Modeling the Solubility of Nitrogen Dioxide in Water …...1000 mol of water. We will use this entity to calculate the solubility of NO 2 in water. In some previous studies, this additional

Modeling the Solubility of Nitrogen Dioxide in Water UsingPerturbed-Chain Statistical Associating Fluid TheorySugata P. Tan* and Mohammad Piri

Department of Chemical and Petroleum Engineering, University of Wyoming, Department 3295, 1000 E. University Avenue,Laramie, Wyoming 82071, United States

ABSTRACT: NO2 is one of the important components in flue gas from combustion in power plants, which together with CO2and SO2 pollute the atmosphere if released and cause the undesired acid rains. NO2 reacts immediately with H2O upondissolution, which prevents direct measurements on the physical phase equilibria of the chemical system. Modeling this reactingsystem is a challenging task due to the complexities arising from the heterogeneous nature of the chemical reaction, the multiplecomponents that are involved in the phase equilibria, ionic dissociation in water, self- and cross-associations among themolecules, and multiple chemical reactions that may occur before reaching the physicochemical equilibria. Therefore, efforts onmodeling this NO2/H2O system have been made so far with no satisfactory progress. In this work, we propose a complete modelof the system using Perturbed Chain Statistical Associating Fluid Theory (PCSAFT) equation of state (EOS). The model isfound to be able to calculate the solubility curves of NO2 in water at various pressures and temperatures, which provide a strongfoundation for a later application in flue gas sequestration into aquifers.

■ INTRODUCTIONDespite its importance in the removal efforts of NOx from theflue gases for a clean environment, in the precipitation processesin the atmosphere, and in the manufacture of nitric acid, theabsorption of NOx in water is perhaps the least understood in allabsorption operations.1 It is probably the most complex case ofabsorption due to the large number of species and reactions thatare involved in the process. NOx is in fact a mixture of all nitrogenoxides (N2O, NO, NO2, N2O3, N2O4, and N2O5), most of whichreact immediately with water upon dissolution resulting inHNO3 (nitric acid) and HNO2 (nitrous acid). Only N2O(nitrous oxide) and NO (nitric oxide) do not react with waterand hardly dissolve in water. Dozens of chemical equilibria, bothin liquid and vapor phases, exist in the absorption and desorptionprocesses that occur simultaneously.2 Therefore, the knowledgeof the process’s physicochemical data such as the solubility ofthose gases in water is still incomplete.1

Among the species that react with water, N2O3 (nitrogentrioxide) and N2O5 (nitrogen petoxide) are the anhydrate formsof nitrous and nitric acids, respectively, while NO2 (nitrogendioxide) and its dimer N2O4 (nitrogen peroxide or nitrogentetroxide) coexist in equilibrium up to about 150 °C:3

↔2NO N O2 2 4 (1)

Generally speaking, the term nitrogen dioxide is meant to includeboth NO2 and N2O4. In this work we denote them with anasterisk to remind us of these duo species, i.e., NO2*.It is customary to summarize the overall chemical equilibrium

in the absorption of NO2* in water as4−7

* + ↔ +3NO H O 2HNO NO2 2 3 (2)

The high reactivity of NO2* in water precludes directmeasurement of physical properties such as the Henry’scoefficient, the magnitude of which is customarily used in theinterpretation of kinetic processes.2 In this case, the coefficient

must be indirectly inferred from kinetic studies, the results ofwhich have large uncertainties.1

The buildup of the products in eq 2 complicates the situation.At high concentration, HNO3 will tend to dissociate accord-ing to8

↔ + +4HNO 4NO 2H O O3 2 2 2 (3)

which is dominant, for example, in the work series of Sage andco-workers.9−14

The resulting oxygenmay involve in another reaction with NOand NO2 following

4

+ ↔2NO O 2NO2 2 (4)

According to this reaction, the availability of O2 is thereforerequired in the production of pure HNO3 using the absorptionprocess eq 2, i.e., to prevent the buildup of NO from halting theformation of HNO3.At moderate temperatures, the resulting NO or O2 from eq 2

or eq 3, respectively, builds the system pressure to levels muchhigher than they would have been if the reactions did not occur.9

Still to worsen the situation, the resulting NO in eq 2 mayassociate with NO2 to form N2O3:

1,2

+ ↔NO NO N O2 2 3 (5)

N2O3 is unstable and reacts with water to form nitrous acid,7

HNO2, which is often considered to involve in intermediatereactions for the overall reaction of eq 2. Both acids, HNO2 andHNO3, in turn also dissociate into their constituting ions inwater.2,7

Furthermore, the overall reaction eq 1 is in fact aheterogeneous equilibrium, in which the aqueous liquid phase

