water systems

Fluid Phase Equilibria 169 Ž2000. 223–236 www.elsevier.nlrlocaterfluid

Improved thermochemical data for computation of phase and chemical equilibria in flue-gasrwater systems J. Krissmann, M.A. Siddiqi ) , K. Lucas Department of Thermodynamics, Gerhard-Mercator-UniÕersity Duisburg, Lotharstraße 1, D-47048 Duisburg, Germany Received 24 August 1999; accepted 25 January 2000

Abstract A thermodynamic model for the computation of phase and chemical equilibrium in aqueous systems based on minimization of the Gibbs energy is developed using new thermochemical data and Pitzer’s activity coefficient model. New data for the thermodynamic standard properties Df G 0 , Df H 0 and Cp0 , are determined from our experimental results, which are based on the spectrometric in situ analysis of both the vapor and the liquid phase. The studies have been made in the concentration range pertinent to flue gas purification processes: p SO 2 between 0.01 and 1 kPa, c HCl up to 1 mol dmy3 , c H 2 SO 4 and cCaCl 2 up to 0.5 mol dmy3 . The temperature varies from 298 to 333 K. In comparison with earlier data, a better correlation of important flue-gasrwater subsystems like SO 2 q water is achieved and a formerly proposed complexation of sulfur dioxide in the SO 2 q HCl q H 2 O system is confirmed. In particular, it is shown that on this basis the phase equilibria of SO 2 q CaCl 2 q H 2 O and SO 2 q HCl q H 2 SO4 q H 2 O can be predicted without further adjustment of parameters. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Vapor–liquid equilibria; Chemical equilibria; Electrolytes; Data; Method of calculation; Sulfur dioxide

1. Introduction The removal of pollutants such as SO 2 , HCl or NO x from flue gases produced by coal fired power plants or incinerating plants often takes place via a wet scrubbing process. In an earlier paper w1x, a thermodynamic model for the computation of phase and chemical equilibrium in aqueous systems

)

Corresponding author. Tel.: q49-203-379-3353, fax: q49-203-379-1594. E-mail address: [email protected] ŽM.A. Siddiqi..

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 0 0 . 0 0 3 1 2 - 5

224

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Fig. 1. Scheme for the investigation of systems.

based on minimization of the Gibbs energy was presented, which used thermodynamic standard properties from literature w2,3x and a modified Debye–Huckel equation w4x for calculating the activity ¨ coefficients of the solutes. The modified Debye–Huckel equation did not require any substance ¨ specific parameter but used a mean value of r s 14.9 for all electrolyte systems. This model is developed further by using newly evaluated thermodynamic data based on our recent experimental investigations and Pitzer’s activity coefficient model for multicomponent strong electrolytes w9–13x. The adjustable binary parameters of Pitzer’s equation are taken from literature for strong electrolyte systems w13–16x. The thermodynamic standard properties needed for the computation are the Gibbs energy of formation Df G T0 0 , the enthalpy of formation Df HT00 and the heat capacities c p,T0 , all in appropriate standard states. These data are determined by a systematic investigation of binary and ternary systems as illustrated in Fig. 1. The purpose of this work is to show the ability of the new model for the correlation of equilibria in SO 2 q H 2 O, HCl q H 2 O, SO 2 q HCl q H 2 O systems as well as for the reliable prediction in SO 2 q H 2 SO4 q H 2 O, SO 2 q CaCl 2 q H 2 O and SO 2 q HCl q H 2 SO4 q H 2 O systems. The experimental data for the cited systems are compared with the calculations done using the original w1x and the modified model.

2. Model description The algorithm for minimization of Gibbs energy, the computation of chemical potentials from standard data and the special simplifications for flue-gasrwater systems are described in detail elsewhere w1x. In this work, four modifications have been made. Ži. The thermodynamic standard data for the solutes are checked and, if needed, improved on the basis of experimental investigations. The new substance specific data are given in Table 1.

