Ind. Eng. Chem. Fundam. 1986, 2 5 , 775-782
eventually chooses the following controller settings to a high degree of precision CY
KL = 1-a!
(7)
where cy
=
~-‘ITS
and
Ts _ -1 TR a!
(8)
In this case, the effect of the disturbance was eliminated in two sampling intervals. In other words, the system exhibited “dead beat” control behavior. The resulting normalized integral absolute error decreased with increasing sampling frequency such that IAE = (1- a ) / w , as predicted by theory. In the limit, continuous system “performance” should result with an optimum IAE of zero. Such a high performance is not achievable in practice because of saturation. The method of predicting the effects of sampling on performance developed in this paper is clearly not applicable to purely first-order systems. Conclusions
We have confirmed that integral “performance” of a number of representative systems under digital PI control continuously improves as sampling frequency increases. We concluded the Roberts’ observed degradation in performance at high sampling frequencies is simply due to the
775
choice of a fixed ratio of reset rate to sampling frequency. It was shown that the performance index originally proposed by Harriott for continuous systems may be applied to the prediction of closed-loop P I controller performance under digital control. Provided that the sum of reduced-order-system equivalent dead time and the semi sampling interval, T,/2, is less than the reduced-ordersystem equivalent time constant T ~a simplified , equation (4) was found to correlate the data well. For example, a 10% reduction in performance of the discrete system (compared with the continuous system) results when the ratio of sampling interval to equivalent dead time is about Literature Cited Harriott, P. Process Control; McGraw-Hill: New York, 1964; p 103. Isermann, R. Automatica 1982, 18, 513. Jeffreson, C. P. Ind. Eng. Chem. Fundam. 1976, 15, 171. Lopez, A. M.; Smith, C. L.; Murrill, P. W. Instrum. ControlSyst. 1969, 42(2), 89. Nelder, J. A.; Mead, R . Comput. J . 1965, 7 , 308. Niederlinski, A. Automatica 1971, 6 , 691. Palmor, Z.J.; Shinnar, R. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 8. Roberts, P. D. Meas. Control 1976, 9 , 227. Saucedo, R.; Schiring, E. E. Introduction to Continuous and Digital Control Systems; Macmillan: New York, 1968; Chapter 10. Thompson, A. G. Proc.-Inst. Mech. Eng. 1973, 187, 129.
Received for review February 27, 1985 Revised manuscript received January 10, 1986 Accepted February 13, 1986
Salting-Out of Oxygen from Aqueous Electrolyte Solutions: Prediction and Measurement Werner Lang’ and Rolf Zander Physiologisches Institut der Johannes-Gutenberg Universitat Mainz, 0-6500Mainz, FRG
On the basis of an independent single-ion parameter model, the parameter k,,,, representing the salting-out of oxygen by an electrolyte, can be calculated from the individual ion parameter Hi, ionic charge zi, and stoichiometric number x, of cations and anions of the same type in the electrolyte. From extensive experimental oxygen solubility data in 68 aqueous electrolyte solutions (20 chlorides, 22 nitrates, 18 sulfates, 3 hydrogen sulfates, and 5 hydroxides) at several concentrations and measured by a photometric method at 310.2 )< with pure oxygen under atmospheric pressure, a set of relative individual ion parameters, Hi, for all of the different cations and anions of the studied electrolytes could be derived, if sodium ion is chosen as a reference ion, HNa+ = 0. Good agreement was found between predicted and experimental k,,, values of the order of f3.5%, and good agreement was also found between predicted and experimental oxygen solubilities.
