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Ind. Eng. Chem. Res. 1997, 36, 4342-4346
Absorption of SO2 into Aqueous Solutions. 2. Gas-Liquid Equilibrium of the MgO-SO2-H2O System and Graphical Presentation of Operation Lines in an Equilibrium Diagram Martin Zidar, Janvit Golob,* Marjan Veber, and Vojko Vlachy Faculty of Chemistry and Chemical Technology, University of Ljubljana, 1001 Ljubljana, Slovenia
A procedure for calculating the relevant concentrations of sulfur dioxide in an MgO-SO2-H2O system and the construction of an equilibrium-operational diagram showing the relation between ctot (the amount of total SO2 per unit mass of solution), ccom (the total concentration of Mg2+ in the solution expressed with SO32- and HSO3- using the corresponding stoichiometric factors), Y (the excess of SO2 over amount necessary to form Mg(HSO3)2 only, per unit mass of solution), pH, pSO2 (the partial pressure of SO2), and the solubility of MgSO3 at different temperatures in the range from 298 to 323 K is described. The procedure uses the Rudzinski method for determining the pH of a complex aqueous solution and Pitzer’s ion interaction model to calculate the activity coefficients in the mixture at various temperatures. The calculated concentrations match closely to those obtained by experiment. The design diagram at 323 K is used for graphical representation of the operating lines for absorption of SO2 taking place within an industrial SO2 absorption unit. Stage efficiency and SO2 removal of commercial Venturi units was computed. The number of overall gas-phase mass transfer units for each stage was found to be in the range from 1 to 3. Introduction The study of absorption of SO2 into aqueous solutions is of basic importance for flue gas desulfurization in power production as also, to some extent, for the pulp production in the cellulose industry. Hagefeldt and coworkers published two papers investigating equilibrium in the MgO-SO2-H2O system at 298 and 323 K (Hagefeldt, 1970; Hagefeldt et al., 1973). In the first paper (Hagefeldt, 1970) the experimental data showing ctot, ccom, Y, and the pH of the solution at 298 K are presented in the diagram. In the second paper (Hagefeldt et al., 1973), they showed measurements of the partial pressure of sulfur dioxide in equilibrium magnesium solutions (cooking acids) at 323 K, together with an extrapolation table for other temperatures. In another contribution of relevance for our study, Pasiuk-Bronikowska and Rudzinski (Pasiuk-Bronikowska and Rudzinski, 1991) described a method of modeling SO2 absorption in aqueous solutions containing sulfites. The method is based on the film theory of gas absorption and the chemical-equilibrium treatment of chemical reactions (Pasiuk-Bronikowska and Rudzinski, 1991). This method can be applied to systems in equilibrium, as well as for the kinetic modeling of complex chemical reactions in aqueous solutions. In their analysis a form of the Debye-Hu¨ckel equation was applied to calculate the activity coefficients of electrolyte solutions. In addition, a method has been proposed for calculating pH in complex aqueous solutions (Rudzinski, 1984). A similar system (NaMgCl-sulfurous acid) has been studied by Roy and co-workers (Roy et al., 1991), who investigated the ionization of sulfurous acids in a NaCl/ MgCl mixture at 25 °C. From the emf measurements they determined the stoichiometric constants for ionization of sulfurous acid in NaCl solutions of varying concentrations of added MgCl2 and in the ionic strength range I ) 0.5-6.0 m. Their experimental results were analyzed by using Pitzer’s ion-interaction model (Pitzer, 1991). The Pitzer parameters for interactions of Mg2+ with SO2 and HSO3- and for the interactions of Mg2+ S0888-5885(97)00121-8 CCC: $14.00
