Mechanism of nitric acid reduction and kinetic modelling

Article abstract of DOI:10.1002/ejic.201402708

In France, the recycling of nuclear waste fuels involves the use of hot concentrated nitric acid. The understanding and prediction of the behaviour of the structural materials (mainly austenitic stainless steels) requires the determination and modelling of the nitric acid reduction process. Nitric acid is indirectly reduced by an autocatalytic mechanism depending on the cathodic overpotential and acid concentration. This mechanism has been widely studied. All the authors agree on its autocatalytic nature, characterized by the predominant role of the reduction products. It is also generally admitted that neither nitric acid nor the nitrate ion is the electroactive species. However, the nature of the electroactive species, the place where the catalytic species regenerates and the thermodynamic and kinetic behaviour of the reaction intermediates remain uncertain. The aim of this study was to clarify some of these uncertainties by performing an electrochemical investigation of the reduction of 4 M nitric acid at 40 °C at an inert electrode (platinum or gold). An inert electrode was chosen as the working electrode in a first step to avoid its oxidation and focus the research on the reduction mechanism. This experimental work enabled us to suggest a coherent sequence of electrochemical and chemical reactions. Kinetic modelling of this sequence was then carried out for a gold rotating disk electrode. A thermodynamic study at 25 °C allowed the composition of the liquid and gaseous phases of nitric acid solutions in the concentration range 0.5-22 M to be evaluated. The kinetics of the reduction of 4 M nitric acid was investigated by cyclic voltammetry and chronoamperometry at an inert electrode at 40 °C. The coupling of chronoamperometry and FTIR spectroscopy in the gaseous phase led to the identification of the gaseous reduction products as a function of the cathodic overpotential. The results showed that the reduction process is autocatalytic for potentials between 0.6 and 1.15 V/NHE. The electroactive species may be regenerated at the surface of the electrode for lower potentials, otherwise this regeneration process occurs in solution by a homogeneous chemical reaction. When the potential is less than 0.6 V/NHE, the fast reduction of nitrogen oxide may lead to rupture of the autocatalytic cycle. The kinetics of the reduction of 4 M nitric acid has been investigated at an inert electrode at 40 °C. The results show that the reduction process is autocatalytic for potentials between 0.6 and 1.15 V/NHE. HNO₂ is the electroactive species and is regenerated at or near the electrode surface by a chemical reaction between HNO₃ and NO_(ads). Kinetic modelling of this mechanism was carried out.

Full text of DOI:10.1002/ejic.201402708

FULL PAPER
DOI:10.1002/ejic.201402708
Mechanism of Nitric Acid Reduction and Kinetic
Modelling
[
a]
[b]
[c]
David Sicsic, Fanny Balbaud-Célérier,* and Bernard Tribollet
Keywords: Autocatalysis / Nitric acid / Nitrogen oxides / Reduction / Reaction mechanisms / Kinetics / Corrosion
In France, the recycling of nuclear waste fuels involves the
use of hot concentrated nitric acid. The understanding and
prediction of the behaviour of the structural materials
search on the reduction mechanism. This experimental work
enabled us to suggest a coherent sequence of electrochemi-
cal and chemical reactions. Kinetic modelling of this se-
quence was then carried out for a gold rotating disk elec-
trode. A thermodynamic study at 25 °C allowed the composi-
(
mainly austenitic stainless steels) requires the determination
and modelling of the nitric acid reduction process. Nitric acid
is indirectly reduced by an autocatalytic mechanism de- tion of the liquid and gaseous phases of nitric acid solutions
pending on the cathodic overpotential and acid concentra-
tion. This mechanism has been widely studied. All the
authors agree on its autocatalytic nature, characterized by
the predominant role of the reduction products. It is also gen-
erally admitted that neither nitric acid nor the nitrate ion is
the electroactive species. However, the nature of the elec-
troactive species, the place where the catalytic species re-
generates and the thermodynamic and kinetic behaviour of
the reaction intermediates remain uncertain. The aim of this
study was to clarify some of these uncertainties by per-
forming an electrochemical investigation of the reduction of
in the concentration range 0.5–22
M to be evaluated. The ki-
netics of the reduction of 4 nitric acid was investigated by
M
cyclic voltammetry and chronoamperometry at an inert elec-
trode at 40 °C. The coupling of chronoamperometry and FTIR
spectroscopy in the gaseous phase led to the identification of
the gaseous reduction products as a function of the cathodic
overpotential. The results showed that the reduction process
is autocatalytic for potentials between 0.6 and 1.15 V/NHE.
The electroactive species may be regenerated at the surface
of the electrode for lower potentials, otherwise this regenera-
tion process occurs in solution by a homogeneous chemical
reaction. When the potential is less than 0.6 V/NHE, the fast
4
M nitric acid at 40 °C at an inert electrode (platinum or
gold). An inert electrode was chosen as the working elec- reduction of nitrogen oxide may lead to rupture of the auto-
trode in a first step to avoid its oxidation and focus the re- catalytic cycle.
Introduction
domain leading to intergranular corrosion. Therefore, to
understand, anticipate and predict the occurrence of such
phenomena, a detailed comprehension and quantitative
modelling of the nitric acid reduction mechanism are essen-
tial.
In a very general way, the behaviour of stainless steels in
concentrated nitric acid can be schematized as shown in
Figure 1.
