h2s Naoh Equilibrium Curve

Ž .Fluid Phase Equilibria 167 2000 263–284www.elsevier.nlrlocaterfluid

Solubility of hydrogen sulfide in aqueous solutions of single strongelectrolytes sodium nitrate, ammonium nitrate, and sodium hydroxideat temperatures from 313 to 393 K and total pressures up to 10 MPa

´ )Jianzhong Xia, Alvaro Perez-Salado Kamps, Bernd Rumpf, Gerd Maurer´Lehrstuhl fur Technische Thermodynamik, UniÕersitat Kaiserslautern, D-67653 Kaiserslautern, Germany¨ ¨

Received 16 August 1999; accepted 17 November 1999

Abstract

New experimental results for the solubility of hydrogen sulfide in aqueous solutions of the single strongelectrolytes sodium nitrate, ammonium nitrate, and sodium hydroxide at temperatures from 313 to 393 K andtotal pressures up to 10 MPa are reported. As in the strong electrolyte-free system, a second — hydrogensulfide-rich — liquid phase is observed at high hydrogen sulfide concentrations. A thermodynamic model fordescribing the phase equilibrium is presented. Calculations are compared with the new experimental data.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Gas solubility; Experimental data; Vapor–liquid equilibrium; Aqueous solutions; Electrolytes; Hydrogen sulfide;Sodium nitrate; Ammonium nitrate; Sodium hydroxide

1. Introduction

The solubility of weak electrolyte gases like ammonia, carbon dioxide, sulfur dioxide, or hydrogenŽ .sulfide in aqueous solutions containing strong electrolytes strong acids and bases and their salts must

Žbe known for designing separation equipment in many technical applications e.g., in the chemical or.oil related industries and in the field of environmental protection . In many cases, the correlation and

prediction of vapor liquid equilibrium in such systems is an extremely difficult task, caused partiallyby chemical reactions in the liquid phase as well as by the possible formation of additional solid or

) Corresponding author. Tel.: q49-631-205-2410; fax: q49-631-205-3835.Ž .E-mail address: [email protected] G. Maurer .

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0378-3812 99 00324-6

( )J. Xia et al.rFluid Phase Equilibria 167 2000 263–284264

Table 1Experimental results for the solubility of hydrogen sulfide in aqueous solutions of sodium nitrate

Ž . Ž . Ž . Ž .T K m molrkg m molrkg 10 p MPa pH S NaNO2 3

313.15 0.088 3.040 1.618 2313.15 0.210 3.040 3.746 2313.16 0.426 3.040 7.64 2313.14 0.469 3.040 8.35 2313.16 0.690 3.040 12.27 2313.17 0.815 3.040 14.62 2313.14 0.946 3.040 16.92 2313.15 1.255 3.040 22.80 2313.16 1.776 3.040 28.29 3313.16 1.820 3.040 28.29 3333.14 0.031 3.040 1.053 2333.14 0.164 3.040 4.050 2333.15 0.404 3.040 9.66 2333.13 0.842 3.040 20.24 2333.15 1.320 3.040 32.71 2333.14 1.596 3.040 40.89 2333.15 1.811 3.040 42.72 3333.15 2.230 3.040 42.72 3353.16 0.087 3.040 3.077 2353.16 0.360 3.040 10.93 2353.16 0.384 3.040 11.83 2353.16 0.834 3.040 25.52 2353.16 1.220 3.040 37.94 2353.16 1.767 3.040 58.82 2353.17 1.918 3.040 61.68 3353.16 2.723 3.040 61.68 3393.15 0.000 3.040 1.780 2393.17 0.123 3.040 6.69 2393.17 0.324 3.040 14.84 2393.17 0.884 3.040 36.50 2393.16 1.181 3.040 49.01 2393.16 1.371 3.040 57.93 2393.19 1.512 3.040 62.16 2393.16 1.763 3.040 71.57 2393.17 1.857 3.040 84.21 2393.17 1.969 3.040 91.06 2313.15 0.064 5.866 1.607 2313.15 0.159 5.866 3.722 2313.17 0.539 5.866 11.69 2313.14 0.838 5.866 18.62 2313.14 0.952 5.866 21.18 2313.15 1.407 5.866 28.34 3313.14 1.528 5.866 28.37 3313.16 1.808 5.866 28.36 3313.16 0.171 5.952 3.785 2313.13 0.336 5.952 7.55 2313.15 0.502 5.952 11.08 2

( )J. Xia et al.rFluid Phase Equilibria 167 2000 263–284 265

Ž .Table 1 continued

Ž . Ž . Ž . Ž .T K m molrkg m molrkg 10 p MPa pH S NaNO2 3

313.15 0.992 5.952 22.50 2333.13 0.073 5.952 2.284 2333.14 0.141 5.952 4.397 2333.15 0.423 5.952 12.28 2333.17 0.439 5.952 12.88 2333.15 0.868 5.952 25.65 2333.15 1.181 5.952 37.67 2333.14 1.279 5.952 42.68 3333.14 1.445 5.952 42.75 3333.14 1.674 5.952 42.97 3353.17 0.080 5.952 3.383 2353.16 0.290 5.952 10.58 2353.16 0.409 5.952 14.86 2353.17 0.672 5.952 24.24 2353.16 0.944 5.952 35.03 2353.15 1.367 5.952 54.26 2353.15 1.523 5.952 61.55 3353.17 1.605 5.952 61.89 3353.16 1.652 5.952 61.86 3393.16 0.000 5.952 1.629 2393.16 0.057 5.952 4.447 2393.18 0.219 5.952 11.87 2393.16 0.365 5.952 18.97 2393.16 0.670 5.952 33.32 2393.19 0.671 5.952 33.56 2393.17 1.069 5.952 54.77 2393.16 1.491 5.952 79.37 2393.15 1.724 5.952 93.93 2

liquid phases. As part of ongoing projects dealing with that kind of phase equilibria, this contributionreports on experimental and theoretical results on the solubility of hydrogen sulfide in aqueoussolutions of the single strong electrolytes sodium nitrate, ammonium nitrate, and sodium hydroxide attemperatures from 313 to 393 K, total pressures up to 10 MPa, and molalities of the strongelectrolytes up to 6 m. For these systems, no similar data are available in the literature.