I n t r o d u c t i o n and T h e o r y
The influence of dissolved electrolytes on oxygen solubility in aqueous solutions is a well-known phenomenon and is called the salting-out effect, if the solubility of oxygen in the electrolyte solution is decreased compared to that in pure water under the same experimental conditions of temperature and pressure. A quantitative treatment of this effect was first given by Setchenov (1889) by an empirical relation for carbon dioxide, which also holds for other gases for a great number of inorganic and organic substances over a wide concentration range. In its logarithmic form to base 10, this relation can be written as log
b 0 / 4= k,,,cs
(la)
where cyo and CY are the Bunsen coefficients of oxygen solubility in pure water and in the salt solution at the same temperature, cs is the molar concentration of the salt in the solution, and k,,, is the salting-out parameter or Setchenov’s constant, which is specific with respect to the gas, electrolyte, and temperature and depends upon the solubility unit of the gas as well on the units of the salt concentration (Clever, 1983). Later, van Krevelen and Hoftijzer (1948), instead of using the molar concentration in eq la, used the ionic strength of the electrolyte, I = 1/2C,c,z,2. c, is the molar concentration of the ith ion with charge number zi. Furthermore, they split up the resulting salting-out parameter into a sum of three independent contributions which are
0196-4313/86/1025-0775$01.50/00 1986 American Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 25, No 4, 1986
specific to the ions, h, and h-, and to the gas, hG. G log ( C U " / C U = ) h I , h = h+ + h- + h (lb) This concept was successfully applied by Danckwerts (1970) and Onda et al. (1970) in predicting the solubility of gases in aqueous solutions of a single electrolyte or in a mixture thereof. However, it was recently shown by Schumpe et al. (1978) that the van Krevelen/Hoftijzer model is inconsistent when applied to mixed electrolyte solutions. They proposed a more general treatment based on the log additivity of the solubility ratio for all of the different ionic species present in the solution. log
(CUO/OC)
= C H J , = YZCSCH~X,Z,' I
(IC)
i
In this equation the H,'s are specific with respect to the different cations and anions and to the gas and depend upon temperature; I, is the ionic strength of the individual ionic species in the solution. For a strong electrolyte, which is assumed to be completely dissociated in aqueous solution, the salting-out parameter, k,,,, for a given gas can be calculated in terms of the singl-ion parameter, H,, and the number, x L , and the charge, z,, of ions of type i in the electrolyte derived from eq l a and IC
Therefore, if a set of single-ion parameters, H,, of a great number of cations and anions would be available for a gas at a given temperature, k,,, values of any combination of electrolytes belonging to that parameter set could be calculated. From electroneutrality and from the fact that no single ionic species can be separated from another in solution, only relative single-ion parameters, Hi, based on a reference ion can be given. In the present study, the salting-out of oxygen in aqueous solutions of a great number of electrolytes differing in size and ionic charge has been investigated with pure oxygen at body temperature, 310.2 K, and atmospheric pressure. From the experimental k,,, values of the single electrolytes determined by a plot of log ( a " / a )vs. salt concentration cs (Setchenov plot), a set of relative single-ion parameters, Hi, for oxygen at 310.2 K with HNa+ = 0 as a reference ion was derived. Good agreement was found between experimental and calculated k,,, values due to the Schumpe model.
Experimental Section Chemicals. The salts, acids, and bases used for preparing the aqueous solutions were obtained from the following: Fluka, Buchs, Switzerland: Ce(N03),.6H20 (99%), Fe(No3),-9H20(99%),La(N0,)3.6H20 (99%),RbN03(98701, Fe2(S04)3-5H20(purum p.a.), CsOH.H,O (90-95 % + 5-10% C S ~ C O ~RbOHa2Hz0 ), (98%). Merck, Darmstadt, FRG: NH4C1, NH,HS04 (reagent grade 99.8%); CaC1,.2H20, CsCl, KCl, NaCl, RbCl, Cu(N03)z.3H20,Cs2S04,MgS04.7H20, (NHJ2SO4,ZnSO4-7H2O (reagent grade 99.5% 1; A1C1,.6H20, BaClZ.2H20, CoC1,6H20,CuC12.2Hz0,FeC1,-6H2O,LiCl, MgCl2.6H20,MnC12.4H20, Ba(NO3I2, Cd(N03)2-4Hz0,CO(NO,)~.~H,O, CsN03, KNO,, Mg(NO3),-6H20, NaNO,, ",NO,, Ni(N03)2.6Hz0,Th(N03)4.5H20,CdS04.8/3H20,CoSO4-7H20, CuS04-5H20, K2S0*,Li,SO,.H,O, MnSO4.H20,Na2S04, NiS04.6Hz0,Rb2S04,NaOH, KHSO,, NaHSO, (reagent grade 99.0%); CeC13.7H20, A1(N03),.9H20, Mn(N03)z. 4H20, Zn(NO3),.4H20 (reagent grade 98.5'70); CdCl2.2HZO, NiC12.6Hz0,ZnCl,, Ca(N0J2.4H20, LiOH (+2% Li,CO,)