Three anodic domains are observed as a function of the
potential. At lower potentials, the active domain is ob-
served; in this domain the steel undergoes homogeneous
dissolution, which can lead to high corrosion rates (around
several hundreds of μm per year). In this potential domain,
the reduction process involves protons. At higher potentials,
austenitic stainless steels such as 304L are in their passive
domain, characterized by very low dissolution rates. Under
these conditions, steels are protected by a very thin oxide
layer (a few nm thick), mainly formed of chromium oxide
In France, the recycling of waste fuel involves the use of
nitric acid at various concentrations (up to the azeotropic
–
1
concentration, 14.8 molL ) and temperatures up to their
[
1]
boiling point. This specific medium can be corrosive
towards structural materials, and for this reason highly cor-
rosion-resistant materials have been selected. For the most
severe conditions (high temperature and highly concen-
trated nitric acid), zirconium has been selected, and for
other conditions stainless steels with very low carbon con-
tents (the carbon level has to be below 0.03 wt.-%) are used,
mainly AISI 304L stainless steel. However, in specific cases
condensation areas,[ non-renewed media ), the autocata-
2]
[3]
(
lytic mechanisms of the reduction of nitric acid may cause
a shift of the steel’s corrosion potential to the transpassive
[
[
a] CEA, DEN, DPC, SCCME,
1191 Gif-sur-Yvette, France
b] CEA, DEN, DADN,
9
(
Cr O ). In this domain, the reduction of nitric acid occurs.
2 3
91191 Gif-sur-Yvette, France
E-mail: fanny.balbaud@cea.fr
The medium can be more oxidizing at higher nitric acid
http://www.cea.fr/
concentrations and temperatures or in the presence of oxid-
[
c] Laboratoire Interfaces et Systèmes Electrochimiques, UPR15
VI
izing ions arising from fuel dissolution, for example, Pu
du CNRS, Université Pierre et Marie Curie,
VI
4
Place Jussieu, 75252 Paris Cedex 05, France
or Np . In this last case, the reduction process is the re-
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one would assume that increasing the quantity of reduction
products would decrease the corrosiveness of the medium.
An understanding of the reduction process of nitric acid is
thus essential and therefore identifying the species and the
mechanisms involved and quantifying the reactions occur-
ring is necessary. This will allow a better anticipation and
prediction of potential corrosion concerns.
Review of the Literature Data
The nitric acid reduction process has been widely studied
[
6–25]
over many years.
All through the 1950s and 1960s, two
German teams supervised by Vetter and Schmid, respec-
tively, made an important effort to determine the nitric acid
reduction mechanism at platinum. Their studies of nitric
Figure 1. Schematic representation of the anodic and cathodic pro-
cesses in nitric acid media.
–1
acid solutions at concentrations of 1–10 molL and con-
taining nitrous acid at 25 °C led to different autocatalytic
[
7–14]
mechanisms.
duction of these oxidizing cations, otherwise it is the nitric
acid reduction process. In this potential domain, called the
transpassive domain, the steel undergoes intergranular cor-
rosion.
According to the literature, the nature of the reduction
mechanism depends on two main parameters: the nitric
acid concentration and the cathodic overpotential. The
studies conducted at low concentrations of nitric acid
One essential result of previous studies[2–5] was the dem-
onstration of the crucial role of the nitric acid reduction
process on the transition between the passive and transpass-
ive domains and thus its impact on the corrosion process.
Indeed, it has been shown that under some specific condi-
tions, an increase in the concentration of the reduction
products leads to an increase in the corrosion rate. This is
the case in a confined and non-renewed medium (even for
nitric acid concentrations at which the corrosion rate gen-
erally remains low) in which it was shown that increasing
the concentration of nitric acid reduction products [nitrite
–1
(
[HNO ]Ͻ1 molL ) are not mentioned because in this
3
case nitrates are directly reduced by a totally different
[
23]
mechanism.
According to Vetter,[7–9] the mechanism is heterogeneous
as the chemical regeneration of NO , assumed to be the
2
electroactive species, occurs at the electrode surface. NO is
2
formed at the interface according to a previous slow hetero-
geneous chemical reaction. In this case, the stirring of the
solution has no influence on the current density. This
mechanism can be described by reactions (1)–(5).
ions were added that convert into nitrous acid (HNO ) in
2
acidic medium] leads to a very important increase in the
cathodic current and also to a very strong shift of the cor-
rosion potential towards higher potentials reaching the
lower end of the transpassive domain.[
3]
Other measurements showed that in nitric acid conden-
[
2]
sates, which are in fact similar to a confined and non-
renewed medium (due to the very high metallic surface/
solution volume ratio), a very strong influence of nitrogen
monoxide flow on the corrosion of samples of 304L was
observed.
According to Schmid and co-workers, the mechanism is
homogeneous, as the chemical regeneration of NO , as-
+
sumed to be the electroactive species, occurs in the bulk.
+
NO (equivalent to HNO ) is obtained from the nitrous
2
Indeed, in the case of N , NO and a 75%O /25%N
[10–14]
2
2
2
2
acid formed in the layer near the electrode.
In this
mixture, there is no influence of the flow on the weight
loss of the different specimens. However, a flow of nitrogen
monoxide causes a sharp increase in the weight loss in the
vapour phase and a high corrosion rate (for which severe
intergranular corrosion occurs) is more quickly reached (af-
ter 15 days) than for the other gases or in the absence of a
gas flow (after 35 days).
case, the stirring of the solution provokes a decrease in the
current density. This mechanism can be described by reac-
tions (6)–(10).