Received: July 26, 2013Revised: September 24, 2013Accepted: October 14, 2013Published: October 14, 2013

Article

pubs.acs.org/IECR

© 2013 American Chemical Society 16032 dx.doi.org/10.1021/ie402417p | Ind. Eng. Chem. Res. 2013, 52, 16032−16043

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is in equilibrium with the vapor phase above it.1 Therefore, thesystem has the physical equilibrium of the phases andsimultaneously the chemical reaction equilibrium in eq 2.In summary, the complexity makes the modeling of this

reacting system more difficult. In this work, we attempt to derivea model for the physical and chemical equilibria of NO2 in water,which is needed to describe the absorption of NO2 into aqueoussolutions. This study will also be the initial step for a laterapplication of the model in flue gas sequestration into aquifers.We apply an equation of state (EOS), namely the perturbed-chain statistical associating fluid theory (PCSAFT),15 which hasbeen widely used in petrochemical industries due to its reliableaccuracy and predictability.16 The kinetics is not considered, aswe are only concerned with the equilibrium state of the system.To the best of our knowledge, it is the first attempt to model thephysicochemical equilibria of this reacting system using astatistical-mechanics based EOS such as PCSAFT.

■ THEORYChemical Equilibrium. The most widely used property of

the reacting system of NO2 in water or in aqueous nitric acidsolutions is the partial equilibrium constant of reaction eq 2defined as4,5

= =KP

P

y

y P( )

( )

( )

( )1

1NO

NO23

NO

NO23 2

(6)

which is actually a factor of the reaction equilibrium constant:

=

Kf f f f

f f f f

( / )( / )

( / ) ( / )NO NO

0HNO3 HNO3

0 2

NO2 NO20 3

H2O H2O0

(7)

In eq 6, y and P are the gas mole fractions and the total pressure,respectively, while f ’s with hats in eq 7 are the fugacities inmixtures and those with superscripts 0 are the fugacities atstandard states, which are the ideal gas at 1 bar in vapor phase, orthe pure-component fugacities at 1 bar and the systemtemperature in the liquid phase. The fugacity and the molefraction of component i are related through

ϕ = f y Pi i i (8)

where ϕ is the fugacity coefficient, which is calculated using anEOS, in our case the PCSAFT. The fugacities in mixtures in eq 7may be calculated in either phase because the vapor and liquidphases are in equilibrium, where the fugacities are equal in bothphases. However, as indicated in eq 7, the value ofK still dependson the standard states of the phases. In this work, the vapor phaseis chosen for convenience because the reaction equilibriumconstant has been determined in the vapor phase,17 which can beexpressed in temperature in the range of interest 293 K <T < 400K as

= − + −K Tlog 8.847 85 2045.883 56 1(9)

The value of K in eq 9 was determined using the experimentalentropy of nitric acid gas and the known thermodynamicproperties of the other reactants,17 but it has never been verifiedin applications due to the lack of reliable EOS in calculating thefugacity coefficients. Instead, K1 is often used to represent thissystem and estimated through eq 6, i.e., the partial pressures ofNO2 and NO in the vapor phase, which may be derived fromexperimental measurements.4,5 Some models for K1 wereproposed using empirical equations18,19 and nomograms.19,20

Whereas K is thermodynamically a function of temperatureonly21 as evident in eq 9, it is not the case with K1. Uponsubstituting the fugacities given by eq 8 into eq 7, K1 in the vaporphase may be calculated as

ϕ

ϕ

ϕ

ϕ=

Ky

yKP

( )

( )

( )

( )1

NO23

NO

H2O

HNO32

H2O

HNO32

(10)

Therefore, without a reliable EOS, it is not possible to connectthe experimentally derived value of K1 with the equilibriumconstant K. In this work, we couple eq 9 for K with PCSAFT tocalculate K1 and match it with the literature data, and thusestablish the EOS validity before making predictions on thesolubility of NO2 in water at various conditions relevant to fluegas geologic sequestration.