2. Experimental

ŽThe experimental equipment and procedure are the same as in previous investigations see forw x.example, Rumpf and Maurer 1 , therefore only a few essentials are repeated here.

Ž 3.In an experiment, a thermostated high-pressure cell material: Hastelloy C4; volume: about 30 cmwith two sapphire windows is partially filled with a known amount of the aqueous solvent. A knownamount of gas is added to the cell from a storage tank. More aqueous solvent is added to the cell by acalibrated high-pressure displacer, until the gas is completely dissolved in the liquid phase. The


amount of solvent charged to the cell is only slightly above the minimum amount needed to dissolvethe gas completely. After equilibration, very small amounts of the liquid mixture are withdrawnstepwise from the cell until the first very small stable bubble appears. That pressure is the equilibriumpressure to dissolve the charged amount of hydrogen sulfide in the charged amount of solvent at thefixed temperature.

Ž .The mass of the charged gas up to about 3.6 g is determined by weighing with an uncertainty of"0.008 g. The volume of the aqueous solvent needed to dissolve the gas is determined by measuringthe position of the high-pressure displacer piston before and after each experiment. The mass of the

Ž .solvent is calculated — with a relative uncertainty of 0.7% at maximum — from its known densityŽ w x . Žeither from Washburn 2 or from own measurements . Three pressure transducers WIKA, Klingen-

.berg, Germany for pressures ranging to 0.6 MPa, to 4 MPa and to 10 MPa, respectively, were used todetermine the solubility pressure. Before and after each series of measurements, the transducers were

Ž .calibrated against a high precision pressure gauge Desgranges & Huot, Aubervilliers, France . Themaximum uncertainty in the pressure measurement is about 1 kPa in the pressure range up to 0.5 MPaand 4 kPa at higher pressures. The temperature is determined with two calibrated platinum resistance

Table 2Experimental results for the solubility of hydrogen sulfide in aqueous solutions of ammonium nitrate

Ž . Ž . Ž . Ž .T K m molrkg m molrkg 10 p MPa pH S NH NO2 4 3

313.15 0.253 5.790 3.198 2313.14 0.435 5.790 5.492 2313.16 0.531 5.790 6.98 2313.14 0.569 5.790 7.29 2313.15 0.602 5.790 7.60 2313.15 1.006 5.790 12.73 2313.15 1.931 5.790 24.34 2313.15 1.972 5.790 24.80 2313.16 2.011 5.790 25.52 2313.16 2.940 5.790 28.46 3313.15 3.111 5.790 28.46 3353.16 0.192 5.790 4.77 2353.15 0.469 5.790 11.06 2353.15 1.273 5.790 28.96 2353.15 1.274 5.790 28.90 2353.16 1.991 5.790 46.89 2353.15 2.162 5.790 51.85 2353.15 2.784 5.790 62.39 3353.16 3.514 5.790 62.36 3393.15 0.000 5.790 1.663 2393.16 0.205 5.790 8.23 2393.16 0.406 5.790 14.74 2393.16 1.013 5.790 34.39 2393.15 1.022 5.790 34.45 2393.16 1.620 5.790 54.95 2393.16 2.268 5.790 77.06 2393.15 2.464 5.790 83.25 2


Table 3Experimental results for the solubility of hydrogen sulfide in aqueous solutions of sodium hydroxide

Ž . Ž . Ž . Ž .T K m molrkg m molrkg 10 p MPa pH S NaOH2

313.14 0.992 0.993 0.459 2313.21 1.028 0.993 1.157 2313.15 1.231 0.993 4.701 2313.15 1.633 0.993 11.57 2313.14 1.758 0.993 13.33 2313.15 2.075 0.993 19.11 2313.15 2.326 0.993 23.59 2313.15 2.606 0.993 28.51 2313.15 2.656 0.993 28.49 3313.15 3.042 0.993 28.51 3313.17 3.254 0.993 28.50 3333.16 0.849 0.993 0.197 2333.15 1.206 0.993 5.140 2333.16 1.396 0.993 9.15 2333.16 1.481 0.993 10.75 2333.15 2.043 0.993 23.91 2333.16 2.373 0.993 32.16 2333.15 2.623 0.993 40.05 2333.15 3.139 0.993 43.02 3333.15 3.319 0.993 43.03 3353.15 0.911 0.993 0.473 2353.15 1.068 0.993 3.195 2353.15 1.393 0.993 11.59 2353.15 1.855 0.993 25.22 2353.15 2.221 0.993 36.08 2353.15 2.259 0.993 37.20 2353.15 2.571 0.993 47.39 2353.16 2.965 0.993 58.96 2353.15 3.214 0.993 62.43 3353.15 3.217 0.993 62.43 3353.15 3.364 0.993 62.45 3393.16 0.000 0.993 1.905 2393.16 0.895 0.993 1.933 2393.15 0.985 0.993 2.557 2393.15 1.089 0.993 5.804 2393.15 1.337 0.993 15.61 2393.16 1.916 0.993 38.17 2393.15 2.366 0.993 55.81 2393.17 2.724 0.993 71.85 2393.16 3.121 0.993 92.50 2393.16 3.115 0.993 92.96 2313.15 1.198 1.957 0.151 2313.15 1.850 1.957 0.205 2313.19 2.248 1.957 5.717 2313.16 2.510 1.957 10.73 2313.16 2.601 1.957 12.83 2

