Absorption of Nitric Oxide into Aqueous Solutions of Ferrous Chelates

Nov 3, 1997 - The absorption leads to stable ferrous NO chelates. ... At elevated T, (DFe(II)chelate/DNO)1/2 decreases due to the ...... The authors t...
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Ind. Eng. Chem. Res. 1997, 36, 4914-4927

Absorption of Nitric Oxide into Aqueous Solutions of Ferrous Chelates Accompanied by Instantaneous Reaction J. F. Demmink, I. C. F. van Gils, and A. A. C. M. Beenackers* Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

The absorption of nitric oxide (NO) into aqueous solutions of ferrous chelates of nitrilotriacetic acid (NTA), ethylenediaminetetraacetic acid (EDTA), hydroxyethylenediaminetriacetic acid (HEDTA), and diethylenetriaminepentaacetic acid (DTPA) was studied in a stirred cell reactor. Experimental conditions were as follows: 0.05 e CFe(II)L e 0.1 kmol/m3, 8 e PNO e 30 kPa, 3 e pH e 10 (NTA), or 7 e pH e 8 (EDTA, HEDTA, DTPA), CL e CFe(II) e 3CL (NTA) or CL ) CFe(II) (EDTA, HEDTA, DTPA), and 293 e T e 333 K (NTA, EDTA, HEDTA) or T ) 294 K (DTPA). The absorption leads to stable ferrous NO chelates. Due to the high reaction rate, in combination with the relatively high PNO applied, the absorption rate is strongly affected by mass transfer limitation only. By applying penetration theory, the ratio of the diffusion coefficients of ferrous chelates and NO was determined: at T ) 294 K, (DFe(II)chelate/DNO)1/2 ) 0.44 ( 0.01, 0.34 ( 0.01, 0.36 ( 0.01, and 0.31 ( 0.015, for the ferrous NTA, HEDTA, EDTA, and DTPA complexes, respectively. At elevated T, (DFe(II)chelate/DNO)1/2 decreases due to the unusual T-dependency of DNO. For ferrous NTA, the formation of the ferrous NO chelate is accompanied by pH effects that can be understood from iron chelate chemistry. In the case of ferrous NTA, pH < 5, or an excess of ligand, these effects lead to local pH gradients at the gas-liquid interface, that substantially affect the NO absorption rates. Kinetic data from the literature on the absorption of NO into ferrous chelates were evaluated using the mass transfer parameters determined. These kinetic data are often unreliable. 1. Introduction Aqueous solutions of iron chelates have found widespread application as catalysts in gas purification processes. Well-known is the oxidative absorption of hydrogen sulfide (H2S) into aqueous solutions of ferric chelates (Wubs and Beenackers, 1994; Demmink et al., 1994; Oostwouder and Hodge, 1995). Another application is the reactive absorption of nitric oxide, NO, into aqueous solutions of ferrous chelates (for instance, Tsai et al., 1989; also see Table 1):

NO(g) a NO(aq) K1

NO(aq) + Fe2+Ln- {\} Fe2+Ln-NO

(1)

Here Ln- stands for an organic ligand, usually ethylenediaminetetraacetic acid (EDTA), hydroxyethylenediamine triacetic acid (HEDTA), diethylenetriaminepentaacetic acid (DTPA), or nitrilotriacetic acid (NTA). The function of the ligand is twofold. It prevents precipitation of ferrous hydroxide and strongly stabilizes the NO complex Fe2+Ln-NO. Table 2 shows that the stability constant of equilibrium reaction 1 increases by a factor of 104 when the ferrous ion is chelated by EDTA or NTA. Removal of NO by ferrous chelates has been considered particularly interesting in the presence of sulfur dioxide (SO2), as is often the case in flue gas, since sulfite (SO32-) and bisulfite (HSO3-) are known to react with ferrous NO complexes. In early studies (for instance, Teramoto et al., 1978; Sada et al., 1984) it was attempted to convert NO to N2:

2Fe2+Ln-NO + 2SO32- f 2Fe2+Ln- + N2 + 2SO42- (2) * To whom correspondence may be addressed. S0888-5885(97)00280-7 CCC: $14.00

However, more recent literature (for instance Weisweiler et al., 1986; Sada et al., 1988; Zang and van Eldik, 1989, 1990a, 1993; Littlejohn and Chang, 1990) emphasizes that a large number of undesired species, such as N2O and N-S compounds, like HON(SO3)22-, are the main products instead. Weisweiler et al. (1986) even explicitly exclude the formation of N2. Also, undesired oxidation of ferrous chelates due to sulfite ions occurs (Weisweiler et al., 1986; Sada et al., 1988; Zang and van Eldik, 1989, 1990a, 1993; Littlejohn and Chang, 1990). Buisman et al. (1996) claim a solution to the above problems in a patent, which describes the simultaneous removal of SO2 and NO by aqueous solutions of ferrous EDTA, in combination with nitrate-reducing bacteria. They claim N2 to be the main nitrogen product, formed according to reaction 2, where, in the absence of SO2, sulfite may be replaced by other electron-donating compounds, such as ethanol, H2, or any reducing sulfur compound, for instance sulfide, sulfur, thiosulfate, or polythionates. The application of ferrous chelates in a biochemical system is particularly interesting if, in a separate vessel, sulfate-reducing bacteria are used to convert SO2 to solid sulfur particles. Undesired oxidation of ferrous chelates may be regenerated by ironreducing bacteria. No information on the combined biochemical/ferrous EDTA system is available in the open literature, and therefore the above claims cannot be verified. Recent studies by Pham and Chang (1994), Shi et al. (1996b), Shi et al. (1996c), and Shi et al. (1996a) mention thiochelate 2,3-dimercapto-1-propanesulfonate (DMPS) as a more successful ligand and NO removal, since its ferrous complex is less susceptible to undesired iron(II) oxidation than ferrous EDTA and NTA. It is reported that no reaction with SO2 takes place, thus avoiding undesired production of N-S compounds. Regeneration takes place at pH ) 4-5, by reaction with © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4915 Table 1. Literature Overview of the Experimental Conditions for the NO Absorption in Aqueous Solutions of Iron(II) Chelate Complexes author

ligand

Kustin et al. (1966) Hikita et al. (1977)

none none

Teramoto et al. (1978)

EDTA

Hishunuma et al. (1979) Sada et al. (1980) Littlejohn and Chang (1982)

EDTA EDTA EDTA, ACAC Cit, none NTA

Lin et al. (1982)

system

T, K

jump in T liquid jet column wetted wall column bubble column stirred cell bubble column stirred cell jump in T

