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Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressures up to 2.5 MPa
241
Fluid Phase Equilibria, 81 ( 1992) 241-260 Elsevier Science Publishers B.V., Amsterdam
Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressures up to 2.5 MPa B. Rumpf and G. Maurer Lehrstuhl ftir Technische Thermodynamik, Universitiit Kaiserslautern, D-6750 Kaiserslautern (Germany) (Received November 4, 1991; accepted in final form May 22, 1992)
ABSTRACT Rumpf, B. and Maurer, G., 1992. Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressures up to 2.5 MPa. Fluid Phase Equilibria, 81: 241-260. The solubilities of hydrogen cyanide and sulfur dioxide in pure water were measured using a static method in the temperature range 313 < T/K < 413 (HCN) and 293 < T/K < 393 ( SOz) at pressures up to 0.6 MPa (HCN) and 2.5 MPa (SO,) corresponding to gas molalities of up to 7 (HCN) and 6 (SO,). Results are reported and compared with literature data and correlations. INTRODUCTION
The solubilities of weak electrolyte gases must be known for designing separation equipment in many technical applications, for example, for the design of sour gas absorption columns and sour water strippers. Experimental data are rarely found in the literature, and therefore models to correlate weak electrolyte gas solubilities in pure water and aqueous salt solutions cannot be tested or improved. This paper reports new experimental data for the boiling point of a gas + liquid mixture measured with a static gas solubility apparatus. EXPERIMENTAL
Apparatus and procedure Figure 1 shows the experimental arrangement for measuring the solubility of a single gas in aqueous solution. In an experiment, a thermostated high Correspondence to: G. Maurer, Lehrstuhl fti Technische Thermodynamik, Kaiserslautern, D-6750 Kaiserslautern, Germany.
Universitit
0378-3812/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
242
B. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
Fig. 1. Scheme of the experimental arrangement for measuring the solubility of a single gas in aqueous solution: A, high pressure optical cell; B, thermostat; C, magnetic stirrer, D, measurement of temperature difference by thermocouples; E, measurement of temperature by platinum resistance thermometers; F, high pressure displacer; G, tank for aqueous solutions; H, pressure transducers, I, tank for rinsing water; J, frequency bridge, K, recorder, L, container for gaseous solute.
pressure optical cell (volume about 30 cm3; material Hastelloy C4) is partially filled with a known amount of the aqueous solvent. Next, a known amount of gas is added from a storage tank. More aqueous solvent is introduced into the cell with a calibrated high pressure displacer until the gas is completely dissolved. The pressure in the cell is then reduced stepwise by withdrawing very small amounts of the liquid until the first stable bubble appears. Typically, about 0.1-7 g of the gas was passed into the cell. The mass of the gas was determined by weighing, with an uncertainty of about 0.008 g. The volume of the solvent needed to dissolve the gas was determined by measuring the position of the high pressure displacer piston before and after each experiment, with an uncertainty of about 0.3 cm3. The density of the solvent was taken from the literature (Schmidt, 1982). The temperature was measured with two calibrated resistance thermometers placed in the heating jacket of the cell. The accuracy of the temperature measurement was fO.l K. The pressure was measured with pressure transducers connected to a frequency bridge. Six transducers were used with pressure ranges of 0.5, 2, 5 MPa (SO,) and 0.25, 0.6, 2.5 MPa (HCN). Before and after each series of measurements, the transducers were calibrated against a pressure gauge. The typical uncertainty in determining the solubility pressure for hydrogen cyanide was 0.3 kPa in the pressure range O-O.25 MPa and 0.6 kPa in the range 0.25-0.6 MPa. For sulfur dioxide, the uncertainty was 1 kPa in the pressure range O-O.5 MPa and 4 kPa at higher pressures.
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
243
Since hydrogen cyanide is an extremely toxic substance, special care had to be taken to avoid any escape of the gas into the atmosphere. Therefore the apparatus was placed into a sealed hood connected to an exhaust fan and operated through gloves. Moreover, warning devices were used to detect any leakage. Materials
High grade sulfur dioxide (99.98 wt.% or more) was purchased from Messer Griesheim, Ludwigshafen, and used without further purification. Hydrogen cyanide was obtained from a production plant from Riihm GmbH, Worms. Since hydrogen cyanide polymerizes (Volker, 1960), it cannot be stored as a liquid for long periods. Therefore, before each series of measurements, small amounts (typically about 40 g) were drawn from the production plant. The purity, as determined by gas chromatography, was better than 99.7%. Furthermore, each sample was degassed at low temperature under vacuum. Water was deionized and further purified by vacuum distillation. RESULTS
The experimental results for the solubility of hydrogen cyanide in water at temperatures between 3 13.15 and 413.15 K at total pressures up to 0.6 MPa are given in Table 1. The results for sulfur dioxide over the temperature range 293.15-393.15 K at pressures up to 2.5 MPa are given in Table 2. Figure 2 shows the total pressure plotted versus the molality of dissolved hydrogen cyanide in the liquid phase. Attempts to extend the experimental investigation to higher concentrations and higher temperatures were discarded owing to the onset of colorization of the liquid mixture, indicating the start of hydrogen cyanide polymerization. Figure 3 shows the results obtained for the system sulfur dioxide-water. The concentration range was limited by the appearance of a second (sulfur dioxide rich) liquid phase at molalities somewhat above the upper limits of the data given in Table 2. METHOD OF CORRELATION AND COMPARISON WITH LITERATURE DATA
The hydrogen cyanide-water
system
To correlate the experimental results for the solubility of hydrogen cyanide in water, the phase equilibrium condition for water (w) and the dissolved gas (G) yields
(1)
3. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
244
TABLE 1 Experimental
results for the solubihty of hydrogen cyanide in water
&iCN
w
&HC!N
1OP
(moi kg-‘)
(MPa)
TK)
(mol kg-‘)
(MPa)
314.12 313.20 313.16 313.16 313.13 313.16 313.15
0.0
0.076 0.269 0.407 0.441 0.609 0.642 0.786
333.03 333.1% 333.22 333.22 333.22 333.23 333.23 333.22
0.0 0.739 1.217 1.497 1.879 2.471 2.877 4.129
0.202 0.431 0.570 0.648 0.747 0.879 0.980 1.197
373.15 373.12 373.15 373.16 373.16 373.13 373.16 373.16 373.14 373.10 373.12 373.10
0.199
1.064 2.117 2.279 3.794 4.009 5.839
1.163 1.524 1.424 1.525 1.700 1.996 1.976 2.004 2.15% 2.523 3.097 3.930
353.19 352.93 353.09 352.99 353.05 352.92 353.17 352.80 353.30 353.23 353.13 353.15
0.0 0.0 1.030 1.905 2.470 2.583 2.669 2.726 3.100 3.245 3.359 4.549
0.479 0.471 0.985 1.30% 1.512 1.565 1.579 1.591 1.720 1.764 1.812 2.073
373.19
0.0
1.022
392.94 393.15 393.16 393.15 393.15 393.13 393.17 393.17 393.16 393.17 393.11 393.16 413.11 413.14 413.14 413.13 413.12
0.731 0.58% 0.685 0.956 1.397 1.399 1.502 1.666 2.485 3.880 6.615 0.0
0.361 0.381 0.609 1,018 1.054 1.211 2.00% 2.393 2.409 3.652 3.785 0.0
0.332 0.693 0.869 1.453
1.964 2.349 2.359 2.575 2.956 3.001 3.123 3.730 3.991 3.986 4.773 4.843 3.611 4.019 4.453 4.676 5.31%
(2) As the equilibrium constant for the dissociation of hydrogen cyanide is small (K = ffn + acN- /ancN M 6 x IO-” (Tsonopoulos et al., 1976)), the true concentration of the gas present in the liquid phase was set equal to the overall concentration directly determined from the measurements. Since the total pressure is always rather low, the fugacity coefficient of water, as well as that of hydrogen cyanide, was set equal to unity and the influence of pressure on Henry’s constant and on the fugacity of liquid
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Fig. 2. Solubility correlation (fit).