with SO32- were determined and are presented in Table III of Roy et al. (1991). Recently, we calculated the relevant concentrations of sulfur dioxide in a MgO-SO2-H2O system and constructed the equilibrium-operational diagram showing the relations between the ctot, ccom, Y, and pH at T ) 298 K. For this purpose Rudzinski’s method (Rudzinski, 1984; Pasiuk-Bronikowska and Rudzinski, 1991) for determining the pH of aqueous solutions was used. The activity coefficients of various ionic species were calculated by using a modified form of Debye-Hu¨ckel expression, with the coefficients A, B, and C obtained from the maximum agreement with experimental results (Hagefeldt, 1970). This way we were able to obtain a reasonably good fit of experimentally determined concentrations of various solutes, however, at the expense of the physical meaning of the fitting parameters. The values of parameters A and B, namely, did not correspond to theoretical values associated with the Debye-Hu¨ckel theory. The equilibrium-operational diagram was used for the graphical representation of mass balances for the industrial absorption process (Zidar et al., 1996). In order to improve the theoretical description of the mixture under study, we propose another model to calculate the activity coefficients, i.e., the so-called ioninteraction approach, developed by Pitzer (Pitzer, 1991). The advantage of this theory is its sound statisticalmechanical basis. With such an approach better description of the concentration of various solutes at 298 K and also at 323 K is to be expected, which was not the case before. Namely, at 323 K where the experimental results (Hagefeldt et al., 1973) were presented as isobaric curves, the old method did not yield good agreement with the experimental data. For this reason, we have not been able to present any results for 323 K so far. Using the refinements the presentation of a mass balance analysis for liquid and gaseous phases would be possible. The aim of the present work is (i) to find the quantitative relations for activity coefficients that would © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4343
yield good agreement with the experimental and predicted values of concentrations in Hagefeldt (1970) and Hagefeldt et al. (1973), (ii) to construct the equilibriumoperational diagram which includes isobaric curves for SO2, iso-pH curves, and the solubility curve for MgSO3 at 298 K, (iii) to conduct a rigorous engineering computation of the stage efficiency for absorption of SO2 in an industrial absorption unit, and (iv) to present a graphical representation of the operating lines for absorption of SO2 at 323 K in the design diagram.
Table 1. Coefficients in Pitzer’s Equations for the MgO-SO2-H2O System with Temperatures Derivatives of Parameters, as Well as Thermodynamic Constants at 298 and 323 K Thermodynamic Constants 298 K K1 ) 0.014 K2 ) 7.1 × 10-8 Kw ) 1 × 10-14 KHe ) 0.808 m3bar/kmol Ksp,MgSO3 ) 3.85 × 10-3
Results and Discussion
(
Kw,c +
ctot )
)
K1,cpSO2 KHe,c
323 K
ref
a a a b c
K1 ) 7.2 × K2 ) 5.4 × 10-8 Kw ) 5.5 × 10-14 KHe ) 1.774 m3bar/kmol Ksp,MgSO3 ) 9.8 × 10-3
d d d b e
10-3
Pitzer Coefficients at 298 K
(a) Equilibrium-Operational Diagram. To obtain the equilibrium-operational diagram in the MgO-SO2H2O system that can be used for graphical presentation of mass balances and for the construction of operational lines in the industrial SO2 absorption process the literature data for Y, ccom, and ctot at different pH at 298 K and different pSO2 at 323 K were used (Hagefeldt, 1970; Hagefeldt et al., 1973). The quantity Y is defined as the excess of SO2 over the amount necessary to form Mg(HSO3)2 only, per unit mass of solution (Y ) cSO2 cSO3), ccom is the total concentration of Mg2+ in the solution expressed with SO32- and HSO3- using the corresponding stoichiometric factors, and ctot is the amount of total SO2 per unit mass of solution. We used the data for ctot, cfree, pH, and pSO2 determined experimentally by Hagefeldt, (1970) and Hagefeldt et al. (1973) to calculate the values for ccom and Y using the equations ccom ) ctot - cfree and Y ) 2cfree - ctot for a set of pH or pSO2 values. The concentrations of Mg2+, H3O+, OH-, HSO3-, SO32-, SO2,aq, and SO2,g were calculated by using the calculation procedure based on the relevant equilibrium relations for the SO2,g-SO2,aq-HSO3--SO32--H2O system, the mass balance equation, the charge balance equation, and the Pitzer ion-interaction model. The relationship between ctot, ccom, and Y can be expressed in two ways: One possible set of equations was applied in our previous work (Zidar et al., 1996) where the quantities of ctot, ccom, and Y were expressed in terms of total SO2, Mg2+, and hydrogen ion concentration. Alternatively, ctot, ccom, and Y can be expressed in terms of pSO2, concentration of Mg2+, and the hydrogen ion concentration, (1)-(4):
