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Determination of Equilibrium Constants for Reactions between Nitric
Oxide and Ammoniacal Cobalt(II) Solutions at Temperatures from
298.15 to 309.15 K and pH Values between 9.06 and 9.37 under
Atmospheric Pressure in a Bubble Column
Hesheng Yu*,† and Zhongchao Tan†,‡,§
†
Department of Mechanical & Mechatronics Engineering, ‡Department of Civil & Environmental Engineering, and §Waterloo
Institute for Sustainable Energy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1
S Supporting Information
*
ABSTRACT: Experiments were conducted in a bubble column to determine the equilibrium constants of reactions between
NO and ammoniacal cobalt(II) solutions at temperatures between 298.15 and 310.15 K and pH values from 9.06 to 9.37 under
atmospheric pressure. The two reactions are 2Co(NH3)5(H2O)2+ + 2NO ⇌ (NH3)5Co(N2O2)Co(NH3)54+ + 2H2O and
2Co(NH3)62+ + 2NO ⇌ (NH3)5Co(N2O2)Co(NH3)54+ + 2NH3, respectively. Their equilibrium constants are calculated on the
fraction molar basis. All experimental data fit well to the equations ln K5NO = 3598.5(1/T) + 16.759 and ln K6NO = 1476.4(1/T) +
26.597, which give the enthalpy of reactions between NO and penta- and hexaamminecobalt(II) nitrates: ΔrH5° =
−29.92kJ·mol−1 and ΔrH6° = −12.27kJ·mol−1.
■
NH4NO3/NH3·H2O buffer solution to ensure a ready supply of
NH3 ligand while avoiding the formation of hydroxide and the
precipitation of cobalt hydroxide. Six reversible step reactions,
as summarized in Table S1 in the Supporting Information (SI),
were involved in the investigated solution. The ultimate
cobalt(II) ammonia system depends on the pH value,
temperature, and concentration of ammonium nitrate.
Although the research work done by Bjerrum is relatively old,
it is the only publicly available literature for analysis of the
cobalt(II) ammonia system. It has been proven by Yatsimirskii
and Volchenskova using absorption spectra17 and used by
Simplicio and Wilkins18 and Ji et al.19
The equilibrium constants for stepwise reactions S1−S6 in
the SI can be correlated at temperatures from room
temperature (295.15 K) to 303.15 K16 as
INTRODUCTION
Current energy consumption pattern leads to great nitrogen
oxide (NOx) emissions.1,2 In response to the increasing
stringent legislations, wet-scrubbing technology is desirable
because of its insensitivity to flue gas particulates, high NOx
reduction efficiency, and ability to simultaneously remove SO2
and NOx.3−6 The selection of a suitable absorbent is crucial to
wet-scrubbing technology. In industrial combustion processes,
inactive nitric oxide (NO) constitutes 95% or so of NOx
emissions.1,7 It requires that the absorbent must quickly react
with NO; commercialization of a wet scrubbing technology can
be restricted by waste-liquor treatment. An excellent absorbent
should also be easily regenerated, which will cut the operational
cost down. Several absorbents such as ClO2 /NaClO2,
KMnO4,8−10 and FeIIEDTA (EDTA = ethylenediaminetetraacetic acid) solutions11 have been reported to be effective for
NOx absorption. Recently, Long’s group reported that a
hexaamminecobalt(II) solution could effectively remove NO
from simulated flue gas and it could be easily regenerated by a
KI solution with ultraviolet light or activated carbon.12−14 Also,
a comparative study of three absorbents by Yu et al.15 showed
that ammoniacal cobalt(II) complexes had advantages over the
two compared absorbents when simulated flue gas was treated
with about 5% oxygen. Moreover, the main byproducts were
nitrite and nitrate, which are sources of fertilizers. Thus, the
hexamminecobalt(II) solution can be considered as an ideal
absorbent for wet flue gas treatment (FGT) technology.
A series of step equilibria exist in solutions containing
ammonia and cobalt(II) salts. In order to determine the
consecutive equilibrium constants as well as the cobalt(II)
ammonia system, Bjerrum16 conducted experiments by adding
ammonia into solutions with small concentrations of cobalt(II)
nitrate and at a high concentration of ammonium nitrate up to
2 mol·L−1. The presence of ammonium nitrate was to form a
© 2013 American Chemical Society
log K n = log K n 0 + 0.062[NH4 +] + 0.005(303.15 − T )
(1)
where the values of log Kn0 can be referred to in Table S1 in the
SI.
Apart from the reactions tabulated in Table S1 in the SI, the
dissociation equilibrium of ammonium can be described as
NH4 + ⇌ NH3 + H+
(2)
Thus, the acid dissociation constant of the ammonium ion can
be presented as
Received:
Revised:
Accepted:
Published:
3663
September 10, 2012
February 11, 2013
February 14, 2013
February 14, 2013
dx.doi.org/10.1021/ie302439u | Ind. Eng. Chem. Res. 2013, 52, 3663−3673
Industrial & Engineering Chemistry Research
k NH4+ =
[NH3][H+]
[NH4 +]
Article
are more likely to react with NO, it is necessary to ensure their
presence in the ammoniacal cobalt(II) solution. According to
the analysis of the cobalt(II) ammonia system elaborated on in
the SI, it can be found that the absorbent system contains only
cobalt(II) complexes with coordination numbers of no more
than 4 at pH values of less than 9. Hence, the pH value of the
absorbent system should be set at 9 or above to ensure the
existence of penta- and hexaamminecobalt(II) ions. On the
other hand, the volatilization of concentrated ammonia at
excessively high pH values will cause errors. Therefore, the pH
value of the current study was set at 9.06−9.37.
In this paper, the theoretical calculation of the equilibrium
constants of reactions between penta- and hexaamminecobalt(II) nitrates and NO is first presented. Then NO is bubbled
through a solution of pH 7.63 in a bubble-column system to
validate the reactivity of the corresponding complexes. At last,
the equilibrium constants measured in the bubble-column
system at temperatures between 298.15 and 310.15 K and pH
values from 9.06 to 9.37 are reported.
(3)
Bjerrum16 provided values of kNH4+ for a 2 mol·L−1 NH4NO3
solution at 295.15 and 303.15 K, respectively. Therefore, values
in or close to this interval can be evaluated by interpolation.
With the corresponding equilibrium constants Kn (n = 1−6)
and the dissociation constant of ammonium, the cobalt(II)
ammonia system can be established. A detailed calculation
scheme can be found in the SI.