298 288-308

pH 35 >2 × 106 313 5.5 (8.7 ( 0.2) × 105 323 5.5 (4.6 ( 0.2) × 105 333 5.5 (2.5 ( 0.2) × 105 Sada et al. (1984) EDTA 308 6-8 9.90 × 105 Weisweiler et al. (1986) EDTA 298 2.5-11 9.4 × 107 b 3.1 × 106 NTA 298 4.5-9 1.6 × 107 b 3.3 × 106 Sada et al. (1987) NTA 293 4-9 1.8 × 106 c 313 4-9 7.7 × 105 c 333 4-9 2.2 × 105 c Yih and Lii (1988) EDTA 298 7 1.24 × 108 313 7 1.35 × 108 333 7 1.43 × 108 353 7 1.47 × 108 Huasheng and Wenchi (1988) EDTA 288 nad 2.18 × 106 298 na 1.53 × 106 308 na 7.82 × 105 328 na 5.31 × 105 348 na 2.52 × 105 Zang and van Eldik (1990a) DTPA 298 5 (2.7 ( 0.2) × 105 1.2 × 104 Nymoen et al. (1993) EDTA 293 na 1.7 × 106 c 313 na 3.9 × 105 c 333 na 1.1 × 105 c Hofele et al. (1996) NTA 295 na 5.9 × 105 c 313 na 3.0 × 105 c 333 na 1.0 × 105 c Shi et al. (1996b) DMPS 323 7.2 1.1 × 108 a Measured at pH 7.6. b For EDTA, pH ) 7; for NTA, pH ) 6. c Recalculated by Hofele et al. (1996). d Not available. e Calculated with He°NO (Fogg and Gerrard, 1990). Kustin et al. (1966) Hikita et al. (1977) Teramoto et al. (1978)

H2O H2O EDTA

105

103

4916 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

metallic iron powder (Shi et al., 1996a):

2Fe2+(DMPS)2NO + 5Fe(s) + 12H+ f 2Fe2+(DMPS)2 + 5Fe2+ + 2NH4+ + 2H2O (3) The excess of ferrous ions produced may be separated by precipitation of ferrous hydroxide (pH ) 6), in a separate vessel. Drawbacks of this process seem to be the production of 2.5 mol of ferrous hydroxide per mol of removed NO, the need of an additional desulfurization step, and several pH adjustments. An alternative application for ferrous chelates in NO removal was suggested by Hofele et al. (1996), who proposed the use of ferrous EDTA or NTA solutions after a desulfurization step, thus in the absence of SO2. The ferrous chelate solution can be regenerated by releasing NO at T > 353 K. The concentrated NO thus obtained may be used for the production of hydroxylamine. Although, after approximately 20 years of research, the application of ferrous chelates in flue gas denitrification still appears to be in the laboratory phase, NO removal by aqueous solutions of ferrous chelates already receives attention from industry. Also, much very recent literature (Pham and Chang, 1994; Buisman et al., 1996; Hofele et al., 1996; Shi et al., 1996a-c) seems to indicate a renewed interest. Only a few kinetic studies deal with reaction 1 in the absence of sulfur oxides. Table 1 gives an overview of the experimental conditions; Table 2 gives information on reaction kinetics and thermodynamics. The spread in the data is considerable, likely due to the very high stability constants and formation rates. Despite these extremely high formation rates, none of the above studies reports a mass transfer limitation of ferrous chelates. Yih and Lii (1988) assume the diffusivities of ferrous chelates and of NO, DB and DA, respectively, to be equal and claim that ferrous chelate mass transfer limitation is negligible. The experimental data presented by Yih and Lii (1988) seem to support this claim, but, as we show below, at T > 313 K, ferrous chelate mass transfer limitation has affected their results. Huasheng and Wenchi (1988) estimated a value for DB, using the Wilke-Chang equation, even though this method is not appropriate for estimating the diffusivity of ionic species (Reid et al., 1987). Moreover, it is unclear what assumptions Huasheng and Wenchi (1988) have made, regarding the molar volume of the ferrous chelate. The gas absorption study by Weisweiler et al. (1986) does not even address the possibility of ferrous chelate mass transfer limitation. Information on mass transfer limitation of iron chelates is desired. Wubs and Beenackers (1994) studied the reaction of H2S with ferric chelates of EDTA and HEDTA:

H2S(g) a H2S(aq) H2S + 2Fe3+Ln- f SV + 2Fe2+Ln- + 2H+

(4)

When applying a relatively high partial pressure, PH2S, ferric chelate mass transfer limitation was induced, which enabled the determination of DB, provided the reaction stoichiometry in reaction 4 at the gas-liquid H2S interface (νFe(III)L ) is known. Wubs and Beenackers H2S (1994) suggested νFe(III) ) 1, since this is the stoichiometry of the rate-determining step. Although ferric chelates of EDTA and HEDTA differ only little in structure and molecular mass, Wubs and Beenackers

(1994) found their diffusivities to be very different (0.54 × 10-9 and 0.88 × 10-9 m2/s, respectively) and reported their observations to be inconsistent. When they studied the regeneration reaction (Wubs and Beenackers, 1993)

O2(g) a O2(aq) O2 + 4Fe2+Ln- + 2H2O f 4Fe3+Ln- + 4OH- (5) they found the diffusivities of ferrous EDTA and HEDTA to be identical but much different from the diffusivities of their ferric chelates. Recently, the oxidation reaction (eq 5) was studied by Demmink and Beenackers (1997) for ferrous NTA, and the diffusivity ratio, DB/ O2 (νFe(II) DA), determined was in good agreement with that of Wubs and Beenackers (1993). However, the calculation of DB from the diffusivity ratio by Wubs and Beenackers (1993) was questioned. Wubs and BeenO2 ackers (1993) argued νFe(II) to be 2 for reaction 5, since this is the stoichiometry of the rate-determining step, whereas Demmink and Beenackers (1997) argue that O2 νFe(II) ) 4, since all ferrous chelate consuming steps take place near the gas-liquid interface. This controversy may be solved by a simple and fast reaction, whose reaction mechanism and (interfacial) stoichiometry are generally agreed on. A candidate for such a reaction is the absorption of NO in ferrous chelate solutions, reaction 1. Leaist and Hao (1994) studied the diffusivity of ferrous EDTA by dispersion experiments in a Teflon capillary at T ) 298 K, low ferrous chelate concentrations (CFe(II)EDTA ) 0.5 mol/m3), and ionic strength values, adjusted with NaCl, between 0 (extrapolated) and 100 mol/m3. They reported DB to decrease with ionic strength: 0.55 e DB × 109 e 0.58 m2/s, which is higher than the values reported by Wubs and Beenackers (1993) and Demmink and Beenackers (1997). The latter two studies, however, used ferrous chelate concentrations that were orders of magnitude higher. NO As shown by Lin et al. (1982), νFe(II) ) 1, and as shown below, the rate of reaction 1 is fast enough for the absorption rate to be completely determined by ferrous chelate mass transfer limitation, even at the lowest NO pressures applied in this work. Here, we report first data on the absorption of NO into solutions of ferrous NTA, EDTA, HEDTA, and DTPA, accompanied by instantaneous reaction. Also, values for DB are reported. Finally, we show how the pH is (locally) affected by reaction 1 and by local concentration gradients. 2. Chemistry of Ferrous Chelates The structure of ferrous chelates depends on T, pH, and the iron to ligand ratio, which all may affect the absorption of NO. For ferrous EDTA and HEDTA, the structure of the chelates shows little pH-dependency within the range 4 < pH < 10 (Handshaw Clark and Martell, 1988; Zang et al., 1988). For ferrous NTA, an overview of ferrous chelate chemistry was given by Motekaitis and Martell (1994). They distinguish the following equilibria: K6