These two examples show the very strong influence of
the reduction products (in these two cases, HNO and NO)
2
on the behaviour of materials in nitric acid under condi-
tions of nitric acid concentration and temperatures at which
the corrosion rate of 304L is usually low. This influence of
At the end of the 1980s, Razygraev et al. started new
the reduction products can appear a little contradictory as research into the behaviour of boiling 2 molL–1 nitric acid
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solutions at a platinum electrode.[15] A voltammetric study
was coupled to chemical, chromatographic and volumetric
analysis of the reduction products. He concluded that the
mechanisms of Vetter and Schmid occur successively at a
The kinetic constants were determined by fitting of the
platinum electrode according to the cathodic overpotential. experimental chronoamperograms and data analysis.
Thus, Razygraev’s observations at lower overpotentials
Finally, according to the literature, the reduction of con-
0.85 Ͻ E/SHE Ͻ 1.15 V) may be characteristic of Vetter’s centrated nitric acid shows the following characteristics.
(
mechanism, whereas at higher overpotentials (0.65 Ͻ
E/SHE Ͻ 0.85 V), Schmid’s mechanism may occur.
At potentials less than 0.65 V/SHE, the significant de-
1) The mechanism is autocatalytic and the oxidation
state of the nitrogenous regenerated species is III.
2) The reduction is indirect: neither nitric acid nor the
crease in current density may be caused by the reduction of nitrate ion is the electroactive species.
NO to N O.
3) Beyond a certain cathodic overpotential, the pro-
2
More recently, Balbaud et al. suggested a mechanism duction of N O leads to a break in the catalytic cycle.
2
[
20]
that is dependent upon the concentration of acid.
A
However, the complexity of the chemical reactions be-
thermodynamic study showed that the final product of the tween nitrogenous species is responsible for discrepancies
–
1
nitric acid reduction is NO for [HNO ]Ͻ6 molL and in the reduction mechanisms presented in the literature. In
3
–
1 [26]
NO for [HNO ] Ͼ 6 molL . A parallel electrochemical particular, the nature of the electroactive species and the
2
3
study was carried out at a platinum electrode in nitric acid place at which the regeneration step takes place are still
–
1
solutions in the range 4–12 molL at 100 °C, which showed poorly determined. In this work, our aim was to clarify
that the charge-transfer step may be the reduction of HNO2 some of these uncertainties, to identify the major species
to NO. The mechanism suggested is described by reac- involved in the reduction of nitric acid, and to propose and
tions (11)–(13). The subscript el indicates that the species is establish a kinetic model for a sequence of reactions that
present in solution near the electrode.
explains the experimental observations.
Results and Discussion
The electrochemical investigation was performed in a
4
molL–1 nitric acid solution at 40 °C. These conditions
were chosen as they are intermediary conditions in the
recycling process and because the reduction kinetics are not
too fast under these conditions, thereby allowing an easier
determination of the elementary steps.
Classical electrochemical techniques were used, namely
cyclic voltammetry and chronoamperometry with a station-
ary electrode and a rotating disk electrode.
These mechanisms are heterogeneous as the regeneration
step takes place at the electrode. The gaseous species NO
–1
A typical cyclic voltammogram of a 4 molL nitric acid
and NO are adsorbed at the surface, and nitrous acid is a
2
solution with a Pt stationary electrode recorded at a sweep
soluble compound formed at the electrode that diffuses into
the solution.
–1
rate v = 20 mVs is represented in Figure 2. The electro-
activity domain of nitric acid is limited by the reduction of
protons (E = 0 V/SHE) and the oxidation of water (E =
Finally, in a recent study, Lange et al. proposed a mecha-
nism in 8 m nitric acid solution at 20 °C to take into ac-
1
.6 V/SHE). Three potential ranges can be observed in the
nitric acid reduction domain.
) –0.9 VϽE/SHEϽ1.15 V: a first reduction wave is ob-
served. The corresponding current densities are relatively
[
25]
count solely the chemical steps that play a kinetic role.
They verified that the huge current enhancement (in the
.95 to –0.45 V/SHE region) is due to autocatalysis and
1
0
stems from the regeneration of HNO in solution. A time-
–2
2
low (Ͻ1 mAcm ).
) –0.6 VϽE/SHEϽ0.9 V: the cathodic current density
and potential-independent current plateau was observed for
low scan rates, which was ascribed to a limitation resulting
from the desorption of NOads. They proposed the following
mechanism based on the Schmid mechanism [reac-
tions (14), (6) and (7)]
2
strongly increases. This transition shows that a different re-
duction mechanism occurs during this second wave.
3) –0.4 VϽE/SHEϽ0.6 V: the marked decrease in the
current density shows that the previous mechanism may be
interrupted by another phenomenon.
This paper is focused on the second range of potentials.
In this range, the sharp increase in the current density cor-
responds to the catalytic part of the reduction process,
which is the interesting part with respect to the corrosion
transition from a passive to a transpassive zone.
and the formation of HNO2 through reactions (15) and
Figure 3 shows the results of a chronoamperometry test
performed at a potential close to the beginning of the sec-
(16).
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away from the electrode leading to the observed decrease in
the current density.
These chronoamperometric measurements were repeated
over a potential range from 1.05 to 0.7 V/SHE (correspond-
ing to the end of the catalytic wave), and the variation in
current densities versus potential are presented in Figure 4
for different rate of rotations of the disk. For each measure-
ment, the stationary current was established 5–10 min after
fixing the polarization potential and the rate of rotation of
the disk.
Figure 2. Cyclic voltammogram obtained at a stationary Pt elec-
trode (4 molL–1 HNO
, T = 40 °C, v = 20 mVs ).
–1
3
ond cathodic wave (E = 0.9 V/SHE) at various rates of rota-
tion of the rotating disk electrode after the addition of
–
3
–1
1
0 molL of nitrites to fix the nitrite concentration dur-
ing the test.