Ž .continued on next page


Ž .Table 3 continued

Ž . Ž . Ž . Ž .T K m molrkg m molrkg 10 p MPa pH S NaOH2

313.14 2.643 1.957 14.12 2313.15 2.653 1.957 14.34 2313.14 3.256 1.957 26.78 2313.15 2.260 1.980 6.46 2313.14 2.649 1.980 13.58 2313.14 2.874 1.980 18.31 2313.16 3.334 1.980 27.66 2313.15 3.526 1.980 28.42 3313.15 3.948 1.980 28.47 3313.15 3.962 1.980 28.55 3333.14 2.202 1.980 5.95 2333.14 2.276 1.980 7.65 2333.15 2.670 1.980 16.74 2333.17 2.929 1.980 23.27 2333.14 3.043 1.980 27.01 2333.16 3.355 1.980 35.86 2333.16 3.601 1.980 43.09 3333.14 3.652 1.980 43.07 3333.14 3.757 1.980 43.08 3333.14 4.071 1.980 43.08 3353.16 1.919 1.980 0.477 2353.15 2.228 1.980 8.14 2353.15 2.577 1.980 19.33 2353.16 2.720 1.980 23.24 2353.16 2.760 1.980 24.85 2353.16 3.050 1.980 34.84 2353.15 3.638 1.980 57.47 2353.16 3.695 1.980 61.76 2353.15 4.386 1.980 62.37 3353.16 4.469 1.980 62.38 3393.16 0.000 1.980 1.836 2393.17 1.541 1.980 1.920 2393.15 2.204 1.980 11.95 2393.16 2.495 1.980 23.99 2393.14 2.584 1.980 28.04 2393.14 2.688 1.980 32.41 2393.14 3.236 1.980 56.89 2393.16 3.280 1.980 59.23 2393.14 3.660 1.980 78.96 2393.15 3.878 1.980 93.19 2

thermometers placed in the heating jacket of the cell with an estimated maximum uncertainty of about"0.1 K.

The strong electrolyte-containing solutions were prepared in a storage tank. The molality of thestrong electrolyte in the aqueous solution was determined gravimetrically with a relative uncertaintynot surmounting 0.1%.


3. Substances

Ž .Hydrogen sulfide G98 mol% was purchased from Messer-Griesheim, Ludwigshafen, Germany,and was used without further purification. Deionized water was degassed by vacuum distillation.

Ž . Ž . ŽSodium nitrate G99.5 mass% , ammonium nitrate G99 mass% and sodium hydroxide G99.mass% were purchased from Riedel de Haen, Seelze, Germany, and were degassed and dried under¨

vacuum.

4. Experimental results

ŽThe solubility of hydrogen sulfide in aqueous solutions of sodium nitrate m f3 and 6NaNO3

. Ž .molrkg and sodium hydroxide m f1 and 2 molrkg was measured at 313, 333, 353, and 393NaOHŽK. The solubility of hydrogen sulfide in aqueous solutions of ammonium nitrate m f6NH NO4 3

.molrkg was measured at 313, 353, and 393 K. The total pressure ranged up to about 10 MPa. Theexperimental results are given in Tables 1–3. For all investigated systems, the formation of a second,hydrogen sulfide-rich liquid phase was observed at higher concentrations of hydrogen sulfide.

Ž .Therefore, the number of observed phases p is also given in Tables 1–3. When there are threeŽ .phases, the number given for m in Tables 1–3 and also in the corresponding figures is no longerH S2

Fig. 1. Solubility of hydrogen sulfide in aqueous solutions of sodium nitrate at T s353 K. `,I Experimental results, thiswork. — Calculated results, this work. - - - Calculated results for the system H S–H O.2 2


Ž .the solubility of H S in the aqueous solution, as all numbers for m are the ratio of moles of2 H S2

Ž .hydrogen sulfide to kilograms of water in the equilibrium cell.As an example, the experimental results for the total pressure above aqueous solutions containing

about 3 and 6 mol of NaNO per kg of H O at 353 K are plotted in Fig. 1 versus the overall amount3 2

of hydrogen sulfide per kilogram of water in the equilibrium cell. Adding hydrogen sulfide to anaqueous salt solution at first causes a nearly linear increase in the total pressure until a second,hydrogen sulfide-rich liquid phase appears. The presence of NaNO has almost no influence on the3

pressure of the three-phase vapor–liquid–liquid equilibrium. Hydrogen sulfide is salted out by sodiumnitrate. The salting out effect increases with increasing salt molality. For example, when 3 or 6 mol ofsodium nitrate are added to 1 kg of water at 353 K, the pressure needed to dissolve 1 mol of hydrogensulfide increases from about 2.5 MPa to about 3.1 and 3.9 MPa, respectively. Vice versa, at a totalpressure of 3.9 MPa, the hydrogen sulfide molality is about 1.6 molrkg in pure water, whereas it isabout 1.2 and 1.0 molrkg in a 3- and 6-m aqueous solution of sodium nitrate, respectively. Anotherexample: when 3 or 6 mol of sodium nitrate are added to 1 kg of water at 353 K, the molality ofhydrogen sulfide required to induce a phase split is reduced from about 2.3 molrkg to about 1.8 and1.5 molrkg, respectively.

Fig. 2 shows the influence of 6 mol sodium nitrate and ammonium nitrate per kilogram of water onthe solubility of hydrogen sulfide in an aqueous solution at 353 K. In contrast to the salting-out effectcaused by sodium nitrate, ammonium nitrate causes a salting-in effect. For example: the pressurenecessary to dissolve 1 mol of hydrogen sulfide in 1 kg of water increases from about 2.5 MPa to

Fig. 2. Solubility of hydrogen sulfide in aqueous solutions of sodium and ammonium nitrate at T s353 K. `,IExperimental results, this work. — Calculated results, this work. - - - Calculated results for the system H S–H O.2 2


Fig. 3. Solubility of hydrogen sulfide in aqueous solutions of sodium hydroxide. ` Experimental results, this work,m s1 molrkg. — Predictions, this work.NaOH

about 3.9 MPa in the presence of sodium nitrate, whereas it decreases to about 2.35 MPa ifammonium nitrate is present.