Physical Equilibrium. The heterogeneous nature of thereaction in eq 1 also requires the system to be in vapor−liquidphase equilibrium (VLE), where the fugacity of component i inthe mixture is the same throughout all phases, in this case vapor(V) and liquid (L) phases:

= f fi iV L

(11)

The equality of the fugacities in eq 11 must be solvedsimultaneously with mass-balance equations to find theequilibrium compositions in both vapor and liquid phases:

+ − =lx l y z(1 )i i i (12)

Here, l is the mole fraction of the liquid phase, and zi is the overallmole fraction of component i. It is also important to realize thatall mole fractions must sum up to unity:

∑ ∑= =x y 1i i (13)

Physicochemical Equilibrium. The VLE of the overallreaction eq 2 has 4 chemical components: H2O, HNO3, NO2*,and NO. As we will show in the model, NO2*may be treated as acomponent instead of two in SAFT framework. Therefore, uponbookkeeping we have 9 independent equations to solve for 9variables: {xi}, {yi}, and l. However, the compositions must alsosatisfy the chemical equilibrium represented by the reactionconstant K, eq 7, and, consequently, the mass balance of thechemical reaction, where the overall mole fractions {zi} in factresult from the chemical reaction and are calculated through

ενεν

=+

∑ +z

n

n( )ii i

i i

0,

0, (14)

In eq 14, {n0,i} is the initial moles before the reaction occurs, νi isthe stoichiometric coefficient of species i in the reaction, and ε isthe extent of reaction. An effective algorithm for thisphysicochemical equilibrium was adopted from Sanderson andChien.22

To know what inputs are needed for the equilibriumcalculations, we must first determine the degree of freedom ofthe reacting system, which follows the Gibbs rule21

π= − + −F N r2 (15)

where N, π, and r are the number of components, phases, andchemical reactions, respectively; in our case, they are 4, 2, and 1,leading to a degree of freedom of 3. This means that, besides thetemperature (T) and pressure (P), we still need another entity asa known variable in order to have the information of the systemcomplete. We may choose, for example, the loading of NO2in water, which can be defined as moles of NO2 injected per

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie402417p | Ind. Eng. Chem. Res. 2013, 52, 16032−1604316033

1000 mol of water. We will use this entity to calculate thesolubility of NO2 in water.In some previous studies, this additional entity was chosen to

be the amount of nitric acid in the liquid phase that is inequilibrium with the gases in the vapor phase.4,5 However, theexperiments were carried out using an inert background gas, i.e.,nitrogen, to dilute NO2 before passing it through the aqueousliquid phase. Though this gas does not participate in the chemicalreaction, its presence affects the concentrations in the equilibriain two ways: first, its mole must be added to the denominator ofeq 14, and second, it participates in the physical phase equilibria,i.e., eqs 11 and 12. Therefore, instead of 4 components, in thiscase we have 5 components, and thus 12 variables ({xi}, {yi}, ε,and l) to solve for from 12 equations, i.e., eqs 11−13 and eq 7with K from eq 9, after applying eq 14 to find {zi} as describedelsewhere.22 Such usage of a background gas increases thesystem’s degrees of freedom by one, so that the reacting systemof NO2 in water now has a degree of freedom of 4, whichmeans we need two known entities in addition to T and P to havethe system information fixed. In reproducing their data, wechoose the concentration of HNO3 in liquid phase (xHNO3) andthe mole fraction of NO in vapor phase (yNO) to accompany thepressure and temperature as the inputs of the calculations.

■ MODELING

Molecular Association. To make all calculations in theprevious section, we apply an EOS, the input of which needssome modeling for the molecules in the system. Because NO2,H2O, NO, and HNO3 are associating molecules, the model forthe molecular association is pivotal in this work.As is commonly done, we model the water molecule to have

two associating sites of proton-donor type and two associatingsites of proton-acceptor type. The association between

molecules, in this case also known as hydrogen bonding,occurs between two sites of different types. The proton-donor sites in water molecules belong to the hydrogen atoms,while the other type belongs to the electron lone-pairs inthe oxygen atoms. Such association scheme is known astype 4C.23

Four electron lone-pairs that are also present in the oxygenatoms of NO2 contribute four associating sites of proton-acceptor type in the molecule. These sites enable NO2 to crossassociate with water molecules, but do not associate amongthemselves. However, NO2 molecules are capable of formingdimers N2O4 through eq 1, which is in fact dominant at lowtemperatures particularly in liquid phase.24 In the SAFTframework, the dimerization is modeled as an associationbonding through a site, in this case on the nitrogen atom, thatis neither proton-donor nor proton-acceptor type, known as type1A,23 which can associate between themselves but not with othertypes of associating sites. This approach provides us with anadvantage that we do not need to consider N2O4 as anindependent species, so that NO2 is actually NO2* in SAFTframework exactly as in the overall reaction eq 2. This treatmenthas been proven to be effective.25 Dimerization also occurs forNO molecules,26 but they do not cross associate with watermolecules as inferred from molecular simulations.27 Themonomer and dimer structures of NO2 and NO in our modelare depicted in Figure 1a.For nitric acid molecules, the presence of a proton-donor site

on the hydrogen atom and some proton-acceptor sites at theoxygen atoms makes both the self-association and cross-association with water molecules possible. There are six electronlone-pairs at three oxygen atoms in the molecule, but only someof them are effective as proton-acceptor sites due to the stericeffects arising from crowded configuration of the oxygen atoms.