Fig. 3. Solubility correlation (fit).
of hydrogen cyanide in water: 0, experimental
of sulfur dioxide in water:
0,
experimental
245
results, this work; -,
results, this work; -,
water was neglected. Thus, eqns. (1) and (2) yield Henry’s constant for hydrogen cyanide from an extrapolation procedure of the direct experimental results: (3)
0.531 0.882 0.891 1.616
0.988 0.982 0.981 0.968 1.377 2.161 2.143 3.640
0.237 0.528 0.767 0.836 1.222 1.348 1.397
393.08 393.08 393.05 393.17 393.33 393.32 393.18
0.595 0.968 0.977 1.736
0.264 0.480 0.700 0.839 0.918 1.763 3.430 4.695 5.554
363.17 363.17 363.17 363.17 363.16 363.17 363.17 363.17 363.16
333.16 333.16 333.15 333.15
0.488 0.545 1.141 1.314 1.537 1.966 2.979 4.001 4.259 4.409 4.603
0.992 0.991 0.982 0.979 0.976 0.970 0.955 0.941 0.935 0.934 0.930
0.309 0.354 0.810 0.943 1.111 1.408 2.237 3.076 3.388 3.466 3.698
0.376 0.427 0.926 1.069 1.250 1.566 2.443 3.323 3.650 3.731 3.973
2.100 2.696 2.968 3.320 4.427 5.310
343.13 343.19 343.13 343.24 343.12 343.23
313.18 313.15 313.16 313.13 313.17 313.29 313.14 313.14 313.11 313.15 313.14
0.356 0.756 1.446 1.623 1.758 2.418 3.076
0.458 1.081 1.903 2.255 2.369 3.454 4.701
0.580 1.279 2.178 2.559 2.680 3.844 5.162
293.17 293.17 293.17 293.14 293.16 293.15 293.16
0.988 0.975 0.959 0.952 0.950 0.931 0.910
Overall
Tru@
Overall
0.223 0.507 0.741 0.809 1.189 1.313 1.361
0.239 0.446 0.657 0.791 0.868 1.691 3.325 4.570 5.417
1.987 2.565 2.829 3.173 4.254 5.119
True*
Molality of SO, (mol kg- ‘)
Molality of SOz (mol kg-‘)
Experimental results for the solubility of sulfur dioxide in water
TABLE 2
0.996 0.990 0.986 0.985 0.978 0.976 0.975
0.995 0.991 0.987 0.984 0.983 0.968 0.941 0.921 0.908
0.962 0.952 0.948 0.942 0.924 0,911
a%
3.428 5.148 6.45 6.90 9.12 9.66 10.29
1.788 2.551 3.498 3.928 4.398 7.12 12.22 14.89 16.40
5.362 6.73 7.45 8.01 10.12 11.09
lOp( MPa)
0.227 0.476 0.733 0.970 1.243 1.663
343.21 343.18 343.21 343.14 343.17 343.14
a Calculated.
2.403 2.748 2.912 3.354 4.500
333.15 333.15 333.15 333.15 333.15
0.195 0.428 0.671 0.898 1.159 1.564
2.238 2.591 2.750 3.178 4.292
0.995 0.991 0.986 0.982 0.977 0.970
0.957 0.951 0.948 0.941 0.923 0.860 1.538 2.239 2.805 3.319 4.541
4.838 5.44% 5.688 6.43 8.06 393.08 393.18 393.09 393.33 393.07 393.09 393.18 393.18 393.18 393.07 393.33
1.551 1.606 1.743 2.500 2.585 2.742 2.777 3.506 4.364 4.707 5.328 1.513 1.567 1.702 2.451 2.535 2.690 2.725 3.447 4.297 4.637 5.254 0.972 0.971 0.969 0.956 0.955 0.952 0.952 0.940 0.926 0.921 0.912
10.70 11.16 11.89 15.38 15.93 16.67 16.89 19.55 22.44 23.60 25.09
248
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 3 Henry’s constants for the solubility of hydrogen cyanide in water 1OH(“) ( MPa mol - ’ kg)
T(K) 313.16 333.21 353.08 373.14 393.15 413.13
_+0.04 _+0.03 f 0.28 * 0.04 rt 0.04 + 0.02
o.210+0.0’5 0010 0.348 2 ;:o”;; 0.583 ‘;:E 0.822 :;:z; 1.088 f o”.;:; 1.320’;:;;;
In the first step, the activity of water a, was approximated by its mole fraction x,. The vapor pressure of water was taken from the literature (Saul and Wagner, 1987). Table 3 gives the values for Henry’s constant of hydrogen cyanide determined from the measurements. The equation BHCN
In H$&+J( MPa mol - ’ kg) = AHCN+ -
(4)
+c~cdT/K)
(T/K)
with coefficients given in Table 4 (Extrapolation) correlates Henry’s constant with an average relative deviation (AHI,1 = 1.7% and a maximum relative deviation of /AHjre,,max= 4.4%. As can be seen from Fig. 2, Henry’s law is obeyed only at concentrations up to about 1 mol HCN per kilogram of water. Therefore activity coefficients had to be taken into account. The model of Pitzer (1973) as modified by Edwards et al. (1978) was used to describe the activity coefficients. When a single gas is dissolved in water (neglecting dissociation as well as any ternary parameters), the equation for the activity coefficients of the dissolved gas and water reduces to
TABLE 4 The temperature
mol- 1kg) = A, + &
In HgQ(MPa
Gas HCN 8%
dependence of Henry’s constant: + C&T/K)
+ Do ln(T/K)
AG
BG
CG
DG
Method
19.411 15.179 - 1203.75 - 154.827
-5189.7 -4493.9 30861.36 321.17
-0.02146 -0.01522 -0.32612 - 0.0634
0.0 0.0 209.74 29.872
Extrapolation Fit Extrapolation Fit
249
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 5 The temperature /gb++bG
Gas HCN so*
Ina,=
dependence of interaction
parameters:
(T/K) + ($)’
aG
bG
CG
0.8893 0.1180 -0.0652 0.0934
-647.10 -115.29 -40.59 - 137.92
1.109. 2.063 1.625 . 3.127.
-m&/Q&G-m
Method 105 lo4 lo4 lo4
Extrapolation Fit Extrapolation Fit
&.J G 1000
where /I& is an adjustable temperature-dependent parameter. Using Henry’s constants calculated from eqn. (4), the interaction parameter was fitted to the experimental results for the total pressure on each isotherm. The equation
P&=aG+bG (T/K) + (&2
(7)
with coefficients given in Table 5 (Extrapolation) was chosen to correlate the results. Combining these results with Henry’s constants from Table 4 results in an average deviation between the experimental and calculated pressure of l&Ire, = 1.3% and a maximum relative deviation IAPI~~,,~~= 5.8% (absolute deviation [Aplabs,max = 2.4 kPa). As the activity of water and in turn the fugacity of the gas are influenced by the value for the interaction parameter /I$&, the extrapolation procedure described previously should normally be performed once more, taking into account activity coefficients. However, we decided to fit the coefficients of eqns. (4) and (7), e.g. I?@&, and /$LN,ncN, simultaneously to the experimental results for the total pressure. The resulting coefficients are also given in Tables 4 and 5 (Fit). Using this set of parameters gives a sligha better description of the experimental results for the total pressure (IAp IreI= 0.8%, (ApIrel,max = 3.2%, IAplabs,max = 1.3 kPa). Simultaneously fitting Henry’s constant and the interaction parameter in most cases results in slightly smaller numbers for Henry’s constant than those obtained from the extrapolation procedure. The typical absolute deviation between Henry’s constants obtained from the different correlations does not exceed 0.004 MPa mol - ’ kg. Results from the simultaneous fit are used for comparison with literature data. Literature data on the solubility of hydrogen cyanide are scarce. Bredig and Shirado ( 1927) investigated the system at 291.15 K using a dynamic
250
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
method. Up to fiHcN x 14 mol kg-’ their results agree well with the correlation of this work. Although the concentration range is more than twice the upper limit of the experimental results on which the correlation is based, the average deviation in total pressure and in the partial pressure of hydrogen cyanide is only 1.9% and 2.4% respectively. Opykhtina and Frost (1936) measured boiling points at a total pressure of about 0.1 MPa in the temperature range from about 312 to 371 K. At low temperatures the hydrogen cyanide concentrations are far beyond the range of the present work, and therefore the comparison is restricted to temperatures between 319 and 371 K. In that temperature range, the partial pressures of hydrogen cyanide as reported by the Qykhtina and Frost agree fairly well with the results of the present work ( [ApHCN/rel = 5.7%, lApnoN Imax = 17.6%), while the differences in total pressure are somewhat larger ( lAp IreI= 7%, (ApIre,,max = 10.2%). Miles and Wilson ( 1975) reported some data for 323.15, 363.15 and 393.15 K. Their results are compared with the correlation of the present work in Figs. 4(a)-4(c). As can be seen from Table 6, relative deviations for the total pressure and the partial pressures of hydrogen cyanide and water amount to a few per cent. The sulfur dioxide -water system
Sulfur dioxide is a stronger acid than hydrogen cyanide; therefore, the simple procedure described previously cannot be applied to determine its Henry’s constant in water from the direct experimental results. The dissociation of sulfur dioxide in the liquid phase must be taken into account. As discussed by Edwards et al. ( 1978), three chemical reactions are considered in the liquid phase: SOz + H,O C$ HSO; + H+ HSO; z$ SO:- + H+ Hz0 z$ H+ + OHTo evaluate the experimental results, the following expressions for chemical equilibrium, mass balance and electroneutrality were used: KI =
mHSOFmH+
?ftSO&+
mSOpw %O$-mH+ &I
=
Y&so,
mH+mOH-?6+Y8H-
*so,= mH+
y&-y&+
mHS0,-
61 =
(8)
740,
(10)
a, mS02
= mHSOT
+ mHSOT + 2mSOz-
(9)
+ mSOj+ mOH-
(11) (12)
B. Rumpf and G. Maurer 1 Fiuid Phase Equilibria 81 (1992) 241-260
251
40
B f 0.
