.
We suppose that charge transfer stage (2) follows a fast chemical
reaction where electroactive complexes (EAC) are formed from ions
Cr(II)init generated in reaction (1):
i1,lim · i1,k
i1
=
(14)
ꢀ
ꢀ
i1,lim + i1,k
Cr(II)init
+
ꢀiXi ꢀ Cr(II)EAC
+
ꢀjXj
(6)
where i1,lim is the limiting diffusion current density of reaction (1),
and i1,k is the current density of the discharge stage in reaction (1).
Expressions for the values of i1,lim and i1,k can be written as
follows:
i
j
where Xi,(j) are possible participants in the EAC formation (organic
ligands, H+ and OH− ions, solvent molecules, etc.), and ꢀi,j are cor-
responding stoichiometric coefficients.
It should be stressed that the complexes of Cr(II) are labile,
so the exchange of ligands in their inner-sphere occurs with very
high rate. Indeed, the rate constant of H2O-ligand exchange for
Cr(II)-ion was estimated to be greater than ca. 109 s−1 [30]. This
FDCCr(III)
i1,lim
=
= kDFCCr(III)
(15)
(16)
ı
ꢃ
ꢄ
˛1F
RT
i1,k = Fk1CCr(III) exp
−
E

5670
V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
where CCr(III) is the Cr(III) concentration in bulk electrolyte; D is
the diffusion coefficient for Cr(III) complex ions (to simplify math-
ematical expressions, we assumed the same diffusion coefficients
for Cr(III) and Cr(II) ions); k1 is the rate constant of reaction (1); i˛1
is the transfer coefficient of reaction (1).
In the general case, some equilibrium chemical reactions can
precede the discharge of Cr(III) ions. To simplify expression (16),
we included into k1 a co-factor that allows for the product of equi-
librium concentrations of reactants.
From (12) and (14)–(16), we have
ꢁ
ꢀ
2Fk1k2ꢀ kDCCr(III)
Ci,j exp[−(˛1F/RT)E] exp[−(˛2F/RT)E]
i,j
ꢅ
ꢆ
i2
=
ꢈ
ꢉ
ꢁ
ꢀ
k2ꢀ
Ci,j exp[−(˛2F/RT)E]+kD
i,j
kD+k1 exp[−(˛1F/RT)E]
·
(17)
As follows from data presented in Fig. 1, the current density
of reaction (1) is close to the limiting diffusion value at the
potentials of chromium electrodeposition. Hence, the rate of the
reaction (1) is determined primarily by transport restrictions, i.e.,
kD ꢁ k1 exp[(−˛1F/RT)E]; then, the expression (17) can be written
Fig. 5. Partial polarization curves, plotted in coordinates of Eq. (13), for chromium
electrodeposition on stationary electrode in electrolytes containing 0.2 M
KCr(SO4)2, 0.5 M H3BO3, 1.0 M Na2SO4, and (1) 0.2 M H2C2O4 (pH 2.5) or (2) 0.4 M
H2C2O4 (pH 3.0).
a
as follows:
ꢁ
ꢀ
2Fk2ꢀ kDCCr(III)
Ci,j exp[−(˛2F/RT)E]
i,j
lines are shown in Fig. 5). The slope of the lines and the intersec-
tions in the ordinate were calculated by the least squares method.
The diffusion mass transfer coefficient kD was calculated with Eq.
(15) on the basis of experimentally determined i1,lim values.
ꢁ
i2
=
(18)
k2ꢀ
Ci,j exp[−(˛2F/RT)E] + kD
ꢀ
i,j
The final expression (18) describes the kinetics of chromium elec-
trodeposition. Based on kinetic equations obtained, it is possible to
explain some peculiarities of the step-wise discharge of Cr(III) ions
to the metal.
It should be stressed that it is impossible to determine accu-
ꢁ
ꢀ
i,j
rately the value of co-factor
Ci,j , because there is no sufficient
information on the composition of the near-electrode layer. There-
fore, the obtained data enable us to calculate only the coefficient
It is clearly from Eq. (18) that the i2 vs. kD dependence is non-
linear and is determined by the balance between the terms in the
ꢁ
ꢀ
k2 = k2ꢀ
˜
Ci,j (Table 1).
i,j
ꢁ
ꢀ
denominator of Eq. (18). If k2ꢀ
Ci,j exp[−(˛2F/RT)E] ꢁ kD, then
i,j
˜
As one can see in the table, the coefficient k2 increases with
a decrease in the H2C2O4 concentration and pH in an oxalate-
containing electrolyte. In a formate-containing electrolyte, the
we obtain:
ꢃ
ꢄ
ꢂ
˛2F
RT
i2 = 2Fk2ꢀ CCr(III)
Ci,j exp
−
E
(19)
ꢀ
i,j
˜
coefficient k2 increases with a decrease in the HCOOH concentra-
tion and with an increase in the pH.