(reagent grade 98.0%); HC1 p.a. (37%, density 1.19), HNO, p.a. (65%, 1.40), H2S0, pea. (95-97%, 1.84). Riedel-de Haen, Seelze-Hannover, FRG: LaC13.7Hz0 (99%), LiN03 (95%). The gases used in the measurements were purified nitrogen (99.9%) and purified oxygen (99.9%), both obtained from Linde, Mainz, FRG. Preparation of the Salt Solutions. The salts were used without further purification. The molar concentration of the solutions was calculated from the weighted amount of salt, corrected by its analytical grade of purity, and from the volume of the measuring bulb filled with deionized, distilled water at room temperature. To prevent hydrolysis in hydrolyzing salts like ZnClz, Z~I(NO,)~, and ZnSO,, a small amount of the corresponding acid was added to a final concentration of about 0.014.04 mol/dm3, a concentration too low to affect the oxygen solubility measurably. The molar concentrations of aqueous solutions of acids and bases were determined by titration against methyl orange as an indicator with volumetric solutions of NaOH and HC1 (Titrisol from Merck, Darmstadt, FRG) and were not corrected for the volume expansion from room temperature to 310.2 K, which is of the order of less than 1% as calculated from density tables for an assumed temperature change from 20 to 40 "C. Equilibration of the Salt Solutions with Oxygen. Equilibration of the solutions with oxygen was performed in a spherical flask of about 44-mL capacity with gas inlet and outlet valves. The gas continuously flowed over the solution under barometric pressure. About 5 mL of a salt solution or pure water was saturated with pure oxygen without prior degassing. In order to prevent concentrating the solutions, the oxygen gas was water vapor saturated. The entire apparatus was in a temperature-controlled water bath at 37 f 0.1 "C. The flask could be rotated to increase the oxygen absorption rate, and normally, equilibrium was reached after 15-20 min. Oxygen Solubility Measurement. The amount of oxygen contained in a liquid or gaseous sample was determined photometrically by a flow injection technique, described in detail by Lang et al. (1979). Optical absorption was due to the sensitive color reaction of oxygen and an alkaline catechol/Fe2+ solution. The maximum absorption occurred at 490-nm wavelength. To increase the selectivity for oxygen, the liquid or gaseous sample was first injected into an elution chamber filled with a mixture of about 20% (v/v) ethanol (95% )/water, and the gaseous components were extracted by purified nitrogen and then combined with the reaction solution. The response of the analyzing system resulted in a peak, the area of which was proportional to the amount of oxygen in the sample. For conversion of peak area into quantity of oxygen, standardized volumes of air (5 and 10 gL) were used for calibration. Considering the volume of the liquid sample, usually 100 KLof pure water or salt solution, and the actual oxygen partial pressure given by the experimental conditions, the Bunsen coefficient, a , of oxygen solubility could be calculated by the law of Henry-Dalton. The effect of lowering the water vapor tension by the dissolved electrolytes compared to pure water was not considered and would lead to only slightly lower values in the order of about 1%. Accuracy and Reliability. The accuracy of the method was checked by determining the oxygen solubility in pure water at the same temperature and pressure as for the salt solutions; a mean value of 0.0241 f 0.0004 mL/ (mL atm) of the Bunsen coefficient was found for 32
Ind. Eng. Chem. Fundam., Vol. 25,
0
l:o
2:o
3.0 cs, mol/dm3
Figure 1. Setchenov plots for oxygen at 310.2 K and 1 atm (101.325 kPa) oxygen partial pressure in aqueous solutions of some representative electrolytes.
measurements a t 310.2 K, which was in excellent agreement with recommended values found in the literature (Zander and Euler, 1976; Battino, 1981). As a criterion for the reliability of the method, the mean reproducibility of all oxygen measurements was taken, which wm in the order of 1-2% for a total number of about 2000. This was, on the average, five to six oxygen measurements per concentration of electrolyte. The mean error of the method used, comprising all the processes such as equilibration, elution, and reabsorption with colorimetric reaction for subsequent analysis and calibration, in the order of about 2% was too high to be a precision measurement. Nevertheless, the results for water were in good agreement with other methods, with the advantage of small sample volumes and a rapid analysis of 2-3 min.