t=
30
20
10
O”m,,,hnollkg” ’
0
40
8o
tii,,./mol/kg
Fig. 4. Solubility of hydrogen cyanide in water: (a) 0, experimental results (total pressure), Miles and Wilson (1975); -, calculated results, this work (fit); (b) 0, experimental results (partial pressure of HCN), Miles and Wilson (1975); -, calculated results, this work (fit); (c) 0, experimental results (partial pressure of water), Miles and Wilson (1975);. 1, calculated results, this work (fit).
Equilibrium constants for the three chemical equilibria were taken from Kawuzuishi and Prausnitz (1988). Activity coefficients for both ionic and molecular species were calculated using the Pitzer model as adapted by Edwards et al. with all interaction parameters set to zero. The dielectric constant D of pure water was taken from Bradley and Pitzer (1979). The resulting “true” molalities of (undissociated) SO2 and the activity of water
252
B. Rumpf and G. Maurer /Fluid Phase Equilibria 81 (1992) 241-260
TABLE 6 Hydrogen cyanide-water: comparison between the experimental results by Miles and Wilson (1975) and those of the present work
I&&NIreI
i”(K) 323.15 323.15 363.15 393.15
13 1 4 2
7.5 7.7 5.8 0.9
_ 9.2 38.4 6.5
10.5 1.9 3.9
are also given in Table 2. Using these values for the activity of water and the experimental results for the total pressure, eqn. (1) was used to calculate the mole fraction y, in the vapor phase in an iterative procedure. The fugacity coefficients in the vapor phase were calculated using the virial equation of state truncated after the second virial coefficient. The second virial coefficient of water II,,, was calculated from a correlation based on data given by Dymond and Smith (1980), whereas the second virial coefficient of sulfur dioxide BSo1,so2 and the mixed second virial coefficient B soz,w were calculated from a correlation of Hayden and O’Connell (1975). The influence of pressure on the fugacity of liquid water was calculated using the molar volume of pure water as given by Saul and Wagner ( 1987). The influence of pressure on Henry’s constant was calculated using the partial molar volume for SO* as described by Brelvi and O’Connell ( 1972). The data used for the determination of H&z& are summarized in Table 7. The next step yielded the fugacity of sulfur dioxide: f*;o, = PexpYSO~ &, Rearranging In -60, mso2
(13)
eqn. (2) results in
_ - ln Go2 + ln HLZ&QG)
+
%o*,w(P -PsH)
(14)
RT
Values for the left-hand side plotted versus the difference (p -p$) and extrapolated to Gso2 = 0 yielded the Henry’s constants given in Table 8. The influence of temperature on Henry’s constant is described by In H&$$,/(MPa mol - ’ kg) = Aso, + &
+
Go,WK)
+
bo,
W’W)
(15) With the coefficients Aso, -Dso, given in Table 4 (Extrapolation), this equation describes the experimental results for Henry’s constant with an average deviation of IdI&, = 0.7% and a maximum deviation IAHIre*,max= 1.4%.
B. Rtmpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
253
B. Rumpf
254
and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 8 Henry’s constants for the solubility of sulfur dioxide in water lOH(“)( MPa mol-’ kg)
T(K) 293.16 313.16 333.15 343.17 363.17 393.17
_+0.02 f 0.13 f 0.01 + 0.06 f 0.01 f 0.16
0.734_‘,q$?; 1.347’Z:E 2.305’;:g 2.901 ‘;:;j; 4.464’;:;;: 6.439’“-382 0.344
As for hydrogen cyanide-water, a strong negative deviation from Henry’s law is observed for the system sulfur dioxide-water at overall concentrations of the dissolved gas greater than about 1 mol per kilogram of water. Therefore the interaction parameter /?&&so2 was fitted to the isothermal results for the total pressure using Henry’s constants calculated from eqn. ( 15). Since most of the dissolved sulfur dioxide is present in molecular rather than in ionic form, parameters for interactions between molecular and ionic species as well as between ionic species were neglected. Thus the activity coefficients of ionic species were calculated from the modified Debye-Htickel term alone as given by Pitzer (1973). This seems to be a reasonable approximation as the ionic strength of the solution does not exceed 0.5 mol per kilogram of water. Equation (7) was used to describe the influence of temperature on /JL!8*,so,.The parameters aso2, bso2 and cso2 were fitted to the isothermal results for p&$J2,so2(cf. Table 5 (Extrapolation)). Combining these parameters with the equation for Henry’s constants (Table 4, (Extrapolation)) results in -an average deviation from the experimental results for the total pressure IAplre,= 2.4% and a maximum relative deviation [ApIrel,max = 7.3% ( JAplabs,max = 5.5 kPa). Since the procedure described before only gives a first estimate for Henry’s constants, the coefficients of eqns (7) and (15) were also fitted simultaneously to the experimental results for the total pressure. The resulting parameters are given in Tables 4 and 5 (Fit). This set of parameters reproduces our experimental results with an average deviation @Ire, = 1.5% and a maximum relative deviation ~~~~~~~~~~ = 5.7% = 4.3 kPa). Henry’s constants calculated with this set of paramew4 abs,max ters are in most cases slightly smaller than those obtained from the extrapolation procedure. However, the difference in Henry’s constants calculated from the two procedures does not exceed 0.03 MPa mol-’ kg at T = 393.15 K, where Henry’s constant obtained from the extrapolation procedure has a value of 0.644 MPa mol - ’ kg.
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Fig. 5. Henry’s constant for sulfur dioxide in water: comparison and Parker (1985) with those of the present work.