Figure 1. Association schemes used in the model: (a) NO2 and NO molecules, stars and triangles are the associating sites (star, dimer type; triangle,proton-acceptor type). The dimer forms are shown on the right next to them. (b) HNO3 molecule, open triangle is the associating site of proton-donortype (hydrogen atom).

Table 1. Pure-Component Parameters

m σ (Å) ε/kBa (K) associating sitesb εA/kB (K) κ ref

H2O 1.2190 c 213.5741 (2, 2, 0) 1851.9773 0.052 246 31NO2* 1.7202 2.793 41 203.6308 (0, 4, 1) 6596.2014 4.335 × 10−6 this workHNO3 2.5859 2.817 49 287.8668 (1, 2.5, 0) 652.6610 0.049 890 this workNO 1.4388 2.768 06 112.0302 (0, 2, 1) 1504.8371 0.000 185 this workN2 1.2414 3.299 20 89.2230 (0, 0, 0) 32

akB: Boltzmann constant. bThe first digit is the number of proton-donor type of associating sites, the second digit is the number of proton-acceptor type of associating sites, and the third digit is the number of type-1A associating sites. cσH2O = 2.798 384 + 120.733 275T−1 −71 515.85T−2 +11 052 303T−3 (Å).



A similar situation has been found in alcohols, in which thepresence of the alkyl group allows only one effective site on theoxygen atom.28 Therefore, one associating site may be assignedon each oxygen atom in HNO3 as shown in Figure 1b. However,this assignment does not give adequate representation of binaryphase equilibria data, particularly that of H2O/HNO3, which isdominant in the investigated chemical systems. It may be causedby the presence of the proton-donor site on the hydrogen atomthat introduces steric shielding to the neighboring proton-acceptor site. The fact that HNO3 undergoes ionic dissociation inwater provides an estimate of the number of proton-acceptor sites tobe between 2 and 3, corresponding tomolecular and ionic structures,respectively. We choose the average value of 2.5 for this number,which is quite unusual being a noninteger, but justifiable as it turnsout to represent the binary H2O/HNO3 very well as discussed laterin the paper. The direct benefit of this assignment is that there is noneed to explicitly treat the ionic dissociation of the acid in the SAFTframework, which makes the calculation tasks much simpler.Cross associations occur betweenHNO3 andH2O, HNO3 and

NO2, as well as NO2 and H2O. The association between HNO3and H2O is made asymmetric, in which the site on the hydrogenatom of HNO3 does not cross associate with oxygen atoms ofwater. Cross association occurs only between hydrogen atoms ofH2O and sites on oxygen atoms of HNO3. This asymmetricassignment is needed to make the model work in representingthe azeotropic binary mixture of HNO3/H2O. In addition to theaforementioned cross associations, the NO2 and NO moleculesare also allowed to cross associate each other through their type-1A associating sites to account for the fact that the molecules maycombine as N2O3 through eq 5.1,2

To validate the model against the experimental K1, wherenitrogen is used as the background gas, the nitrogen molecule isto be included. But because nitrogen is a nonassociatingmolecule, it does not have any association sites.PCSAFT EOS. In the following, we will briefly introduce the

PCSAFT EOS that we use to apply the model for this particular

system. The EOS calculates the residual Helmholtz free energy ofthe chemical system, as follows.

= + + + A A A A Ares hs chain disp assoc (16)

Here, the superscripts of the free energy terms on the right-handside of eq 16 are hard-sphere, chain, dispersion, and association,respectively. These refer to the molecular interactions in thesystem: the hard-core repulsion, the chain-forming covalentbond, the van der Waals type of dispersive attraction, and thehighly directed associating interaction through hydrogen bondsor dimerization, respectively.For each associating species in the system, the EOS has five

parameters: the segment numberm, the segment diameter σ, thesegment energy ε, the association volume κ, and the associationenergy εA. Nitrogen, which is the only nonassociating moleculein the system, does not have the latter two parameters. In a strictsense, the number of associating sites may be considered as aparameter that may be fitted from experimental phase-equilibriadata, but as shown earlier in the previous section it may also beestimated from the molecular structures. This estimation helpsthe other EOS parameters with more physical values.The details of the EOS can be found in the original work,15

while the whole association scheme can be handled using thegeneralized approach.29 As a note, the dimerization ofNO2 andNO,as well as the cross association between NO2 and NO, is not ofdonor−acceptor type, and therefore needs caution andmodificationexplained in the generalized approach.29 We apply an assumptionhere that this non-donor−acceptor association occurs independ-ently from that of the hydrogen-bond type of association. In otherwords, an occurrence of one cross-association type does not affectthe occurrence probability of the other type.