33{\} Fe2+LNTA Fe2+ + LNTA K7

333Fe2+LNTA + LNTA {\} Fe2+(LNTA )2 K8

33Fe2+LNTA + H2O \ { } Fe2+LNTA OH- + H+

(6) (7) (8)

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4917

Figure 2. Stirred cel reactor used for absorption experiments (reactor I). Table 3. Chemicals Used

Figure 1. Concentration of ferrous and NTA species at 2 < pH < 10, T ) 293 K, CFe(II) ) 50 mol/m3: (a) CNTA ) CFe(II); (b) CNTA 33) 2CFe(II). Components: (1) Fe2+; (2) Fe2+LNTA ; (3) Fe2+(LNTA )2; 2+ 32(4) Fe LNTAOH ; (5) H3LNTA; (6) H2LNTA; (7) HLNTA. The con3centration of “free” LNTA is negligible. 3with LNTA denoting the nitrilotriacetate ion, N(CH2COO-)3. Protonated ferrous NTA chelates report-

edly do not exist at pH > 2 (Motekaitis and Martell, 1994). The equilibrium constants and the formation rates used in this work are taken from Demmink and Beenackers (1997); at T ) 294 K, log K6 ) 7.47 (with k1,1(6) ) 5 × 103 m3/(mol s)), log K7 ) 3.63 m3/kmol, with k1,1(7) ) 2 m3/(mol s), and log K8 ) -10.63 kmol/m3. NTA is deprotonated according to K9,i

(3-i)(3-i+1)HiLNTA {\} Hi-1LNTA + H+

(9)

with pK9,i ) 1.5, 2.52, and 9.59 kmol/m3, for i ) 3, 2, and 1, respectively (Motekaitis and Martell, 1994, T ) 298 K). Figure 1 shows the appearance of the various ferrous NTA species as a function of pH at T ) 293 K and CFe(II) ) 0.050 kmol/m3. For ferrous DTPA, protonated chelates were reported by Zang and van Eldik (1990b), with pKDTPA,1 ) 3.5 and pKDTPA,2 ) 5.7 (kmol/m3), for the first and second

compound

company

NTA HEDTA(Na)3‚2H2O EDTA FeSO4‚7H2O Na2SO4 NaOH N2O NO H 2O

Acros Chimica Acros Chimica Acros Chimica Merck Merck Acros Chimica AGA AGA

purity >97% >99% 99% >99.5% >99% >97% >98% >99% reverse osmosis, degassed

protonation of Fe2+(H2LDTPA)3-, respectively (CFe(II) ) 2 × 10-3 kmol/m3, T ) 298 K). However, assuming these equilibrium constants to be valid at high concentrations (CFe(II) ) 0.050 kmol/m3), it can be shown that protonation of ferrous DTPA is significant at pH < 4 only. 3. Experimental Section Kinetic experiments were carried out in a glass reactor, denoted as reactor I, shown in Figure 2. A centrally located axis equipped with two six-bladed stirrers was used to mix both the gas and the liquid phases. Four symmetrically placed baffles were used to increase the effectiveness of mixing and to avoid the formation of a vortex, thus retaining a flat surface. Valve 1 was connected to an Olivetti PCS 386 SX computer, enabling automatic reactor operation. A pressure indicator (Druck) and a Pt-100 thermocouple were connected to the computer for automatic operation and data collection. The computer was equipped with a Burr Brown PCI 20089 W-1 interface. Some preliminary experiments were carried out in a smaller, but otherwise similar reactor, denoted as reactor II. Aqueous solutions were prepared by dissolving ligand, FeSO4 and NaOH in degassed water (see Table 3). Background salt Na2SO4 (0.1 kmol/m3) was added to get at similar conditions as used by Wubs and Beenackers (1993) and Demmink and Beenackers (1997). The preparations were carried out under nitrogen. The experiments in reactor I were carried out similarly to those by Wubs and Beenackers (1993). First,

4918 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 4. Reactor Dimensions and Reaction Conditions total reactor volume gas phase volume liquid impeller gas impeller a Ns T pH PNO CFeL total reactor volume gas phase volume liquid impeller gas impeller a Ns T pH PNO CFeL

Reactor I 1.77 × 10-3 m3 0.77 × 10-3 m3 six-bladed turbine, dLs ) 4 × 10-2 m six-bladed turbine, -2 m dG s ) 6 × 10 2 3 8.34 m /mliquid 10 s-1 293-333 K 2-10 (8.0-30) × 103 Pa 0.010-0.100 kmol/m3 Reactor II 0.525 × 10-3 m3 0.275 × 10-3 m3 flat disk, dLs ) 5.0 × 10-2 m six-bladed turbine, -2 m dG s ) 4.6 × 10 3 20.12 m2/mliquid 17 s-1 293-333 K 2-10 1, the absorption of NO is enhanced by reaction 1. The relationship between EA and the concentration of active ferrous chelate, CB, depends on the reaction regime. If sufficient ferrous chelate is present, the reaction is pseudo-first-order in NO and EA equals the Hatta number, Ha. Since reaction 1 is first order in both ferrous chelate and NO (Littlejohn and Chang, 1982), Ha is given by (Westerterp et al., 1984)

EA ) Ha )

x

k1,1DACB k2L

(12)

If the condition of sufficient ferrous chelate no longer holds, depletion of ferrous chelate occurs close to the gas-liquid interface and EA < Ha. Finally, as the interfacial reactive ferrous chelate concentration CiB f 0, the enhancement factor is completely determined by diffusion of the reactive components, which is expressed by the instantaneous enhancement factor:

EA ) EA,∞

(13)

Equations 12 and 13 hold for 2 < Ha , EA,∞ and Ha > EA,∞, respectively (Westerterp et al., 1984). For penetration theory, exact, but implicit, expressions for EA,∞ are available (Westerterp et al., 1984). An explicit approximation is given by (Danckwerts, 1970)

EA,∞ )

1 + qAxrB xrB

(14)

with

rB )

CB DB and qA ) i DA νB(CA,L - CA)

(15)

where, for instantaneous, irreversible reactions, CA ) 0. For EA > 20 and rB ) 0.2, the accuracy of the approximate eq 14 is within 0.2% (DeCoursey and Thring, 1989). For reversible reactions, an approximate implicit solution for EA was given by DeCoursey and Thring (1989), which, rewritten for reaction 1, reads

qA

(

(

CBK1β CB

)

E2A - 1

CP -

qA(EAxrP + 1)

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4919

qACA -

) CB

βHa2 - R2DC + 1

(

2

βHa RDC(RDC - 1) 1 -

1

(

1-

)

)

x1 + βHa2

EA

He )

×

)

x1 + βHa2

(16)

with β given by

β)1-

E2A - 1 q(EAxrB + 1)

(17)

rB given by eq 15, and rP given by

rP )