Results and Discussion The Bunsen coefficient of oxygen in aqueous solutions of 68 electrolytes was measured at a constant temperature of 310.2 K and under barometric pressure with pure oxygen a t varying concentrations: the solutions included 20 chlorides, 22 nitrates, 18 sulfates, 3 hydrogen sulfates, and 5 hydroxides of various cations of different valency (see Table I). The concentrations of the dissolved electrolytes were in the molar range and far from Debye-Huckel behavior, corresponding to a solubility range of oxygen from about 98% to 10% of that in pure water. The effect of the different electrolytes on oxygen solubility was best demonstrated in the Setchenov plots (Figure 1)where the logarithmic ratio of the oxygen solubility in pure water and in the salt solution was plotted vs. molar concentration of the electrolyte. Straight lines were obtained for almost all electrolytes with the exception of ZnC1, and CdC12, even at high concentrations. The slopes of the lines, which were determined by a best linear fit through the origin, yielded the salting-out parameters,
No. 4, 1986 777
k,,,, for oxygen based on a molarity scale. Large k,,, values indicate low oxygen solubilities in the salt solutions, and vice versa. From Figure 1, which is only a representative selection of all the electrolytes studied, it is evident that, with increasing concentration and increasing ionic charge of the electrolyte, the oxygen solubility is decreased. The experimental k,,, values for oxygen of all studied electrolytes are shown in Table 11; all of the electrolytes salted out (k,,, > 0). The salting-out effect for oxygen of electrolytes with a common cation increased in the order NO3 < C1- < HS04- z OH- < SO:-, and with a common anion among the alkali ions, the order was H+ < NH4+< Li' < Cs' < Rb' < K+ < Na+. It is seen from Table I1 that k,,,, for some uni-bivalent electrolytes, e.g., Na2S04 or KzS04,is larger than for bi-univalent electrolytes, e.g., MgCl, or Mg(N03),, larger than for bi-bivalent electrolytes, e.g., MgSO,, larger than for some tri-univalent electrolytes, e.g., AlCl, or A1(N03)3,and even larger than for a tetraunivalent electrolyte like Th(N03)4.Obviously, the overall salting-out parameter, k,,,, is determined both by an individual effect of the ion as well as by its charge and its concentration in solution. Low k,,, values were found for FeCl,, Fe(N03)3,and Fe2(S04)3and, similarly, for ZnC12 and CdCl,, and may be explained by the existence of a complex mixture of positively and negatively charged ionic and neutral species in aqueous solutions (Cotton and Wilkinson, 1970). In Table I11 are summarized all experimental k,,, values at 310.2 K and 1 atm (101.325 kPa) oxygen partial pressure, which could be compared with available literature data at 298.2 K and, preferably, a temperature at or near 310.2 K (Battino, 1981). The effect of temperature on k,,, in the range 20-40 "C is small, and the values at 310.2 K should be slightly lower than at 298.2 K. Agreement was good to moderate for most of the chlorides, nitrates, and hydroxides with more or less negligible deviations from author to author. Larger deviations to much lower k,,, values were those for KC1, CaC12, BaC12, and AlC13 by Yasunishi (1977), determined by a volumetric saturation method; the value for MnCl, was derived by Murray et al. (1968) from only one concentration, and values for LiN03, LiOH, and CsNO, were derived by Khomutov and Konnik (1974), all at 298.2 K, who worked with air-saturated solutions and used the classical Winkler method for the determination of oxygen. However, the peculiar salting behavior of LiNO, solutions on oxygen solubility (to salt-out between 0 and 0.1 mol/dm3 and to salt-in above 0.15 mol/dm3) could not be observed. In the low concentration range the method used was insufficient to detect oxygen solubility changes, which in dilute solutions decreased by only a few percent (98-100%) from that in pure water. In a higher concentration range (1-3 mol/dm3) LiN03 solutions salted-out and no salting-in of oxygen was observed. For the sulfates, the agreement with literature data was poor. The k,,, values at 298.2 and 323 K by Bruhn et al. (1965) were comparable only for (NH4)2S0, but were too low by more than half for the values found for CoSO,, NiSO,, and CuSO, in this work. Those values were of the order of KC1 and RbCl and can be considered as doubtful for a bi-bivalent electrolyte, if one accepts a value of 0.280 dm3/mol for MgSO, as of the right order (Yasunishi, 1977). Low lz,,, values were also found for MnS0, by Murray et al. (1968), which were calculated from only one concentrated solution, and for Li2S04and Cs2S04 by Khomutov and Konnik (1974), whereas for A12(S04)3Yasunishi (1977) and for Na,SO, all authors but McArthur (1916) found higher values, even at 308.2 K (Yasunishi, 1977).