■ RESULTS AND DISCUSSIONParameter Derivation. The pure-component parameters of

all species in the system are tabulated in Table 1. They are derivedfrom fitting the literature vapor pressure and saturated-liquid

Table 2. Fitting of the Pure-Component Parameters

fitting range

T (K) Psat (bar) refAADa

PsatAADvL,sat

NO2* 294−388 1−31.28 DIPPR30 0.09% 0.07%HNO3 233−373 0.0007−1.783 DIPPR30 1.23% 0.24%NO 110−172 0.24−43.93 DIPPR30 0.47% 0.53%

aAverage absolute deviation = (βexp − βcalc)/ βexp × 100% (exp =experimental; calc = calculated); β is the vapor pressure Psat or thesaturated liquid volume vL,sat.

Table 3. Coefficients of Binary Interaction Parameters in Equation 18 and the References of the Experimental Data Used ToDerive Them

binary a b c d data ref T range (°C)

H2O−HNO3 −0.264 16 5.097 0 0 34 24.6−120.6H2O−NO −1.1144 64.235 −8.5220 0 37 0−100H2O−N2 −0.892 15 40.205 −4.316 0 35 5−89.8HNO3−NO2* 75.486 75 −6911.961 94 2114.659 23 −2.1614 38 21.5−76.6HNO3−NO 0 0 0 0HNO3−N2 0 0 0 0NO2*−NO 2.345 −141.6 20.57 0 40 37.7−104.4NO2*−N2 0 0 0 0NO−N2 0.04 0 0 0 39 (−159.4)−(−153.6)H2O−NO2* kij = 0.33743 − 4.827 × 107 × exp(−0.060 92T) 33 20−80

Table 4. Cross-Association Parametersa

H2O NO2* HNO3 NO

H2O 900.00 2340.00b

NO2* 0.05 881.0923 5450.437c

HNO3 0.05b 0.049 89NO 0.000 15c

aThe diagonally upper-right entries are the cross-association energyεAij/kB (K) and the lower-left entries are the cross-association volumeκij.

bOnly between proton-donor sites in H2O and proton-acceptorsites in HNO3 (see text). cType 1A cross association.



specific volume data.30 The fitting properties, references, and thequalities of fit are tabulated in Table 2. As defined before, NO2* isin fact a mixture of NO2 and its dimer N2O4. The parameters ofH2O and N2 are directly taken from previous studies.31,32

In mixtures, where interactions between unlike species occur,binary interaction parameters kij are needed and derived frombinaryVLE data for interactions between species. The binary interactionparameters are used to correct the molecular interactions and areimplemented in the combining rule of the energy parameters:

ε ε ε= − k(1 )ij i j ij (17)

The binary interactions are generally functions of temperature,which are in the form of polynomials

= + × + × + ×− − −k T a b T c T d T( ) 10 10 10ij4 6 2 6 3

(18)

where the coefficients a, b, c, and d are listed in Table 3. Theexception is for H2O−NO2*, which is also given in the last row ofthe table. The use of a high-order polynomial in the parametercorrelation is necessary in our case to obtain acceptableaccuracies for several binary mixtures due to the limitedavailability of their experimental data as described later.Moreover, as our applications fall within the correlationtemperature range, the use of eq 18 is safe and justified for ourmodel. Greater data availability in the future will definitelyimprove the correlation quality and extend the applicability to awider temperature range.Among the binary parameters, the kij between H2O and NO2*

is the only one that was derived from the experimental physicalVLE of ternary mixture, which is in this case H2O/HNO3/NO2*,

33 because the data of physical VLE of the binary H2O/NO2* do not exist due to the high reactivity of the system. Thereare three binary mixtures that do not have experimental data, i.e.,NO/HNO3, N2/HNO3, and NO2*/N2, the binary parameters ofwhich could fortunately be set to zero. This fortunate fact isjustified in parameter sensitivity tests of the quinary mixture ofN2/H2O/HNO3/NO2*/NO discussed later in this paper.The cross-association parameters, which are commonly

derived from mixing rules, have to be directly fitted from theexperimental data due to the high complexity of the reactingsystem. The parameters are listed in Table 4. No crossassociation occurs between NO and H2O or HNO3.

EOS Performance. The EOS performance is presented herefor both the correlations in deriving the parameters and theirextrapolations to independent data, not included in the correlations,using the derived parameters without additional adjustments.The most important binary mixture is H2O/HNO3, which

contains the dominant species in the liquid phase. Although

Figure 2. VLE of H2O/HNO3: experimental data,34 open symbols are

the dew points; filled symbols are the bubble points. Curves arePCSAFT correlations.