As was to be expected, the addition of hydrogen sulfide to a solution containing a fixed overallŽ .molality of the strong base sodium hydroxide cf. Fig. 3 at first results only in a slight change in the

Ž .total pressure, as nearly all hydrogen sulfide is dissolved in ionic form, i.e., as bisulfide and sulfideions. When the overall amount of hydrogen sulfide in the liquid phase nearly equals the overallamount of sodium hydroxide, the total pressure above the aqueous solution steeply increases. As inthe system hydrogen sulfide–water, the solubility decreases with increasing temperature.

As can also be seen from Figs. 1 and 2, the pressure at the three-phase equilibrium is the same inthe salt-free system as in the salt containing systems. This indicates that the second liquid phase isnearly pure hydrogen sulfide.

5. Modeling

5.1. Systems H S–H O–NaNO and H S–H O–NH NO2 2 3 2 2 4 3

Fig. 4 shows a scheme of the model applied to correlate the new data. At the concentrationsdiscussed here, the dissociation of dissolved hydrogen sulfide in the aqueous phase can be neglected.However, for very small amounts of dissolved hydrogen sulfide the dissociation of H S and HSy can2


Ž q q y.Fig. 4. VLLE in the system H S–H O–M X MsNa or NH , XsNO .2 2 n n 4 3q y

Ž .be taken into account cf. Section 5.2 . It is assumed that the salts sodium nitrate and ammoniumŽ .nitrate are fully dissociated in the aqueous phase. The second hydrogen sulfide-rich liquid phase and

the vapor phase are treated as binary mixtures of hydrogen sulfide and water.

5.1.1. Vapor–liquid equilibriumThe vapor–liquid equilibrium conditions for water and hydrogen sulfide are:

sÕ pypŽ .w w X Zs sp w exp a spy w 1Ž .w w w w wRT

` sÕ pypŽ . XH S,w w X Z2Žm . s Žm . ,H T , p exp m g spy w . 2Ž .Ž .H S,w w H S H S H S H S2 2 2 2 2RT

Žm. Ž s .H T , p denotes Henry’s constant for the solubility of hydrogen sulfide in pure water. It wasH S,w w2

w x Ž .adopted from Edwards et al. 3 cf. Table 4 . The influence of pressure on that Henry’s constant wasestimated using the partial molar volume of hydrogen sulfide in water as given by Brelvi and

w x Ž .O’Connell 4 cf. Table 5 . The vapor pressure and molar volume of pure liquid water werew xcalculated from the equations of Saul and Wagner 5 . Fugacity coefficients in the vapor phase were

calculated from the virial equation of state truncated after the second virial coefficient. The secondvirial coefficient of pure water B was calculated from a correlation based on the data collection byw,w

Table 4Henry’s constant of hydrogen sulfide in pure water

H Žm . T , ps BŽ .H S,w w2ln s Aq qC TrK q D ln TrKŽ . Ž .y1 TrKMPakg mol Ž .Ž .A B C D

340.292 y13236.8 0.0595651 y55.0551


Table 5Pure component and mixed second virial coefficients, partial molar volumes of H S at infinite dilution in water2

3 3 ` 3Ž . Ž . Ž . Ž .T K B cm rmol B cm rmol Õ cm rmolH S,H S H S,w H S,w2 2 2 2

313.15 y182 y381 35.9333.15 y162 y318 37.2353.15 y145 y270 38.9393.15 y118 y203 43.7

w x Ž .Dymond and Smith 6 cf. Table 6 . The second virial coefficient of pure hydrogen sulfide BH S,H S2 2

and the mixed second virial coefficient B were estimated as recommended by Hayden andH S,w2

w x Ž .O’Connell 7 cf. Table 5 .w xA modified Pitzer model 8 for the excess Gibbs energy of aqueous solutions containing strong

electrolytes is applied to calculate the activities of all species in the liquid phase:

EGŽ0. Ž1. Ž2.s f I q m m b qb f x qb f xŽ . Ž . Ž .Ý Ý1 i j i , j i , j 2 1 i , j 2 2n RTMw w i/w j/w

q m m m t . 3Ž .Ý Ý Ý i j k i , j ,ki/w j/w k/w

The resulting expressions for the activity coefficient of a dissolved species and for the activity ofwater are given in Appendix A. f and f are functions of ionic strength I. The dielectric constant of1 2

Ž . w x Ž0. Ž1. Ž2.pure water is required for calculating f I . It was taken from Bradley and Pitzer 9 . b , b , b ,1 i, j i, j i, j

and t are binary and ternary interaction parameters.i, j,kw xInteraction parameters for the binary system NaNO –H O were taken from Sing et al. 10 , and for3 2

w x Ž . ŽNH NO –H O from Kim and Frederick 11 cf. Appendix B . According to Pitzer’s equation cf.4 3 2. Ž .Appendix A , the activity coefficient of a gas G molality m dissolved in pure water isG

Žm . Ž0. 2lng m s0 s2m b q3m t , 4Ž .Ž .G s G G,G G G,G,G

whereas it is

Žm . Ž0. Ž1. Ž2. Ž0. Ž1.lng s2m b qb f x qb f x q2m B qB f xŽ . Ž . Ž .G G G,G G,G 2 1 G,G 2 2 s G,MX G,MX 2 1

Ž2. 2 2qB f x q3m t q3m G q6m m G 5Ž . Ž .G,MX 2 2 G G,G,G s G,MX ,MX G s G,G,MX

Ž .in an aqueous solution containing a strong electrolyte M X salt molality m .n n sq y

Table 6Pure component second virial coefficient of water

dc3B r cm rmol s aq bŽ .w,w ž /TrKŽ .

a b c d

y53.53 y39.29 647.3 4.3


Ž0. w x Ž .The binary parameter b was taken from Kuranov et al. 12 cf. Table 7 . The ternaryH S,H S2 2

parameter t was neglected. The parameters BŽ0. , BŽ1. , BŽ2. , G and GH S,H S,H S G,MX G,MX G,MX G,G,MX G,MX,MX2 2 2

are combinations of the second and third virial coefficients and are given by:

BŽi. sn b Ži. qn b Ži. is0,1,2 6Ž .G,MX q G ,M y G ,X

G sn 2 t q2n n t qn 2 t 7Ž .G,MX ,MX q G ,M ,M q y G ,M ,X y G ,X ,X

G sn t qn t . 8Ž .G,G,MX q G ,G ,M y G ,G ,X

The parameters b Ž1. , b Ž2. , BŽ1. , BŽ2. , and G were neglected, i.e., they were set to zero.G,G G,G G,MX G,MX G,G,MX

5.1.2. System H S–H O–NaNO2 2 3Ž0. Ž Ž0. .The remaining parameters B and G i.e., B and G were fittedG,MX G,MX,MX H S,NaNO H S,NaNO ,NaNO2 3 2 3 3

to the new results for the total pressure above H S–H O–NaNO . For the parameter determination,2 2 3

only vapor–liquid equilibrium data, i.e., no experimental data in the three-phase region wereconsidered. The influence of temperature on the interaction parameters was expressed by

q2,if T sq q . 9Ž . Ž .1,i TrKŽ .

The resulting numbers for q and q are given in Table 7.1,i 2, i

5.1.3. System H S–H O–NH NO2 2 4 3Ž0. Ž .The following expression for B is obtained by applying Eq. 6 to the systemsH S,NH NO2 4 3

Ž .H S–H O–salt, with single salts Na SO , NH SO , NaNO , and NH NO :2 2 2 4 4 2 4 3 4 3

1Ž0. Ž0. Ž0. Ž0.B s B yB qB . 10Ž .H S,NH NO H S,ŽNH . SO H S,Na SO H S,NaNO2 4 3 2 4 2 4 2 2 4 2 32

Ž0. Ž0. w x Ž0.B and B were taken from Xia et al. 13 . B was taken from theH S,Na SO H S,ŽNH . SO H S,NaNO2 2 4 2 4 2 4 2 3

correlation presented above. Thus BŽ0. was predicted.H S,NH NO2 4 3

Table 7Interaction parameters for Pitzer’s equation for the systems H S–NaNO –H O, H S–NH NO –H O and H S–NaOH–2 3 2 2 4 3 2 2

H O2q2,i

f T s q qŽ . 1,i TrKŽ .Parameter q q TrK Subsystem Source1,i 2, i

Ž0. w xb y0.26156 69.751 283–453 H S–H O Kuranov et al. 12H S,H S 2 22 2Ž0. w xB 0.05147 y21.2928 313–393 NH –H S–H O Rumpf et al. 15H S,NH HS 3 2 22 4Ž0. w xB y0.08436 115.72732 313–393 H S–H O–Na SO Xia et al. 13H S,Na SO 2 2 2 42 2 4Ž0. Ž . w xB 0.14091 4.70824 313–393 H S–H O– NH SO Xia et al. 13H S,ŽNH . SO 2 2 4 2 42 4 2 4Ž0. Ž .B 0.00163 10.45166 313–393 H S–H O–NaNO fitted this workH S,NaNO 2 2 32 3y5G y2=10 –H S,NaNO ,NaNO2 3 3Ž0. Ž .B 0.114265 y45.05788 313–393 H S–H O–NH NO prediction from Eq. 10H S,NH NO 2 2 4 32 4 3y3 Ž .G 1.16=10 – fitted this workH S,NH NO ,NH NO2 4 3 4 3


Table 8Distribution coefficients of hydrogen sulfide and water in H S–H O2 2

g2,iXY ,ln K s g qi 1, i TrKŽ .i g g1,i 2, i

H S y1.0711 173.13562

H O 3.44803 y2429.7412

The ternary parameter G cannot be calculated in a similar way. This parameterH S,NH NO ,NH NO2 4 3 4 3

was fitted to the new experimental results for the total pressure above H S–H O–NH NO . Only2 2 4 3

vapor–liquid but no vapor–liquid–liquid equilibrium data were considered for determining thatparameter. The parameters are given in Table 7.

5.1.4. Vapor–liquid–liquid equilibriumThe phase equilibrium between the coexisting liquid phases is expressed by:

X YY ref , ref ,a m ymi i iXY ,K s sexp isH S, H O 11Ž .Xi 2 2a RTi

Y ,X Ž .where K is the distribution coefficient of component i either hydrogen sulfide or water betweeniŽX. ŽY.the water-rich and the hydrogen sulfide-rich phases.

In the hydrogen sulfide-rich phase, concentrations are expressed through mole fraction and theunsymmetric convention for normalization is chosen: For hydrogen-sulfide, the reference state is the

ref,Y Ž . ref,Ypure liquid m sm T , p ; for water, it is the infinitely diluted solution m sH S H S pure liquid w2 2` Ž .m T , p . As the second liquid phase is nearly pure hydrogen sulfide, it is assumed that this phasew,H S2

behaves like an ideal solution. Therefore, the activities of hydrogen sulfide and water were replacedby the mole fractions:

a Y sxY isH S, H O. 12Ž .i i 2 2

Y ,X w x Ž .The distribution coefficients K were taken from Xia at al. 13 cf. Table 8 .i

5.2. System H S–H O–NaOH2 2

Fig. 5 shows a scheme of the model applied to predict the solubility of hydrogen sulfide in aqueoussolutions of sodium hydroxide. Here, the chemical reactions in the liquid phase, which converthydrogen sulfide to bisulfide and sulfide ions as well as the autoprotolysis of water have to be takeninto account.

H S|HqqHSy R1Ž .2

HSy|HqqS2y

R2Ž .

H O|HqqOHy R3Ž .2


Fig. 5. VLLE in the system H S–H O–NaOH.2 2

Sodium hydroxide is assumed to be present only in the aqueous phase, where it is completelyŽ .dissociated. The second hydrogen sulfide-rich liquid phase and the vapor phase are treated as binary

mixtures of hydrogen sulfide and water.

