Determination of Equilibrium Constants for Reactions between Nitric

Article pubs.acs.org/IECR

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

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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 3664

dx.doi.org/10.1021/ie302439u | Ind. Eng. Chem. Res. 2013, 52, 3663−3673

Industrial & Engineering Chemistry Research

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.

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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)


Industrial & Engineering Chemistry Research 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 3666



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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.

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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 3668



Article 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: 3669

(49)



Article 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 3670



Article

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) 3671



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

REFERENCES

(1) U.S. EPA. Nitrogen oxides (NOx), why and how they are controlled; EPA-456/F-99-006R; U.S. Environmental Protection Agency: Research Triangle Park, NC, 1999. (2) U.S. EIA. Electric power annual 2008; DOE/EIA-0348(2008); U.S. Government Printing Office: Washington, DC, 2010. (3) WBG. Pollution prevention and abatement handbook; 19128; U.S. Government Printing Office: Washington, DC, 1998. (4) Pham, E. K; Chang, S. G. Removal of NO from flue gases by absorption to an iron(II) thiochelate complex and subsequent reduction to ammonia. Nature 1994, 369, 139−141. (5) Reese, J. L. State of art of NOx emission control technology. ASME Joint International Power Generation Conference, Phoenix, AZ, 1994. (6) Perlmutter, H. D.; Ao, H. H.; Shaw, H. Absorption of NO promoted by strong oxidizing agentsorganic tertiary hydroperoxides in n-hexadecane. Environ. Sci. Technol. 1993, 27, 128−133. (7) Roy, S.; Hegde, M. S.; Madras, G. Catalysis for NOx abatement. Appl. Energy 2009, 86, 2283−2297. (8) Sada, E.; Kumazawa, H.; Hayakawa, N.; Kudo, I.; Kondo, T. Absorption of NO in Aqueous Solutions of KMnO4. Chem. Eng. Sci. 1977, 32, 1171−1175. (9) Sada, E.; Kumazawa, H.; Kudo, I.; Kondo, T. Absorption of lean NOx in aqueous solutions of NaClO2 and NaOH. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 275−278. (10) Sada, E.; Kumazawa, H.; Kudo, I.; Kondo, T. Absorption of NO in aqueous mixed solutions of NaClO2 and NaOH. Chem. Eng. Sci. 1978, 33, 315−318. (11) Teramoto, M.; Hiramine, S. I.; Shimada, Y.; Sugimoto, Y.; Teranishi, H. Absorption of dilute nitric monoxide in aqueous solutions of Fe(II)-EDTA and mixed solutions of Fe(II)-EDTA and Na2SO3. J. Chem. Eng. Jpn. 1978, 11, 450−457. (12) Long, X. L.; Cheng, H.; Yuan, W. K. Reduction of Hexamminecobalt(III) Catalyzed by Coconut Activated Carbon. Environ. Prog. Sust. Energy 2010, 29, 85−92. (13) Long, X. L.; Xiao, W. D.; Yuan, W. K. Removal of nitric oxide and sulfur dioxide from flue gas using a hexamminecobalt(II)/iodide solution. Ind. Eng. Chem. Res. 2004, 43, 4048−4053. (14) Long, X. L.; Xiao, W. D.; Yuan, W. K. Simultaneous absorption of NO and SO2 into hexamminecobalt(II)/iodide solution. Chemosphere 2005, 59, 811−817. (15) Yu, H. S.; Zhu, Q. Y.; Tan, Z. C. Absorption of nitric oxide from simulated flue gas using different absorbents at room temperature and atmospheric pressure. Appl. Energy 2012, 93, 53−58. (16) Bjerrum, J. Metal ammine formation in aqueous solution; P. Haase and Son: Copenhagen, Denmark, 1957. (17) Yatsimirskii, K. B.; Volchenskova, I. I. Absorption spectra and band type in Co(II) aquoamino complexes. Theor. Exp. Chem. 1968, 6, 808−815. (18) Simplicio, J.; Wilkins, R. G. Uptake of Oxygen by Ammoniacal Cobalt(II) Solutions. J. Am. Chem. Soc. 1969, 91, 1325−1329. (19) Ji, X. B.; Buzzeo, M. C.; Banks, C. E.; Compton, R. G. Electrochemical response of cobalt(II) in the presence of ammonia. Electroanalysis 2006, 18, 44−52. (20) Ford, P. C.; Lorkovic, I. M. Mechanistic aspects of the reactions of nitric oxide with transition-metal complexes. Chem. Rev. 2002, 102, 993−1017. (21) Asmussen, R. W.; Bostrup, O.; Jensen, J. P. The Magnetic Properties of [Co(NH3)5(NO)]Cl2 (Black) and [Co(NH3)5(NO)](NO3)2.1/2H2O (Red)Studies in Magnetochemistry. 21. Acta Chem. Scand. 1958, 12, 24−30.

Greek Letters

Bunsen absorption coefficient, cm3 of gas·cm−3 of solution, significance level of Grubbs’ testing, or assumed uncertainty in quantity β quantity defined in eq 67 η NO absorption efficiency ρ density of the solution, kg·m−3 ΔrH° reaction enthalpy, kJ·mol−1 α

Superscripts

° ground state at which ammonium nitration concentration = 0 and T = 303.15 K 5 reaction between pentaamminecobalt(II) nitrate and NO 6 reaction between hexaamminecobalt(II) nitrate and NO 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 reaction between hexaamminecobalt(II) nitrate and NO chem chemical absorption e equilibrium state G gas i ith species in inlet L liquid n number of reactions, n = 1−6, unless otherwise stated NO nitric oxide out outlet phy physical T total w water + cation − anion 3672



Article

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