Figure 3. EOS extrapolation on the behavior of dilute HNO3 aqueous solutions: symbols are experimental data;4 curves are PCSAFT calculation.



many authors have discussed this particular system,9−11 most ofthem did not provide the physical equilibria data that we need toderive the binary interaction parameter. The performance ofPCSAFT correlation for this binary, which has an azeotropicbehavior, is shown in Figure 2 at various T and P along with theexperimental data.34 The performance is then extrapolated to thedilute HNO3 aqueous solutions at atmospheric pressure andcompared with the data of Burdick and Freed4 in Figure 3.Figures 4 and 5 show the EOS performance in N2/H2O and

NO/H2O systems, respectively, both of which have small gas

solubility in the aqueous phase. While the experimental data forN2/H2O are abundantly available in the literature, for example,those shown in Figure 4,35,36 there is only one set of data availablefor NO/H2O.

37 It is also the case for HNO3/NO2*, for whichonly one set of physical equilibrium data is available,38 whilemany others are physicochemical data at high concentration ofHNO3

11−14 that follow the dissociation reaction of eq 3irrelevant to flue gas geologic sequestration. The EOS perform-ance for HNO3/NO2* is shown in Figure 6, where it exhibitsliquid−liquid equilibrium (LLE) at low temperatures.

Figure 4. VLE of N2/H2O: (a) solubility of N2 in liquid phase, curves are PCSAFT correlation; (b) mole fraction of water in vapor phase, curves arePCSAFT extrapolation. Symbols are experimental data.35,36

Figure 5. Solubility of NO in H2O: symbols are experimental data;37

curves are PCSAFT correlation.Figure 6. Phase equilibria of HNO3/NO2*: symbols are experimentaldata;38 curves are PCSAFT correlation.



TheVLEof the gases,N2/NOandNO2*/NO, arewell representedalong with the experimental data39,40 in Figure 7a,b, respectively.Due to the unavailability of physical VLEdata asmentioned before,

the binary parameter of NO2* in water was derived from the NO2*/H2O/HNO3 ternary. Since we already have the binary parameters forNO2*/HNO3 and H2O/HNO3, the derivation of that of NO2*/H2O from the ternary data is straightforward. Caution must be takenfor this ternary, however, becausemost of the data in the literature arephysicochemical rather than physical VLE. The physical VLE data33

are shown in Figure 8 together with the EOS representation.Up to this point, all parameters have been derived, except for

the binary parameters of N2/HNO3,NO/HNO3, andN2/NO2*, the

experimental data of which are not available in the literature. We ranparameter sensitivity tests over the quinary mixtures N2/H2O/HNO3/NO2*/NO, from which we conclude that those remainingthree binary parameters have very small effects on the phase equilibriacalculations. Therefore, we safely set them to zero for simplicity.

EOS Validation.Now, using the parameters listed in Tables 1,3, and 4, along with the equilibrium constant K in eq 9, thelogarithm of K1 can be calculated and matched with theexperimental data. The available data were all obtained by varyingthe temperature and liquid concentration of HNO3 (xHNO3) atatmospheric pressures. Due to the use of N2 as the background gas,as discussed before, the degree of freedom of the chemical system is

Figure 7. Binary VLE: (a) N2/NO; (b) NO2*/NO. Symbols are experimental data;39,40 curves are PCSAFT correlation.

Figure 8.VLE of H2O/HNO3/NO2*: (a) data used to derive the binary parameter of NO2*/H2O; symbols are experimental data,33 curves are PCSAFT

correlation. (b) EOS extrapolation examples at other compositions compared with experimental data.33



in fact 4, not 3, so that the data were not measured systematically asthey should have been if another property was fixed in theexperiments in addition to the system P, T, and xHNO3. Theresearchers assumed that the presence of the background gas couldsafely be neglected due to the small N2 solubility in water as well asthe inert nature of the N2 in the chemical reaction eq 2.Unfortunately, this assumption produced experimental data

with obvious scattered distribution, as can be seen in the originalpaper,4 in which experiments at the same condition (P, T, xHNO3)give very different concentrations in the vapor phase. Even worse,

the determination of gas concentration in the vapor phase isinaccurate in some cases, particularly when the gas exists in smallquantities, i.e., at low concentration of HNO3 (<10 wt %) forNO2* and at high concentration of HNO3 (>55 wt %) for NO.