DP DA

(18)

where P pertains to Fe2+Ln-NO. The parameter RDC is arbitrarily set to 1.5, as suggested by DeCoursey and Thring (1989). Equation 16 was tested, for the equilibrium A + B a P′ + Q′, by Winkelman et al. (1992), who compared their results with a numerical solution. For CA ) 0, deviations typically were within 2%, with maximum deviations up to 11%. For CA > 0, the deviation generally was higher. As shown below, Ha . 2 and reaction 1 therefore takes place very close to the gas-liquid interface. In a previous paper (Demmink and Beenackers, 1997) we reported that, for ferrous NTA, the oxidation reaction (eq 5) sometimes has a strong impact on interfacial complex equilibria, which may affect the rate of gas absorption. We observed similar phenomena for the absorption of NO from solving the transport equations in the mass transfer zone, accounting for the electric field potential induced by ions. For all species a mass balance was constructed, which, in combination with the dynamic and static charge balances, could be solved numerically using NAG Routine D03PGE (NAG Fortran Library) on a Cray J932. Details on this approach, including boundary conditions, were given by Demmink and Beenackers (1997), and it will be referred to in this work as the comprehensive interfacial complex chemistry model (C.I.C.C. model). 5. Gas Solubility and Mass Transfer Coefficients 5.1. Gas Solubility. For the solubility of NO in pure water the correlation suggested by Fogg and Gerrard (1990) (PA ) 1.013 × 105 Pa) was used. It is assumed that, within the pressure range applied in this work, the solubility is independent of partial pressure. For mixed salt solutions, the approach suggested by Demmink and Beenackers (1997) was used. This approach is based on the model by Schumpe (1993) and Weisenberger and Schumpe (1996) and requires an absorption experiment with the inert gas N2O prior to each experiment:

HeNO 0 HeNO

) AG

HeN2O 0 HeN 2O

with He the Henry coefficient defined as

(19)

PA

(20)

i CA,L

From gas-specific salting-out parameters from Weisenberger and Schumpe (1996), it could be concluded that, at 298 K, 1 e AG e 1.05, which is close to unity. Since the value of a T-dependent salting-out parameter is not known for NO, the validity of the suggested approach is uncertain at elevated temperatures. Typical values for HeNO obtained are 6.5 × 104, 1.4 × 105, and 2.4 × 105 Pa m3/mol, at T ) 294, 313, and 333 K, respectively. 5.2. Liquid and Gas Phase Mass Transfer Coefficients. The liquid side mass transfer coefficient, kL, for NO was estimated by absorbing the inert gas N2O in the liquid. The appropriate value of kL for NO was calculated from penetration theory (Westerterp et al., 1984):

kL,NO ) kL,N2O

x

DNO DN2O

(21)

The diffusivities of N2O and NO in water are given by Versteeg and van Swaaij (1988) and Wise and Houghton (1968), respectively. The diffusion coefficients were corrected for viscosity according to Ho et al. (1988). The viscosity of ferrous chelate solutions was measured with an Ubbelohde viscosimeter. For 293 < T < 323 K the value of η/η° remained practically constant; see Table 5. Typical values for kL, obtained in both reactors I and II, were 3.5 × 10-5, 7 × 10-5, and 1.2 × 10-4 m/s, for T ) 294, 313, and 333 K, respectively. Values for kG were estimated from Versteeg (1987). Typical values were kG ≈ 0.02 m/s. With this value, kGHe/(RTkLEA) . 1 under all circumstances, proving that gas phase resistance never played a role. 6. Results and Discussion Experiments were carried out with ferrous EDTA, HEDTA, DTPA, and NTA. Except for the latter chelant, no excess of ligand was applied: CFe(II) ) Cligand and 6.5 e pH e 8.5. For NTA, the complex chemistry was studied more extensively: 1 e CNTA/CFe(II) e 3 and 2 e pH e 10. Except for DTPA, studied at T ) 293 K only, all ligands were studied at 293 e T e 333 K. 6.1. Ferrous NTA: T ) 293 K. With DB ≈ 0.3 × 10-9 m2/s (Demmink and Beenackers, 1997) and k1,1 ) 1.6 × 104 m3/(mol s) (from Weisweiler et al. (1986)), which seems a lower value, see Table 2, values for EA,∞ and Ha were estimated for reaction 1 with L ) NTA. With CB typically 0.050 kmol/m3 and CiA,L ) 1.3 × 10-4 kmol/m3, Ha g 1100, while EA,∞ e 180. EA values were calculated from eqs 16 and 14, using the equilibrium constant for eq 1 with L ) NTA, given by Hofele et al. (1996) (which seems to represent a lower value, CNTA ) CFe(II); see Table 2). CA values were calculated from equilibrium equations discussed below. Even at the highest conversions applied, (EA,(16)/EA,(14)) g 0.95. Instantaneous, irreversible reaction therefore appears to hold for ferrous NTA with no excess of NTA. Preliminary experiments with ferrous NTA were carried out in reactor II with 3 e pH e 8, 293 < T < 333 K, and CNTA/CFe(II) ) 1 or 2. After the gas phase was evacuated, NO was let in, until P ) 90 kPa, and allowed to absorb completely until P ) PH2O. This procedure was repeated until all ferrous NTA was 3converted to Fe2+LNTA NO. No uptake of NO was ob-

4920 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 5. Viscosity of Ferrous Chelate Solutions Relative to That of Pure Water, η/η°, 293 e T e 323 K, CNa2SO4 ) 100 mol/m3, pH ) 7 ligand

CFe(II), mol/m3

(η/η°)

(η/η°)a

NTA NTA HEDTAb EDTAb EDTAb DTPA

50 100 100 100 200 50

1.08 1.22 1.39 1.47 1.79 1.13

1.13 1.36

a

CFe(II) ) 1/2CNTA. b Wubs and Beenackers (1993).

Figure 4. Experimental curves: EA as a function of CB for ferrous NTA. CB decreases with time due to absorption of NO. CFe(II) ) i CNTA, T ) 294 K, kL ) 3.5 × 10-5 m/s, and CA,L ) 0.13 mol/m3. Curves: (1) pH ) 2.83, CB,0 ) 51.8 mol/m3; (2) pH ) 3.42, CB,0 ) 48.2 mol/m3; (3) pH ) 6.58, CB,0 ) 45.9 mol/m3; (4) pH ) 6.62, CB,0 ) 17.7 mol/m3.

Figure 3. Final pH, pHf, as a function of initial pH, pH0: change in pH as a result of NO absorption for ferrous NTA and T ) 294 K. Closed symbols: CNTA ) CFe(II), 0.060 e CFe(II) e 0.080 kmol/ m3, ∑CNO/CFe(II) ) 1.0. Open symbols: CNTA ) 2CFe(II), CFe(II) ) 0.046 kmol/m3, ∑CNO/CFe(II) ) 0.26. Lines: (1) pHf ) pH0 (hypothetical); (2) calculated from equilibria 1, 6, and 9, eq 22, and mass balances over Fe(II) and NTA with ∑CNO/CFe(II) ) 1.0 and CFe(II) ) CNTA ) 0.072 kmol/m3; (3) as for 2 but with ∑CNO/CFe(II) ) 0.99, indicating a high sensitivity to small experimental errors at pH > 6; (4) as for 2 but with CNTA ) 2CFe(II), CFe(II) ) 0.046 kmol/m3, and ∑CNO/CFe(II) ) 0.26.