255
of the results of Goldberg
In a recent publication, Goldberg and Parker (1985) proposed a correlation for Henry’s constant of sulfur dioxide in water, based on selected literature data. As shown in Fig. 5, Henry’s constants determined from the new experimental data are generally larger than those given by Goldberg and Parker. The deviations are about 5%. Several authors have reported measurements on the solubility of sulfur dioxide in water, mainly at low temperatures and at pressures around, or less than, 0.1 MPa. Table 9 gives a comparison between calculated results from our correlation (Fit) and some selected literature data. In most cases, good agreement is observed, especially with the authors also selected by Goldberg and Parker. The measurements of Bunsen (1855), Conrad and Beuschlein (1934) and Smith and Parkhurst (1922) result in values for the partial pressure of sulfur dioxide which are predominantly larger than the results of the correlation. The opposite is observed for the more recent measurements of Douabul and Riley (1979), Tokunaga (1974) and Vosolsobe et al. (1965). The best agreement between our correlation and literature data is observed for the measurements of Hudson (1925), Maas and Maas (1928) and Rabe and Harris (1963) for both total pressures and partial pressures of sulfur dioxide. As an example, Fig. 6 shows the measurements of Rabe and Harris (1963) together with calculated isotherms. CONCLUSIONS
An apparatus for measuring gas solubilities in aqueous solutions is described. The apparatus was used to determine the solubilities of hydrogen cyanide and sulfur dioxide in water over a wide range of temperature and
308.1%3813,15 273.15-293.15 298.15-323X$ 298_2@ 278-R-303.u 283.15-363.15 298.15-323.15 313.15-363,15 283.1%300.113; 273.15-298.15 3mt5-353.15 278.20-X33,20 283.15-313,15 293.20-333.20
Comparison between c&ulated
TABLE 9
5.3 3.3 3,O 3.2 13.0
3.@ 23.4 1.1 5,2 1.7
4.9 3.7
13.2
5.0
23.6 +I-t-l+ /+I+.i+f+
+I+ t/+
rim&s and Iiteratuxe data for the au!,& dioxide-‘l;rater system
Beuschlein and Sjmenson (1940) b Bunsen (1855) Bye&q et al. (1980) 6 Cm& ;urb arch (fY_%) b Dmabul and R&q (1979) Huds0n (1925) h Johnstone and Leppla (1934) b Lavrovra md Tudorovskaya (1977) Maas and Maas (1928) b xGorga= and Mws ffY31) b Rabe and IMar& (lY63) b Snith and Parkhurst (1922) Tokunaga ( X974) Yosolsobe et zil. (1965) b
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
251
06
01
"0
02
Ob
iiiso,/mollkg OB
Fig. 6. Solubility of sulfur dioxide in water: 0, (1963); -, calculated results, this work (fit).
experimental
results, Rabe and Harris
pressure. Henry’s constants as well as the interaction parameters of the Pitzer model were determined for both gases. A comparison with literature data yields fair to good agreement. ACKNOWLEDGMENTS
Financial support of this investigation by the government of the Federal Republic of Germany (BMFT-Contract No. 312-4@3-0326558), BASF AG and Lurgi AG is gratefully acknowledged. The authors also owe thanks to Rohm GmbH for the use of their facilities while investigating the system hydrogen cyanide-water. LIST OF SYMBOLS
a
activity coefficients for temperature dependence of interaction parameter for gas G AG, BG, CG, DG coefficients for temperature dependence of Henry’s constant for gas G second virial coefficient for interactions between species i 4j and j relative dielectric constant ‘of .pure water fugacity H(m) Henry’s constant on molality scale chemical equilibrium constant for reaction R KR aG9
bG,CG
f”
258
B. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
true molality of component i overall molality of component i molar mass number of data points pressure partial pressure of component i universal gas constant temperature partial molar volume mole fractions in liquid and vapor
mi tii A4
N P Pi R T V x,
Y
Greek letters (0) P Y cp
interaction parameter activity coefficient fugacity coefficient
Subscripts
absolute calculated experimental gas hydrogen cyanide component i data point k maximum relative water sulfur dioxide
abs Cal exp G HCN L max rel W so2
Superscripts *
normalized to infinite dilution saturation gas phase
S II
De$nition of average absolute deviation
I&s = $ i IXk,cal - Xk,exp( k-l
Definition of average relative
B. Rumpf and G. Maurer 1Fluid Phase Equilibria 81 (1992) 241-260
259
REFERENCES Beuschlein, W.L. and Simenson, L.O., 1940. The solubility of sulfur dioxide in water. J, Am. Chem. Sec., 62: 610-612. Bradley, D.J. and Pitzer, K.S., 1979. Dielectric properties of water and Debye-Hiickel parameters to 350°C and 1 kbar. J. Phys. Chem., 83: 1599-1603. Bredig, G. and Shirado, M., 1927. Dampfdrticke und spezifisches Gewicht wassriger Blausaure. Z. Elek~~hem., 33: 209-211. B&vi, SW. and O’Connell, J.P., 1972. Corresponding states correlation for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE J., 18: 1239-1243. Bunsen, R., 1855. As cited by Young, CL., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Byerley, J-J., Rempet, G.L. and Lee, T.V., 1980. Solubility of sulfur dioxide in water-acetonitrile solutions. 3. Chem. Eng. Data, 25: 55-56. Conrad, F-H, and Beuschlein, W.L., 1934. As cited by Young, CL., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Douabul, A. and Riley, J., 1979. Solubility of sulfur dioxide in distilled water and decarbonated sea water. J. Chem. Eng. Data, 24: 274-276. Dymond, J.H. and Smith, E.B., 1980. The Virial C~~cients of Pure Gases and Mixtures. Oxford University Press, Oxford. Edwards, T.J., Maurer, G., Newman, J. and Prausnitz, J.M., 1978. Vapor-liquid equilibria in multicompon~t aqueous solutions of volatile weak electrolytes. AIChE J., 24: 966976. Goldberg, R.V. and Parker, V.B., 1985. Thermodynamics of solution of SO,(g) in water and of aqueous sulfur dioxide solutions. I. Res. Natl. Bur. Stand., 90: 341-357. Hayden, J.G. and O’Connell, J.P., 1975. A generalized method for pr~i~ting second virial coefficients. Ind. Eng. Chem. Process. Des. Dev., 14: 209-216. Hudson, J.C., 1925. The ~lubility of sulfur dioxide in water and in aqueous solutions of potassium chloride and sodium sulfate. J. Chem. Sot., 127: 1332-1347. Johnstone, HF. and Leppla, P.W., 1934. As cited by Young, C.L., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Kaw~sh~, K. and Prausnitz, J.M., 1988. Correlation of vapor liquid equiIib~a for the system ammonia-carbon dioxide-water. Ind. Eng. Chem. Res., 26: 1482-1485. Lavrovra, EM. and Tudorovskaya, L.L., 1977. As cited by Young, C.L., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Maas, C.E. and Maas, G., 1982. Sulfur dioxide and its aqueous solutions, I. Analytical methods, vapor density and vapor pressure of sulfur dioxide. Vapor pressure and concentrations of solutions. J. Am. Chem. Sot., 50: 1352-1368. Miles, D.H. and Wilson, G., 1975, Vapor liquid ~uilib~~ data for design of sour water strippers. 1974 Annu. Rep. to API, Brigham Young University, Provo, UT. Morgan, GM. and Maas, O., 1931. Au inv~tigation of the equilibria existing in gas water systems forming electrolytes. Can. J. Res., 5: 162-199. Opykhtina, M.A. and Frost, D.I., 1936. &3IcOCTb I4 TeMjIeparypa roinenmr nombrx pacracB HCN. Zh. Obshch. Khim., 6: 1778-1783. Pitzer, K. S., 1973. ~e~~ynarni~ of electrolytes. I. Theoretical basis and genera1 equations. J. Phys. Chem., 77: 268-277. Rabe, A.E. and Harris, J.F., 1963. Vapor liquid ~uilib~~ data for the binary system, sulfur dioxide and water. J. Chem. Eng. Data, 8: 333-336. Saul, A. and Wagner, W., 1987. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data, 16: 893-901. ~h~dt, E., 1982. Properties of Water and Steam in SI-units. Sponger-Verlag, Berlin.
260
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Smith, W.T. and Parkhurst, R.B., 1922. The solubility of sulfur dioxide in suspensions of calcium and magnesium hydroxides. J. Am. Chem. Sot., 44: 1918- 1927. Tokunaga, J., 1974. Solubilities of sulfur dioxide in aqueous alcohol solutions. J. Chem. Eng. Data, 19: 162-165. Tsonopoulos, C., Coulson, D.M. and Inmon, L.B., 1976. Ionization constants of water pollutants. J. Chem. Eng. Data, 21:190-193. Viilker, Th., 1960. Polymere Blausiiure. Angew. Chem., 11: 379-384. Vosolsobe, J., Simecek, A., Michalek, J. and Kadlec, B., 1965. Rozpustnost kyslicniku siriciteho ve vode. Chem. Prum., 15: 401-404.