Figure 4. Steady-state current densities vs. potential and influence
–
1
3
of the rate of rotation of a gold rotating disk (4 molL HNO +
–
3
–1
1
2
0 molL NaNO , T = 40 °C).
To check if a nitrogen(III) species is created near the elec-
trode, samples of the solution were collected 1 mm from the
platinum plate during the chronoamperometry measure-
ment and analysed by the Griess method. The potential was
fixed at 0.65 V/SHE, which corresponds to the catalytic
wave. Table 1 presents the results of the analysis of nitrites
during the test.
Table 1. Concentrations of the nitrogen(III) species during the
chronoamperometry test presented in Figure 5.
Figure 3. Influence of the rate of rotation of the current density
during a chronoamperometry measurement (E = 0.9 V/SHE, gold
–
1
–3
–1
[NIII] [molL–1]
rotating disk, 4 molL HNO
3
+ 10 molL NaNO
2
, T = 40 °C).
t [min]
–
6
0
8
9
5.81ϫ10
1.86ϫ10
7.62ϫ10
2.09ϫ10
During this measurement the rate of disk rotation was
changed from 1000 to 50 rpm. It is worth noting that, in
–
4
–5
–
4
general, the electroactive species diffuses from the solution 20
towards the electrode and the limiting current is then pro-
1
/2
[27]
portional to ω according to the Levich law. In the pres-
The current densities and nitrogen(III) concentrations
ent case it is clear that the current density does not follow are presented in Figure 5 under the condition of stirring (+)
III
the Levich law as its absolute value increases when the rate or non-stirring (–). The results confirm that a dissolved N
of rotation decreases. Only a few dozen rpm are sufficient species may be the electroactive species and that it is regen-
to produce important variations of the current density, thus, erated close to the electrode by a chemical reaction as its
the reduction process occurring in this potential range is concentration increases strongly when the solution is not
III
partly controlled by the diffusion of the reactive species. stirred. We will assume that the major N species present
The inverse effect of the rate of rotation shows that this in solution is nitrous acid (HNO ), but as was said pre-
2
+
species would not diffuse from the solution to the electrode, viously, NO could also be considered an active species as
but that it would be generated close to or at the electrode. it is always in equilibrium with HNO in acidic medium
2
This species could be either the electroactive species or a [reaction (5)]. In contrast, when the solution is stirred, this
reaction intermediate leading to the formation of the elec- species is chased away from the electrode and so the cata-
troactive species by a chemical reaction. In both cases, by lytic cycle is disrupted and both the current density and the
increasing the rate of rotation, this species would be chased concentration of the nitrogen(III) species decrease.
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is not produced during the process or does not diffuse
through the medium. During the catalytic wave, as ex-
pected, the concentration increases strongly and then drops
because of a break in the catalytic cycle.
Figure 5. Measurements of nitrogen(III) during a chronoampero-
metry test at a Pt electrode (E = 0.65 V/SHE, 4 molL–1 HNO
, T
40 °C).
3
=
Other chronoamperometry measurements were per- Figure 7. Concentration of nitrogen(III) in the solution at the end
formed over the potential range of 0.05 to 1.05 V/SHE to of the chronoamperometric measurements versus potential
–
1
(
3
4 molL HNO , T = 40 °C).
study the evolution of the current density over 5000 s at
different stages of the reduction process. The working elec-
trode was a gold stationary plate and the medium
The gaseous reduction products were also analysed by
FTIR spectroscopy. The spectra were recorded during
chronoamperometric measurements of a 4 molL nitric
–
1
(
4 molL HNO at 40 °C) was renewed between each mea-
–1
3
surement. The current densities measured at different times
as a function of potential are presented in Figure 6. The
steady state was quickly obtained for potentials between 0.7
and 1.05 V/SHE. However, for lower potentials, the current
densities increase until the end of the measurements. Al-
though the catalytic cycle is supposed to be broken in this
potential range, a new slow catalytic reduction process may
occur. At the end of each test, a sample of the solution was
collected to measure the concentration of nitrogen(III). The
results are presented in Figure 7 as a function of potential.
The concentrations obtained follow the variation in the cur-
rent density. At the beginning of the reduction process, the
concentration of nitrogen(III) is the same as that of a
freshly made nitric acid solution, which means that HNO2
acid solution in the potential range of 1.05 to 0.15 V/SHE.
Different gases were detected depending on the potential
imposed, thereby defining three potential domains.
Typical spectra corresponding to these domains are rep-
resented in Figure 8. From 1.05 to 1 V/SHE, absorption
bands are observed at the vibrational frequencies of water
–1
(
(
3756, 3657 and 1595 cm ) and carbon dioxide
–1 [28]
2349 cm ). These compounds are already present in the
atmosphere above the nitric acid solution, which means that
no gaseous reduction products are detected at these poten-
tials. From 0.95 to 0.7 V/SHE, a band characteristic of NO
–1
(
1880 cm ) can be observed in addition to the bands of
water and carbon dioxide. NO is a very unstable species in
the atmosphere of nitric media and is rapidly oxidized by
Figure 6. Voltammograms plotted from chronoamperometric
–1
measurements at a stationary gold electrode (4 molL HNO
40 °C).
3
, T
Figure 8. FTIR spectra of the reduction products in the gas phase
–
1
=
at different potentials (4 molL HNO
3
, T = 40 °C).
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nitric acid or oxygen.[29] Therefore it cannot be produced Figure 10, and agree well with the literature data and the
by a chemical reaction in the gaseous phase, but must be spectra described above. It would be interesting to quantify
the product of an electrochemical reaction. From 0.65 to these analyses by calibrating the FTIR spectrometer for
0
.15 V/SHE, typical bands corresponding to N O (2277 NO, NO and N O to access the kinetic constants.