Of the complexes with different coordination numbers in the
cobalt(II) ammonia system, only penta- and
hexaamminecobalt(II) ions were referred to as reactants that
react with NO to form nitrosyl by Ford and Lorkovic,20
Asmussen et al.,21 and Gans.22 Besides, it has been reported by
Simplicio and Wilkins18 that penta- and hexaamminecobalt(II)
nitrates were the only compounds reactive with oxygen. A trial
performed at pH 7.5 or so and T = 303.15 K is able to confirm
the reactive substances in a cobalt(II) ammonia system because
of the fact that the system nearly contains only complexes with
coordination numbers of less than 5 at pH 7.5 according to the
analysis of the cobalt(II) ammonia system in the SI. It can be
verified that only penta- and hexaamminecobalt(II) ions have
the ability to react with NO if no evident absorption of NO
occurs at pH values close to 7.5.
Additionally, a number of studies on the preparation23−25
and structure21,22,26−36 of cobalt nitrosyl by a reaction between
NO and ammoniacal cobalt(II) complexes have been
conducted. It has been well accepted that there were two
series of cobalt nitrosyl: the black series formed at low
temperature (273.15 K and below) and the red series at high
temperatures (room temperature or above).24 Almost all of the
researchers who considered isomerization believed that the red
isomer was the dicobalt μ-hyponitrite complex with a formula
of [(NH3)5Co(NO)2Co(NH3)5]4+22,28,31,32,34,36,37 with only
one exception.38
Because the experimental results showed that an ammoniacal
cobalt(II) solution was a promising option for NO abatement,
it is of importance to determine its corresponding equilibrium
constants for the understanding of NO absorption mechanism.
Mao et al.39 have reported the equilibrium constant of the
reaction between a hexaamminecobalt(II) ion and NO. In their
work, first, they ignored the analysis of the cobalt(II) ammonia
system. Second, they stated that the product was a monomer,
[Co(NH3)5NO]2+, at temperatures higher than 303.15 K,
which conflicts with most aforementioned earlier publications.
Therefore, it is worthwhile to study the equilibrium constants
of reactions between ammoniacal colbalt(II) solutions and NO
again by taking into account analysis of the cobalt(II) ammonia
system.
The bubble-column reactor has been used to determine the
equilibrium constant of the reaction between the absorbent and
NO by several authors.11,39,40 A bubble column is also utilized
in the present study. Because parameters for cobalt(II)
ammonia system analysis are only available at temperatures
from 295.15 and 303.15 K and for ammonium nitrate
concentrations up to 2 mol·L−1, our experiments were
conducted at temperatures close to this applicable range,
which are between 298.15 and 310.15 K. Also, we reported in
the last paper16 that low temperature favored NO absorption.
The ammonium nitrate concentration was 2 mol·L−1 for all
experiments. Because penta- and hexaamminecobalt(II) ions
■
EXPERIMENTAL SECTION
All of the chemicals mentioned herein were purchased from
Sigma-Aldrich Co. LLC. A continuous water purification
system (model S-99253-10) from Thermo Scientific Inc. was
used to produce deionized water. An oxygen-free condition is
necessary because cobalt(II) complexes are able to react with
oxygen. With this in mind, the deionized water was degassed
with pure nitrogen (Grade 4.8 from Praxair Inc.) for around 30
min before use. Because the oxidation rates of cobaltous
complexes were relatively slow without catalysts, it was
reasonable to assume that the oxidation of cobalt(II) complexes
was negligible in a short period.15 The cobalt(II) ammonia
system was prepared in a 500 mL beaker by step reversible
reactions between cobalt(II) nitrate hexahydrate [Co(NO3)2·6H2O; ACS reagent, ≥98%] and aqueous ammonia
(NH3·H2O; ACS reagent, 28−30% NH3 basis) with the
addition of 2 mol·L−1 ammonium nitrate (NH4NO3; ACS
reagent, ≥98%), which in this case was used to form a
NH4NO3/NH3·H2O buffer solution. This solution was
produced to ensure a ready supply of the NH3 ligand while
avoiding the formation of hydroxide and precipitation of cobalt
hydroxide.
For ease of operation and the acceptance of uncertainty,
calculated amounts of Co(NO3)2·6H2O and NH4NO3 based on
the desired experimental substance concentrations were
weighed by an analytical balance with a readability of 0.0001
g (model RK-11422-01 from Denver Instrument Inc.) and a
top-loading balance with a readability of 0.01 g (model RK11421-93 from Denver Instrument Inc.), respectively, and
dissolved in the 500 mL beaker placed on a stirring hot plate
(model SP142025Q from Thermo Scientific Cimarec Inc.) by
deionized water to around 100 mL. The beaker was then sealed
to isolate oxygen, and the solution was heated to a temperature
slightly higher than the desired one. The pH values of the
liquids were measured by a benchtop pH meter with an
accuracy of ±0.01 (model pH 700) manufactured by Oakton
Instruments. This pH meter had temperature compensation.
The reading was taken under mild magnetic stirring. Aqueous
ammonia was added into the solution to reach a pH value just
slightly above the desired one. Then water was used to dilute or
ammonia to concentrate alternatively, until the solution ended
up with a 300 mL volume with a pH value close to the one
desired. Because the concentration of aqueous ammonia given
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dx.doi.org/10.1021/ie302439u | Ind. Eng. Chem. Res. 2013, 52, 3663−3673
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Article
(model SS-4BMG) purchased from Swagelok Inc. The gas was
fed at a flow rate of approximately 2.60 L·min−1.
Downstream the metering valve was a three-way valve that
could be switched between bypass and gas feeding. The nitrosyl
formation reactions took place in the bubble-column reactor
mentioned above. Because of volatilization of the concentrated
aqueous ammonia, a glass bottle filled with deionized water was
placed to absorb NH3 to eliminate its interference before the
exhaust entered the gas analyzer. The NO concentrations at the
outlet were measured by a gas analyzer (model CAI 650
NOXYGEN, which had a range of 3000 ppm and a repeatability
of around 0.5% of full scale) from California Analytical
Instruments Inc. Because the CAI 650 NOXYGEN analyzer
could only work properly under atmospheric pressure, a “Tee”
conjunction was added for a pressure dump with a flow rate of
around 1 L·min−1. The analyzer required an extra air or oxygen
supply for ozone generation. A data logger was used to collect
data every 2 s. The operation terminated when the outlet
concentration reached 605 ppm or so and remained invariable,
which indicated that the reaction reached equilibrium. Experiments for determination of the equilibrium constants were
conducted at temperatures from 298.15 to 310.15 K and pH
values between 9.06 and 9.37. To validate the assumption that
only penta- and hexaamminecobalt(II) nitrates contribute to
NO absorption, a trial run was performed at pH 7.63, T =
304.15 K, a total cobalt(II) concentration of aqueous absorbent
of 0.04 mol·L−1, and a concentration of ammonium nitrate of 2
mol·L−1. The duration of a typical run varied from 13 to 28 min
depending upon the temperature and NO and absorbent
concentrations. Only one test lasted for 2.5 min in a trial run
conducted at pH 7.63. The same pH meter measured the final
pH value of the solvent used. The corresponding NO
absorption efficiency was then calculated as
by the supplier was between 28% and 30% on an NH3 basis, the
accurate volume of aqueous ammonia needed for an assigned
pH value could not be calculated. Instead, the pH value
mentioned above was used to indicate the dosage of ammonia.