Fluid Phase Equilibria, 81 ( 1992) 241-260 Elsevier Science Publishers B.V., Amsterdam
Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressures up to 2.5 MPa B. Rumpf and G. Maurer Lehrstuhl ftir Technische Thermodynamik, Universitiit Kaiserslautern, D-6750 Kaiserslautern (Germany) (Received November 4, 1991; accepted in final form May 22, 1992)
ABSTRACT Rumpf, B. and Maurer, G., 1992. Solubilities of hydrogen cyanide and sulfur dioxide in water at temperatures from 293.15 to 413.15 K and pressures up to 2.5 MPa. Fluid Phase Equilibria, 81: 241-260. The solubilities of hydrogen cyanide and sulfur dioxide in pure water were measured using a static method in the temperature range 313 < T/K < 413 (HCN) and 293 < T/K < 393 ( SOz) at pressures up to 0.6 MPa (HCN) and 2.5 MPa (SO,) corresponding to gas molalities of up to 7 (HCN) and 6 (SO,). Results are reported and compared with literature data and correlations. INTRODUCTION
The solubilities of weak electrolyte gases must be known for designing separation equipment in many technical applications, for example, for the design of sour gas absorption columns and sour water strippers. Experimental data are rarely found in the literature, and therefore models to correlate weak electrolyte gas solubilities in pure water and aqueous salt solutions cannot be tested or improved. This paper reports new experimental data for the boiling point of a gas + liquid mixture measured with a static gas solubility apparatus. EXPERIMENTAL
Apparatus and procedure Figure 1 shows the experimental arrangement for measuring the solubility of a single gas in aqueous solution. In an experiment, a thermostated high Correspondence to: G. Maurer, Lehrstuhl fti Technische Thermodynamik, Kaiserslautern, D-6750 Kaiserslautern, Germany.
Universitit
0378-3812/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved
242
B. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
Fig. 1. Scheme of the experimental arrangement for measuring the solubility of a single gas in aqueous solution: A, high pressure optical cell; B, thermostat; C, magnetic stirrer, D, measurement of temperature difference by thermocouples; E, measurement of temperature by platinum resistance thermometers; F, high pressure displacer; G, tank for aqueous solutions; H, pressure transducers, I, tank for rinsing water; J, frequency bridge, K, recorder, L, container for gaseous solute.
pressure optical cell (volume about 30 cm3; material Hastelloy C4) is partially filled with a known amount of the aqueous solvent. Next, a known amount of gas is added from a storage tank. More aqueous solvent is introduced into the cell with a calibrated high pressure displacer until the gas is completely dissolved. The pressure in the cell is then reduced stepwise by withdrawing very small amounts of the liquid until the first stable bubble appears. Typically, about 0.1-7 g of the gas was passed into the cell. The mass of the gas was determined by weighing, with an uncertainty of about 0.008 g. The volume of the solvent needed to dissolve the gas was determined by measuring the position of the high pressure displacer piston before and after each experiment, with an uncertainty of about 0.3 cm3. The density of the solvent was taken from the literature (Schmidt, 1982). The temperature was measured with two calibrated resistance thermometers placed in the heating jacket of the cell. The accuracy of the temperature measurement was fO.l K. The pressure was measured with pressure transducers connected to a frequency bridge. Six transducers were used with pressure ranges of 0.5, 2, 5 MPa (SO,) and 0.25, 0.6, 2.5 MPa (HCN). Before and after each series of measurements, the transducers were calibrated against a pressure gauge. The typical uncertainty in determining the solubility pressure for hydrogen cyanide was 0.3 kPa in the pressure range O-O.25 MPa and 0.6 kPa in the range 0.25-0.6 MPa. For sulfur dioxide, the uncertainty was 1 kPa in the pressure range O-O.5 MPa and 4 kPa at higher pressures.
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
243
Since hydrogen cyanide is an extremely toxic substance, special care had to be taken to avoid any escape of the gas into the atmosphere. Therefore the apparatus was placed into a sealed hood connected to an exhaust fan and operated through gloves. Moreover, warning devices were used to detect any leakage. Materials
High grade sulfur dioxide (99.98 wt.% or more) was purchased from Messer Griesheim, Ludwigshafen, and used without further purification. Hydrogen cyanide was obtained from a production plant from Riihm GmbH, Worms. Since hydrogen cyanide polymerizes (Volker, 1960), it cannot be stored as a liquid for long periods. Therefore, before each series of measurements, small amounts (typically about 40 g) were drawn from the production plant. The purity, as determined by gas chromatography, was better than 99.7%. Furthermore, each sample was degassed at low temperature under vacuum. Water was deionized and further purified by vacuum distillation. RESULTS
The experimental results for the solubility of hydrogen cyanide in water at temperatures between 3 13.15 and 413.15 K at total pressures up to 0.6 MPa are given in Table 1. The results for sulfur dioxide over the temperature range 293.15-393.15 K at pressures up to 2.5 MPa are given in Table 2. Figure 2 shows the total pressure plotted versus the molality of dissolved hydrogen cyanide in the liquid phase. Attempts to extend the experimental investigation to higher concentrations and higher temperatures were discarded owing to the onset of colorization of the liquid mixture, indicating the start of hydrogen cyanide polymerization. Figure 3 shows the results obtained for the system sulfur dioxide-water. The concentration range was limited by the appearance of a second (sulfur dioxide rich) liquid phase at molalities somewhat above the upper limits of the data given in Table 2. METHOD OF CORRELATION AND COMPARISON WITH LITERATURE DATA
The hydrogen cyanide-water
system
To correlate the experimental results for the solubility of hydrogen cyanide in water, the phase equilibrium condition for water (w) and the dissolved gas (G) yields
(1)
3. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
244
TABLE 1 Experimental
results for the solubihty of hydrogen cyanide in water
&iCN
w
&HC!N
1OP
(moi kg-‘)
(MPa)
TK)
(mol kg-‘)
(MPa)
314.12 313.20 313.16 313.16 313.13 313.16 313.15
0.0
0.076 0.269 0.407 0.441 0.609 0.642 0.786
333.03 333.1% 333.22 333.22 333.22 333.23 333.23 333.22
0.0 0.739 1.217 1.497 1.879 2.471 2.877 4.129
0.202 0.431 0.570 0.648 0.747 0.879 0.980 1.197
373.15 373.12 373.15 373.16 373.16 373.13 373.16 373.16 373.14 373.10 373.12 373.10
0.199
1.064 2.117 2.279 3.794 4.009 5.839
1.163 1.524 1.424 1.525 1.700 1.996 1.976 2.004 2.15% 2.523 3.097 3.930
353.19 352.93 353.09 352.99 353.05 352.92 353.17 352.80 353.30 353.23 353.13 353.15
0.0 0.0 1.030 1.905 2.470 2.583 2.669 2.726 3.100 3.245 3.359 4.549
0.479 0.471 0.985 1.30% 1.512 1.565 1.579 1.591 1.720 1.764 1.812 2.073
373.19
0.0
1.022
392.94 393.15 393.16 393.15 393.15 393.13 393.17 393.17 393.16 393.17 393.11 393.16 413.11 413.14 413.14 413.13 413.12
0.731 0.58% 0.685 0.956 1.397 1.399 1.502 1.666 2.485 3.880 6.615 0.0
0.361 0.381 0.609 1,018 1.054 1.211 2.00% 2.393 2.409 3.652 3.785 0.0
0.332 0.693 0.869 1.453
1.964 2.349 2.359 2.575 2.956 3.001 3.123 3.730 3.991 3.986 4.773 4.843 3.611 4.019 4.453 4.676 5.31%
(2) As the equilibrium constant for the dissociation of hydrogen cyanide is small (K = ffn + acN- /ancN M 6 x IO-” (Tsonopoulos et al., 1976)), the true concentration of the gas present in the liquid phase was set equal to the overall concentration directly determined from the measurements. Since the total pressure is always rather low, the fugacity coefficient of water, as well as that of hydrogen cyanide, was set equal to unity and the influence of pressure on Henry’s constant and on the fugacity of liquid
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Fig. 2. Solubility correlation (fit).