served when ∑CNO ) CFe(II), indicating νNO B ) 1, which is in agreement with the data of Lin et al. (1982). Although, at pH < 4, the ferrous ion is only partially chelated (see Figure 1) and “free” ferrous ions do not form stable NO complexes (see Table 2), full conversion was obtained even at the lowest pH applied. Samples drawn from the ferrous NTA solutions, after the experiments where CNTA ) CFe(II), showed a pH decrease as a result of NO absorption; see Figure 3. Also shown in Figure 3 are experiments with an excess of NTA and pH > 7, which showed the opposite effect: the pH appeared to increase during reaction 1. Formation of NOx is unlikely under the anaerobic conditions applied (no oxidation of Fe(II) was observed) and may be excluded by the latter observation of increasing pH. 3Apparently the formation of Fe2+LNTA NO is more complex than expected from reaction 1. Mass balances over NO, Fe(II), and NTA, as well as the electroneutrality condition N

ziCi ) 0 ∑ i)1

(22)

with zi the charge of ion i and Ci its concentration, and 3equilibria 1, for Fe2+LNTA and Fe2+, as well as equilibria 6 and 9 result in a set of algebraic equations, which can be solved by a Newton-Raphson technique. The pH calculated this way appears to match experimental values reasonably well; see Figure 3. Figure 3 also shows that, for the initial pH, pH0 > 6, the pH decrease at high conversions is very steep and therefore sensitive to small errors in initial pH, CFe(II), and CNTA. The decrease of pH with conversion appears to be a result of shifting equilibria 6 and 9. In contrast, the increase of pH, observed for excess NTA only (pH0 > 6), may result from a combination of equilibria 1 and 7 K23

333)2 + NO \ { } Fe2+LNTA NO + LNTA Fe2+(LNTA

(23)

followed by consumption of a proton via reaction 9. This 3suggests that the ferrous NO complex Fe2+(LNTA )2NO is not produced. A gas absorption experiment, carried out in reactor I (P constant) with CNTA ) 3CFe(II), pH ) 10, and CiA,L ) 1.1 × 10-4 kmol/m3, appears to support this hypothesis. As shown in Figure 8 (curve 6), the uptake of NO stops when ∑CNO/CFe(II) ≈ 0.3, which turns 3out to be the equilibrium value if Fe2+LNTA NO is the only NO complex produced. The stability constant for equilibrium 23 is given by K23 ) K1/K7. Some observed and calculated pH values, for CFe(II) ) 1/2CNTA(∑CNO/ CFe(II) ) 0.26) are given in Figure 3. The experimental and calculated pH appear to match reasonably well. Since all experiments were performed for Ha > EA,∞, the ferrous chelate is locally completely converted to 3Fe2+LNTA NO. Therefore, local pH effects occur within the mass transfer zone at the gas-liquid interface. The impact of these local effects is discussed below. Figure 4 shows some typical (batch) experiments carried out in reactor I, for CFe(II) ) CNTA, where CB decreases with time, while CiA,L remains constant. The straight lines observed are consistent with eq 14, even

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4921

Figure 5. EA as a function of pH, CNTA ) CFe(II) ) 50 mol/m3, T i ) 294 K, CA,L ) 0.13 mol/m3, and kL ) 3.5 × 10-5 m/s. Line A1 results from eq 14, [(DB/DNO)]1/2 ) 0.44. Lines B1 and B2 are calculated from the C.I.C.C. model, DB ) 0.38 × 10-9 m2/s. B1 is 3calculated assuming that Fe2+LNTA is formed through eqs 1 and 6 3only. Line B2 is calculated assuming Fe2+LNTA NO can be formed 32+ directly from Fe NO and LNTA (eq 25) with k1,1(25) ) k1,1(6).

though this equation may be a simplified approach due to pH effects both in the bulk and at the gas-liquid interface. The slopes of the lines may therefore be used for estimating [(DB/DNO)]1/2:

dEA 1 ) dCB Ci

A,L

x(DB/DNO)

(24)

At pH ) 7 and T ) 294 K, [(DB/DNO)]1/2 ) 0.44 ( 0.01 (also see Table 6) and may be compared to the value O2 for [(DB/DNO)]1/2/νFe(II)L ) 0.09 for reaction 5 (Demmink O2 and Beenackers, 1997). It indicates that νFe(II)L ) 4, as suggested earlier by Demmink and Beenackers (1997), rather than 2, as suggested by Wubs and Beenackers (1993). Now it is possible to calculate EA values, using eq 14, the [(DB/DNO)]1/2 given above, the equilibrium constants for reactions 6-8 given by Demmink and Beenackers (1997), and the NTA protonation constants given by Motekaitis and Martell (1994), and to compare these values with the experimental values of EA. The result of calculating EA from eq 14 is shown in Figure 5, line A1. As may be expected from the high capacity of ferrous NTA solutions at low pH, for pH < 5, eq 14 appears to be invalid. Apparently, the approximate eq 14 is invalid for pH < 5, and a more comprehensive approach should be followed. Also, the observed pH dependency of the NO absorption, in combination with the observed decrease in pH (Figure 3) requires that we test the validity of eq 24 for pH > 5. Figure 6 shows the local concentration profiles, as calculated from the set of mass balances using DB ) 0.38 × 10-9 m2/s for ferrous NTA, as determined above. “Free” ferrous ion and ligand are assumed to have nearly similar diffusivities as ferrous chelate (Leaist and Hao, 1994). In Figure 6a, pH ) 7.02. In the mass

Figure 6. Near interface concentration profiles calculated from a set of mass balances (C.I.C.C. model), after a contact time, θ, given by θ ) 4DA/(πk2L). Relative penetration depth rp is given by rp ) x/[πDAθ]1/2 (Demmink and Beenackers, 1997). For readability, some concentrations have been omitted from the plots, although i they were incorporated in the calculations. CA,L ) 0.13 mol/m3, kL ) 3.5 × 10-5 m/s, and DB ) 0.38 × 10-9 m2/s. (a) pH ) 7.02 and CFe(II) ) 40 mol/m3. (b) pH ) 2.83 and CFe(II) ) 50 mol/m3.

transfer zone, CFe2+LNTA3- decreases as a result of reaction 1. Consistent with the observations at pH ) 7, shown in Figure 3, the pH sharply decreases with conversion, until an interfacial value of pHi ) 4.61. Fe2+ and 33LNTA are rapidly interconverted to Fe2+LNTA , according to equilibria 6 and 9. Figure 6b shows local concentration profiles for pH ) 2.83. Consistent with the preliminary experiments (Figure 3), the pH gradient is not as steep as that in Figure 6a. Although practically no 3Fe2+LNTA is present, the major product formed in the mass transfer zone appears not to be Fe2+NO ()Fe2+LH2O3NO) but Fe2+LNTA NO. The maximum concentration of H2LNTA at rp ) 0.4 is a result of production from 2HLNTA due to the decreasing pH and consumption resulting from reactions 6 and 1. EA values, calculated from a set of mass balances (Demmink and Beenackers, 1997), are shown in Figure 5, line B1, and show that, for pH < 5, EA still is underestimated. This is different from the observation for ferrous NTA oxidation (Demmink and Beenackers, 1997), where the above approach, with the same equilibrium and rate constants for equilibria 9 and 6, yielded good results at low pH. It should be noted, however, that, for NO absorption, it is implicitly assumed that 3Fe2+LNTA NO is formed via equilibria 1 and 6 only.