2
2
2
–
1 [28]
–1 [28]
and 1300 cm )
and NO (1610 cm )
are observed.
2
These results confirm the hypothesis of Razygraev and co-
workers that the break in the catalytic cycle is caused by the
Reduction Mechanism and Kinetic Modelling
reduction of NO to N O. Nevertheless, NO is still present in
2
In the potential domain studied, the evolution of NO
was detected and colorimetric titration measurements con-
the gaseous phase, which means that these two mechanisms
could be in competition in this potential range.
firmed that HNO is involved in the charge-transfer step
2
A spectrum of a 6 molL–1 nitric solution was recorded
in the catalytic domain (Figure 9). A band corresponding
and regenerated at or near the electrode by a chemical reac-
tion. The act of stirring chases HNO away from the elec-
2
to NO is observed in addition to the band of NO, so at
2
trode, which decreases the catalytic effect and the current
nitric acid concentrations greater than or equal to
densities. The mechanism considered for the modelling is
–
1
6
molL , this species could be a reduction product accord-
[20]
similar to that of Balbaud et al. at low HNO concentra-
3
[20]
ing to the mechanism described by Balbaud et al.
tions and is described by reactions (17) and (18). The sub-
scripted a indicates that the species is considered in its
aqueous state.
There are three hypotheses that are important to con-
sider in this mechanism.
1) NO is supposed to be an adsorbed intermediate at the
electrode. The ability of NO to adsorb at inert electrodes in
nitric media has already been suggested and validated in
the literature by in situ FTIR measurements at inert elec-
[
22]
trodes.
) Reaction (18) is heterogeneous: HNO regenerates at
2
2
the electrode.
Figure 9. FTIR spectrum of the reduction products in the gas
phase (6 molL–1 HNO
3) Both reactions are supposed to be irreversible. This
hypothesis is reasonable as the cathodic overpotential is im-
portant and because the inverse kinetic constant of the
homogeneous reaction corresponding to reaction (8) in
solution is very low [the kinetic constants for the hetero-
geneous reaction (18) have not been found in the literature].
The desorption of adsorbed NO to gaseous NO should
be included in the mechanism, but it will not be considered
in the following modelling.
3
, E = 0.8 V/SHE, T = 40 °C).
Finally, to confirm the assignment of the different ab-
sorption bands to the species detected, pure water vapour
and industrial preparations of NO, NO and N O dissolved
2
2
in 100 ppm N (Messer) were directly analysed in the FTIR
2
gas cell. The spectra obtained for each gas are presented in
Having proposed a mechanism for the reduction of nitric
acid at an inert electrode, the objective was then to develop
a kinetic model for this mechanism. Comparison between
the model and the experimental results at a gold rotating
disk will enable support for the mechanism and eventually
allow its modification. The approach adopted in this work
deliberately set out to develop analytical modelling (as
much a possible) to achieve a better mastering of the model
in this first step of the modelling procedure.
Nitrous acid is supposed to diffuse from the electrode to
the solution along the axis y. Thus, its concentration C is a
solution of the convective-diffusion equation. Considering
cylindrical coordinates, for reasons of symmetry and uni-
form accessibility of the disk, the angular and radial com-
ponents of the equation can be neglected. When the steady-
state current value is reached, the concentration near the
electrode no longer varies and dC/dt = 0. These considera-
Figure 10. FTIR spectra of gaseous H
ambient temperature.
2 2 2
O, NO, NO and N O at
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tions lead to a simplification of the convective-diffusion
equation, which can be written as Equation (19).
dC
dy
d2C
v
y
(
) = D(
)
(19)
The cathodic steady-state current is proportional to the
electrochemical reaction rate, given by Equation (29).
2
d y
–2
in which D is the diffusion coefficient of HNO (molcm )
2
0
i
s
= –FSk
1
ЈC (1 – θ)
(29)
and v is the normal component of the fluid velocity profile
y
given by Levich, see Equation (20).[27]
in which S is the disk area (cm2).
= –0.51ω3
/2 –1/2
y2
Combination of Equations (22), (27) and (28) leads to
Equation (30).
v
y
v
(20)
–1
2
in which ν is the kinematic viscosity of the liquid (cm s ).
Integration of Equation (19) leads to Equation (21).
0
in which C* and C are the concentrations of HNO in the
2
An expression for the steady-state current is obtained by
combining Equations (29) and (30) to give Equation (31).
bulk solution and at the electrode, respectively.
It is assumed that the concentration profile of HNO is
linear and decreases across the diffusion layer of thickness
2
0
i
s
= 2DFS(C* – C )/δ
(31)
δ, see Equation (22).
0
Moreover, C can be expressed as a function of the sta-
0
0
C(y) = C + (C* – C )y/δ
(22) tionary current and the kinetic parameters according to
Equation (32).
The analogy between the derivative for y = 0 in Equation
(22) and Equation (21) gives the thickness of the diffusion
layer [Equation (23)].
δ = 1.61D1
/3 1/6
v
ω–1/2
(23)
By inserting Equation (32) into (31), an expression for δ
is obtained, see (33).
+
–
The activities a(H ), a(NO ) and a(H O) are supposed
3
2
to be constant, so the apparent kinetic parameters k Ј and
1
k2Ј are introduced through Equations (24) and (25).
k
1
2
Ј = k
Ј = k
1
2
a(H)
(24)
(25)
[a(H )a(NO
3 2
–)a(H O)]1/2
+
k
Equations (23) and (33) can then be combined to give a
relationship between the rate of rotation and the stationary
current, see Equation (34).