Fig. 3. Solubility correlation (fit).
of hydrogen cyanide in water: 0, experimental
of sulfur dioxide in water:
0,
experimental
245
results, this work; -,
results, this work; -,
water was neglected. Thus, eqns. (1) and (2) yield Henry’s constant for hydrogen cyanide from an extrapolation procedure of the direct experimental results: (3)
0.531 0.882 0.891 1.616
0.988 0.982 0.981 0.968 1.377 2.161 2.143 3.640
0.237 0.528 0.767 0.836 1.222 1.348 1.397
393.08 393.08 393.05 393.17 393.33 393.32 393.18
0.595 0.968 0.977 1.736
0.264 0.480 0.700 0.839 0.918 1.763 3.430 4.695 5.554
363.17 363.17 363.17 363.17 363.16 363.17 363.17 363.17 363.16
333.16 333.16 333.15 333.15
0.488 0.545 1.141 1.314 1.537 1.966 2.979 4.001 4.259 4.409 4.603
0.992 0.991 0.982 0.979 0.976 0.970 0.955 0.941 0.935 0.934 0.930
0.309 0.354 0.810 0.943 1.111 1.408 2.237 3.076 3.388 3.466 3.698
0.376 0.427 0.926 1.069 1.250 1.566 2.443 3.323 3.650 3.731 3.973
2.100 2.696 2.968 3.320 4.427 5.310
343.13 343.19 343.13 343.24 343.12 343.23
313.18 313.15 313.16 313.13 313.17 313.29 313.14 313.14 313.11 313.15 313.14
0.356 0.756 1.446 1.623 1.758 2.418 3.076
0.458 1.081 1.903 2.255 2.369 3.454 4.701
0.580 1.279 2.178 2.559 2.680 3.844 5.162
293.17 293.17 293.17 293.14 293.16 293.15 293.16
0.988 0.975 0.959 0.952 0.950 0.931 0.910
Overall
Tru@
Overall
0.223 0.507 0.741 0.809 1.189 1.313 1.361
0.239 0.446 0.657 0.791 0.868 1.691 3.325 4.570 5.417
1.987 2.565 2.829 3.173 4.254 5.119
True*
Molality of SO, (mol kg- ‘)
Molality of SOz (mol kg-‘)
Experimental results for the solubility of sulfur dioxide in water
TABLE 2
0.996 0.990 0.986 0.985 0.978 0.976 0.975
0.995 0.991 0.987 0.984 0.983 0.968 0.941 0.921 0.908
0.962 0.952 0.948 0.942 0.924 0,911
a%
3.428 5.148 6.45 6.90 9.12 9.66 10.29
1.788 2.551 3.498 3.928 4.398 7.12 12.22 14.89 16.40
5.362 6.73 7.45 8.01 10.12 11.09
lOp( MPa)
0.227 0.476 0.733 0.970 1.243 1.663
343.21 343.18 343.21 343.14 343.17 343.14
a Calculated.
2.403 2.748 2.912 3.354 4.500
333.15 333.15 333.15 333.15 333.15
0.195 0.428 0.671 0.898 1.159 1.564
2.238 2.591 2.750 3.178 4.292
0.995 0.991 0.986 0.982 0.977 0.970
0.957 0.951 0.948 0.941 0.923 0.860 1.538 2.239 2.805 3.319 4.541
4.838 5.44% 5.688 6.43 8.06 393.08 393.18 393.09 393.33 393.07 393.09 393.18 393.18 393.18 393.07 393.33
1.551 1.606 1.743 2.500 2.585 2.742 2.777 3.506 4.364 4.707 5.328 1.513 1.567 1.702 2.451 2.535 2.690 2.725 3.447 4.297 4.637 5.254 0.972 0.971 0.969 0.956 0.955 0.952 0.952 0.940 0.926 0.921 0.912
10.70 11.16 11.89 15.38 15.93 16.67 16.89 19.55 22.44 23.60 25.09
248
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 3 Henry’s constants for the solubility of hydrogen cyanide in water 1OH(“) ( MPa mol - ’ kg)
T(K) 313.16 333.21 353.08 373.14 393.15 413.13
_+0.04 _+0.03 f 0.28 * 0.04 rt 0.04 + 0.02
o.210+0.0’5 0010 0.348 2 ;:o”;; 0.583 ‘;:E 0.822 :;:z; 1.088 f o”.;:; 1.320’;:;;;
In the first step, the activity of water a, was approximated by its mole fraction x,. The vapor pressure of water was taken from the literature (Saul and Wagner, 1987). Table 3 gives the values for Henry’s constant of hydrogen cyanide determined from the measurements. The equation BHCN
In H$&+J( MPa mol - ’ kg) = AHCN+ -
(4)
+c~cdT/K)
(T/K)
with coefficients given in Table 4 (Extrapolation) correlates Henry’s constant with an average relative deviation (AHI,1 = 1.7% and a maximum relative deviation of /AHjre,,max= 4.4%. As can be seen from Fig. 2, Henry’s law is obeyed only at concentrations up to about 1 mol HCN per kilogram of water. Therefore activity coefficients had to be taken into account. The model of Pitzer (1973) as modified by Edwards et al. (1978) was used to describe the activity coefficients. When a single gas is dissolved in water (neglecting dissociation as well as any ternary parameters), the equation for the activity coefficients of the dissolved gas and water reduces to
TABLE 4 The temperature
mol- 1kg) = A, + &
In HgQ(MPa
Gas HCN 8%
dependence of Henry’s constant: + C&T/K)
+ Do ln(T/K)
AG
BG
CG
DG
Method
19.411 15.179 - 1203.75 - 154.827
-5189.7 -4493.9 30861.36 321.17
-0.02146 -0.01522 -0.32612 - 0.0634
0.0 0.0 209.74 29.872
Extrapolation Fit Extrapolation Fit
249
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 5 The temperature /gb++bG
Gas HCN so*
Ina,=
dependence of interaction
parameters:
(T/K) + ($)’
aG
bG
CG
0.8893 0.1180 -0.0652 0.0934
-647.10 -115.29 -40.59 - 137.92
1.109. 2.063 1.625 . 3.127.
-m&/Q&G-m
Method 105 lo4 lo4 lo4
Extrapolation Fit Extrapolation Fit
&.J G 1000
where /I& is an adjustable temperature-dependent parameter. Using Henry’s constants calculated from eqn. (4), the interaction parameter was fitted to the experimental results for the total pressure on each isotherm. The equation
P&=aG+bG (T/K) + (&2
(7)
with coefficients given in Table 5 (Extrapolation) was chosen to correlate the results. Combining these results with Henry’s constants from Table 4 results in an average deviation between the experimental and calculated pressure of l&Ire, = 1.3% and a maximum relative deviation IAPI~~,,~~= 5.8% (absolute deviation [Aplabs,max = 2.4 kPa). As the activity of water and in turn the fugacity of the gas are influenced by the value for the interaction parameter /I$&, the extrapolation procedure described previously should normally be performed once more, taking into account activity coefficients. However, we decided to fit the coefficients of eqns. (4) and (7), e.g. I?@&, and /$LN,ncN, simultaneously to the experimental results for the total pressure. The resulting coefficients are also given in Tables 4 and 5 (Fit). Using this set of parameters gives a sligha better description of the experimental results for the total pressure (IAp IreI= 0.8%, (ApIrel,max = 3.2%, IAplabs,max = 1.3 kPa). Simultaneously fitting Henry’s constant and the interaction parameter in most cases results in slightly smaller numbers for Henry’s constant than those obtained from the extrapolation procedure. The typical absolute deviation between Henry’s constants obtained from the different correlations does not exceed 0.004 MPa mol - ’ kg. Results from the simultaneous fit are used for comparison with literature data. Literature data on the solubility of hydrogen cyanide are scarce. Bredig and Shirado ( 1927) investigated the system at 291.15 K using a dynamic
250
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
method. Up to fiHcN x 14 mol kg-’ their results agree well with the correlation of this work. Although the concentration range is more than twice the upper limit of the experimental results on which the correlation is based, the average deviation in total pressure and in the partial pressure of hydrogen cyanide is only 1.9% and 2.4% respectively. Opykhtina and Frost (1936) measured boiling points at a total pressure of about 0.1 MPa in the temperature range from about 312 to 371 K. At low temperatures the hydrogen cyanide concentrations are far beyond the range of the present work, and therefore the comparison is restricted to temperatures between 319 and 371 K. In that temperature range, the partial pressures of hydrogen cyanide as reported by the Qykhtina and Frost agree fairly well with the results of the present work ( [ApHCN/rel = 5.7%, lApnoN Imax = 17.6%), while the differences in total pressure are somewhat larger ( lAp IreI= 7%, (ApIre,,max = 10.2%). Miles and Wilson ( 1975) reported some data for 323.15, 363.15 and 393.15 K. Their results are compared with the correlation of the present work in Figs. 4(a)-4(c). As can be seen from Table 6, relative deviations for the total pressure and the partial pressures of hydrogen cyanide and water amount to a few per cent. The sulfur dioxide -water system
Sulfur dioxide is a stronger acid than hydrogen cyanide; therefore, the simple procedure described previously cannot be applied to determine its Henry’s constant in water from the direct experimental results. The dissociation of sulfur dioxide in the liquid phase must be taken into account. As discussed by Edwards et al. ( 1978), three chemical reactions are considered in the liquid phase: SOz + H,O C$ HSO; + H+ HSO; z$ SO:- + H+ Hz0 z$ H+ + OHTo evaluate the experimental results, the following expressions for chemical equilibrium, mass balance and electroneutrality were used: KI =
mHSOFmH+
?ftSO&+
mSOpw %O$-mH+ &I
=
Y&so,
mH+mOH-?6+Y8H-
*so,= mH+
y&-y&+
mHS0,-
61 =
(8)
740,
(10)
a, mS02
= mHSOT
+ mHSOT + 2mSOz-
(9)
+ mSOj+ mOH-
(11) (12)
B. Rumpf and G. Maurer 1 Fiuid Phase Equilibria 81 (1992) 241-260
251
40
B f 0.