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Table 1 Thermodynamic data at T 0 s 298.15 K and p 0 s 0.1 MPa Species

State a

D f G T0 0 , kJ moly1

D f HT00 , kJ moly1

H 2O

g

y228.572

y241.818

H 2O SO 2

l g

SO 2 N2

y237.129 y300.090

aq g

y285.830 y296.810

y300.503 0

y323.160 0

0 y1 0 , J mol c p,T Ky1

b

33.656 75.291

0 b

39.765 194.8

1.69 b

29.177 HCl

g

y95.299

y92.307

Hq HSOy 3 SO 32y S 2 O52y HSO4y SO42y OHy Cly Ca2q

aq aq aq aq aq aq aq aq aq

0 y527.032 y486.092 y808.405 y755.910 y744.530 y157.244 y131.228 y553.580

0 y626.790 y630.440 y972.350 y887.340 y909.270 y229.994 y167.159 y542.830

SO 2 Cly

aq

y426.991

y490.320 d

Žd c p0 rdT .T 0 , J moly1 Ky2

b

29.527 0 y1.9 y263.9 y100.0 y84 y293 y148.8 y136.4

0 3.39 0.69 4.88 0 0 0 0 0 1.69 d

y8.40 58.40 d

Source w2x w6x w2x w7x w6x w5x convention w6x w2x w6x convention w7x c w7x c w7x c w2x w2x w2x w2x w2x w8x w5x

a

The corresponding standard states are as follows: ‘‘g’’ — ideal gas, ‘‘l’’ — pure liquid, ‘‘aq’’ — hypothetical ideal aqueous solution of unit molality. b The temperature dependence of gaseous components is taken from Ref. w6x. c Converted from given equilibrium constant. d These values are estimated by assuming K s const. for reaction: SO 2 Žaq.qCly°SO 2 Cly.

Žii. The activity coefficients of the ionic species are now calculated using Pitzer’s equation for multicomponent strong electrolytes w9–11x. Restriction to binary interaction parameters for ions of opposite charge leads to the following equation for the molal activity coefficient of ion i: lng i) s yAf Ž T . z i2

ž

= b

ž

Ž 0. ij q

'I 1 q 1.2'I

bi jŽ 1 . 2I

2 q 1.2

/

ln Ž 1 q 1.2'I . q 2

Ž 1 y Ž1 q 2'I . exp Žy2'I . .

= Ž 1 y Ž 1 q 2'I q 2 I . exp Ž y2'I . .

Ý mj j/w

/

y

z i2 4I 2

Ý Ý m j m k b jkŽ1. j/w k/w

Ž1.

where Is

1 2

Ý m j z j2 j

Ž2.

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Table 2 Debye–Huckel coefficient and ion–ion interaction parameters for Pitzer’s equation ¨ Parameter

298.15 K

313.15 K

323.15 K

333.15 K

Source

Aw . b Ž0. ŽHq, HSOy 3 . b Ž1. ŽHq, HSOy 3 b Ž0. ŽHq, HSO4y . b Ž1. ŽHq, HSO4y . b Ž0. ŽHq, SO42y . b Ž1. ŽHq, SO42y . b Ž0. ŽHq, Cly . b Ž1. ŽHq, Cly . b Ž0. ŽHq, SO 2 Cly . b Ž1. ŽHq, SO 2 Cly . . b Ž0. ŽCa2q, HSOy 3 . b Ž1. ŽCa2q, HSOy 3 b Ž0. ŽCa2q, Cly . b Ž1. ŽCa2q, Cly .

0.3909 0.1500 0.4000 0.2106 0.5320 0.0217 0 0.1754 0.3004 0.1694 0.5365 0.4380 1.7600 0.3053 1.7081

0.4022 0.1500 0.4000 0.2029 0.4580 0.0123 0 0.1690 0.3119 0.1694 0.5365 0.4380 1.7600 0.3065 1.7684

0.4104 0.1500 0.4000 0.1981 0.4154 0.0066 0 0.1647 0.3215 0.1694 0.5365 0.4380 1.7600 0.3069 1.8165

0.4190 0.1500 0.4000 0.1937 0.3776 0.0012 0 0.1604 0.3326 0.1694 0.5365 0.4380 1.7600 0.3068 1.8710

w12x w13x w13x w14x w14x w14x w14x w15x w15x w5x w5x w13x w13x w16x w16x

is the ionic strength in terms of molality. The bi j parameters are binary interaction parameters, which are taken from literature for aqueous single electrolyte solutions and listed in Table 2. The activity coefficients of all molecular dissolved solutes are set equal to unity. Žiii. The activity of the solvent is calculated from the Gibbs–Duhem equation w11x: aQw s wQ x w s Mw

g

ž

2 Af Ž T . I 1.5 1 q 1.2'I

y

Ý Ý m i m j ž bi jŽ 0 . q bi jŽ 1 . exp Žy2'I . /

i/w j/w

/

y Mw

Ý mi

Ž3.

i/w

Živ. For an accurate representation of thermodynamic equilibrium at elevated temperatures, the temperature dependence of the molar heat capacity for the main solutes, like SO 2 Ž aq. and HSOy 3 , are now calculated by a Taylor series: 0 c pi Ž T . s c p0 i Ž T 0 . q

0 d c pi

ž / dT

ŽT y T 0 . .