In this case, i2 is independent of the solution stirring, because an
increased generation of Cr(II) ions in reaction (1) with a more inten-
sive stirring accelerates the diffusion removal of Cr(II) ions from the
electrode surface. Hence, the values of CS,init and i2 do not depend on
the electrolyte stirring conditions in the initial segment of an i2 vs.
E curve. However, intensifying the mass transfer by increasing con-
vection can alter surface concentrations of reactants Xi(j) involved in
reaction (6), which affects i2. An analysis of these relations can pro-
vide valuable information on the formation of Cr(II) electroactive
complexes.
The calculated apparent transfer coefficients ˛2 lie in the range
from 0 to 1. It seems that from this we could have assumed that
the transfer of the first electron is the limiting stage at the dis-
charge of Cr(II) ions. However, one must compare apparent transfer
coefficients both for cathodic reaction and for anodic one in order
to determine the limiting stage of the multi-electron process [28].
Therefore, it must be stressed that the available kinetic data are
insufficient for a reliable determination of slow stage in the two-
electron reaction (2).
At
a sufficiently negative electrode potentials, we have
Ci,j exp[−(˛2F/RT)E] ꢂ kD, and as follows from Eq. (18):
ꢁ
3.4. Mechanism of the chromium electrodeposition
k2ꢀ
ꢀ
i,j
i2 → i2,lim = 2kDFCCr(III) = 2i1,lim
(20)
When generalizing the results of the analysis of kinetic data
obtained, we conclude that despite many common features, the
where i2,lim is the limiting current density of reaction (2) deter-
mined by convection–diffusion limitations of reaction (1). At this
Table 1
conditions, the value of i2,lim depends on the same factors as i1,lim
,
Kinetic parameters of the Cr(II) discharge at 298 K.
in particular, on solution stirring intensity. As follows from Eqs. (5)
and (20), v = 0, i.e. no intermediates are accumulated in the bulk
electrolyte.
Organic ligand concentration (M)
pH
Parameters
˜
˛
2
k2 (×106 cm/sa)
One can observe a chromium deposition at the limiting diffu-
sion current, as a rule, on a dropping mercury electrode [18–22].
On a solid electrode, the limiting diffusion current of chromium
electrodeposition appears in some cases in electrolytes of certain
composition [8,31].
H2C2O4
0.2
0.4
2.5
2.5
3.0
0.32
0.28
0.37
0.55
0.38
0.09
0.4
HCOOH
0.2
0.4
2.5
2.5
3.0
0.28
0.23
0.38
20.06
11.90
38.16
3.3. Calculation of kinetic parameters
0.4
a
0 = −0.91 V of the reaction
˜
Coefficient k2 is given for standard potential
E
Kinetic parameters of the reaction (2) were determined by lin-
earizing the experimental data in the coordinates of Eq. (13) (some
ꢁ
ꢀ
Cr2+ + 2e− ⇔ Cr0. We assume here that the co-factor
Ci,j is dimensionless.
1,j

V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
5671
kinetics and mechanism of chromium electrodeposition from the
oxalate and formate baths are different. These distinctions are likely
to be caused by the different nature of the electroactive complexes
participating in the discharge that yields the metal.
We believe that the electroactive complexes in the formate
bath are hydroxocomplexes of bivalent chromium formed at
the electrode surface as the products of the dissociation of
inner-sphere-coordinated water molecules, which precedes the
discharge. Then the mechanism of the chromium electrodeposi-
tion can be conditionally presented by the following approximate
reaction scheme2:
2−m
)
[Cr(II)(HCOO)m(H2O) ](
n
ads
1−m+k
↔ [Cr(II)(HCOO)m−k(H2O)n−1(OH)](
)+kHCOO− + H+ (21)
ads
Fig. 6. The value of i2,max as a function of disk rotation velocity for (1) formate bath
and (2) oxalate bath.
1−m+k
[Cr(II)(HCOO)m−k(H2O)n−1(OH)](
) + 2e−
ads
It should be stressed that the presence of a peak in the i2 vs. E
curves does not follow from the above equations, thus indicating
that the adopted kinetic model fails to account for all the features
of the chromium electrodeposition process.
The dependence of i2,max on the disk electrode rotation veloc-
ity ω cannot be described by the Levich equation [33] (see Fig. 6).
Hence, the formation of a current peak in the partial polarization
curves is not related with the convection–diffusion limitations of
the transport of some chromium-containing ions.