t=
30
20
10
O”m,,,hnollkg” ’
0
40
8o
tii,,./mol/kg
Fig. 4. Solubility of hydrogen cyanide in water: (a) 0, experimental results (total pressure), Miles and Wilson (1975); -, calculated results, this work (fit); (b) 0, experimental results (partial pressure of HCN), Miles and Wilson (1975); -, calculated results, this work (fit); (c) 0, experimental results (partial pressure of water), Miles and Wilson (1975);. 1, calculated results, this work (fit).
Equilibrium constants for the three chemical equilibria were taken from Kawuzuishi and Prausnitz (1988). Activity coefficients for both ionic and molecular species were calculated using the Pitzer model as adapted by Edwards et al. with all interaction parameters set to zero. The dielectric constant D of pure water was taken from Bradley and Pitzer (1979). The resulting “true” molalities of (undissociated) SO2 and the activity of water
252
B. Rumpf and G. Maurer /Fluid Phase Equilibria 81 (1992) 241-260
TABLE 6 Hydrogen cyanide-water: comparison between the experimental results by Miles and Wilson (1975) and those of the present work
I&&NIreI
i”(K) 323.15 323.15 363.15 393.15
13 1 4 2
7.5 7.7 5.8 0.9
_ 9.2 38.4 6.5
10.5 1.9 3.9
are also given in Table 2. Using these values for the activity of water and the experimental results for the total pressure, eqn. (1) was used to calculate the mole fraction y, in the vapor phase in an iterative procedure. The fugacity coefficients in the vapor phase were calculated using the virial equation of state truncated after the second virial coefficient. The second virial coefficient of water II,,, was calculated from a correlation based on data given by Dymond and Smith (1980), whereas the second virial coefficient of sulfur dioxide BSo1,so2 and the mixed second virial coefficient B soz,w were calculated from a correlation of Hayden and O’Connell (1975). The influence of pressure on the fugacity of liquid water was calculated using the molar volume of pure water as given by Saul and Wagner ( 1987). The influence of pressure on Henry’s constant was calculated using the partial molar volume for SO* as described by Brelvi and O’Connell ( 1972). The data used for the determination of H&z& are summarized in Table 7. The next step yielded the fugacity of sulfur dioxide: f*;o, = PexpYSO~ &, Rearranging In -60, mso2
(13)
eqn. (2) results in
_ - ln Go2 + ln HLZ&QG)
+
%o*,w(P -PsH)
(14)
RT
Values for the left-hand side plotted versus the difference (p -p$) and extrapolated to Gso2 = 0 yielded the Henry’s constants given in Table 8. The influence of temperature on Henry’s constant is described by In H&$$,/(MPa mol - ’ kg) = Aso, + &
+
Go,WK)
+
bo,
W’W)
(15) With the coefficients Aso, -Dso, given in Table 4 (Extrapolation), this equation describes the experimental results for Henry’s constant with an average deviation of IdI&, = 0.7% and a maximum deviation IAHIre*,max= 1.4%.
B. Rtmpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
253
B. Rumpf
254
and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
TABLE 8 Henry’s constants for the solubility of sulfur dioxide in water lOH(“)( MPa mol-’ kg)
T(K) 293.16 313.16 333.15 343.17 363.17 393.17
_+0.02 f 0.13 f 0.01 + 0.06 f 0.01 f 0.16
0.734_‘,q$?; 1.347’Z:E 2.305’;:g 2.901 ‘;:;j; 4.464’;:;;: 6.439’“-382 0.344
As for hydrogen cyanide-water, a strong negative deviation from Henry’s law is observed for the system sulfur dioxide-water at overall concentrations of the dissolved gas greater than about 1 mol per kilogram of water. Therefore the interaction parameter /?&&so2 was fitted to the isothermal results for the total pressure using Henry’s constants calculated from eqn. ( 15). Since most of the dissolved sulfur dioxide is present in molecular rather than in ionic form, parameters for interactions between molecular and ionic species as well as between ionic species were neglected. Thus the activity coefficients of ionic species were calculated from the modified Debye-Htickel term alone as given by Pitzer (1973). This seems to be a reasonable approximation as the ionic strength of the solution does not exceed 0.5 mol per kilogram of water. Equation (7) was used to describe the influence of temperature on /JL!8*,so,.The parameters aso2, bso2 and cso2 were fitted to the isothermal results for p&$J2,so2(cf. Table 5 (Extrapolation)). Combining these parameters with the equation for Henry’s constants (Table 4, (Extrapolation)) results in -an average deviation from the experimental results for the total pressure IAplre,= 2.4% and a maximum relative deviation [ApIrel,max = 7.3% ( JAplabs,max = 5.5 kPa). Since the procedure described before only gives a first estimate for Henry’s constants, the coefficients of eqns (7) and (15) were also fitted simultaneously to the experimental results for the total pressure. The resulting parameters are given in Tables 4 and 5 (Fit). This set of parameters reproduces our experimental results with an average deviation @Ire, = 1.5% and a maximum relative deviation ~~~~~~~~~~ = 5.7% = 4.3 kPa). Henry’s constants calculated with this set of paramew4 abs,max ters are in most cases slightly smaller than those obtained from the extrapolation procedure. However, the difference in Henry’s constants calculated from the two procedures does not exceed 0.03 MPa mol-’ kg at T = 393.15 K, where Henry’s constant obtained from the extrapolation procedure has a value of 0.644 MPa mol - ’ kg.
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Fig. 5. Henry’s constant for sulfur dioxide in water: comparison and Parker (1985) with those of the present work.