Ž4.

T0

This form for the temperature dependence of c p0 is chosen to facilitate the representation of K Ž T . Rln K Ž T . s A q

B T

q CT q DlnT

Ž5.

in terms of the standard thermodynamic data. The K-value is related to the Gibbs energy of the corresponding reaction via RT ln K Ž T . s yDr G 0 Ž T .

Ž6.

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In Eq. Ž6. the pressure dependence of the liquid phase is neglected. Expressing Dr G 0 Ž T . in terms of standard Gibbs energy of reaction, standard heat of reaction, molar heat capacities according to Eq. Ž4. and integrating with respect to the temperature yields Rln K Ž T . s y =

Dr G T0 0 T0

ž

q Dr HT00

T T

y 0

T0 T

ž

y 2ln

1 T0 T T0

1 y T

/

/

q Dr c p0 ,T 0

ž

T0 T

y 1 q ln

T T0

/

q

T 0 d Dr c p0 2

ž

dT

/

T0

Ž7.

A comparison of the coefficients in Eqs. Ž 5. and Ž7. leads to the standard thermodynamic data of the reaction and, finally, to the substance specific data, if an appropriate reference point is chosen.

3. Data evaluation For testing the extrapolation ability of the thermodynamic model, accurate measurements for binary, ternary and quaternary systems are needed. The experimental results for the ternary systems SO 2 q H 2 SO4 q H 2 O, SO 2 q HCl q H 2 O and SO 2 q CaCl 2 q H 2 O have already been published w17,18x. Some additional measurements on the quaternary system SO 2 q HCl q H 2 SO4 q H 2 O are reported here. For the study of phase equilibria, a closed circulation apparatus was used, which allows an in situ measurement of the concentrations of SO 2 in both the liquid and the vapor phase simultaneously by coupling UV spectroscopy with a special fibre optic-based technique. The method for the measurements is the same as described earlier w17,18x. The total pressure at thermodynamic equilibrium results mainly from inert nitrogen and is about 103 kPa. The equilibrium partial pressure of sulfur dioxide P SO 2 is calculated by P SO 2 s cSO2 ,2 RT2

Ž8.

where T2 is the equilibrium temperature and cSO2 ,2 is the concentration of SO 2 in the gas phase. This equation differs from that given in some former communications w17,18x, where the partial pressures were wrongly transformed using a standard pressure of 100 kPa. The experimental partial pressures reported there can be easily corrected by multiplication with Ž prp 0 ., where p 0 s 100 kPa is the standard pressure. The corrected data are given in the Results section.

4. Results 4.1. Binary systems Our calculations for the activity coefficients in aqueous systems containing a single strong electrolyte Ž HCl, H 2 SO4 or CaCl 2 . have shown the Pitzer model w9–11x to be the most suitable for the representation of combined phase and chemical equilibrium in the concentration range up to 2 molrkg. Therefore, we use this model for the following calculations. In contrast with this model, the modified Debye–Huckel equation w4x, which was used in Ref. w1x, is limited to high dilution, as it is ¨

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Table 3 Partial pressure of hydrogen chloride above aqueous solutions T, K

m HClŽtot. , mol kgy1

calc g" wthis modelx

w x p exp HCl , kPa 19

calc p HCl , kPa wthis modelx

calc p HCl , kPa w1x

293.15 293.15 293.15 293.15 293.15 293.15 323.15 323.15 323.15 323.15 323.15 323.15

0.01 0.05 0.10 0.20 0.50 1.00 0.01 0.05 0.10 0.20 0.50 1.00

0.906 0.832 0.798 0.770 0.763 0.817 0.900 0.822 0.784 0.752 0.736 0.773

0.245P10y8 0.517P10y7 0.191P10y6 0.704P10y6 0.435P10y5 0.199P10y4 0.447P10y7 0.933P10y6 0.336P10y5 0.125P10y4 0.721P10y4 0.327P10y3

0.249P10y8 0.527P10y8 0.194P10y6 0.721P10y6 0.443P10y5 0.203P10y4 0.453P10y7 0.944P10y6 0.344P10y5 0.127P10y4 0.756P10y4 0.334P10y3