Therefore, it was difficult to obtain the exact value appointed
and a value close to the desired one was accepted. In our
experiments, the pH values investigated varied from 9.06 to
9.37.
The prepared solution was then transferred to a Pyrex 500
mL bubble-column reactor with coarse-fritted cylinder
distributor (product 31770-500C from Corning Inc.). A glass
bubble-column reactor with a 29/40 standard taper stopper,
which incorporated a central vertical tube with a 12-mmdiameter coarse-fritted cylinder as the distributor in the lower
end, was used to seal the top to the base. The gas entered the
bottom of the bottle through the top of the tube in the form of
bubbles and exited via the side arm of the bottle stopper. This
coarse-fritted cylinder had a nominal pore distribution of 40−
60 μm and provided uniform dispersion of gas bubbles for
complete absorption. Most importantly, it could be conveniently seated in the water bath for temperature regulation. The
water bath (Cole-Parmer) with a temperature stability of ±0.2
K could maintain temperatures between room temperature and
373.15 K. The readout was given by a thermometer. The
concentration of total cobalt(II) was between 0.04 and 0.05
mol·L−1. The solution in the reactor was replaced by fresh
absorbent after equilibrium every time.
Figure 1 shows the experimental setup for determination of
the equilibrium constants. The operation was performed
η=
yin − yout
yin
(4)
This measured efficiency would be used in eq 25 for
[(NH3)5Co(N2O2)Co(NH3)54+]e calculation.
■
CALCULATION
As introduced above, penta- and hexaamminecobalt(II) ions are
to react with NO; therefore, the following equilibria might take
place in the cobalt(II) ammonia system.
2Co(NH3)5 (H 2O)2 + + 2NO
⇌ (NH3)5 Co(N2O2 )Co(NH3)5 4 + + 2H 2O
Figure 1. Laboratory setup for measurement of the equilibrium
constants.
(5)
2Co(NH3)6 2 + + 2NO
⇌ (NH3)5 Co(N2O2 )Co(NH3)5 4 + + 2NH3
continuously with respect to the gas phase and batchwise
with respect to the liquid phase. All gases were from Praxair Inc.
The compressed air cylinder was of grade zero for ozone
generation. In order to reduce errors, a certified 605 ppmv NO
cylinder (with an accuracy of ±2%) with a nitrogen balance was
used. A regulator relieved the deliver pressure of each cylinder
before entering the process line. The gas flow rate was
measured using a mass flow controller from the Cole-Parmer
(model S-32648-16) instrument, which had a range of 5
L·min−1 and an accuracy of ±1.5% of full scale. The flow
controller was regulated by a bellows-sealed metering valve
(6)
The equilibrium constants of reactions S6 in the SI and 5 and 6
then can be defined as41
K6 =
a{Co(NH3)62+ }ea w
a{Co(NH3)5(H2O)2+ }ea{NH3}e
5
KNO
=
3665
(7)
a{(NH3)5Co(N2O2)Co(NH3)54+ }ea w 2
a{Co(NH3)5(H2O)2+ }e 2a{NO}e 2
(8)
dx.doi.org/10.1021/ie302439u | Ind. Eng. Chem. Res. 2013, 52, 3663−3673
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6
KNO
=
Article
a{(NH3)5Co(N2O2)Co(NH3)54+ }ea{NH3}e 2
a{Co(NH3)62+ }e 2a{NO}e 2
and applicability. First, it is accepted by other researchers such
as Sada et al.,43 Onda et al.,44 Sattler and Feindt,45 and Fogg.46
Second, compared to the Pitzer model,47 the relatively simpler
form of the Bunsen coefficients to describe the solubility of NO
in an electrolyte solution makes the calculation easier.
(9)
The water activity, aw, is a measure of the energy status of the
water in a system. It can be assumed to be unity in a 2 mol·L−1
NH4NO3 solution at low ammonia concentration (less than 1
mol·L−1). This assumption will lead to erroneous results at
higher ammonia concentrations.16,18 The activity of free
ammonia is presented in terms of the activity coefficient, as
in eq 10. One way to estimate the values of the water activity
and activity coefficient of free ammonia is interpolation
according to 10 sets of experimental data obtained between
1.01 and 10.57 mol·L−1 of free ammonia in 2 mol·L−1
NH4NO3.16 These available experimental data correspond to
our experimental conditions; the interpolated values are
deemed straightforward.
a{NH3}e = [NH3]e fNH
⎛α ⎞
log⎜ ⎟ = −(k1I1 + k 2I2)
⎝ αw ⎠
where the ionic strength of a solution can be determined by
I = 1/2 ∑ cizi 2
k = x+ + x− + xG
5
KNO
=
xNH4
6
KNO
=
2
2
[NO]e =
From eqs 11−13, one can get
(20)
PTyin
(21)
H
Second, the concentration of (NH3)5Co(N2O2)Co(NH3)54+ at
equilibrium is equal to half of the amount of NO chemically
absorbed based on the stoichiometry in reactions 5 and 6. The
total amount of NO absorbed can be calculated through the
graphic integration of a NO absorption efficiency curve, which
is given by the continuous measurement of the outlet NO
concentration, using the trapezoid method.
(14)
In eq 12, the solution of K5NO necessitates the knowledge of
aw and the concentrations of NO, (NH3)5Co(N2O2)Co(NH3)54+, and Co(NH3)5(H2O)2+ at equilibrium.
The equilibrium NO concentration in water can be obtained
from its solubility in terms of Henry’s constant of NO in water,
which can be presented as42
⎡
⎛1
1 ⎞⎤
⎟⎥
H w = 526.32 exp⎢ − 1400⎜ −
⎝T
⎣
298.15 ⎠⎦
−0.1825
Then the equilibrium NO concentration in the solution is
(13)
5
6
KNO
= K 6 2KNO
xNO
0.3230
⎛H ⎞
log⎜
⎟ = k1I1 + k 2I2
⎝ Hw ⎠
2
3
[Co(NH3)6 ]e [NO]e
−0.0534
xNO3−
The Bunsen absorption coefficient is another parameter
commonly used to represent gas solubility in a liquid solution;
the conversion between the Bunsen absorption coefficient and
Henry’s Law constant can be realized by45
1 ρ
αi = 22.4
Hi M
(19)
(12)
[(NH3)5 Co(N2O2 )Co(NH3)5 ]e [NH3]e fNH
2
2+
Substituting eq 19 into 16 gives
2
[Co(NH3)5 (H 2O)2 + ]e [NO]e 2
2+
xCO
+
−0.0737
value
[(NH3)5 Co(N2O2 )Co(NH3)5 4 + ]e a w 2
4+
are summarized in Table 1.