4922 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

Figure 7. Parity plot for EA: open symbols, eq 14; closed symbols, C.I.C.C. model. T ) 294 K. Parameters given in Table 6. NTA: i CL ) CFe(II), pH g 6, 1.2 × 10-4 e CA,L e 1.0 × 10-3 kmol/m3, 0.017 e CB e 0.076 kmol/m3. EDTA and HEDTA: 6.8 e pH e i 7.6, 0.02 e CB e 0.1 kmol/m3, 1.2 × 10-4 e CA,L e 2.5 × 10-4 3 kmol/m .

Figure 8. Experimental curves of EA as a function of CB, where CB decreases with time due to absorption of NO, with ferrous NTA, T ) 294 K, and kL ) 3.5 × 10-5 m/s. (curves 1-5) CFe(II) ) 1/2CNTA; i (curve 6) CFe(II) ) 1/3CNTA, CA,L ) 0.13 mol/m3, 45 e CB,0 e 50 mol/m3. Curves: (1) pH0 ) 3.58; (2) pH0 ) 5.01; (3) pH0 ) 6.08; (4) pH0 ) 7.91; (5) pH0 ) 9.03; (6) pH0 ) 10.03.

3However, if formation of Fe2+LNTA NO directly from 32+ Fe NO and LNTA is accounted for

K25

33Fe2+NO + LNTA {\} Fe2+LNTA NO with K1(Fe2+LNTA3-)K6 (25) K25 ) K1(Fe2+)

with a forward rate constant k1,1(25) ) k1,1(6) (which, for reasons of steric hindrance, is an upper limit), the resulting calculated line matches nicely over the entire range 3 e pH e 8 (line B2, Figure 5). Establishing equilibrium 1 through reaction 25 therefore may account for the very high EA values observed for pH < 5. Despite sharp interfacial pH gradients, shown in Figure 6a, for pH > 5 and no excess of NTA, both eq 14 and the C.I.C.C. model give good results (see Figure 7). Therefore, for pH > 5, eq 24 may be applied for determining [(DB/DNO)]1/2, even though reaction 1 is shown to be complex. Some experiments with CNTA ) 2CFe(II) are shown in Figure 8. EA generally decreases with increasing pH (see also Figure 9). Line A2 in Figure 9 is the result of eq 14, with single-coordinated ferrous NTA as the only reactive component. This approximate approach appears to be invalid over the entire range 2 e pH e 10 for excess NTA. Lines B3-B5 in Figure 9 are calculated from the C.I.C.C. model. Line B3 was obtained assuming Fe2+ 3(LNTA )2 reacts through local dissociation (equilibrium 7) only. This approach appears to underestimate the absorption rate at pH > 8, indicating an active role of 3Fe2+(LNTA )2. Most likely, equilibrium 23 involves a substitution reaction, where NO actively removes a 33ligand LNTA , with Fe2+NO(LNTA )2 as an unstable intermediate. Line B4 was calculated, assuming k1,1(23) ) k1,1(1) (given in Table 2, Weisweiler et al. (1986)), thus

Figure 9. EA as a function of pH with CFe(II) ) 1/2CNTA ) 50 mol/ i m3, T ) 294 K, CA,L ) 0.13 mol/m3, and kL ) 3.5 × 10-5 m/s. Line 3A2 is calculated from eq 14, [(DB/DNO)]1/2 ) 0.44; Fe2+LNTA is the only reactive component. Lines B3-B5 are calculated from the C.I.C.C. model, DB ) 0.38 × 10-9 m2/s. Line B3 is 3calculated assuming Fe2+(LNTA )2 reacts through equilibrium 7 only. Line B4 is calculated with k1,1(23) ) k1,1(1) (see Table 2, Weisweiler et al. (1986)). Line B5 is calculated with k1,1(23) ) 0.5k1,1(1).

implying that the second-coordinated ligand does not 3hinder the formation of Fe2+LNTA NO. This assumption may be considered as an upper limit, and as shown in Figure 9, line B4, overestimates the absorption rate at pH > 7. Line B5 was calculated with k1,1(23) ) 7.7 × 103 m3/(mol s), where it should be noted that, from equilibrium considerations

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4923

K23 )

k1,1(23) k1,1(-23)

)

K1 ) 7.7 × 102 K7

(26)

at T ) 294 K (values for K1,NTA and K7 given by Weisweiler et al. (1986) and Demmink and Beenackers (1997), respectively). Although for pH < 7 line B5 still appears to overestimate the experimental data, it reasonably matches over the range 3 e pH e 10. 6.2. Ferrous EDTA and HEDTA: T ) 294 K. Figure 10 shows some typical NO absorption experiments with ferrous EDTA at T ) 294 K and pH ) 7.5. Initially, until ∑CNO/CFe(II) ≈ 0.1-0.2, the absorption rate deviates from linearity. These initial values typically are twice the enhancement predicted by eq 14, taking DB from Wubs and Beenackers (1993), as recalculated by Demmink and Beenackers (1997), and 4. A few exdecrease with consumption of Fe2+LEDTA periments were interrupted once EA linearly decreased with conversion (i.e. for ∑CNO/CFe(II) > 0.2). After thorough degassing, these experiments were continued, but now the extra fast initial absorption rate did not reoccur. This excludes adsorption phenomena on the reactor. Experiments 1-4 in Figure 10 have been carried out with CiA,L ) 1.3 × 10-4 kmol/m3. Irrespective of the 4, the experimental initial concentration of Fe2+LEDTA curves eventually follow the same straight line. Furthermore, from eq 14 it follows that i i ) CA,L EACA,L

x

DA + CB DB

x

DB DA

Figure 10. Experimental curves of EA as a function of CB with ferrous EDTA. CB decreases with time due to absorption of NO. i T ) 294 K, kL ) 3.5 × 10-5 m/s, CA,L ) 0.13 mol/m3, 7 e pH e 7.5. 3 Curves: (1) CB,0 ) 17.6 mol/m ; (2) CB,0 ) 29.2 mol/m3; (3) CB,0 ) i 40.6 mol/m3; (4) CB,0 ) 45.8 mol/m3; (5) CB,0 ) 95.4 mol/m3; CA,L ) 0.10 mol/m3.

(27)

therefore, for CB[DB/DA]1/2 . CiA,L[(DA/DB)]1/2, EACiA,L should be independent of CiA,L. Figure 11 shows EACiA,L as a function of CB for CiA,L ) 1.3 × 10-4 and 2.5 × 10-4 kmol/m3, respectively. It is seen that, except for the initial values (∑CNO/CFe(II) < 0.2), the experimental lines match very nicely. From these observations, it is concluded that not the initial rate but the straight line obtained after some NO uptake represents “regular” instantaneous reaction. As far as we know, the extraordinarily large initial rate in absorption is not reported in the literature and remains yet unexplained. From the slope of lines 1-4 in Figure 10, a value for [(DB/DNO)]1/2 was determined; see Table 6. Experiment 5 in Figure 10 was carried out with CiA,L ) 1.0 × 10-4 kmol/m3. The line through these experimental points was calculated with the [(DB/DNO)]1/2 value obtained from experiments 1-4 and matches the experiment very well. Figure 12 shows some typical absorption experiments with ferrous HEDTA. Again, the phenomenon of nonlinear absorption rates occurred initially. The observed [(DB/DNO)]1/2 is very similar to the value found for ferrous EDTA; see Table 6. Different from the case for ferrous NTA, little pH effects were observed during the experiments with ferrous EDTA and HEDTA, and except for the initial absorption rate, the observed EA matches well with values predicted from both eq 14 and the C.I.C.C. model; see Figure 7. 6.3. Ferrous NTA, EDTA, and HEDTA: 293 e T e 333 K. Figure 13 (closed symbols) shows that,

i Figure 11. EACA,L as a function of CB with ferrous EDTA, showing the validity of eq 14 for ∑CNO/CFe(II) > 0.2 with ferrous EDTA, kL ) 3.6 × 10-5 m/s, T ) 294 K, and pH ) 7.1.