cH3 + 2cMgcH2 -
ref
K1,cK2,cpSO2
cH - 2
KHe,c
pSO2(cH2 + K1,ccH + K1,cK2,c) cH2KHe,c
) 0 (1)
(2)
ccom ) cSO3 + 0.5cHSO3
(3)
Y ) ctot - 2ccom
(4)
Equation 1 is the charge balance equation with the relevant thermodynamic equilibrium constants for the SO2,g-SO2,aq-HSO3--SO32--H2O system and with the mass balance equation, eq 2 results from dissociation and dissolution equilibrium in the H2O-SO2 system, and eqs 3 and 4 are additional equations which are important for description of the literature data for ccom and Y (Hagefeldt et al., 1973). In eqs 1-4, K1,c )
salt
β(0)
β(1)
β(2)
CΦ
ref
MgSO3 Mg(HSO3)2
-2.8 0.35
12.9 1.22
-250
0 -0.072
f f
i H i Mg
j Mg j SO2
ref f ref g
Θi,j 0.062 λi,j 0.28
Temperature Derivatives of Pitzer Parameters salt
β(0)L
β(1)L
β(2)L
103CΦL
ref
MgSO3 Mg(HSO3)2
-0.7 × 10-3 -4.0 × 10-3
0.15 -0.016
-10.5
0.0 0
g g
a Zidar et al., 1996. b Pitzer, 1991. c Dean, 1992. d Pasiuk-Bronikowska and Rudzinski, 1991. e Ksp has been calculated according to equation Ksp/γMgγSO3 ) cMgcSO3 with activity coefficients calculated with Pitzer’s equations and solubility data given in Markant et al. (1965). Note, however, that the solid phase was not included in the mass-molar balance equations. This information might be of some interest of practical work. f Roy et al., 1991. g The best fit of experimental data given in Hagefeldt et al. (1973).
(K1γH2OγSO2/γHγHSO3), K2,c ) (K2γHSO3/γHδSO3), and Kw,c ) (KwγH2O/γHγOH) are the concentration equilibrium constants and Khe,c is the concentration Henry constant, here defined as Khe,c ) KheγSO2. Thermodynamic constants are taken from the literature (cf. Table 1) and refer to T ) 298 and 323 K, respectively. Industrial magnesium-based pulping solutions usually have an ionic strength between 0.5 and 2 mol/L. To calculate concentration equilibrium constants the activity coefficients are required. In the present study, the Pitzer ion-interaction theory is used to calculate the activity coefficients for all species in the solution, since the previously applied modified Debye-Hu¨ckel expression is not applicable for calculation of partial pressure of SO2 (pSO2), which is studied in this paper. The best correlation between the experimental (Hagefeldt, 1970) and calculated values of ccom and Y at T ) 298 K for certain values of ctot and pH is obtained when the quantities of ctot, ccom, and Y are expressed with the equations given in Zidar et al. (1996) using the activity coefficients calculated with the Pitzer ion-interaction model and with Pitzer parameters β(0), β(1), β(2), and Cφ taken from literature (Roy et al., 1991). For good agreement the parameter λ has to be modified from the value 0.085 used by Roy et al. to 0.28 in our study. The results of linear regression analysis comparing the experimental and computed concentrations show an acceptable agreement between the two sets of values at temperature T ) 298 K: ccom,exp ) 0.998ccom,model + 0.007 (Rval ) 0.9999); Yexp ) 0.918Ymodel - 0.001 (Rval ) 0.9957). The best correlation between the experimental (Hagefeldt et al., 1973) and calculated values for Y and ccom at T ) 323 K for certain values of ctot and pSO2 is obtained when the quantities of ctot, ccom, and Y are expressed with eqs 1-4 by using the activity coefficients
4344 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
Figure 2. Graphical representation of operating lines for absorption of SO2 taking place in an industrial SO2 absorption unit at 323 K. (ccom,1 - ccom,5 ) equilibrium curves of each absorption unit, B1C1 - B5C5 ) operating lines of each absorption unit, D1 - D5 ) crossing points with equilibrium curves). Figure 1. Equilibrium operational diagram of MgO-SO2-H2O at 298 K.