quantity
(11)
3
xG8,43,44
Table 1. Values of x+, x−, and xG
[Co(NH3)6 2 + ]e a w
[Co(NH3)5 (H 2O)2 + ]e [NH3]e fNH
(18)
The values of x+, x−, and
Although the existence of 2 mol·L−1 NH4NO3 affects the
activities of Co(NH3)62+, Co(NH3)5(H2O)2+, and (NH3)5Co(N 2 O 2 )Co(NH 3 ) 5 4+, unlike the activity of water, this
simplification is believed to cause negligible error as proposed
by Bjerrum16 and used by Simplicio18 for absorption of oxygen
into ammoniacal cobalt(II) solutions. Therefore, the activities
of Co(NH3)62+, Co(NH3)5(H2O)2+, and (NH3)5Co(N2O2)Co(NH3)54+ can be replaced by the concentrations at
equilibrium of these three substances. Equations 7−9 can
then be rewritten as follows:
K6 =
(17)
and the salting-out parameter k is the summation of
contributions of cation, anion, and gas, respectively:
(10)
3
(16)
n = Gmyin
(15)
∫0
∞
η dt
(22)
According to the ideal gas law,
The solubility in an electrolyte solution can then be predicted
by taking the ionic strength into account. In this study, the
solution can be regarded as a mixed solution of cobaltous
nitrate and ammonium nitrate, where the concentration of
NH4NO3 is higher than that of Co(NO3)2. According to Sada
et al.43 and Onda et al.,44 the Bunsen absorption coefficient in
an electrolyte can be associated with that in water at the same
temperature by the following equation. The Bunsen coefficient
method was accepted as a compromise between simplification
Gm =
PTQ G
(23)
RT
then the amount of NO absorbed by chemical reaction is
nchem = Gmyin
∫0
∞
η dt − VL[NO]e
(24)
Then the equilibrium concentration of (NH3)5Co(N2O2)Co(NH3)54+ can be described as
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Table 2. Cobalt(II) Ammonia System at pH 7.63, T = 304.15 K, and [NH4+] = 2 mol·L−1
Co2+
Co(NH3)2+
Co(NH3)22+
Co(NH3)32+
Co(NH3)42+
Co(NH3)52+
Co(NH3)62+
4.30%
24.01%
44.38%
21.58%
5.38%
0.35%
0%
[(NH3)5 Co(N2O2 )Co(NH3)5 4 + ]e
∞
⎞
1 ⎛ Gmyin
= ⎜
η dt − [NO]e ⎟
0
2 ⎝ VL
⎠
∫
(25)
Last, the combination of Table S1 in the SI and the known
equilibrium concentration of (NH3)5Co(N2O2)Co(NH3)54+
provides the concentration of Co(NH3)5(H2O)2+ at equilibrium. The corresponding calculation is described in detail in
the SI. As a result, the value of K5NO can be obtained following
eq 12, and K6NO is then given by eq 14.
■
RESULTS AND DISCUSSION
Determination of Reactive Complexes in the Cobalt(II) Ammonia System. According to the calculation scheme
Figure 3. Uncertainties in the measured equilibrium constant K5NO
with different α values.
will dissolve into an aqueous solvent even though its solubility
is low. Because the NO concentration is in the order of parts
per million, these two contributions to the NO absorption
cannot be neglected. Therefore, it is concluded that only pentaand hexaamminecaoblt (II) nitrates in a cobalt(II) ammonia
system react with NO to form nitrosyl products.
The rationality of reversible step reactions proposed by
Bjerrum16 can be proved by findings of the trial run conducted
at pH 7.63. However, the assumption that only
hexaamminecobalt(II) existed at pH values of around 9.14
made by Mao et al. is contrary to Bjerrum’s theory. It means
that the results of the trial at pH 7.63 opposed Mao’s
assumption. Thus, the assumption made in the analyses by Mao
et al.39 needs clarifications.
Equilibrium Constants. On the basis of the aforementioned calculation scheme, the equilibrium constants of
reactions 5 and 6 at different temperatures from 298.15 to
310.15 K and pH values between 9.06 and 9.37 are tabulated in
Table S2 in the SI. It is noteworthy that there are four replicates
for each temperature. In order to eliminate experimental error,
the outliers are first detected and abandoned using Grubbs’
test48,49 at the significance level, α, of 0.1. Then, the mean of
the remaining data at each temperature is used for further
analysis. The largest ratio of standard deviation to the
corresponding mean is less than 13.6%, while most are within
5%. As for the equilibrium constant, its order of magnitude is
more practical because it is usually presented in terms of the
logarithm format. It can be seen that K5NO has an order of
magnitude of 1012 and K6NO of 1013.
It is well-acknowledged that the temperature dependence of
the chemical reaction equilibrium constant can be described by
the van’t Hoff equation.50 Specifically, this expression of
temperature dependence has also been accepted by Nymoen et
al.,40 who used FeIIEDTA to absorb NO and by Mao et al.39 for
NO control utilizing a hexamminecobalt(II) solution. Thus
Figure 2. Time series plot of the outlet NO and oxygen
concentrations (at pH 7.63, T = 304.15 K, and feeding NO
concentration = 605 ppm).
described in the SI, the cobalt(II) ammonia system for the trial
performed at pH 7.63, T = 304.15 K, and [NH4+] = 2 mol·L−1
is summarized in Table 2; it shows that complexes of
coordination numbers of less than 5 constitute 99.65% of the
system, with 0.35% of pentaamminecobalt(II) nitrate. The
ineffectiveness of small coordination number complexes can be
proved if there is no evident NO absorption taking place.
Figure 2 shows changes of the outlet NO and oxygen
concentrations with time. It can be seen that the outlet NO
concentration reaches 605 ppm in around 2.5 min. The
relatively low NO concentrations in the first minute is a result
of the existence of oxygen in the headspace at the beginning of
the test. The NO concentration is then diluted. The glass
bubble column is open to the air at each absorbent loading, and
the volume of the solution inside is 300 mL out of the 500 mL
column capacity; therefore, there may be some residual oxygen
present in the headspace.