The parameter k is the heterogeneous rate constant for
reduction, and can be expressed by Equation (26).
1
αFη
k
1
= k 0
1
exp(
)
(26)
RT
0
in which k is the standard electrochemical rate constant
1
–
1
(
cms ), α is the charge-transfer coefficient, F is the Faraday
–
1
–1 –1
constant (Cmol ), R is the gas constant (Jmol K ), T is
the temperature (K), η is the cathodic overpotential (V),
which is the difference between the electrode potential E
The representation of ω–1/2 as a function of the station-
ary current measured experimentally allows the determi-
(
V/SHE) and the apparent normal potential E , which is
0
equal to 1.09 V/SHE.
nation of A, B and C, and then the adjustement of kЈ and
1
The two species with interfacial concentrations that im-
kЈ , which have not been found in the literature.
2
pact on the reaction kinetics are NO and HNO . In the
2
Finally, the expression of the stationary current as a
stationary regime, the surface coverage of NO(ads), θ, is con-
stant at the steady-state. Thus, βdθ/dt = 0, which leads to
Equation (27).
function of potential (implicitly expressed in kЈ ) and the
1
rate of rotation of the disk (implicitly expressed in δ) is
given by the negative solution of Equation (33), that is, (35).
0
k
1
ЈC (1 – θ) = k
2
Јβθ
(27)
–2
in which β (molcm ) is the maximum surface concentra-
tion of NO(ads)
.
The flux of HNO at the surface of the disk can be
2
written as Equation (28).
The parameters used in the model are given in Table 2.
Eur. J. Inorg. Chem. 2014, 6174–6184
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Table 2. Values of input data for the heterogeneous model.
Model parameter
Value
–
1
F [Cmol ]
96485
8.314
313[
R [Jmol–1 K ]
–1
a]
T [K]2
[a]
S [cm ]
0.196
7.4ϫ10
0.5[
2
–1
–3[b]
ν [cm s ]
c]
α
–
2
–9[d]
β [molcm ]
C* [molcm ]
a(H ) = a (NO
2ϫ10
–3
–6[a]
10
+
–)
–3[e]
3
5.27ϫ10
0.816[
e]
a(H
2
O)
[
a] Measured. [b] See ref.[30] [c] Adjusted. [d] See ref.[31] [e] See ref.[32]
The results obtained from the chronoamperometry tests
at the rotating disk (Figure 4) were fitted to Equation (34)
at different potentials to obtain values of A, B and C. The
Figure 11. Variation of the stationary current density as a function
of the cathodic overpotential. Comparison of the model presented
in Equation (35) with the experimental results obtained at a gold
–
1
–3
–1
mean values of these parameters are as follows: A = rotating disk electrode (4 molL HNO + 10 molL NaNO , T
3
2
–
5
1/2
–2
1/2
= 40 °C).
3
3
.43ϫ10 As
,
B
=
1.48ϫ10 As
and
C
=
–
5
.52ϫ10 A.
By using A, B and C it is possible to determine k Ј, k Ј
1
2
pected by the model. This difference can be explained by
the fact that under these conditions, the heterogeneous
mechanism proposed herein would not represent the global
process. In fact, the chemical reaction allowing the regener-
and the diffusion coefficient of HNO , D. Then, by using
2
Equation (24), k can be determined, and finally, the stan-
1
0
dard electrochemical rate constant k1 can be determined
by using Equation (26). The diffusion layer thickness, δ, can
also be calculated (numerical application for ω = 100 rpm).
ation of HNO may not occur only at the surface of the
2
electrode as considered here, but in the solution close to the
electrode. Indeed, the intermediate NO quickly and abun-
dantly formed at the electrode would diffuse into solution
and the homogeneous regeneration reaction would be pre-
dominant.
The
following
values
were
obtained:
D
=
–
5
2
–1
0
–1
(
9
1.81Ϯ0.56)ϫ10 cm s , k = 0.02Ϯ0.01 cms , k Ј =
00Ϯ600 s and δ = 60 μm.
1
2
–
1
The diffusion coefficient of HNO , D, at 40 °C is missing
2
from the literature, but the value obtained in this study is
In that case, the mechanism of reduction would be given
by reactions (17), (36) and (37).
–
1
in accordance with measurements in a 4 molL nitric acid
[
20]
–6
–5
2 –1
solution at 100 °C: 8ϫ10 ϽDϽ9ϫ10 cm s .
Finally, having defined and evaluated all the parameters,
it is possible to calculate the theoretical stationary current
density as a function of the overpotential. These plots and
experimental data from Figure 4 are represented in Fig-
ure 11 for four different rates of rotation.
At low overpotentials, the kinetic parameter k is low,
1
so the electrochemical reaction is slow compared with the
chemical reaction, and the current densities remain rela-
tively low. Thus, the kinetics of the reduction process is
limited by the rate of the charge-transfer step. For higher
overpotentials, the current density of the plateau is deter-
As in the previous modelling of a heterogeneous mecha-
nism, the system is considered to be stationary and the con-
centrations of NO and HNO are assumed to be indepen-
2
dent of the radius, r, and the angle, φ, of the cylindrical
coordinates.
mined by the value of k , so the kinetics of the process are
2
By considering C = [HNO ] and C = [NO ], the
1
2(a)
2
(a)
limited by the rate of the catalytic chemical reaction. This
value does not depend on the rate of rotation of the disk,
as shown by Equation (28) for high overpotentials: in this
convective-diffusion equations have to be modified because
at a given point of the solution, HNO2(a) is produced and
NO(a) is consumed according to reaction (37). According to
case, the term B/(C + i ) tends towards zero. Between these
s
[33]
the literature, this reaction would itself be the result of a
two domains, the kinetics is controlled by the rates of both
the chemical and electrochemical steps and by the diffusion
of HNO2.