5.2.1. Vapor–liquid equilibriumThe condition for chemical equilibrium yields the following equation for a chemical reaction R:

K T s a n i ,R . 13Ž . Ž .ŁR ii

The balance equations for the overall number of moles of sodium hydroxide, hydrogen sulfide, andwater result in:

Xqn sn , 14Ž .NaOH Na

X X Xyy 2n sn qn qn , 15Ž .H S H S HS S2 2

X X Xy qn sn qn yn . 16Ž .H O H O OH Na2 2

The condition for electroneutrality of the aqueous phase gives:

n qX qn q

X sn yX qn y

X q2n 2yX . 17Ž .H Na OH HS S

Solving this set of equations for given temperature and overall mole numbers n of componentsiŽ .i.e., H S, H O and NaOH results in the ‘‘true’’ composition of the liquid phase, i.e., the molalities2 2

of true species i.ŽThe conditions of vapor–liquid equilibrium between the aqueous phase and the gas phase cf. Eqs.

Ž . Ž ..1 and 2 can then be applied to calculate the total pressure and the composition of the gas phase.Apart from the information already given in Section 5.1, the calculation requires the knowledge of

w xthe temperature-dependent equilibrium constants K –K , which were taken from Edwards et al. 31 3


Table 9Chemical equilibrium constants

ARln K s q B ln TrK qC TrK q DŽ . Ž .R R R RTrKŽ .

2Reaction A B C =10 DR R R R

y qH S|HS qH y18034.72 y78.07186 9.19824 461.71622y 2y qHS |S qH y406.0035 33.88898 y5.411082 y214.5592

q yH O|H qOH y13445.9 y22.4773 0 140.9322

Ž . E w xcf. Table 9 . Activity coefficients were calculated from the G equation of Pitzer 8 . Parametersdescribing interactions in H S–H O–NaOH can be divided into different groups.2 2

Ž .1 Interaction parameters for the binary subsystem H S–H O. They were taken from Kuranov et2 2w x Ž .al. 12 cf. Table 7 .Ž .2 Interaction parameters for the binary subsystem NaOH–H O. They were taken from Pabalan2

w x Ž .and Pitzer 14 cf. Table 10 and Appendix B .Ž . w x3 The following parameters were determined by Rumpf et al. 15 from VLE data in the ternary

Ž0. Ž0. Ž1. Ž .q y q y q q ysystem NH –H S–H O: B , b , b , and t . According to Eq. 6 :3 2 2 H S,NH HS NH ,HS NH ,HS NH ,NH ,HS2 4 4 4 4 4

BŽ0. sb qŽ0. qb y

Ž0. . As in this system the concentrations of NHq and HSy ions areH S,NH HS H S,NH H S,HS 42 4 2 4 2

practically the same, b qŽ0. was arbitrarily set to zero without losing any generality,H S,NH2 4

b qŽ0. s0 18Ž .H S,NH2 4

Ž .and consequently cf. Table 7 :

b yŽ0. sBŽ0. . 19Ž .H S,HS H S,NH HS2 2 4

Ž . Ž0. Ž0. Ž0. Ž . Ž .q4 b was determined from B and B with Eqs. 6 and 18 :H S,Na H S,NaNO H S,NH NO2 2 3 2 4 3

b qŽ0. sBŽ0. yBŽ0. . 20Ž .H S,Na H S,NaNO H S,NH NO2 2 3 2 4 3

Ž . q5 Due to the very small amounts of H ions, all interaction parameters involving this specieswere set to zero.

Ž . 2y Ž Ž ..6 As the equilibrium constant for the formation of S ions reaction R2 is rather small, allinteraction parameters involving this species were set to zero.

Ž .7 All interaction parameters involving only charged species of the same sign were neglected.Ž . Ž0. Ž0.

y q y8 There remain two unknown binary parameters: b and b . When both areH S,OH Na ,HS2

Ž .neglected i.e., set to zero , the model can be used to predict the solubility of H S in aqueous NaOH.2

Neglecting b yŽ0. causes no serious problems, as H S and OHy never appear simultaneously inH S,OH 22

high concentrations. This is demonstrated in Fig. 6, where the predictions for the ‘‘true’’ molalities ofall the important species in an aqueous solution of 1 mol of NaOH at 313 K are plotted versus the‘‘overall’’ molality of H S.2


Fig. 6. Predictions for the aqueous phase molalities of the most important species in the system H S–H O–NaOH at 313.152 2

K and m s1 molrkg.NaOH

5.2.2. Vapor–liquid–liquid equilibriumŽ .The same procedure was applied as for the systems H SqH Oq NaNO or NH NO , allowing2 2 3 4 3

a prediction of pressure and compositions of the coexisting phases.

Fig. 7. Solubility of hydrogen sulfide in a 6-m aqueous solution of sodium nitrate. ` Experimental results, this work. —Calculated results, this work.


6. Comparison of experimental data with model calculations

A comparison between the new experimental results for the total pressure and calculated resultsŽ .from the correlation for the system H S–H O–NaNO see Fig. 7 for m f6 molrkg yields an2 2 3 NaNO3

average relative deviation of 3.2%. The maximum relative deviation in the total pressure is 15.6%,occurring at Ts333.14 K, and ps0.1053 MPa, where the calculated pressure is too small by about16 kPa. Typical relative deviations range from 1% to 4%. The model predicts the pressure at the

Ž .three-phase-line VLLE with an average relative deviation of 1.8%.The experimental results for the total pressure above H S–H O–NH NO are correlated with an2 2 4 3

average relative deviation of 9.3%. The maximum relative deviation is 16% corresponding to anŽ .absolute deviation of 0.112 MPa at Ts313.16 K, ps0.698 MPa . The average relative deviation

between predicted and measured pressures at the three-phase line is 1.8%. Fig. 8 shows a comparisonbetween the new experimental results for the total pressure above an aqueous solution containingabout 6 mol of NH NO per kg of H O and the results from the correlation. It is worthwhile to4 3 2

mention that the correlation can be improved by fitting BŽ0. together with GH S,NH NO H S,NH NO ,NH NO2 4 3 2 4 3 4 3

to the experimental data instead of predicting that parameter. The average relative deviation in thetotal pressure is then reduced from 9.3% to 1.9%.