The presence of 520 ppm NO at the 60th second could be
attributed to two factors. First, according to Table 2, the
solution still contains 0.35% of pentaamminecobalt(II) nitrate,
which can react with NO. Another possible reason is that NO
Table 3. Cobalt(II) Ammonia System at pH 9.14, T = 303.15 K, and [NH4+] = 2 mol·L−1
Co2+
Co(NH3)2+
Co(NH3)22+
Co(NH3)32+
Co(NH3)42+
Co(NH3)52+
Co(NH3)62+
0%
0%
0.21%
3.24%
25.61%
53.34%
17.60%
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Table 4. Uncertainties in Measured K5NO with Different Uβ/β Values at α = 2%
Uβ/β
UK5NO/K5NO
2%
68.2%
3%
68.4%
4%
68.6%
5%
68.8%
5
ΔH°
d ln KNO
= r 25
dT
RT
(26)
6
d ln KNO
ΔH°
= r 26
dT
RT
(27)
6%
69.2%
Δr H5° 1
+ constant 5
R T
(28)
6
ln KNO
=−
Δr H6° 1
+ constant 6
R T
(29)
Regression analysis of the experimental data gives the following
equilibrium constant equations:
5
= 3598.5
ln KNO
1
+ 16.759
T
R2 = 0.994
6
= 1476.4
ln KNO
(30)
1
+ 26.597
T
2
R = 0.970
⎛ 1476.4 ⎞
6
⎟
= 3.56 × 1011 exp⎜
KNO
⎝ T ⎠
(33)
10%
71.0%
(34)
They provide values of the standard enthalpy of reaction:
ΔrH5° = −29.92kJ·mol−1 and ΔrH6° = −12.27kJ·mol−1, which
means that these two reactions are exothermic in nature. It
indicates that high temperatures are not favorable to the
removal of NO using ammoniacal cobalt(II) solutions. This is
consistent with the experimental findings in our earlier
5
publication.15 Then, the temperature dependences of KNO
6
and KNO can be given by
(32)
9%
70.5%
Co(NH3)6 2 + + NO ⇌ [(NH3)5 Co(NO)]2 + + NH3
(31)
⎛ 3598.5 ⎞
5
⎟
KNO
= 1.90 × 107 exp⎜
⎝ T ⎠
8%
70.0%
(yet without a known concentration) when preparing the
ammoniacal cobalt(II) solutions. They assumed that the end
product of ammonical cobalt(II) complexes was
hexaamminecobalt(II) alone, but according to the calculation
procedure described in the SI, the complex distribution in a
solution at pH 9.14, T = 303.15 K, and [NH4+] = 2 mol·L−1 is
tabulated in Table 3. It can be seen that the largest contributor
is the pentaamminecobalt(II) ion, which is 53.34%, whereas the
hexaamminecobalt(II) ion only accounts for 17.60%, less than
25.61% of the tetraamminecobalt(II) ion. Therefore, the
assumption made by Mao et al.39 that the end product was
hexaamminecobalt(II) alone seemed problematic, unless
otherwise they prepared the absorbent in a different way,
which was not explicitly mentioned.
Second, the molecular structure of generated nitrosyl
proposed by them is different from ours. They reported that
the product of the reaction between the hexamminecobalt(II)
ion and NO is a monomer, [Co(NH3)5NO]2+, in reaction 34,
while we believe that the nitrosyl is more likely to be a dicobalt
μ-hyponitrite complex with the formula [(NH3)5Co(NO)2Co(NH3)5]4+ in reaction 6.
Integration of eqs 26 and 27 gives
5
ln KNO
=−
7%
69.5%
As mentioned above, high temperature (room temperature
or above) favors the formation of a red series nitrosyl
compound.22,24 Many previous investigations proved the
molecular structure of the red series as μ-hyponitrite dimeric
formulation [(NH3)5Co(NO)2Co(NH3)5]4+ from various
aspects. Feltham28 reported that the red salt was a 4:1
electrolyte in the form of [(NH3)5Co(NO)2Co(NH3)5]X4 by
conductivity measurement. Mercer et al.31 stated that a dimeric
structure had been definitely assigned to the red isomer
through IR and chemical investigation. The crystal structure
reported by Hoskins and Whillans32,34 showed that the red
nitrosyl ion was binuclear: the two crystallographically
independent cobalt atoms, each surrounded by five ammonia
molecules, were bridged asymmetrically through a hyponitrite
ion. Raynor37 determined the red nitrosylpentaammines of
cobalt as [(NH3)5Co(NO)2Co(NH3)5]4+ with a trans hyponitrite bridging group and a metal−nitrogen bond from IR
evidence. Recently, Chacon Villalba et al.36 confirmed the red
nitrosyl compound as [(NH3)5Co(NO)2Co(NH3)5]4+ once
more by X-ray diffraction methods. Hence, the square of [NO]e
is present in the denominator in our study instead of [NO]e.
Because [NO]e is in the order of 10−7 mol·L−1, our result is in
the order of 1013 instead of 104.
In addition, omission of the temperature dependence on
Henry’s constant, as shown in eq 15, and negligence of the
effect of the ionic strength on the NO solubility, as described in
eq 20, might also lead to the difference.
Although our study gives acceptable results regarding the
equilibrium constants of reactions between NO and ammoniacal cobalt(II) complexes, the accuracy can be further enhanced
by direct measurement of the corresponding concentrations at
equilibrium with liquid-phase Fourier transform IR spectroscopy. It may reduce uncertainties caused by the empirical
constants adopted in the concentration calculation scheme.
These two equations can be used to calculate the equilibrium
constant at certain temperatures between 298.15 and 309.15 K.
In literature available to the public, the authors only found
that Mao et al.39 had measured the equilibrium constants of the
reaction between NO and the hexaamminecobalt(II) ion in the
temperature interval from 303.15 to 353.15 K at pH 9.14.
Although our experimental setup is similar to theirs, the results
are quite different. At a temperature of 303.15 K, for example,
the calculated value of K6NO using eq 33 in our study is 4.63 ×
1013 L·mol−1, whereas that computed according to Mao et al.39
is 5.16 × 104 L·mol−1. The main causes of this difference are as
follows.
First, they ignored the analysis of the cobalt(II) ammonia
system and thus did not consider the contribution of the
pentaamminecobalt(II) ion to NO absorption. Nevertheless,
the rationality of using the method established by Bjerrum16 to
analyze the compound composition of a solution containing a
cobalt(II) ion and aqueous ammonia in high-concentration
ammonium salt was proven in the last subsection and by other
researchers.17−19 Likewise, Mao et al. added ammonium salt
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2
⎛ UH ⎞2 ⎛ UHw ⎞
⎜
⎟ = ⎜
⎟ + 5.3(I1Uk1)2 + 5.3(k1UI1)2
⎝H⎠
⎝ Hw ⎠
Uncertainty Analysis. Because of the complexity of this
experimental system, only general uncertainty analysis that
contains propagation of bias errors is elaborated on in this
section. In general, a data reduction equation, as described in eq
35, for determination of the experimental result, r, from N
measured variables Xi is needed for an uncertainty analysis.
r = r(X1 , X 2 , ..., XN )
+ 5.3(I2Uk 2)2 + 5.3(k 2UI2)2
Equation 41 shows that the uncertainty in H depends not only
on the uncertainties in Hw, k1, I1, k2, and I2 but also on the
values of k1, I1, k2, and I2. According to Table 1 and eq 18, k
values for NH4NO3 and Co(NO3)2 are 0.0668 and 0.0871,
respectively.