4

Figure 9 shows the comparison between theEOS-calculated logK1

with that of Burdick andFreed,4 aswell as that ofTereshchenko et al.5

We calculated log K1 at the original experimental conditions (P, T,xHNO3) and one of the published mole fractions of NO that wasexperimentally derived in the vapor phase (yNO) to satisfy the systemdegree of freedom of 4. In Figure 9a, the data of Tereshchenko et al.5

Figure 9. Logarithm of partial equilibrium constant K1 versus nitric acid concentration at P = 1 atm: (a) Tereshchenko et al.;5 (b) Burdick and Freed.4

Symbols with connecting curves are calculated using the EOS.

Figure 10.Calculated values of log K1 at 25 °C based on the choice of yNO: (a) comparison with Burdick and Freed,4 dotted curve from Figure 9b, dash-

dotted curve for quaternary H2O/HNO3/NO2*/NO, solid curve for quinary with yNO from part b. (b) The corresponding choices of yNO (for thequaternary, yNO is fixed by the experimental conditions, not by choice).



are well reproduced except at low temperature (20 °C) and high acidconcentration, where the resulting NO in the vapor phase is so smallthat may be buried in the uncertainty of the measurements.As shown in Figure 9b for the data of Burdick and Freed,4 a

similar symptom occurs at 25 °C and high HNO3 concentration,as well as at 75 °C, the very reason why no data was measured at57.8 wt % of HNO3. Considering the omission of some databefore averaging the values of log K1, the apparent order of thelogarithm of K1 data in Figure 9b may be deceptive.Regarding the deviation observed above at high acid

concentrations, particularly at low temperatures, we recalculatedthe logK1 at 25 °C at the same conditions (P, T, xHNO3) as that inBurdick and Freed, but now with a systematic choice of yNO. Inaddition, we also calculated log K1 at the conditions forquaternary H2O/HNO3/NO2/NO, in which we have a degreeof freedom of 3, so that the input (P, T, xHNO3) is sufficient to fix thesystem properties; in this case log K1 does not depend on yNO. Theresults are shown in Figure 10a with the corresponding yNO used inthe calculations in Figure 10b. The yNO curve for the quaternary inFigure 10b is not by choice, but fixed by the conditions (P,T, xHNO3).As seen in Figure 10a, the values of Burdick and Freed at high acid

concentration can be reproduced (solid curve) only if we use muchsmaller yNO (solid curve) as shown in Figure 10b. In other words,the experimentally derived yNO is inaccurate due to the diminishingamount of NO in the gas phase. The dependency of log K1 on yNOcan be clearly observed if the acid concentration is lowered whileyNO is increased as we track the solid curves upward in Figure 10a,b.When yNO is larger than that of Burdick and Freed, logK1 gets lowerapproaching the fixed value given by the quaternary system, whereNO is the dominant gas in the vapor phase replacing N2. From thisdiscussion, we learn that the presence of N2 cannot be neglected incalculating K1, particularly at low and high acid concentrations.The calculated K1 values matching with that derived from

experiments provide us with two pieces of information. First, theliterature values of K in eq 9 are verified for use in the main reactionof eq 2. Second, the EOS is validated that allows us to proceed withcalculations predicting the solubility of NO2* in water.

Predictions on the Solubility of NO2* inWater.The totalNO2* that dissolves in water also includes the reaction products(HNO3 and NO), and can be calculated through the molebalance:

*

= * + +n n n

total NO mole dissolved

(liquid) (liquid) (liquid)2

NO2 HNO3 NO (19a)

εν= + +

∑ +*

*x x x

l n

n( )

( )i iNO2 HNO3 NO

0,

0,NO2 (19b)

Figure 11. Prediction of solubility curves of NO2* in water: (a) bubble pressure vs NO2* loading at different temperatures, (b) bubble pressure vstemperature at different NO2* loadings.

Figure 12. Predicted portion of injected NO2* that dissolves in water at25 and 75 °C for ζ = 0.001.



The solubility of NO2* in water is calculated from thequaternary system of H2O/HNO3/NO2*/NO with P, T, and theNO2* loading as the input, which makes more sense for absorptionpurposes rather than xHNO3. The NO2* loading ζ is defined here asmoles of NO2* injected into every 1000 mol of water:

ζ = *n

1000 mol H O0,NO2

2 (20)