As can be seen from Fig. 3, for the system H S–H O–NaOH, a good agreement is achieved2 2

between the new experimental data and the prediction. The average relative deviation in the total

Fig. 8. Solubility of hydrogen sulfide in a 6-m aqueous solution of ammonium nitrate. ` Experimental results, this work. —Calculated results, this work.


pressure is 8.8%. However, that deviation mostly results from a few data points at hydrogen sulfidemolalities m -m , where the total pressure is nearly not changed by the addition of hydrogenH S NaOH2

sulfide. In that low-pressure range, the absolute uncertainty in the pressure readings can reach up toŽ .5%. The pressure at three-phase equilibrium VLLE is predicted with an average relative deviation of

about 2%.

7. Conclusions

The solubility of hydrogen sulfide in aqueous solutions containing the single strong electrolytessodium nitrate, ammonium nitrate and sodium hydroxide was measured at temperatures from 313 to393 K, and total pressures up to 10 MPa. The salt molalities were about 3 and 6 for sodium nitrate,about 6 for ammonium nitrate, and about 1 and 2 for sodium hydroxide. The maximum ratio ofhydrogen sulfide to water in the equilibrium cell was about 4.5 molrkg. In some experiments, theconcentration was above the solubility limit for hydrogen sulfide and therefore, a second, hydrogensulfide-rich liquid phase was observed. Thermodynamic models are used to describe the vapor–liquidand vapor–liquid–liquid equilibria. Interaction parameters for Pitzer’s GE–equation were determinedfrom the new experimental results for the systems H S–H O–NaNO and H S–H O–NH NO .2 2 3 2 2 4 3

The model successfully predicts the pressures above H S–H O–NaOH within the experimental2 2Ž .uncertainties. Furthermore, the model reliably predicts the three-phase VLLE pressure.

List of symbolsa . . . d coefficients for the temperature dependence of second virial coefficients of waterA . . . D coefficients for the temperature dependence of Henry’s constant for the solubility of

hydrogen sulfide in pure waterA . . . D coefficients for the temperature dependence of chemical equilibrium constantsR R

A Debye–Huckel parameter¨w

a activity of component ii

b constant in modified Debye–Huckel expression¨BŽi. effective second osmotic virial coefficient for interactions between a gas G and a saltG,MX

Ž .MX is0,1,2Cf third osmotic virial coefficient in Pitzer’s equationD relative dielectric constant of watere charge of protonf function for the temperature dependence of an interaction parameterf , f , f functions in Pitzer’s equation1 2 3

g coefficients for the temperature dependence of distribution coefficientsiŽ .G gas here hydrogen sulfide

GE excess Gibbs energyŽm. Ž .H Henry’s constant for the solubility of gas i in pure water on molality scalei,w

Ž .I ionic strength on molality scalek Boltzmann constantK distribution coefficienti


Ž .K equilibrium constant for chemical reaction R on molality scaleR

M cation MŽ .M molar mass of water kgrmolw

m overall molality of component ii

m true molality of component ii

n overall number of moles of component i in equilibrium celli

n true number of moles of component ii

N Avogadro’s numberA

p pressureq coefficients for the temperature dependence of interaction parametersi

R universal gas constantT absolute temperatureÕ partial molar volumeX anion Xx, x , x variables in Pitzer’s equations1 2

y mole fraction in vaporz number of charges of component ii

Greek lettersa , a constants in Pitzer’s equation1 2

b Ž0., b Ž1., b Ž2. binary interaction parameters in Pitzer’s equationŽm. Ž .g activity coefficient normalized to infinite dilution on molality scale

G third osmotic virial coefficient´ vacuum permittivity0

l second osmotic virial coefficient in Pitzer’s equationi, j

m chemical potential of component ii

n stoichiometric coefficient of component i in reaction Ri,R

n , n number of cations and anions in salt M Xq y n nq y

p number of phasesr mass densityt ternary interaction parameter in Pitzer’s equationw fugacity coefficient

SubscriptsG gasi, j,k components i, j, kR reaction Rs saltw water

SuperscriptsŽ .m on molality scales saturation` infinite dilutionX water-rich liquid phaseY hydrogen sulfide-rich liquid phase


Z gas phaseref reference state

Acknowledgements

ŽFinancial support of this investigation by the Volkswagen-Stiftung, Hannover, Germany Grant No.. ŽIr70 877 , as well as by the government of the Federal Republic of Germany BMFT Grant No..0326558 C , and BASF AG, Ludwighafen; Bayer AG, Leverkusen; Degussa AG, Hanau; Hoechst

AG, Frankfurt; Linde KCA, Dresden; and Lurgi AG, Frankfurt is gratefully acknowledged. J.X.Ž .thanks the Deutscher Akademischer Austauschdienst DAAD for granting a scholarship.

Appendix A. Brief outline of Pitzer’s model

w xThe equation of Pitzer 8 for the excess energy of an aqueous, salt containing system is

GE

s f I q m m l I q m m m t . 21Ž . Ž . Ž .Ý Ý Ý Ý Ý1 i j i , j i j k i , j ,kRTn Mw w i/w j/w i/w j/w k/w

Ž .f I is a modified Debye–Huckel term¨1

4 I 'f I syA ln 1qb I 22Ž . Ž .Ž .1 w b

where I is the ionic strength

12Is m z . 23Ž .Ý i i2 i

Ž .1r2b is 1.2 kgrmol for all electrolytes. A is the Debye–Huckel parameter for the osmotic¨w

coefficient1.521 e0.5

A s 2p N r . 24Ž . Ž .w A w ž /3 4p´ DkT0

Ž .l I is the ionic strength dependent second virial coefficient:i, j

l I sb Ž0.qb Ž1. f x qb Ž2. f x 25Ž . Ž . Ž . Ž .i , j i , j i , j 2 1 i , j 2 2

where b Ž0., b Ž1. and b Ž2. are binary interaction parameters. The function f is defined asi, j i, j i, j 2