0.253P10y8 0.541P10y8 0.198P10y6 0.720P10y6 0.391P10y5 0.140P10y4 0.458P10y7 0.971P10y6 0.354P10y5 0.128P10y4 0.688P10y4 0.244P10y3

) not able to reproduce the typical increase in the mean ionic activity coefficient g " at higher y1 molalities Ž) 0.5 mol kg . due to intermolecular short range interactions in the solution. For this reason, the Debye–Huckel based model was adjusted in Ref. w1x by introducing an empirical ¨ correction for the HCl q H 2 O system. This system is pertinent to the absorption of flue-gases in acidic scrubbers, which are frequently found behind waste incinerating plants. Table 3 and Fig. 2 show the calculated vapor pressures of HCl above aqueous solutions based on Pitzer’s model as ) compared to the results given in Ref. w1x. As the Pitzer model yields a better correlation of g " over the whole concentration range, the calculated vapor pressures of HCl are also much closer to the experimental data of Fritz and Fuget w19x up to 1 mol kgy1 HCl.

Fig. 2. Comparison of model calculations with the experimental data for HClqH 2 O system at 298 and 323 K.

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The binary system SO 2 q H 2 O is most relevant for the modeling of flue-gasrwater systems. In Ref. w1x, a comparison with the experimental data of Johnstone and Leppla w20x and Rabe and Harris w21x was presented. These data are listed in Table 4 along with some of our recent measurements at higher dilution w22x. Our experimental results for phase equilibrium and the dissociation of SO 2 in aqueous phase in the temperature range 25–608C were used to select the most reliable equilibrium constant for HSOy 3 formation, via SO 2 Ž aq . q H 2 O Ž l . | Hqq HSOy 3. This was subsequently used to obtain Henry’s constant HSO2 for sulfur dioxide in water w5x. The Henry constant agrees within about "1% Ž298–333 K. with the value given by Rumpf and Maurer w23x and is about 5% Ž at 298 K. higher than the value of Goldberg and Parker w7x. As the determined or selected K-values for the chemical reaction and the physical absorption are related directly to 0 0 0 and Ž d D c rdT . 0 Ž cf. Eq. 7. , we can convert these into substance specific Dr G T0 0 , Dr HT00 , Dr c p,T r p T parameters, which are needed here for using direct minimization of the Gibbs energy. For this purpose we chose the well known value for SO 2 Ž g. as reference point. The resulting thermochemical data for dissolved sulfur species are listed in Table 1. A comparison of the calculations based on the new model and the old model w1x with the experimental data is presented in Table 4. It may be seen that both the measurements done in this laboratory at high dilution and the measurements of other authors w20,21x are in good agreement with those calculated using the new model. On the other hand, the equilibrium calculations according to Ref. w1x differ significantly from the experimental data for the partial pressure as well as for the degree of dissociation. The predicted values for the degree of dissociation according to the old model are too high and, consequently, the calculated partial Table 4 Phase and chemical equilibria for absorption of sulfur dioxide in water T, K

p, kPa

m SO 2Žt ot., mol kgy1

exp a SO 2

calc a SO 2 wthis modelx

calc a SO 2 wold modelx

exp p SO , 2 kPa

calc p SO , kPa 2 wthis modelx

calc p SO , kPa 2 wold modelx

Source for exp. data

298.15 298.15 298.25 298.05 298.15 298.15 298.15 298.15 298.15 298.15 322.60 323.00 322.80 322.60 322.70 322.60 323.15 323.15

104.96 105.56 105.52 104.72 105.84 101.30 101.30 101.30 101.30 101.30 103.68 101.55 102.19 102.72 102.93 101.90 101.30 101.30

0.00154 0.00357 0.00661 0.00991 0.0121 0.0271 0.0854 0.1663 0.2873 0.5014 0.00113 0.00344 0.00540 0.00717 0.00724 0.0100 0.0921 0.501

0.909 0.840 0.761 0.697 – 0.524 0.363 0.285 0.230 0.184 0.876 0.759 0.693 0.644 0.646 0.594 – –

0.915 0.839 0.762 0.703 0.672 0.543 0.373 0.291 0.234 0.186 0.888 0.758 0.692 0.648 0.646 0.594 0.277 0.137

0.929 0.863 0.793 0.738 0.709 0.583 0.411 0.325 0.266 0.215 0.908 0.794 0.732 0.690 0.688 0.638 0.308 0.158