At low values of ω (30 to 70 rpm), the model fits well
with the experimental points. In particular, the sudden in-
crease in the current density and the surprising influence of
the rate of rotation are well described. However, at higher
values of ω (Ն100 rpm) and overpotentials, the experimen-
tal current densities of the plateau are lower than those ex-
more complex catalytic process. The kinetics of this process
would be first order in HNO and zero order in NO. To
2
simplify the resolution, only reaction (37) will be considered
and it will be assumed to be zero order in NO.
The rate of production of HNO by the chemical reac-
2
tion is thus given by Equation (38).
dC1
(
) = 3/
2
k
5
Ј
(38)
dt
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in which k Ј = k [a(H )a(NO )a(H O)]1/2.
+
–
dC
dC
2
5
5
3
2
1
)
D
1
(
0
+ D
2
(
)
0
= 0
(48)
The consumption of NO by the chemical reaction is de-
scribed by Equation (39).
dy
dy
Once the stationary concentration profiles C (y) and
1
dC
dt
2
C
2
(y) have been numerically determined, the stationary cur-
(
) = –k
5
Ј
(39)
rent density can be calculated according to Equation (49).
The convective-diffusion equations for NO and HNO2
can thus be described by Equation (40).
dC
1
i
s
= –FSD
1
(
)
0
(49)
dy
The input data of the model are the same as for the
heterogeneous model previously described. The adjusted or
calculated parameters have also been adjusted to the same
values as in the heterogeneous model (α, D = D ; Table 3):
1
2
in which D and D are diffusion coefficients of HNO and
1
–1
2
2
2
NO (cm s ) and v is the normal component of the fluid Table 3. Values of input data for the homogeneous model.
y
velocity given by Levich [Equation (20)].[
27]
Model parameter
Value
The concentration profiles C (y) and C (y) were calcu-
1
2
F [Cmol–1]
R [Jmol K ]
96485
8.314
313[
lated numerically by using the Mathematica software. This
–1 –1
a]
resolution requires four boundary conditions. In solution T [K]
2
[a]
(
yǞϱ), the concentrations of HNO and NO are constant, S [cm ]
0.196
7.4ϫ10
0.5[
2
2
–1
–3[b]
ν [cm s ]
whatever the overpotential, see Equations (41) and (42).
c]
α
–
2
–9[d]
(ϱ) = 10–6 molcm–3
β [molcm ]
2ϫ10
C
C
1
2
(41)
–
3
–6[a]
C* [molcm ]
10
+
–)
–3[e]
–5[f]
(ϱ) = K
(42) a(H ) = a(NO
3
5.27ϫ10
e]
a(H O)
= D
2
0.816[
2
–1
C (ϱ) was measured experimentally. The resolution tests
D
1
2
[cm s ]
1.81ϫ10
0.02
1
0
–1
k
1
[cms ]
of this system showed that the current density is indepen-
dent of K. However, K has to be fixed to a non-zero value [a] Measured. [b] See ref.[30] [c] Adjusted. [d] See ref.[31] [e] See ref.[32]
[f] Calculated.
to ensure the convergence of the calculation. The value of
–
4
–3
K was fixed to 3ϫ10 molcm , which allows the conver-
Finally, the kinetic constants of the chemical reactions
gence of the calculations. The concentrations of HNO and
2
were adjusted with the experimental values of the current
0
0
NO for y = 0 at the stationary state (C1 and C , respec-
–1
–4 –1
2
density: k = 900 s and k Ј = 1.86ϫ10 s .
4
5
tively) are not known, and thus the two other boundary
conditions have to be determined from the expression of
the flux of these species at the electrode surface, see Equa-
tions (43) and (44).
Calculated values of i = f(η ) according to Equation (49)
s
c
together with experimental measurements of the stationary
current density by chronoamperometry are presented in
Figure 12 as a function of overpotential for two rates of
rotation of the disk electrode.
For low overpotentials, the homogeneous model does not
allow the variation of the current density to be represented,
dC
1
D
1
(
(
)
0
= k
= k
1
ЈC
1
0(1 – θ)
(43)
(44)
dy
dC
dy
2
)
D
2
0
4
βθ
The desorption reaction of NO(ads) at the stationary state
leads to Equation (45).
k
1
ЈC
1
0(1 – θ
s
) = k
4
βθ
s
(45)
The stationary surface coverage of NO(ads) can thus be
expressed by Equation (46).
By combining Equations (43) and (46), the first bound-
ary condition for y = 0 is obtained, see Equation (47).
Figure 12. Variation of the stationary current density as a function
of the cathodic overpotential. Comparison of the model Equa-
tion (44) with the experimental results obtained at a gold rotating
The second boundary condition for y = 0 is obtained
from Equations (43), (44) and (45), see Equation (48).
–
1
–3
–1
disk electrode (4 molL HNO
3 2
+ 10 molL NaNO , T = 40 °C).