2yxf x s 1y 1qx e 26Ž . Ž . Ž .2 2x

' 'where x sa I and x sa I .1 1 2 2

For salts with at least one univalent cation or anion, a has the value 2.0 and the binary parameter1

b Ž2. is usually set to zero except at very high temperatures.i, j


Table 10Ion interaction parameters for aqueous solutions of NaNO and NH NO3 4 3

TRf T s q q q 1yŽ . 1 2 ž /T

Salt Parameter q q Source1 2

Ž0. w xNaNO b 0.00388 0.04938 Sing et al. 103Ž1.b 0.21151 8.6493fC y0.00006 y0.0003Ž0. w xNH NO b y0.01476 – Kim and Frederick 114 3Ž1.b 0.13826 –fC 0.00029 –

Ž .Differentiation of Eq. 21 yields the activity coefficient of a dissolved species i:

'I 2Žm . 2 Ž0. Ž1. Ž2.'lng syA z q ln 1qb I q2 m b qb f x qb f xŽ . Ž .Ž . Ýi w i j i , j i , j 2 1 i , j 2 2' b1qb I j/w

2 Ž1. Ž2.yz m m b f x qb f x q3 m m t . 27Ž . Ž . Ž .Ý Ý Ý Ýi j k j,k 3 1 j ,k 3 2 j k i , j ,kj/w k/w j/w k/w

where f is3

21 xyxf x s 1y 1qxq e . 28Ž . Ž .3 2 ž /Ix 2

Table 11Ž w x.Ion interaction parameters for aqueous solutions of NaOH Pabalan and Pitzer 14

q q q q p10 11 122f T s q q q pq q q q p rT q q lnT q q q q p T q q q q p T q qŽ . Ž . Ž . Ž .1 2 3 4 5 6 7 8 9 T y227 647yTŽ . Ž .Ž0. Ž1. fb b C

2 2 1q 2.7682478=10 4.6286977=10 y1.6686897=101y3 y4q y2.8131778=10 0.0 4.0534778=1023 4 2q y7.3755443=10 y1.0294181=10 4.5364961=103y1 y2q 3.7012540=10 0.0 y5.1714017=1041 1q y4.9359970=10 y8.5960581=10 2.96807725y1 y1 y3q 1.0945106=10 2.3905969=10 y6.5161667=106y6 y6q 7.1788733=10 0.0 y1.05530373=107y5 y4 y6q y4.0218506=10 y1.0795894=10 2.3765786=108y9 y10q y5.8847404=10 0.0 8.9893405=1091 y1q 1.1931122=10 0.0 y6.8923899=1010

y2q 2.4824963 0.0 y8.1156826=1011y3q y4.821740=10 0.0 0.012


The activity of water follows from the Gibbs–Duhem equation1.5I

Ž . Ž . Ž .0 1 yx 2 yx1 2lna sM 2 A y m m b qb e qb eÝ Ý ž /w w w i j i , j i , j i , j'1qb I i/w j/w

y2 m m m t y m . 29Ž .Ý Ý Ý Ýi j k i , j ,k ii/w j/w k/w i/w

For systems containing a single salt M X , the binary and ternary parameters involving two orn nq y

more species of the same sign of charge are usually set to zero. The ternary parameters t , tM,X,X M,M,X

are usually reported as third virial coefficients Cf for the osmotic coefficient:1 1

1 n nq y2 2fC s t q t . 30Ž .M,M,X M,X ,Xž / ž /3 n ny q

Ž . Ž . fInstead of rewriting Eqs. 27 and 29 in terms of C , we preferred to set t to zero andM,X,X

calculated the ternary parameter t from the reported values for Cf:M,M,X

1f1:1 salt: t s C 31Ž .M,M,X 3

Appendix B. Interaction parameters for Pitzer’s equation

Literature data for the temperature dependent ionic interaction parameters b Ž0., b Ž1. and Cf forthe systems NaNO qH O, NH NO qH O, and NaOHqH O are given in Tables 10–11. T is the3 2 4 3 2 2

Ž .temperature in kelvin T s298.15 K . p is the pressure in bar. In the present work, for theR

calculation of interaction parameters, p was approximated by the saturation pressure of pure water.

References

w x Ž .1 B. Rumpf, G. Maurer, Fluid Phase Equilib. 81 1992 241–260.w x2 E.W. Washburn, International Critical Tables of Numerical Data, McGraw-Hill, New York, 1928.w x Ž .3 T.J. Edwards, G. Maurer, J. Newman, J.M. Prausnitz, AIChE J. 24 1978 966–976.w x Ž .4 S.W. Brelvi, J.P. O’Connell, AIChE J. 18 1972 1239–1243.w x Ž .5 A. Saul, W. Wagner, J. Phys. Chem. Ref. Data 16 1987 893–901.w x6 J.H. Dymond, E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Oxford Univ. Press, Oxford, UK, 1980.w x Ž .7 J.G. Hayden, J.P. O’Connell, Ind. Eng. Chem. Proc. 14 1975 209–216.w x Ž .8 K.S. Pitzer, J. Phys. Chem. 77 1973 268–277.w x Ž .9 D.J. Bradley, K.S. Pitzer, J. Phys. Chem. 83 1979 1599–1603.

w x Ž .10 R. Sing, B. Rumpf, G. Maurer, Ind. Eng. Chem. Res. 38 1999 2098–2109.w x Ž .11 H.T. Kim, W.J. Frederick Jr., J. Chem. Eng. Data 33 1988 177–184.w x Ž .12 G. Kuranov, B. Rumpf, N. Smirnova, G. Maurer, Ind. Eng. Chem. Res. 35 1996 1959–1966.

´w x13 J. Xia, A. Perez-Salado Kamps, B. Rumpf, G. Maurer, Ind. Eng. Chem. Res., in press.´w x Ž .14 R.T. Pabalan, K.S. Pitzer, Geochim. Cosmochim. Acta 51 1987 829–837.

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h2s Naoh Equilibrium Curve

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