We assume that there is no product species (HNO3 and NO)in the system before the chemical reaction eq 2 as it should be inthe absorption of NO2 in water. The results are presented assolubility curves in bubble-point diagrams in Figure 11a,b. Thebubble-point pressure is the pressure above which all the gasdissolves in water. In Figure 11a, the solubility curve can also beinterpreted as the maximum loading below which all injectedNO2* dissolves in water. In Figure 11b, it can be understood asthe maximum temperature above which some of the gas escapesto the vapor phase.It is clear from Figure 11b that the bubble pressure

dramatically increases at temperatures between 25 and 40 °C.Consequently, the solubility of NO2* hugely drops from 25 to40 °C.The percentage of dissolved NO2* relative to the injected

amount, i.e., the dissolved species for every 1000 molecules ofH2O on the right-hand side of eq 19a divided by 1000 × ζ, ispresented in Figure 12 as a function of pressure for loading ζ =0.001. The percentage reaches 100% at the bubble pressures. Thecorresponding composition of the dissolved portion of NO2* ispresented in Figure 13a,b. The top lines in these figures are thesame as those in Figure 12.It can be seen in Figure 13a,b that most of the dissolved NO2*

is in the form of HNO3. The acid concentration decreases withpressure as the amount of unreacted NO2* increases, whichdoubles from atmospheric pressure to the bubble pressure at25 °C. At 75 °C, this behavior is not obvious in Figure 13b due tothe minute amount of unreacted NO2*. The percentage of theresulting HNO3 at 75 °C approaches 66.67% at all pressures,which means the reaction of NO2* with H2O is practically

complete according to eq 2 even at atmospheric pressure. It alsoconfirms that the reaction in eq 2 does occur in the liquid phase.The completion of the reaction is the cause of the dramaticincrease of the bubble pressure at 25−40 °C in Figure 11, asdemonstrated in Figure 14 where the acid concentration quicklyapproaches 66.67% (xHNO3 = 0.004 for ζ = 0.006, and xHNO3 =0.000 67 for ζ = 0.001) in this range of temperature. Thecorresponding maximum weight fraction of the resulting HNO3 is1.38% and 0.23%, respectively. The curves in Figure 14 werecalculated at their bubble pressures; the behavior at other pressuresis very similar to that at bubble pressures.The compositions of vapor and liquid phases at different

pressures corresponding to the conditions in Figure 12 are given

Figure 13. Predicted composition of the dissolved portion of NO2* in water: (a) at 25 °C, (b) at 75 °C for ζ = 0.001.

Figure 14. Predicted concentration of HNO3 in liquid phase at bubblepressures: ζ = 0.001 (right vertical axis) and ζ = 0.006 (left vertical axis).



in Figure 15a,b, respectively. The calculations start atatmospheric pressure up to the bubble pressure at eachtemperature. Since the aqueous liquid phase consists of mostlywater (more than 99.9 mol %) at both temperatures, water molefraction in liquid is not included in Figure 15b for clarity.The order of abundances is NO, H2O, NO2*, and HNO3 in

the vapor phase, and H2O (not shown in Figure 15b), HNO3,NO, and NO2* in the liquid phase. At 25 °C and lower pressureregion, however, NO2* is more than NO in the liquid phase. Asthe pressure increases, the concentrations of NO and NO2*increase in both phases; the increase is not so obvious at 75 °C inthe vapor phase due to the scale of Figure 15a. On the contrary,the concentrations of water and HNO3 in the vapor phasedecrease with pressure, while they are relatively constant in theliquid phase.

■ CONCLUSIONS

The model using PCSAFT is found capable of describing thephysicochemical equilibria of an important reacting chemicalsystem of NO2 in water, which involves the reaction productsHNO3 and NO. Several important findings are as follows: (1) Inthis model, the total reaction eq 2 is effective to represent thereacting system of NO2* in water in the dilute region of theresulting HNO3. The reaction is confirmed to occur in the liquidphase. (2) The literature value of the reaction constant K in eq 9is verified for applications. (3) The use of an inert background gasintroduces an additional degree of freedom. Despite the inertnature of the gas with respect to the chemical reaction and thelow solubility of the gas in the aqueous liquid phase, the presenceof the gas has substantial effects that cannot be neglected.Therefore, the use of partial reaction constant K1 is notrecommended. With the availability of the new model, K1 is nolonger needed, and should be replaced by the total constant K.(4) Without an inert background gas, the solubility of NO2* inwater dramatically drops in the temperature range 25−40 °C dueto the completion of the reaction in eq 2 at higher temperatures. (5)In equilibrium without an inert background gas, NO dominates the

vapor phase, while HNO3 trails water in dominating the liquidphase.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by DOE Financial AssistanceAgreement DE-FE0004832. The authors also acknowledge thefinancial support of the School of Energy Resources and theEnhanced Oil Recovery Institute at the University of Wyoming.

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Figure 15. Predicted compositions of NO2*/H2O system at 25 and 75 °C for ζ = 0.001: (a) vapor phase, (b) liquid phase.



mailto:[email protected]

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