Eur. J. Inorg. Chem. 2014, 6174–6184
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whereas the heterogeneous model is well adapted. The higher overvoltages on the stainless-steel electrode than on
chemical regeneration of HNO would therefore occur at the platinum electrode to obtain comparable current densi-
2
the electrode surface. However, for higher overpotentials, ties. Chronoamperometric measurements were performed
(
|η | Ͼ 0.3 V), the homogeneous model represents the cur- to study the effect of stirring of the electrode. The rotation
c
rent density well, contrary to the heterogeneous model, of the electrode led to a sharp decrease (in magnitude) of
which predicts a constant value for the current density (see the current density, which shows that the electroactive spe-
Figure 11) whatever the rate of rotation of the disk, this cies is not nitric acid. Moreover, a series of experiments
value being far from the experimental values for ω Ն were performed in nitric acid solutions containing nitrous
00 rpm. Under these conditions of high overpotential (|ηc| acid at a concentration close to 10–2 molL . In these ex-
–1
1
Ͼ 0.3 V) and rates of rotation (ω Ն 100 rpm), the nitrogen periments, the corrosion potential was shifted towards high
monoxide formed by the electrochemical reaction in high potentials. Moreover, in the presence of nitrites, the current
quantities would be chased away from the electrode by con- densities in oxidation as well as in reduction were higher
[
20]
vection to react in the homogeneous phase with nitric acid (as has already been observed for platinum ). This in-
to regenerate nitrous acid.
crease shows that nitrous acid promotes the reduction of
nitric acid on stainless steel.
As the chronoamperometric measurements showed that
nitric acid was not the electroactive species, and that it was
a soluble species formed at the electrode that diffuses
Conclusions
To gain a better understanding of corrosion mechanisms through solution, it was possible to assume that, as at plati-
of stainless steels in concentrated nitric acid and to develop num, nitrous acid is the electroactive species.
a predictive and quantitative approach to these phenomena,
Finally, it is possible to assume that the reduction mecha-
a model of the nitric acid reduction process has been devel- nism is identical at both electrodes except that it proceeds
oped. In a first approach, only measurements at an inert at a much lower rate at the 304L stainless-steel electrode.
electrode (platinum or gold) were taken to focus on the re- Of course, it is now necessary to verify that the modelling
duction process. In agreement with the literature data, the established for platinum in this paper would be the same in
catalytic nature of the reduction process was evidenced and the case of stainless steel.
a mechanism was proposed for the catalytic part of the
global reduction mechanism. The results suggest that
HNO is the electroactive species and that it is regenerated
at or near the electrode surface by a chemical reaction be-
2
Experimental Section
General: Classical electrochemical techniques were used: cyclic vol-
tammetry and chronoamperometry with a stationary electrode and
a rotating disk electrode.
tween HNO and NO(ads). In particular, stirring has an un-
3
usual and significant effect as it chases away HNO from
2
the electrode and slows down the kinetics of the process. A
two-step mechanism involving an electrochemical and Electrochemical experiments were conducted at 40 °C in a reactor
–
1
containing 4 molL nitric acid (200 mL). The gas volume above
the reactor was also 200 mL. The stationary working electrodes
chemical reaction, both heterogeneous and irreversible, was
suggested. The kinetic modelling of this mechanism carried
out for a rotating disk system fits well with the experimental
data at low rates of rotation. The potential of the transition
between the two kinetic regimes is shifted towards higher
overvoltages when ω is increased. However, when ω is
greater than 100 rpm, the limiting current density of the
plateau is not well described by the model. Indeed, for these
conditions, the kinetic model including the regeneration of
2
consisted of a platinum plate (area 0.5 cm ) or a gold plate (area
cm ). A Radiometer EDI-101 gold rotating disk (diameter 5 mm)
was used to study the hydrodynamic effects of the reduction pro-
cess.
2
2
In very acidic and corrosive media, such as concentrated nitric acid,
an oxide layer PtO
2
may form on the platinum.[ Indeed, the open
34]
–
1
circuit potential of an inert electrode in a 4 molL nitric acid solu-
tion at 40 °C is about 1.15 V/SHE. At this acidity, platinum can be
oxidized at potentials above 1 V/SHE and gold for potentials above
.3 V/SHE. Thus, it is preferable to use gold as the working elec-
trode material in these media to avoid the reduction of PtO during
HNO in solution and not at the electrode allows a good
2
description of the experimental results. However, these are
the first calculations and they need to be consolidated, for
1
2
example, specific experimental work could be performed to electrochemical measurement.
determine the kinetic constants that were adjusted from
The working electrode was treated electrochemically before each
test to clean it and then afterwards to remove the eventual ad-
sorbed species at its surface. This treatment consisted of imposing
a potential of –0.5 V/SHE at the electrode so that bubbles of
these calculations.
Finally, considering the applicability of this work to aus-
tenitic stainless steel 304L, electrochemical tests (cyclic vol-
tammetry and chronoamperometry) were performed at a hydrogen produced in the reduction of water can clean it. Thus,
stainless-steel electrode to confirm the proposed mecha- the condition of the surface of the electrode is the same for each
[
2]
nism. These electrochemical measurements were carried measurement.
–
1
[2]
out in 4 molL HNO at 100 °C. The results obtained
3
The counter electrode was a platinum wire and the reference elec-
trode was a mercurous sulfate electrode (SSE) separated from the
showed that the reduction process is much slower at the
stainless-steel electrode than at the platinum electrode at the nitric media by a salt bridge filled with a saturated KNO solution.
3
same temperature. Indeed, it was necessary to impose much The potential of this reference electrode versus the standard
Eur. J. Inorg. Chem. 2014, 6174–6184
6183
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FULL PAPER
hydrogen electrode (SHE) at 25 °C was ESSE = 0.65 V/SHE.[34] All
the measurements were made with a Bio-logic VSP potentiostat.
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[
[
[
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35]
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Received: July 25, 2014
Published Online: November 25, 2014
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