different from [DB/DO2]1/2, [(DB/DNO)]1/2 decreases with T (293 e T e 333 K, ferrous NTA, HEDTA, and EDTA). Neither ferrous NTA (Demmink and Beenackers, 1997) nor ferrous EDTA and HEDTA (Wubs and Beenackers, 1993) show significant T-dependency in O2 [(DB/DNO)]1/2/νFe(II) , measured via reaction 5; see Figure 13, dashed line. Therefore, the temperature dependencies of DB and DO2 appear to be similar, whereas DNO increases faster with T than DB and DO2. This is supported by data on DO2 and DNO (Wise and Houghton, 1966, 1968); Figure 13, solid line. Also, back calculating

4924 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 Table 6. Values for (rB)1/2, DB, M, z, and RB for Ferrous NTA, HEDTA, EDTA, and DTPA, pH ) 7, T ) 294 K, and 0.02 e CFe(II) e 0.1 kmol/m3 NTA HEDTA EDTA DTPA

[(DB/DNO)]1/2 a

109DB,a m2/s

1010RB,b m

109DB,c m2/s

M, kg/mol

zFe(II)L

0.44 ( 0.01 0.34 ( 0.01 0.36 ( 0.01 0.31 ( 0.015

0.37 ( 0.015 0.22 ( 0.015 0.24 ( 0.02 0.19 ( 0.02

5.1 8.9 8.2 10.3

0.84 ( 0.02 0.65 ( 0.02 0.68 ( 0.02

0.247 0.331 0.348 0.448

-1 -1 -2 -3

a Determined from penetration theory: eq 14 for ferrous NTA, EDTA, and HEDTA or eq 16 for ferrous DTPA. D ) 1.90 × 10-9 m2/s A (Wise and Houghton, 1968, corrected for viscosity). b Calculated with DB from penetration theory, RB ) kT/(6πηDB) (Atkins, 1982). c Determined from film theory: E A,∞ ) 1 + rBqA (Westerterp et al., 1984).

Figure 12. Experimental curves of EA as a function of CB with ferrous HEDTA. CB decreases with time due to absorption of NO. i CA,L ) 0.13 mol/m3, 6.8 e pH e 7.3. Curves (1-3) T ) 294 K, kL ) 3.5 × 10-5 m/s; (1) CB,0 ) 25.0 mol/m3; (2) CB,0 ) 27.6 mol/m3; (3) CB,0 ) 47.5 mol/m3; (4) CB,0 ) 47.7 mol/m3, T ) 314 K, kL ) 7.4 × 10-5 m/s; (5) CB,0 ) 47.4 mol/m3, T ) 333 K, kL ) 1.4 × 10-4 m/s.

[(DB/DO2)]1/2, from the values for [(DB/DNO)]1/2, according to

(x ) (x ) (x ) DB DO2

)

calc

DB DNO

obs

DNO DO2

(28)

indeed shows [DB/DO2]1/2 to be temperature independent (Figure 13, open symbols) and to scatter around the experimental values determined with reaction 5, for ferrous EDTA, HEDTA, and NTA. The low [(DB/DNO)]1/2 at high T explains the lack of data on k1,1(1) at elevated temperatures; see Table 2. Huasheng and Wenchi (1988) report experiments at elevated T, but no values for k1,1. Yih and Lii (1988) reported k1,1 values for reaction 1 for ferrous EDTA at 298 e T e 353 K. At T ) 333 K, these authors used CB ) 0.05 kmol/m3 and 4 × 10-7 e CiA,L e 15 × 10-7 kmol/ m3. Therefore, with [(DB/DNO)]1/2 ) 0.22 (see Figure 13), it follows that 7 × 103 e EA,∞ e 2.8 × 104. From the kL and k1,1 reported by Yih and Lii (1988) and the DA reported by Wise and Houghton (1968), it can be shown that Ha ≈ 1.2 × 104, indicating that the k1,1 reported by Yih and Lii (1988) is underestimated due to ferrous chelate mass transfer limitation. The determination of the activation energy, Ea, for reaction 1 is based on an underestimated k1,1 at elevated temperatures. This

1/2 i Figure 13. CA,L (dEA/dCB) ) (1/νNO as a function of B )[(DB/DNO)] T: black points, NO data; dashed line, values for [DB/DO2]1/2 determined for EDTA, HEDTA, and NTA (Wubs and Beenackers, 1993; Demmink and Beenackers, 1997); solid line, [DO2/DNO]1/2 (data from Wise and Houghton, 1966, 1968); white points, [DB/ DO2]1/2 calculated from NO data (eq 28), showing the consistency of NO absorption data with ferrous chelate oxidation.

explains the low Ea reported by Yih and Lii (1988): Ea ) 2.7 kJ/mol. This value probably is too low. 6.4. Ferrous DTPA. For ferrous DTPA, approximate values for K1 and k1,1 are given by Zang and van Eldik (1990b); see Table 2. These values are considerably lower than those for ferrous NTA and EDTA. Therefore, for ferrous DTPA, the assumption of instantaneous, irreversible reaction is unlikely to hold. As a preliminary experiment, a ferrous DTPA solution (CB ) 9.3 mol/m3, T ) 294 K, pH0 ) 7.77) was allowed to react with NO in batch, until equilibrium was reached. From this experiment it was concluded that K1,DTPA ) 23.4 m3/mol, which is close to the approximate value given by Zang and van Eldik (1990b); see Table 2. Checks on eq 16, with the approximate k1,1 given in Table 2, showed negligible sensitivity to k1,1, even for the lowest PNO applied. This implies that a more accurate value for k1,1 is not needed within the scope of this paper. Remarkably, during the NO absorption experiments, the pH rose significantly. For instance, for CFe(II) ) 0.049 kmol/m3, T ) 294 K, and ∑CNO/CFe(II) ) 0.19, pH0 ) 7.87 increased to pHf ) 8.86. This observation cannot be understood from known complex chemistry and 5indicates that the formation of Fe2+LDTPA NO is accompanied by a proton transfer reaction. An explanation may follow from the structure of ferrous DTPA. Unlike ferrous NTA, HEDTA, and EDTA, the ferrous DTPA complex has no water coordinated (Zang and van Eldik, 1990b). The heptacoordinated complex involves three N atoms and four carboxylate groups. The fifth

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4925

theory (Westerterp et al., 1984). This leads to much higher values of DB. The value for DFe(II)EDTA found by Leaist and Hao (1994) lies in between these two extremes. This observation is of importance in determining ferrous chelate mass transfer limitation; consistent use of either of the models appear to be crucial. 7. Conclusions