0.012 0.050 0.134 0.254 0.335 1.05 4.56 9.84 18.1 33.7 0.021 0.147 0.297 0.457 0.457 0.721 11.5 77.9

0.011 0.049 0.134 0.248 0.336 1.05 4.53 9.98 18.6 34.6 0.023 0.150 0.298 0.450 0.458 0.723 12.0 78.1

0.009 0.040 0.113 0.213 0.290 0.933 4.14 9.24 17.4 32.4 0.018 0.126 0.256 0.391 0.398 0.637 11.4 75.4

w22x w22x w22x w22x w22x w20x w20x w20x w20x w20x w22x w22x w22x w22x w22x w22x w21x w21x

230

J. Krissmann et al.r Fluid Phase Equilibria 169 (2000) 223–236

Fig. 3. Comparison of model calculations with the experimental data for SO 2 qH 2 O system at 298 and 323 K.

pressures are too low. Typical results at 298 and 323 K for the concentration range most relevant to flue-gasrwater system are also shown graphically in Fig. 3. 4.2. Ternary systems and quaternary system From the knowledge of standard data and interaction parameters obtained from the consideration of the binary electrolyte systems H 2 SO4 q H 2 O, HCl q H 2 O, CaCl 2 q H 2 O and SO 2 q H 2 O, the phase equilibrium for the ternary systems, i.e. the absorption of sulfur dioxide in aqueous solutions of H 2 SO4 , HCl or CaCl 2 , may be predicted. As shown in a former communication, the prediction of SO 2 q H 2 SO4 q H 2 O is possible w18x. To perform the same calculations using the described algorithm for minimization of the Gibbs energy, it is necessary to differentiate between the two valency states of sulfur, namely tetravalent SŽ IV. and hexavalent SŽVI.. This differentiation is done to prevent the oxidation of sulfite to sulfate ion Ž as is the case in the absence of oxygen and in acidic solutions. , which is known to be kinetically inhibited. Table 5 shows the complete matrix for the species to be considered. The results of phase and chemical equilibrium calculations are compared with the experimental data and the calculations based on the old model w1x in Table 6. At very high dilution of the sulfuric acid, the degree of dissociation for SO 2 is found to be important and, consequently, the corresponding partial pressures of SO 2 calculated according to Ref. w1x are too small compared with experimental values. With increasing molarity of sulfuric acid, the degree of dissociation for SO 2 decreases as a consequence of the more acidic solution. The predicted partial pressures according to Ref. w1x are then in better agreement with the measurements. This may be a consequence of the negligible influence of the dissociation reaction in strongly acidic solutions. The predictions based on the model presented in this work are throughout in excellent agreement with the experimental data. Table 7 shows a similar comparison between the experimental and the calculated values for the SO 2 q HCl q H 2 O system. Again the measured partial pressures show an increase in more acidic

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Table 5 Atom and charge matrix Species

zi

H

O

N

S ŽIV.

S ŽVI.

Cl

Ca

H 2O SO 2 N2 HCl Hq HSOy 3 SO 32y S 2 O52y HSO4y SO42y OHy Cly Ca2q SO 2 Cly

0 0 0 0 1 y1 y2 y2 y1 y2 y1 y1 q2 y1

2 0 0 1 1 1 0 0 1 0 1 0 0 0

1 2 0 0 0 3 3 5 4 4 1 0 0 2

0 0 2 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 1 1 2 0 0 0 0 0 1

0 0 0 0 0 0 0 0 1 1 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 1 0 1

0 0 0 0 0 0 0 0 0 0 0 0 1 0

Table 6 Phase and chemical equilibria for system SO 2 qH 2 SO4 qH 2 O T, K

exp calc calc exp calc calc p, kPa c H 2 SO4 , m SO 2 Žtot. , a SO , a SO a SO p SO , p SO , kPa p SO , 2 2 2 2 2 2 mol dmy3 mol kgy1 mol kgy1 w18x wthis modelx wold modelx kPa w18x wthis modelx wold modelx

298.35 298.55 298.05 298.35 298.25 298.25 298.05 298.45 298.15 298.35 298.15 298.25 298.05 298.15 298.15 298.15 298.05 298.15 298.15 298.15 298.25 298.05 298.05 298.25

105.75 104.55 103.41 104.55 104.67 104.11 104.74 104.89 104.58 105.76 105.15 104.67 104.39 104.67 105.42 104.98 104.95 104.66 103.89 104.76 105.27 105.16 104.74 104.87