255
of the results of Goldberg
In a recent publication, Goldberg and Parker (1985) proposed a correlation for Henry’s constant of sulfur dioxide in water, based on selected literature data. As shown in Fig. 5, Henry’s constants determined from the new experimental data are generally larger than those given by Goldberg and Parker. The deviations are about 5%. Several authors have reported measurements on the solubility of sulfur dioxide in water, mainly at low temperatures and at pressures around, or less than, 0.1 MPa. Table 9 gives a comparison between calculated results from our correlation (Fit) and some selected literature data. In most cases, good agreement is observed, especially with the authors also selected by Goldberg and Parker. The measurements of Bunsen (1855), Conrad and Beuschlein (1934) and Smith and Parkhurst (1922) result in values for the partial pressure of sulfur dioxide which are predominantly larger than the results of the correlation. The opposite is observed for the more recent measurements of Douabul and Riley (1979), Tokunaga (1974) and Vosolsobe et al. (1965). The best agreement between our correlation and literature data is observed for the measurements of Hudson (1925), Maas and Maas (1928) and Rabe and Harris (1963) for both total pressures and partial pressures of sulfur dioxide. As an example, Fig. 6 shows the measurements of Rabe and Harris (1963) together with calculated isotherms. CONCLUSIONS
An apparatus for measuring gas solubilities in aqueous solutions is described. The apparatus was used to determine the solubilities of hydrogen cyanide and sulfur dioxide in water over a wide range of temperature and
308.1%3813,15 273.15-293.15 298.15-323X$ 298_2@ 278-R-303.u 283.15-363.15 298.15-323.15 313.15-363,15 283.1%300.113; 273.15-298.15 3mt5-353.15 278.20-X33,20 283.15-313,15 293.20-333.20
Comparison between c&ulated
TABLE 9
5.3 3.3 3,O 3.2 13.0
3.@ 23.4 1.1 5,2 1.7
4.9 3.7
13.2
5.0
23.6 +I-t-l+ /+I+.i+f+
+I+ t/+
rim&s and Iiteratuxe data for the au!,& dioxide-‘l;rater system
Beuschlein and Sjmenson (1940) b Bunsen (1855) Bye&q et al. (1980) 6 Cm& ;urb arch (fY_%) b Dmabul and R&q (1979) Huds0n (1925) h Johnstone and Leppla (1934) b Lavrovra md Tudorovskaya (1977) Maas and Maas (1928) b xGorga= and Mws ffY31) b Rabe and IMar& (lY63) b Snith and Parkhurst (1922) Tokunaga ( X974) Yosolsobe et zil. (1965) b
B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
251
06
01
"0
02
Ob
iiiso,/mollkg OB
Fig. 6. Solubility of sulfur dioxide in water: 0, (1963); -, calculated results, this work (fit).
experimental
results, Rabe and Harris
pressure. Henry’s constants as well as the interaction parameters of the Pitzer model were determined for both gases. A comparison with literature data yields fair to good agreement. ACKNOWLEDGMENTS
Financial support of this investigation by the government of the Federal Republic of Germany (BMFT-Contract No. 312-4@3-0326558), BASF AG and Lurgi AG is gratefully acknowledged. The authors also owe thanks to Rohm GmbH for the use of their facilities while investigating the system hydrogen cyanide-water. LIST OF SYMBOLS
a
activity coefficients for temperature dependence of interaction parameter for gas G AG, BG, CG, DG coefficients for temperature dependence of Henry’s constant for gas G second virial coefficient for interactions between species i 4j and j relative dielectric constant ‘of .pure water fugacity H(m) Henry’s constant on molality scale chemical equilibrium constant for reaction R KR aG9
bG,CG
f”
258
B. Rumpf and G. Maurer / Fluid Phase Equilibria 81 (1992) 241-260
true molality of component i overall molality of component i molar mass number of data points pressure partial pressure of component i universal gas constant temperature partial molar volume mole fractions in liquid and vapor
mi tii A4
N P Pi R T V x,
Y
Greek letters (0) P Y cp
interaction parameter activity coefficient fugacity coefficient
Subscripts
absolute calculated experimental gas hydrogen cyanide component i data point k maximum relative water sulfur dioxide
abs Cal exp G HCN L max rel W so2
Superscripts *
normalized to infinite dilution saturation gas phase
S II
De$nition of average absolute deviation
I&s = $ i IXk,cal - Xk,exp( k-l
Definition of average relative
B. Rumpf and G. Maurer 1Fluid Phase Equilibria 81 (1992) 241-260
259
REFERENCES Beuschlein, W.L. and Simenson, L.O., 1940. The solubility of sulfur dioxide in water. J, Am. Chem. Sec., 62: 610-612. Bradley, D.J. and Pitzer, K.S., 1979. Dielectric properties of water and Debye-Hiickel parameters to 350°C and 1 kbar. J. Phys. Chem., 83: 1599-1603. Bredig, G. and Shirado, M., 1927. Dampfdrticke und spezifisches Gewicht wassriger Blausaure. Z. Elek~~hem., 33: 209-211. B&vi, SW. and O’Connell, J.P., 1972. Corresponding states correlation for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE J., 18: 1239-1243. Bunsen, R., 1855. As cited by Young, CL., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Byerley, J-J., Rempet, G.L. and Lee, T.V., 1980. Solubility of sulfur dioxide in water-acetonitrile solutions. 3. Chem. Eng. Data, 25: 55-56. Conrad, F-H, and Beuschlein, W.L., 1934. As cited by Young, CL., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Douabul, A. and Riley, J., 1979. Solubility of sulfur dioxide in distilled water and decarbonated sea water. J. Chem. Eng. Data, 24: 274-276. Dymond, J.H. and Smith, E.B., 1980. The Virial C~~cients of Pure Gases and Mixtures. Oxford University Press, Oxford. Edwards, T.J., Maurer, G., Newman, J. and Prausnitz, J.M., 1978. Vapor-liquid equilibria in multicompon~t aqueous solutions of volatile weak electrolytes. AIChE J., 24: 966976. Goldberg, R.V. and Parker, V.B., 1985. Thermodynamics of solution of SO,(g) in water and of aqueous sulfur dioxide solutions. I. Res. Natl. Bur. Stand., 90: 341-357. Hayden, J.G. and O’Connell, J.P., 1975. A generalized method for pr~i~ting second virial coefficients. Ind. Eng. Chem. Process. Des. Dev., 14: 209-216. Hudson, J.C., 1925. The ~lubility of sulfur dioxide in water and in aqueous solutions of potassium chloride and sodium sulfate. J. Chem. Sot., 127: 1332-1347. Johnstone, HF. and Leppla, P.W., 1934. As cited by Young, C.L., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Kaw~sh~, K. and Prausnitz, J.M., 1988. Correlation of vapor liquid equiIib~a for the system ammonia-carbon dioxide-water. Ind. Eng. Chem. Res., 26: 1482-1485. Lavrovra, EM. and Tudorovskaya, L.L., 1977. As cited by Young, C.L., 1983. Solubility Data Series, Vol. 12. Pergamon, Oxford. Maas, C.E. and Maas, G., 1982. Sulfur dioxide and its aqueous solutions, I. Analytical methods, vapor density and vapor pressure of sulfur dioxide. Vapor pressure and concentrations of solutions. J. Am. Chem. Sot., 50: 1352-1368. Miles, D.H. and Wilson, G., 1975, Vapor liquid ~uilib~~ data for design of sour water strippers. 1974 Annu. Rep. to API, Brigham Young University, Provo, UT. Morgan, GM. and Maas, O., 1931. Au inv~tigation of the equilibria existing in gas water systems forming electrolytes. Can. J. Res., 5: 162-199. Opykhtina, M.A. and Frost, D.I., 1936. &3IcOCTb I4 TeMjIeparypa roinenmr nombrx pacracB HCN. Zh. Obshch. Khim., 6: 1778-1783. Pitzer, K. S., 1973. ~e~~ynarni~ of electrolytes. I. Theoretical basis and genera1 equations. J. Phys. Chem., 77: 268-277. Rabe, A.E. and Harris, J.F., 1963. Vapor liquid ~uilib~~ data for the binary system, sulfur dioxide and water. J. Chem. Eng. Data, 8: 333-336. Saul, A. and Wagner, W., 1987. International equations for the saturation properties of ordinary water substance. J. Phys. Chem. Ref. Data, 16: 893-901. ~h~dt, E., 1982. Properties of Water and Steam in SI-units. Sponger-Verlag, Berlin.
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B. Rumpf and G. Maurer 1 Fluid Phase Equilibria 81 (1992) 241-260
Smith, W.T. and Parkhurst, R.B., 1922. The solubility of sulfur dioxide in suspensions of calcium and magnesium hydroxides. J. Am. Chem. Sot., 44: 1918- 1927. Tokunaga, J., 1974. Solubilities of sulfur dioxide in aqueous alcohol solutions. J. Chem. Eng. Data, 19: 162-165. Tsonopoulos, C., Coulson, D.M. and Inmon, L.B., 1976. Ionization constants of water pollutants. J. Chem. Eng. Data, 21:190-193. Viilker, Th., 1960. Polymere Blausiiure. Angew. Chem., 11: 379-384. Vosolsobe, J., Simecek, A., Michalek, J. and Kadlec, B., 1965. Rozpustnost kyslicniku siriciteho ve vode. Chem. Prum., 15: 401-404.