Figure 14. Experimental curves of EA as a function of CB with ferrous DTPA. CB decreases with time due to absorption of NO. T ) 294 K, kL ) 3.4 × 10-5 m/s, CB,0 ) 50 mol/m3, 7.6 e pH0 e i i 7.8. Curves: (1) CA,L ) 0.13 mol/m3; (2) CA,L ) 0.25 mol/m3; (3) i CA,L ) 0.52 mol/m3. Solid lines are calculated with eq 16, with rB ) rP ) 0.1, K1 ) 23.4 m3/mol, and k1,1 ) 270 m3/(mol s). CA values are calculated from mass balances, including ∑CNO and CFe(II), equilibria 1 and 29, and the electroneutrality condition (eq 22).

carboxylate group is not coordinated and is protonated at pH < 4. Whereas, for ferrous NTA, HEDTA, and EDTA, reaction 1 involves the substitution of a water molecule, this cannot be the case for ferrous DTPA. Apparently, one of the coordinated carboxylate groups is substituted by NO and may now be protonated: K29

45Fe2+HLDTPA NO {\} Fe2+LDTPA NO + H+

(29)

From the rise in pH as a function of NO absorption, we calculated pK29 ) 7.2-7.4 kmol/m3. Although calculation of near-interface concentration gradients, from the C.I.C.C. model and accounting for equilibrium 29, shows a significant rise in local pH, the resulting EA does not show significant deviation from the result of eq 16: 0.96 e EA,C.I.C.C./EA,eq 16 e 1. This is within the accuracy limits of eq 16 (Winkelman et al., 1992). Equilibrium 29 therefore has no significant effect on the NO absorption under the conditions applied. DB could be calculated from the experiments, using eq 16; see Table 6. As shown in Figure 14, the EA values thus calculated agree with the experimental data, for all PNO applied. As shown in Table 6, the diffusivity of ferrous chelates decreases according to ferrous NTA > ferrous EDTA, HEDTA > ferrous DTPA, which appears to be consistent with the increasing molecular mass of these ferrous chelates; see Table 6. From the very similar diffusivities of ferrous HEDTA and EDTA, it is concluded that the diffusivity of ferrous chelates is determined by mass rather than charge (also see Wubs and Beenackers, 1993). Also given in Table 6 is the hydrodynamic radius of ferrous chelates, RB, that can be estimated from the Stokes-Einstein equation (Atkins, 1982). Our data have been interpreted with penetration theory. Table 6 also gives the results from applying film

At 294 e T e 333 K, 0.020 e CFe(II) e 0.100 kmol/m3, and 8 e PNO e 30 kPa, the absorption of NO into aqueous solutions of ferrous chelates of NTA, EDTA, HEDTA, and DTPA appears to be accompanied by instantaneous reaction. For ferrous EDTA, HEDTA, and DTPA, the absorption rate is well described by the approximate expression EA,∞ ) 1/xrB + xrB(CB/CiA,L) (Danckwerts, 1970). Despite observed pH gradients, for ferrous NTA, this expression is valid as well, provided, however, that ligand is not present in excess and pH > 5. For pH < 5 and NTA present in excess, a more comprehensive penetration mass transfer model, in parallel with complex chemical reactions, resulting in pH and concentration gradients at the interface, appeared to be necessary. NO Comparing the values for [(DB/DNO)]1/2/νFe(II) with 1/2 O2 those for [(DB/DNO)] /νFe(II), found for ferrous EDTA and HEDTA (Wubs and Beenackers, 1993) and ferrous O2 NTA, showed that νFe(II) ) 4. At T > 294 K, the value of DB/DNO decreases with T as a result of the unusual T dependency of DNO. From this observation it can be shown that the scarce kinetic data available from the literature at elevated T are unreliable. The reversible binding of NO to ferrous DTPA involves the substitution of a coordinated carboxylate group, which may be protonated. As a result, a significant increase in pH is observed, which, however, appears to have no significant effect on the NO absorption rate. Acknowledgment The authors thank the financial support of The Netherlands Foundation for chemical research (SON). They thank M. Hoogland for experimental contributions. Nomenclature 3 a ) specific surface, m2/mliquid AG ) parameter defined in eq 19, unitless C ) concentration, kmol/m3 C ) concentration in the bulk of the liquid, kmol/m3 3 ∑CNO ) total uptake NO, kmol/mliquid L G ds , ds ) diameter of stirrer, m D ) diffusivity, m2/s Ea ) activation energy, kJ/mol EA ) chemical enhancement factor, unitless EA,∞ ) EA at instantaneous reaction, unitless Ha ) Hatta number, see eq 12, unitless 3 He ) Henry coefficient, see eq 20, Pa mliquid /mol 2 JA ) specific absorption rate of gas A, mol/(mliquid s) -23 k ) Boltzmann constant ()1.3806 × 10 ), J/K kL ) liquid side mass transfer coefficient, m/s kG ) gas side mass transfer coefficient, m/s k1,1 ) rate constant for reaction first order in liquid and gas phase reactant, m3/(mol s) Ke ) stability constant for equilibrium e, kmol/m3 for eqs 8 and 9; (e ) 1, 2, ...) m3/kmol for eqs 1, 6, and 7; unitless for eq 23

4926 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 M ) molecular mass, kg/m3 Ni ) number of ionic species, unitless Ns ) stirring rate, s-1 PA ) partial pressure of gas A, Pa pH ) pH in bulk pKe ) -log Ke qA ) stoichiometric ratio, see eq 15, unitless rp ) relative penetration depth (≡x/xπDAθ), unitless rB, rP ) diffusivity ratio, see eqs 15 and 18, unitless R ) gas constant ()8.314), J/(mol K) Ri ) reaction rate for component i, kmol/(m3 s) RB ) hydrodynamic radius, m t ) time, s T ) temperature, K V ) volume, m3 x ) distance from gas-liquid interface, m z ) ion charge, unitless Greek Symbols RDC ) parameter in eq 16 ()1.5), unitless β ) parameter in eq 16, unitless η ) viscosity, Pa s θ ) average contact time (≡4DA/(πk2L)), s A′ A′ νB′ ) (interfacial) stoichiometry for reaction A′ + νB′ B′ f P′, unitless Super- and Subscripts A ) NO A′ ) arbitrary gas phase reactant B ) active ferrous chelate B′ ) arbitrary liquid phase reactant f ) final G ) gas phase i ) interfacial (supercript) i ) species i (subscript) j ) species j L ) liquid phase m ) species m P ) product Fe2+Ln-NO P′, Q′ ) arbitrary products ° ) pertaining to pure water (superscript) 0 ) pertaining to t ) 0 (subscript) Ligands ACAC ) acetylacetonate Cit ) citrate DMPS ) 2,3-dimercapto-1-propanesulfonate DTPA ) diethylenetriaminepentaacetic acid EDTA ) ethylenediaminetetraacetic acid HEDTA ) hydroxyethylenediaminetriaacetic acid NTA ) nitrilotriacetic acid

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Received for review April 14, 1997 Revised manuscript received July 29, 1997 Accepted August 10, 1997 IE9702800

X Abstract published in Advance ACS Abstracts, October 15, 1997.