Propagation of the uncertainty in salting-out parameters to k
described in eq 18 is expressed as
(35)
Then the uncertainty in the result is given by eq 36.51,52
⎛ ∂r
⎞2
⎞2
⎞2 ⎛ ∂r
⎛ ∂r
UX1⎟ + ⎜
UX 2⎟ + ... + ⎜
UXN ⎟
Ur 2 = ⎜
⎠
⎝ ∂X 2
⎠
⎝ ∂X1
⎝ ∂XN
⎠
Uk 2 = Uxc 2 + Uxa 2 + UxG 2
(36)
⎞2
⎞2 ⎛ 1 ∂r
⎛ Ur ⎞2 ⎛ 1 ∂r
⎜
⎟ = ⎜
UX ⎟ + ⎜
UX 2⎟ +
⎝r ⎠
⎠
⎝ r ∂X 2
⎝ r ∂X1 1⎠
(37)
Specifically, the uncertainty of K5NO described in eq 12 can be
presented in eq 38, in which A denotes [(NH3)5Co(N2O2)Co(NH3)54+]e and B denotes [Co(NH3)5(H2O)2+]e for the
ease of presentation.
⎛ UK 5 ⎞
⎛ U[NO]e ⎞
⎛ Ua ⎞
⎛U ⎞
⎛U ⎞
⎜ 5NO ⎟ = ⎜ A ⎟ + 4⎜ w ⎟ + 4⎜ B ⎟ + 4⎜
⎟
⎝A⎠
⎝ B⎠
⎝ aw ⎠
⎝ [NO]e ⎠
⎝ KNO ⎠
2
2
2
2
2
It can be seen from the right-hand side of eq 38 that the
uncertainties of A, aw, B, and [NO]e are needed. aw is the value
of the water activity experimentally given by Bjerrum;16
however, information of its uncertainty is unavailable. It is
well-accepted that a reasonable assumption can be made if an
uncertainty in quantity is unknown and/or unachievable. In the
case where multiple uncertainties in quantities are unobtainable, it is natural and universal to assign the same value to all
unknown uncertainties if possible.51 The uncertainty in aw is set
to be a variable α% herein, and all of the unknown uncertainties
hereafter in this section will be assumed to be α % for
simplicity.
Uncertainty in [NO]e. The uncertainty in [NO]e presented
in eq 21 can be given by
⎛ U[NO]e ⎞
⎛ UP ⎞2 ⎛ Uy ⎞
⎛ U ⎞2
⎜
⎟ = ⎜ T ⎟ + ⎜⎜ in ⎟⎟ + ⎜ H ⎟
⎝H⎠
⎝ PT ⎠
⎝ [NO]e ⎠
⎝ yin ⎠
(43)
I2 = 3c 2
(44)
⎛ UI1 ⎞2 ⎛ Uc1 ⎞2
⎜ ⎟ =⎜ ⎟
⎝ c1 ⎠
⎝ I1 ⎠
(45)
⎛ UI2 ⎞2 ⎛ Uc2 ⎞2
⎜ ⎟ =⎜ ⎟
⎝ c2 ⎠
⎝ I2 ⎠
(46)
The concentrations of NH4NO3 and Co(NO3)2 are
calculated by measured compound mass and solution volume,
as shown in eq 47.
m
c=
MVL
(47)
Propagation of the uncertainties in m, M, and VL to the
concentration can be written as
2
⎛ Uc ⎞2 ⎛ Um ⎞2 ⎛ UM ⎞2 ⎛ UVL ⎞
⎟ + ⎜
⎜
⎟ = ⎜
⎟ + ⎜
⎟
⎝M⎠
⎝c⎠
⎝m⎠
⎝ VL ⎠
(48)
The repeatability of ±0.02 g is provided by Denver
Instrument Inc. to the top-loading balance for the weighing
of NH4NO3. A repeatability of ±0.0002 g is also provided by
the manufacturer to the analytical balance for the weighing of
Co(NO3)2·6H2O. They can be taken as reasonable estimates of
the uncertainty. All of the glassware is from Corning Inc., and
5% is given as the bias limit of the volume. It is noted that the
values of universal constants such as molecular weight, gas
constant, etc., are known with a much greater accuracy than the
measurements made in most experiments. So, it is justifiable to
assume that the uncertainties in such quantities are negligible.
Assuming that UM is zero and substituting it into eq 48 gives
2
(39)
The uncertainty in the total pressure PT, which is atmospheric
pressure, can be assumed to be zero. The uncertainty in yin of
2% was given by the gas supplier Praxair Inc. The uncertainty in
H is derived as follows.
Rewriting eq 20 gives
H = H w × 10k1I1+ k 2I2
I1 = c1
Thus,
(38)
2
(42)
Values of xc, xa, and xG are available in the literature without
uncertainty; it is assumed again that Uxc/xc = Uxc/xa = UxG/xG =
α % for further calculation.
The valence of the ion for a given electrolyte solution is
constant with an uncertainty of zero. Substituting the value of
the ion valence in eq 17 gives eqs 43 and 44 for the ionic
strengths of NH4NO3 and Co(NO3)2, respectively. For
simplicity, the subscripts are defined as 1 = NH4NO3 and 2
= Co(NO3)2.
Dividing both sides of eq 36 by the square of the
experimental result, r, gives,
⎛ 1 ∂r
⎞2
... + ⎜
UXN ⎟
⎝ r ∂XN
⎠
(41)
(40)
2
⎛ Uc ⎞2 ⎛ Um ⎞2 ⎛ UVL ⎞
⎜
⎟ = ⎜
⎟ + ⎜
⎟
⎝c⎠
⎝m⎠
⎝ VL ⎠
Then the uncertainty in H is described in the following
equation:
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2
⎛ Uy ⎞2 ⎛ UV ⎞2
⎛ UA ⎞2 ⎛ UGm ⎞
⎜
⎟ = ⎜
⎟ + ⎜⎜ in ⎟⎟ + ⎜ L ⎟
⎝A⎠
G
⎝ m⎠
⎝ VL ⎠
⎝ yin ⎠
UHw is needed to determine UH. The temperature dependence on Henry’s law constant of gas into water can be
expressed as42
⎡
⎛1
1 ⎞⎤
⎟⎥
H w = C1 exp⎢ −C2⎜ −
⎝T
⎣
298.15 ⎠⎦
⎛ Uη + 2Uη + ... + 2Uη + Uη ⎞2
2
N
N+1
⎟⎟
+ ⎜⎜ 1
⎝ η1 + 2η2 + ... + 2ηN + ηN + 1 ⎠
(50)
As mentioned above, Uyin/yin = 2% is provided by Praxair, and
UVL/VL = 5% by Corning Inc.
The uncertainty in Gm is computed based on eq 23.
It can be seen from eq 11 that C1 = 526.32 and C2 = 1400 for
NO. The uncertainties of these two empirical constants are
unknown and are assumed to be α % too. Then the uncertainty
of Hw can be described in eq 51.