0.005 0.005 0.005 0.005 0.005 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.500 0.500 0.500 0.500 0.500

0.00123 0.00455 0.00761 0.01066 0.01545 0.00092 0.00097 0.00335 0.00495 0.00593 0.00596 0.00824 0.01237 0.01253 0.00079 0.00401 0.00483 0.00787 0.01163 0.00081 0.00316 0.00485 0.00740 0.01112

– – 0.578 – 0.522 – 0.299 – 0.255 – – – 0.233 0.234 0.152 0.162 0.145 0.161 0.155 0.012 0.035 0.043 0.043 0.038

0.657 0.617 0.589 0.563 0.532 0.248 0.249 0.246 0.246 0.246 0.245 0.245 0.244 0.242 0.158 0.157 0.157 0.157 0.156 0.040 0.040 0.040 0.040 0.040

0.703 0.663 0.636 0.610 0.578 0.300 0.301 0.298 0.298 0.296 0.297 0.295 0.293 0.293 0.204 0.204 0.204 0.203 0.202 0.073 0.073 0.073 0.073 0.073

0.035 0.146 0.263 0.390 0.620 0.053 0.057 0.210 0.316 0.369 0.375 0.536 0.804 0.801 0.056 0.280 0.333 0.558 0.830 0.067 0.262 0.394 0.599 0.906

0.036 0.150 0.264 0.397 0.615 0.059 0.062 0.216 0.316 0.382 0.381 0.530 0.791 0.804 0.056 0.286 0.343 0.562 0.831 0.066 0.258 0.393 0.599 0.907

0.030 0.128 0.228 0.345 0.539 0.053 0.056 0.196 0.286 0.346 0.345 0.480 0.718 0.730 0.052 0.263 0.316 0.517 0.764 0.062 0.243 0.370 0.564 0.854

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Table 7 Partial pressure of SO 2 above aqueous hydrochloric acid solutions T, K

p, kPa

c HCl , mol dmy3

m SO 2 Žtot. , mol kgy1

exp p SO , 2 kPa w18x

calc p SO , kPa 2 wthis modelx

calc p SO , kPa 2 wold modelx

298.15 298.15 298.25 298.15 298.15 298.25 298.25 298.15 298.25 298.25 298.15 298.15 298.45 298.35 298.35 298.25 298.25 298.25 298.15 298.15 298.25 298.15 298.25 297.95 298.15 298.15 298.05

105.94 106.29 105.64 105.45 106.54 105.96 105.54 105.80 105.84 105.84 106.21 106.18 105.98 106.28 105.87 105.43 105.73 105.50 105.44 105.52 104.88 104.69 104.82 105.11 104.90 105.28 104.17

0.001 0.001 0.001 0.001 0.010 0.010 0.010 0.010 0.010 0.050 0.050 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.100 0.500 0.500 0.500 0.500 1.000 1.000 1.000 1.000

0.00150 0.00530 0.00863 0.01176 0.00114 0.00433 0.00748 0.01052 0.01052 0.00086 0.00347 0.00608 0.00854 0.00081 0.00081 0.00322 0.00565 0.00805 0.00807 0.00081 0.00296 0.00534 0.00753 0.00087 0.00501 0.00674 0.01002

0.017 0.108 0.222 0.345 0.037 0.156 0.288 0.417 0.421 0.053 0.208 0.368 0.532 0.055 0.055 0.221 0.390 0.557 0.555 0.063 0.234 0.407 0.579 0.062 0.365 0.492 0.734

0.017 0.107 0.220 0.341 0.037 0.155 0.284 0.418 0.420 0.052 0.210 0.369 0.526 0.056 0.056 0.223 0.391 0.557 0.556 0.062 0.226 0.406 0.574 0.064 0.368 0.495 0.734

0.014 0.090 0.188 0.295 0.032 0.133 0.246 0.364 0.366 0.047 0.190 0.334 0.477 0.052 0.052 0.207 0.363 0.517 0.516 0.062 0.226 0.407 0.576 0.060 0.395 0.531 0.787