We believe that a decrease in the partial current density
of chromium electrodeposition is probably caused by blocking
the electrode surface with poorly soluble adsorbed hydroxide
compounds of Cr(III) [14]. This phenomenon is due to the above-
mentioned local increase in pHS near the electrode layer. At the
electrode potential range corresponding to the descendent seg-
ments in the i2 vs. E curves, we observed the deterioration of the
deposit appearance. The particles of the Cr(III) hydroxide sol cover
the electrode surface and are incorporated into coating structure,
which causes cracking and darkening of deposits.
With an increase in the acidity and the concentration of buffer-
ligand (HCOOH or H2C2O4) in the electrolyte, the amount of Cr(III)
hydroxide adsorbed on the cathode decreases. That is the reason
for the corresponding increase in the value of peak current density
i2,max. Obviously, such effects must be highly sensitive to changes
in the convective mass transfer, which agrees well with our data.
Indeed, the pHS value and the cathode blocking by adsorbed Cr(III)
hydroxide evidently decrease with increasing ω.
→ Cr0 + (m − k)HCOO− + (n − 1)H2O + OH−
(22)
where m = 1, 2; k = 0, 1, 2; n = 1, 2, . . ..
According to this mechanism, an increase in pH and a decrease
in the formic acid concentration in the bath must result in the shift
of the equilibrium (21) to the right, thus contributing to the increase
in the electrochemically active complex concentration. Hence, the
ꢁ
ꢀ
˜
i,j
co-factor
Ci,j and the rate constant k2 increase. This agrees well
with the experimental data obtained.
We note that the composition of chromium complexes is
shown in the scheme provisionally. It is possible that certain other
adsorbed complexes different from those shown above or several
Cr(II) hydroxocomplexes of different composition concurrently can
also be electroactive.
As follows from Fig. 4, the rate of the chromium deposi-
tion decreases with an increase in the disk rotation velocity ω
(for ascending section of i2 vs. E curve). Due to a parallel dis-
charge of hydrogen ions, chromium electrodeposition from aqueous
solutions is always accompanied by an increase in pHS in the near-
electrode solution layer [32]. An increase in the disk electrode
rotation velocity favors the lowering of pHS. This naturally leads
to the lowering of the electroactive complexes concentration; thus,
the rate of the chromium deposition reaction diminishes.
A thermodynamic stability of the Cr(II) oxalate complexes
exceeds that of the corresponding formate complexes by several
orders of magnitude [2]; therefore, the formation of a significant
amount of the hydroxocomplexes is questionable; we may assume
that it is the oxalate complexes of bivalent chromium that directly
discharge (involving hydrogen ions):
The phenomenon involved is rather complex and can be
described quantitatively by introducing additional terms into above
kinetic equations, which would take into account the blocked
electrode surface and a decreased Cr(III) concentration in the near-
electrode layer caused by the Cr(III) hydroxide formation. This
problem must be considered in detail in a separate communica-
tions.
[Cr(II)(C2O4)(H2O)n]ads + 2H+ + 2e− → Cr0 + H2C2O4 + nH2O
(23)
The suggested reaction scheme (23) agrees with the data obtained:
in particular, the rate of chromium deposition from oxalate bath
increases with an increase in the solution acidity and a decrease in
the H2C2O4 concentration.
Due to a high buffer capacity of the oxalate-containing elec-
trolyte, the pHS deviation from the solution pH is probably small
and, therefore, hardly changes with an increase in the disk elec-
trode rotation velocity ω. Hence, the chromium electrodeposition
rate is independent of ω in the electrolytes containing oxalic acid
(see Fig. 4).
4. Conclusions
(1) The electroreduction of Cr(III) complex ions in aqueous solu-
tions is demonstrated to proceed step-wise, via the formation
of relatively stable intermediates—Cr(II) compounds. Only a
part of the total amount of Cr(II) complexes formed at the
first stage of Cr(III) discharge is reduced further to the metal.
Hence, the rate of the chromium deposition is determined by
the current density of Cr(II) ions electroreduction. The corre-
sponding kinetic equations were derived and compared with
the experimental data obtained on a stationery and rotating
disk electrode. Kinetic parameters for the Cr(II) ions discharge
were calculated.
2
A similar reaction scheme has been proposed by us for the electrodeposition
process in trivalent chromium baths containing aminoacetic acid [14].

5672
V. Protsenko, F. Danilov / Electrochimica Acta 54 (2009) 5666–5672
(2) The kinetics and mechanism of chromium deposition from
oxalate and formate baths proved to be different. In case of
formate electrolyte, the metal chromium deposits probably via
the discharge of electroactive hydroxocomplexes of bivalent
chromium which are formed in the near-cathode layer due to
the dissociation of inner-sphere-coordinated water molecules.
In case of oxalate electrolyte, the formation of a significant
amount of the hydroxocomplexes is questionable. Therefore,
the reaction of chromium deposition from oxalate bath is
assumed to proceed with the participation of oxalate complexes
of Cr(II). The reaction schemes proposed agree well with the
experimental data obtained.
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