calculated with the Pitzer ion-interaction model. Pitzer parameters β(0), β(1), β(2), and Cφ were taken from literature (Roy et al., 1991); parameter λ with value 0.28 and temperature derivatives of Pitzer’s parameters β(0)L, β(1)L, and β(2)L are presented in Table 1. Temperature derivatives β(0)L, β(1)L, and β(2)L were determined as the best fit of experimental data at T ) 323 K (Hagefeldt et al., 1973). The result of linear regression analysis comparing the experimental and computed data at T ) 323 K are as follows: ccom,exp ) 0.998ccom,model - 0.006 (Rval ) 0.9999); Yexp ) 1.003Ymodel + 0.019 (Rval ) 0.9966). Besides the iso-pH curve and isobars of SO2 we wish to show also “the solubility curve” for MgSO3 on the same graph. The information might be of some relevance for practical operation. The best fit between experimental (Markant et al., 1965) and calculated values for Y at T ) 323 K is obtained when the quantities ctot, ccom, and Y are expressed with an additional equation of the solubility product of magnesium sulfite (Ksp/γMgγSO3 ) cSO3cMg) in the equations (Zidar et al., 1996) using the activity coefficients calculated with the Pitzer ion-interaction model (Pitzer, 1991) and with Pitzer parameters β(0), β(1), β(2), Cφ, and λ. Again temperature derivatives of Pitzer’s parameters β(0)L, β(1)L, β(2)L, and Ksp for MgSO3 are presented in Table 1. The solubility product for MgSO3 with a value of 0.0098 at T ) 323 K in Table 1 was determined as the best fit of the experimental data (Markant et al., 1965). The detail scheme of calculation procedures used in this section is given as Supporting Information. The parameters used in the calculations are listed in Table 1. The expressions for activity coefficients of all species are given in the Appendix 2, together with temperature derivatives of the model parameters. Expressions based on the molar scale were used. A graphical representation of the calculated concentrations at 298 K is displayed in the equilibriumoperational diagram (Figure 1) which is presented as a relation between Y and ccom for different ctot and pH or pSO2 values as parameters. The diagram contains (a) iso-pH curves, calculated from equations of our previous
work (Zidar et al., 1996), (b) isobaric curves of SO2 calculated by eqs 1-4 of this paper, and (c) the solubility curve as described at a temperature of ∼298 K. (b) Industrial Application. The flow diagram of a commercial Venturi absorption system and of the fortification tower of the magnesia pulping process is the same as in our previously published paper (Zidar et al., 1996). In the same publication measured and calculated data from the operation of the commercial Venturi absorption and fortification system are given in Table 1. The graphical representation of liquid flows in the Venturi absorption units is also shown. Note that in the absorption tower, as well as in the fortification tower, the gas and liquid flow is countercurrent but in each commercial Venturi of the absorption tower the gas and liquid flows are cocurrent. The