2
⎛ UP ⎞2 ⎛ U ⎞2 ⎛ U ⎞2
⎛ UGm ⎞2 ⎛ UQ G ⎞
⎟⎟ + ⎜ T ⎟ + ⎜ R ⎟ + ⎜ T ⎟
⎟ = ⎜⎜
⎜
⎝T ⎠
⎝R⎠
⎝ PT ⎠
⎝ Gm ⎠
⎝ QG ⎠
2
⎛ UHw ⎞
⎛ UC ⎞
⎡⎛ 1
1⎞ ⎤
− ⎟UC2 ⎥
⎜
⎟ = ⎜ 1 ⎟ + ⎢⎜
⎣⎝ 298.15
T⎠ ⎦
⎝ C1 ⎠
⎝ Hw ⎠
2
2
+ (C2T −2UT )2
2
⎛ UGm ⎞2 ⎛ UQ G ⎞
⎛ U ⎞2
⎟⎟ + ⎜ T ⎟
⎟ = ⎜⎜
⎜
⎝T ⎠
⎝ Gm ⎠
⎝ QG ⎠
2
Uη = (yout yin
t
where N = e
Δt
(52)
A=
2VL
(58)
⎛ f ⎞5
2+
= K1K 2K3K4K5[NH3] ⎜
⎟ [Co(H 2O)6 ]
a
⎝ w ⎠
5 ⎜ NH3 ⎟
(59)
The uncertainty in [Co(NH3)5(H2O)2+]e is then given by
following equation where B = [Co(NH3)5(H2O)2+]e.
(53)
2
⎛ UK ⎞2 ⎛ UK ⎞2 ⎛ UK ⎞2
⎛ UB ⎞2 ⎛ UK1 ⎞
⎜
⎟ = ⎜
⎟ + ⎜ 2⎟ + ⎜ 3⎟ + ⎜ 4⎟
⎝ B⎠
⎝ K2 ⎠
⎝ K1 ⎠
⎝ K3 ⎠
⎝ K4 ⎠
⎛ U f ⎞2
⎛ UK5 ⎞2
⎛ U[NH3] ⎞2
NH3
⎟
+⎜
⎟ + 25⎜
⎟ + 25⎜⎜
⎟
f
⎝ K5 ⎠
⎝ [NH3] ⎠
⎝ NH3 ⎠
⎛ Ua ⎞2 ⎛ U[Co(H2O)62+ ] ⎞2
⎟
+ 25⎜ w ⎟ + ⎜
2+
⎝ aw ⎠
⎝ [Co(H 2O)6 ] ⎠
(η1 + 2η2 + ... + 2ηN + ηN + 1)
t
where N = e
2
⎛ 1
⎞2
Uy ) + ⎜⎜ − Uy ⎟⎟
in
⎝ yin out⎠
2
[Co(NH3)5 (H 2O)2 + ]e
Further simplification of eq 53 is performed by neglecting
[NO]e because the value of [NO]e is much less than the first
item in the braces. Besides, in the calculation, Δt is equal to 2 s,
which is a constant. So, the uncertainty of time interval Δt is
zero. The data reduction expression of A then becomes
Gmyin
−2
where Uyin/yin = 2%, and Uyout is 0.5% of full scale provided by
CAI Inc.
Uncertainty in [Co(NH3)5(H2O)2+]e. According to eqs S7−
S12 in the SI, the data reduction equation of [Co(NH3)5(H2O)2+]e is presented as
1 ⎧ Gmyin Δt
⎨
(η1 + 2η2 + ... + 2ηN + ηN + 1)
2 ⎩ 2VL
⎫
− [NO]e ⎬
⎭
(57)
According to product specifications given by manufacturers,
the uncertainty in QG is 1.5% of full scale. Recall that UT = 0.5
K. The uncertainty in the NO removal efficiency η is calculated
by propagation of the uncertainties in yin and yout, as shown in
following equation.
Rearranging and combining terms give
A=
(56)
It is well-acknowledged that quantities like the atmospheric
pressure and gas constant are quite accurate, and their
uncertainties can be assumed to be zero. Then eq 56 further
transforms into
(51)
A comparison between the readings of the thermometer and
a calibrated thermal couple shows a difference of less than 0.5
K. In the absence of any other information, it is assumed that
UT = 0.5 K.
Uncertainty in [(NH3)5Co(N2O2)Co(NH3)54+]e. The data
reduction expression of [(NH3)5Co(N2O2)Co(NH3)54+]e, as
shown in eq 25, is very complex because of the presence of the
integral item. The partial derivative with respect to η is difficult
to obtain. In practice, the calculation of the integral item is
graphically solved by using the trapezoid method. The time for
the reaction to reach equilibrium is discretized into grids with
an interval of 2 s (which is the sampling interval). Then eq 25
can be numerically rewritten as in eq 52, in which A =
[(NH3)5Co(N2O2)Co(NH3)54+]e for ease of presentation.
i=1
⎫
⎧
⎞
⎪
1 ⎪ Gmyin ⎛
1
⎜
⎟
⎬
(
)
[NO]
t
A= ⎨
∑
η
+
η
Δ
−
e
⎜
⎟
i
i+1
⎪
⎪
2 ⎩ VL ⎝ N 2
⎠
⎭
t
where N = e
Δt
(55)
(60)
Because there is no information on the uncertainties in
empirical constants K1, K2, K3, K4, K5, f NH3, and aw, it is
assumed that UK1/K1 = UK2/K2 = UK3/K3 = UK4/K4 = UK5/K5 =
Uf NH3/f NH3 = Uaw/aw = α %.
(54)
Propagation of the uncertainties of the quantities in the righthand side of eq 54 to A is then described as
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The uncertainty in [Co2+]T can be estimated by eq 49, and
that in A has already been elaborated on above. It is shown that
the data reduction expression of quantity β is very complex and
the task of obtaining the partial derivatives in eq 67 is tedious.
In order to continue the uncertainty analysis of the equilibrium
constant, it is assumed that Uβ/β = 2α % to avoid the timeconsuming calculations. This simplification will then be
validated by examining the sensitivity of Uβ/β to the ultimate
UK5NO/K5NO. Eventually, all of the unknown variables in eq 38 can
be determined.
As an example, Figure 3 shows the uncertainties in the
5
measured equilibrium constant of reaction 5, KNO
, with
2+
different assumed α values at T = 298.2 K, [Co ]T = 0.04
mol·L−1, and pH 9.23. It can be seen that UK5NO/K5NO greatly
depends on the assumed uncertainty in the empirical constant,
α %. The smallest UK5NO/K5NO of 57.3% is given at α = 0, under
which none of the empirical coefficients contributes to the
ultimate uncertainty in K5NO. As α value increases from 0 to 6%,
the uncertainty in K5NO (UK5NO/K5NO) rapidly rises from 57.3 to
126.9%. The sensitivity of Uβ/β to UK5NO/K5NO at α = 2% is
summarized in Table 4. The uncertainty in K5NO slightly
increases from 68.2% to 71.0%, with the uncertainty in β
increasing from 2% (=α) to 10% (=5α). Therefore, it can be
5 /K 5
concluded that the effect of Uβ/β) on (UKNO
NO is
insignificant, which justifies the assumption of Uβ/β = 2α.