solutions, but — in contrast to the simple SO 2 q H 2 SO4 q H 2 O system — they decrease again at higher HCl content. This anomaly is caused by a strong interaction between molecular dissolved sulfur dioxide and chloride ions in the aqueous solutions and is interpreted in terms of a complexation reaction forming SO 2 ClyŽaq. by the authors w18x. The equilibrium constant for this reaction, as determined at standard temperature, yields the value for Df G T0 0 ,SO 2 Cly Žaq.. For performing calculations at elevated temperatures using the described algorithm, values for the standard enthalpy of formation and the molar heat capacity for SO 2 ClyŽaq. are needed as well. They are estimated by assuming Dr HT00 s 0 and Dr c p0 Ž T . s 0 for the complexation reaction. This is believed to be a good approximation as the degree of complexation is only a few percent. As the new thermochemical data result from equilibrium constants, which are fitted to the experimental data in Table 7, they are in very good agreement. On the other hand, the values that are calculated according to Ref. w1x differ from the experimental data in a characteristic manner. At very small molarities of hydrochloric acid, the calculated partial pressures are again too small, while at a high molarity Ž 1 mol dmy3 HCl. the predicted values are too large. This is due to the missing interaction between SO 2 and chloride in the old model w1x. The predicted values at 0.5 mol dmy3 HCl according to old model w1x agree with the

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experimental values. It is believed that the error due to the use of an incorrect dissociation constant for the formation of HSOy 3 is compensated by the error caused by neglecting the interaction between SO 2 Ž aq. and Cly. At still higher HCl concentrations, the model w1x, which does not take into account SO 2 Ž aq. –Cly interactions, predicts SO 2 partial pressures that are too high. To test the extrapolation ability of the new model, including the proposed chemical complexation reaction, the absorption of sulfur dioxide into aqueous CaCl 2-solutions is calculated and compared with experimental data Ž see Table 8. . The chloride content in aqueous solutions is similar to those of system SO 2 q HCl q H 2 O, but the pH of the solutions is totally different. None of the measured data is used for the correlation. Therefore, an agreement between measurement and calculation indicates the extrapolation ability of the proposed model. The calculations according to Ref. w1x differ by about 40% from the measurements at 0.5 mol dmy3 CaCl 2 . On the other hand, the new model allows a very reliable and accurate prediction of phase and chemical equilibrium for the ternary system SO 2 q CaCl 2 q H 2 O. For an overview of ternary systems, some representative P SO 2 vs. m SO2 Žtot. plots for SO 2 q H 2 O, SO 2 q HCl q H 2 O, SO 2 q H 2 SO4 q H 2 O and SO 2 q CaCl 2 q H 2 O systems at 298 K and high

Table 8 Partial pressure of SO 2 above aqueous calcium chloride solutions T, K

p, kPa

cCaCl 2 , mol dmy3

m SO 2 Žtot. , mol kgy1

exp p SO , 2 kPa w17x

calc p SO , kPa 2 wthis modelx

calc p SO , kPa 2 wold modelx

298.25 298.25 298.45 298.25 298.05 298.05 298.25 298.15 298.15 298.25 298.15 298.35 298.25 298.25 298.05 298.35 298.05 298.25 298.35 298.25 298.05 298.05 298.15 298.05 298.05 298.15

105.74 105.03 104.29 104.41 105.06 104.87 104.76 104.27 104.20 105.43 103.94 104.89 104.43 104.18 104.18 104.86 104.73 104.79 104.43 104.51 105.30 105.18 105.01 104.20 104.88 104.61

0.001 0.001 0.001 0.001 0.010 0.010 0.010 0.010 0.010 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.500 0.500 0.500 0.500 0.500 0.500

0.00190 0.00621 0.01346 0.01918 0.00355 0.00783 0.01385 0.01383 0.01958 0.00213 0.00807 0.00810 0.01429 0.02015 0.02015 0.00200 0.00807 0.00814 0.01440 0.02057 0.00210 0.00391 0.00822 0.00843 0.01495 0.02103

0.016 0.121 0.389 0.642 0.040 0.153 0.377 0.376 0.623 0.014 0.137 0.142 0.357 0.596 0.595 0.012 0.134 0.135 0.342 0.582 0.011 0.036 0.137 0.139 0.363 0.608

0.016 0.119 0.393 0.648 0.048 0.156 0.382 0.379 0.632 0.014 0.147 0.149 0.365 0.610 0.605 0.012 0.140 0.143 0.357 0.606 0.015 0.044 0.148 0.153 0.364 0.591

0.013 0.100 0.341 0.568 0.040 0.130 0.326 0.323 0.546 0.010 0.114 0.116 0.295 0.504 0.500 0.008 0.102 0.104 0.273 0.479 0.006 0.019 0.077 0.080 0.217 0.386