equilibrium-operational diagram has two useful applications. First, by using the diagram it is possible to describe the commercial Venturi absorption system and the fortification system (Zidar et al., 1996). Note that the operational variable Y in the equilibriumoperational diagram can be put in the form (Y ) ctot 2ccom), which contains two terms: first is ctot, which is constant during the reaction with MgO, and, second, is ccom, which is constant during the absorption of SO2. The second application of the diagram is presented below. The equilibrium operational diagram is reconstructed in design diagram characteristic for gas absorption processes with ccom as a parameter. The design diagram (Figure 2) was constructed by using eqs 1-3 and activity coefficients calculated by the Pitzer ioninteraction model (Pitzer, 1991) as described in the in section (a). In Figure 2, a typical design diagram for each cocurrent absorber (from 1 to 4), in which gas and liquid are fed to the center of the Venturi stage, is shown. The variables in Figure 2 are ySO2 (the volume fraction of SO2 in gas flow), ctot (the amount of total SO2 per unit mass of solution), and ccom (the total concentration of Mg2+ in the solution expressed with SO32- and HSO3- using the corresponding stoichiometric factors). ccom is constant during the absorption process. Each value of ccom yields the equilibrium curve in an absorption unit. This way we obtained the family of iso-ccom equilibrium curves. With the design diagram and using process data, the commercial Venturi absorption system and fortification system can be quantitatively described.
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4345
The operating lines in Figure 2 (BiCi; i is from 1 to 5), which represent mass balance equations, were constructed by using recently published experimental data (Zidar et al., 1996). The fractional solute removal for a dilute system, defined as (1 - pSO2,output/pSO2,input), is given by eq 5 (Perry, 1984):
removal ) E(1 - KHe,c,totctot*/pSO2,input)/(1 + Khe,c,tot fG/L) (5) where the mass transfer efficiency E is defined by eq 6 (Perry, 1984)
E ) (pSO2,input - pSO2,output)/(pSO2,input - pSO2*) ) 1 - e-NG (6) with NG ) number of overall gas-phase mass transfer units and KHe,c,tot is defined by eq 7, which is obtained by modification of eq 2
KHe,c,tot ) KHe,ccH2/(cH2 + K1,ccH + K1,cK2,c)
(7)
The number of overall gas-phase mass transfer units that were achieved in a Venturi scrubber was found to be in the range from NG ) 1 to NG ) 3 (NG,1 ) 1.39, NG,2 ) 1.02, NG,3 ) 2.81, NG,4 ) 1.10), calculated by using eq 6. The values of Khe,c,tot (KHe,c,tot,1 ) 0.000 84, KHe,c,tot,2 ) 0.000 53, KHe,c,tot,3 ) 0.002 97, KHe,c,tot,4 ) 0.009 84 bar m3/kmol) were calculated by using eq 7, as well as the values for ctot,1* ) 1.1 wt %, ctot,2* ) 2.35 wt %, ctot,3* ) 4.1 wt %, and ctot,4* ) 5.0 wt %, respectively. Finally, using these results in eq 5, the fractional solute removal for each Venturi scrubber may be calculated (removal1 ) 0.66, removal2 ) 0.59, removal3 ) 0.74, removal4 ) 