The data reduction expression for [NH3] is shown in eq S14
in the SI. Thus, the corresponding uncertainty in [NH3] is
shown as follows:
2
⎛ U[NH3] ⎞2 ⎛ Uk NH4+ ⎞
⎛ U + ⎞2 ⎛ U + ⎞2
⎟⎟ + ⎜ [NH4+] ⎟ + ⎜ [H+ ] ⎟
⎜
⎟ = ⎜⎜
⎝ [H ] ⎠
⎝ [NH3] ⎠
⎝ [NH4 ] ⎠
⎝ k NH4+ ⎠
(61)
As usual, the assumption of UkNH4+/kNH4+ = α % is made, and
U[NH4+]/[NH4+] is calculated by using eq 49.
The concentration of the hydrogen ion in the aqueous
solution is calculated using a pH value measured by an Oakton
pH meter in eq S13 in the SI. Hence, the uncertainty in [H+] is
described as
⎛ U[H+] ⎞2
2
⎜ + ⎟ = ( −ln 10 × UpH)
⎝ [H ] ⎠
(62)
The specification of the pH meter (model pH-700) gives UpH =
0.01.
From eq 60, one can see that the uncertainty in B
necessitates the knowledge of uncertainty in [Co(H2O)62+].
The achievement of the data reduction expression for
[Co(H2O)62+] is summarized as follows. According to the
mass balance of Co2+,
■
i=1
2+
2+
[Co ]T = [Co(H 2O)6 ] +
∑ [Co(NH3)i (H2O)6 − i 2 + ]
CONCLUSIONS
Analysis of the cobalt(II) ammonia system for solutions
containing cobalt(II) nitrate, ammonium hydroxide, and 2
mol·L−1 ammonium nitrate is reviewed. The characteristics of
reactions between NO and ammoniacal cobalt(II) complexes
are analyzed through the molecular structure of the
corresponding nitrosyl. It is validated that only penta- and
hexaamminecobalt(II) complexes have the ability to react with
NO, as shown in reactions 5 and 6. Moreover, the equilibrium
constants of such reactions are determined. K5NO has an order of
magnitude of 1012 and K6NO of 1013. All experimental data fit eqs
30 and 31 well.
6
4+
+ 2[(NH3)5 Co(N2O2 )Co(NH3)5 ]e
(63)
As defined in eqs S7−S12 in the SI, the concentration of
different ammoniacal cobalt(II) complexes is a function of
[Co(H2O)62+] and
[Co(NH3)i (H 2O)6 − i 2 + ]
j=1
⎛ f ⎞i
i ⎜ NH3 ⎟
2+
= ∏ Kj[NH3] ⎜
⎟ [Co(H 2O)6 ]
a
⎝ w ⎠
i
i = 1−6
■
(64)
Substituting eq 64 into eq 63 gives the data reduction
expression of [Co(H2O)62+].
S Supporting Information
*
Step reversible reactions involved in the cobalt(II) ammonia
system, calculated equilibrium constants at NO = 605 ppm,
[NH4NO3] = 2 mol·L−1, and A = NH3 based on cobalt(II)
ammonia analysis, detailed absorbent system information for
each run, and analysis of the cobalt(II) ammonia system. This
material is available free of charge via the Internet at http://
pubs.acs.org.
2+
[Co(H 2O)6 2 + ] =
[Co ]T − 2A
β
(65)
where
A = [(NH3)5 Co(N2O2 )Co(NH3)5 4 + ]e
⎫
⎧ j=1
⎛ f ⎞i ⎪
⎪
i ⎜ NH3 ⎟
⎨
⎬
β = 1 + ∑ ∏ Kj[NH3] ⎜
⎟
⎪
⎝ aw ⎠ ⎪
6 ⎩ i
⎭
(66)
■
i=1
The uncertainty in
[Co(H2O)62+]
ASSOCIATED CONTENT
AUTHOR INFORMATION
Corresponding Author
(67)
*Phone: (519) 888-4567 ext. 38723. E-mail: h48yu@
uwaterloo.ca.
is then described as
Notes
⎛ U[Co(H O) 2+ ] ⎞2
2
6
⎟
⎜
2+
⎝ [Co(H 2O)6 ] ⎠
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The authors acknowledge financial support provided by the
Natural Sciences and Engineering Research Council of Canada
(NSERC) Collaborative Research and Development Program
⎞2 ⎛ Uβ ⎞2
⎛
⎞2
⎛
U[Co2+]T
UA
⎟ +⎜ ⎟
⎜
⎟
4
=⎜
+
2+
2+
⎝β⎠
⎝ [Co ]T − 2A ⎠
⎝ [Co ]T − 2A ⎠
(68)
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dx.doi.org/10.1021/ie302439u | Ind. Eng. Chem. Res. 2013, 52, 3663−3673
Industrial & Engineering Chemistry Research
Article
Abbreviations
and Imperial Oil Ltd. The authors also thank Chao Yan for
assistance in data collection.
A
CAA
FGT
NO
NOx
■
NOMENCLATURE
a
activity of substance
c, [ ] concentration, mol·L−1
f NH3 activity coefficient of ammonia
Gm total molar flow rate of gas, mol·s−1
H
Henry’s law constant, L·atm·mol−1
I
ionic strength, mol·L−1
k
salting-out parameter, L·mol−1
K
equilibrium constant, L·mol−1 or L3·mol−3
m
mass, g
M
molar mass of the solution, g·mol−1
n
amount of NO absorbed, mol
P
pressure, atm
Q
flow rate, L·s−1
r
experimental result
R
universal gas constant = 0.08205 L·atm·K−1·mol−1 =
8.314 J·K−1·mol−1
t
time, s
T
temperature, K
Ur
uncertainty in the experimental result
UXi uncertainty in the measured variable Xi
V
volume, L
x
contribution to the salting-out parameter, L·mol−1
Xi
ith measured variables
y
concentration of NO in the gas phase, ppm
z
ionic valency
■
NH3
Clean Air Act
flue gas treatment
nitric oxide
nitrogen oxide
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Greek Letters
Bunsen absorption coefficient, cm3 of gas·cm−3 of
solution, significance level of Grubbs’ testing, or
assumed uncertainty in quantity
β
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η
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ρ
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Superscripts
° ground state at which ammonium nitration concentration =
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5 reaction between pentaamminecobalt(II) nitrate and NO
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Subscripts
1
2
5
NH4NO3, in eqs 16 and 20
Co(NO3)2, in eqs 16 and 20
reaction between pentaamminecobalt(II) nitrate and
NO
6
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T
total
w
water
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−
anion
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