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Fig. 4. Typical plots of p SO 2vs. m SO 2 Žtot. for SO 2 qH 2 O Žv ., SO 2 qHClqH 2 O ŽI., SO 2 qH 2 SO4 qH 2 O Ž`. and SO 2 qCaCl 2 qH 2 O Ž^. systems at 298 K.

concentrations of the strong electrolyte are shown in Fig. 4. It may be seen that the phase equilibrium for SO 2 q H 2 SO4 q H 2 O and SO 2 q CaCl 2 q H 2 O systems can be predicted very satisfactorily. Finally, the extrapolation ability of the presented model is tested through comparison with the new experimental data for the quaternary system SO 2 q HCl q H 2 SO4 q H 2 O. The results for this aqueous mixture are given in Table 9. The prediction of SO 2 partial pressures is quite good and better than the calculations according to Ref. w1x. The predicted values at higher chloride content according to the old model w1x are satisfactory. This is due to the compensation of errors as mentioned for SO 2 q HCl q H 2 O system. The new model presented here yields a reliable prediction for the absorption of sulfur dioxide in all discussed aqueous solutions and is believed to deliver a reliable prediction in more complex electrolyte systems as well. Table 9 Partial pressures of SO 2 above aqueous HClqH 2 SO4 solutions T, K

p, kPa

c HCl , mol dmy3

c H 2 SO4 , mol dmy3

m SO 2 Žtot. , mol kgy1

exp p SO , 2 kPa

calc p SO , kPa 2 wthis modelx

calc p SO , kPa 2 wold modelx

298.15 298.15 298.25 298.05 298.05 298.15 298.55 298.55 298.55 298.55

104.85 104.82 104.73 105.31 105.18 105.11 104.06 104.65 105.86 105.21

0.05 0.05 0.05 0.25 0.10 0.10 0.25 0.25 0.50 0.50

0.05 0.05 0.25 0.05 0.10 0.10 0.25 0.25 0.25 0.25

0.00377 0.00771 0.00365 0.00373 0.00233 0.00450 0.00225 0.00435 0.00225 0.00452

0.266 0.551 0.292 0.289 0.170 0.344 0.172 0.343 0.174 0.351

0.265 0.541 0.288 0.283 0.175 0.339 0.179 0.347 0.176 0.354

0.244 0.500 0.271 0.273 0.154 0.320 0.174 0.337 0.178 0.358

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5. List of symbols ai Aw ci c p0 0 0 c p,T Žd c p0rdT . T 0 Dr c p0 cSO2 ,2 Df G T0 0 Dr G T0 HSO2 Df HT00 Dr HT0 I K mi Mi p pi R T xi zi

activity of species i w – x Debye–Huckel coefficient wkg 0.5 moly0.5 x ¨ molarity of species i wmol dmy3 x molar heat capacity Ž p 0 , T . wJ moly1 Ky1 x standard molar heat capacity Ž p 0 , T 0 . wJ moly1 Ky1 x derivative of molar heat capacity with respect to temperature at T s T 0 wJ moly1 Ky2 x molar heat capacity due to reaction wJ moly1 Ky1 x concentration of sulfur dioxide in the gas phase at equilibrium state wmol dmy3 x standard Gibbs energy of formation Ž p 0 , T 0 . wkJ moly1 x Gibbs energy of reaction Ž p 0 , T . wkJ moly1 x molal Henry’s constant wkPa kg moly1 x standard heat of formation Ž p 0 , T 0 . wkJ moly1 x heat of reaction Ž p 0 , T . wkJ moly1 x ionic strength wmol kgy1 x K-value, equilibrium constant w – x molality of species i wmol kgy1 x molecular weight of species i wg moly1 x pressure wkPax partial pressure wkPax molar gas constant Žs 8.31448. wJ moly1 Ky1 x temperature wKx mole fraction of species i w – x number of charges of species i w – x

Greek letters a Ž1. biŽ0. j , bi j ) gi ) g" g iQ

degree of dissociation w – x binary interaction parameter in Pitzer’s equation w – x molal activity coefficient of species i w – x molal mean ionic activity coefficient w – x activity coefficient of i with respect to the ideal solution w – x

Subscripts i, j w 2 tot aq

species i, j water equilibrium state for measurements totally dissolved Žmolecular and ionic. molecular dissolved Žundissociated.

Superscripts )

Q 0 exp calc

standard state of the hypothetical ideal aqueous solution of unit molality standard state of the pure component standard state at standard pressure Ž p 0 s 100 kPa. experimental value calculated value

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