0.26). Conclusions A quantitative method for the construction an equilibrium-operational diagram for a MgO-SO2-H2O system based on thermodynamic relations was described. The model calculation for the concentrations of various solutes yielded good agreement with the experimental data, providing that Pitzer’s ion-interaction approach was applied. The equilibrium-operational diagram, which includes isobaric curves for SO2, iso-pH curves, and a solubility curve for MgSO3 at 298 K, was constructed. The stage efficiency for absorption of SO2 and removal of SO2 in an industrial Venturi absorption unit was computed and graphically presented in the design diagram at 323 K. In this way the efficiency of a commercial Venturi absorption tower was analyzed. Nomenclature a ) activity (kmol/m3) BMX, BMX′, CMX, E, f, f′ ) parameters of Pitzer equations (dimensionless) E ) mass transfer efficiency (dimensionless) c ) concentration (kmol/m3 or wt %) G ) flow of gas (m3/h) K1,c, K2,c, Kw,c ) concentration equilibrium constants (dimensionless) Khe,c ) concentration Henry constant (m3bar/kmol), defined as Khe,c ) KheγSO2 in pSO2 ) Khe,ccSO2,aq KHe,c,tot ) slope of equilibrium curve (m3bar/kmol), defined as KHe,c,tot ) KHe,ccH2/(cH2 + K1,ccH + K1,cK2,c) in equation pSO2 ) Khe,c,totctot
Khe,c,totf ) dimensionless slope of equilibrium curve defined by eq 7 where f is the conversion factor equal to 0.0372 kmol/m3 bar K1, K2, Kw ) thermodynamic equilibrium constants (dimensionless) Khe ) Henry constant (m3bar/kmol) defined as pSO2 ) KheaSO2 Ksp,MgSO3 ) solubility product of MgSO3 (dimensionless) L ) flow (m3/h) NG ) number of overall gas-phase mass transfer units (dimensionless) pSO2 ) partial pressure of SO2 (mbar or bar) removal ) fractional solute removal (dimensionless) Y ) the excess of SO2 over amount necessary to form Mg(HSO3)2 only, per unit mass of solution (wt %) ySO2 ) volume fraction of SO2 in gas flow (vol %) Greek Letters β(0), β(1), β(2), CΦ, λ, θ ) parameters of Pitzer’s equation β(0)L, β(1)L, β(2)L, CΦL ) temperature derivatives of the parameters of Pitzer’s equations Subscripts H, OH, HSO3, SO3, Mg ) species of H3O+, OH-, HSO3-, SO32-, and Mg2+ in solutions com ) the total concentration of Mg2+ in the solution expressed with SO32- and HSO3- using the corresponding stochiometric factors exp ) experimental values input ) before absorption of SO2 output ) after absorption of SO2 model ) calculated values tot ) amount of total SO2 per unit mass of solution c ) cation (Mg2+, H3O+) a ) anion (OH-, HSO3-, SO32-) N ) inert species (SO2) 1, 2, 3, 4 ) first, second, third, fourth commercial Venturi Superscript * ) equilibrium
Appendix The activity coefficients can be analyzed by using Pitzer’s ion-interaction model. The activity coefficients for H2O, H3O+, Mg2+, SO32-, HSO3-, OH-, and SO2 in solutions are given by the following equations (Pitzer, 1991), here based on the molar scale:
(1000/Mw) ln(γw) ) f - 2µf′ - cMg(cSO3BMg-SO3 + cHSO3BMg-HSO3) µ(B′Mg-SO3 + B′Mg-HSO3) - cMgcHθMg-H 2E(CMg-HSO3cMgcHSO3 + CMg-SO3cMgcSO3) ln(γH ) ) ZH2f′ + ZH2(B′Mg-HSO3cMgcHSO3 + B′Mg-SO3cMgcSO3) + 2cHθMg-H + |ZH|(CMg-HSO3cMgcHSO3 + CMg-SO3cMgcSO3) ln(γMg) ) ZMg2f′ + 2(cSO3BMg-SO3 + cHSO3BMg-HSO3) + 2cHθMgH + 2E(CMg-HSO3cHSO3 + CMg-SO3cSO3) ln(γSO3) ) ZSO32f′ + 2cMgBSO3-Mg + ZSO32(B′HSO3-MgcMgcHSO3) + |ZSO3|(CHSO3-MgcHSO3cMg) + 2ECSO3-MgcMg
4346 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
ln(γHSO3) ) ZHSO32f′ + 2cMgBHSO3-Mg +
BLMX ) β(0)L +
ZHSO32(B′SO3-MgcMgcSO3) + |ZHSO3|(CSO3-MgcSO3cMg) + 2ECHSO3-MgcMg
(β(1)L/0.98µ)[1 - (1 + 1.4µ0.5) exp(-1.4µ0.5)] + (β(2)L/72µ)[1 - (1 + 12µ0.5) exp(-12µ0.5)] CLMX ) (∂CΦMX/∂T)P/(2|ZMZX|)0.5
ln(γOH) ) ZOH2f′ + ZOH2(B′SO3-MgcMgcSO3 + B′HSO3-MgcHSO3cMg) + |ZOH|(CSO3-MgcSO3cMg + CHSO3-MgcHSO3cMg) ln(γSO2) ) 2cMgλSO2,Mg The parameters of these equations are given by the following equations (Pitzer, 1991):
f ) -0.392(4µ/1.2)[ln(1 + 1.2µ0.5)] f′ ) -0.392[µ0.5/(1 + 1.2µ0.5) + (2/1.2) ln(1 + 1.2µ0.5)] BMX ) β(0) + (β(1)/2µ)[1 - (1 + 2µ0.5) exp(-2µ0.5)] B′MX ) (β(1)/2µ2)[1 - (1 + 2µ0.5 + 2µ) exp(-2µ0.5)] CMX ) CΦ/(2|ZMZX|)0.5
∑ci|Zi|
E ) 0.5 BMX ) β(0) +
(β(1)/0.98µ)[1 - (1 + 1.4µ0.5) exp(-1.4µ0.5)] + (β(2)/72µ)[1 - (1 + 12µ0.5) exp(-12µ0.5)] B′MX ) (β(1)/0.98µ2)[1 (1 + 1.4µ0.5 + 0.98µ) exp(-1.4µ0.5)] + (β(2)/72µ2)[1 - (1 + 12µ0.5 + 72µ) exp(-12µ0.5)] Temperature derivatives of the parameters for the activity coefficients needed to calculate these quantities at other temperatures are given (Pitzer, 1991) by the following:
Supporting Information Available: Detail scheme of calculation procedures used in the Results and Discussion section, part a (5 pages). Ordering information is given on any current masthead page. Literature Cited Dean, J. A. Lange’s Handbook of Chemistry, 14th ed; McGrawHill: New York, 1992; 5.16. Hagefeldt, K. Fast Analysis of Magnesium Bisulphite. Sven. Papperstidn. 1970, 73 (13-14 (Jul 15)), 435-437. Hagefeldt, K.; Simmons, T.; So¨derlund, U. Absorption of Sulfur Dioxide into Magnesium Cooking Acids. Sven. Papperstidn. 1973, 8, 292-296. Markant, H. P.; Phillips, N. D.; Shah, S. I. Physical and Chemical Properties of Magnesia-Base Pulping Solutions. Tappi 1965, 48 (11), 648-653. Pasiuk-Bronikowska, W.; Rudzinski, K. J. Absorption of SO2 into Aqueous Systems. Chem. Eng. Sci. 1991, 46 (9), 2281-2291. Perry, J. H. Chemical Engineers’ Handbook, 6th ed; McGrawHill: New York, 1984; pp 14-39. Pitzer, K. S. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991; pp 75-155. Roy R. N.; Zhang, J.-Z.; Millero, F. J. The Ionisation of Sulfurous Acid in Na-Mg-Cl Solutions at 25 °C. J. Solution Chem. 1991, 20, 361-373. Rudzinski, K. J. Calculation of the pH Value of a Mixture of SolutionssA Supplement. Chem. Eng. Sci. 1984, 39 (1), 196198. Zidar, M.; Golob, J.; Veber, M. Absorption of Sulfur Dioxide into Aqueous Solutions: Equilibrium MgO-SO2-H2O and Graphical Presentation of Mass Balances in an Equilibrium Diagram. Ind. Eng. Chem. Res. 1996, 35, 3702-3706.
Received for review February 11, 1997 Revised manuscript received June 4, 1997 Accepted June 11, 1997X IE970121G
X Abstract published in Advance ACS Abstracts, August 1, 1997.