778
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
Table I. Oxygen Solubility Measurements in Aqueous Electrolyte Solutions with 310.2 K concn of solution, concn of solution. mol/dm3 n" io4& salt mol/dm3 na 1 0 salt 2.005 11 211 f 4 1.502 5 158 f 5 HC1 3.050 4 198 f 7 1.992 4 134 f 3 3.910 2 191 f 4 2.976 4 105 f 1 4.000 6 185 f 2 LaC1, 0.514 6 162 f 2 0.501 5 173 f 1 0.992 4 112 f 1 AlC1, 0.745 6 144 f 3 1.993 4 50f1 1.006 4 119 f 2 2.478 4 37f2 1.081 8 113 f 3 LiCl 0.985 6 194 f 4 2.009 10 63 f 3 1.069 14 189 f 8 2.503 5 41f2 1.482 8 174 f 6 0.507 6 178 f 3 1.993 13 159 f 7 BaCI, 0.997 6 131 f 2 2.336 5 150 f 3 1.509 7 96f2 3.978 9 109 f 3 0.494 4 184 zk 2 MgCI, 0.503 6 190 f 3 CaCI, 0.747 5 162 f 2 0.523 5 187 f 4 0.987 4 144 f 1 0.982 5 153 f 1 1.021 5 141 f 1 0.998 1 2 149 f 3 1.421 5 110 f 2 1.463 8 120 f 2 1.490 4 107 f 1 1.592 5 113 f 2 2.985 4 5lf2 1.745 4 106 f 3 3.557 3 37fl 2.126 5 9lfl 3.894 8 34fl 2.879 13 64 f 2 4.477 3 23 f 1 MnCI, 0.840 4 159 f 2 0.260 4 213 f 4 1.230 4 134 f 3 CdC1, 0.479 6 196 f 1 1.756 5 106 f 2 0.505 12 194 f 3 2.127 3 88 f 1 0.523 12 193 f 3 NaCl 1.001 6 177 f 4 0.747 11 179 f 3 1.265 6 164 f 8 0.760 3 178 f 2 1.503 3 152 f 2 0.966 5 164 f 1 2.016 3 130 f 3 0.997 14 163 f 2 2.989 4 100 f 2 1.025 3 161 f 3 3.030 3 98f3 1.046 5 164 f 3 1.017 4 7lf2 1.264 4 149 f 3 NH4C1 1.002 9 200 f 3 1.457 5 141 f 3 2.008 4 172 f 1 1.491 7 141 f 3 2.215 4 160 f 1 1.503 11 138 f 3 3.001 4 144 f 2 1.922 5 120 f 1 NiCI, 0.744 4 167 f 2 1.996 11 1 1 6 f 2 0.991 6 145 f 1 2.041 4 116 f 2 1.490 4 117 f 2 2.029 3 115 f 1 RbCl 0.990 4 187 f 3 0.498 5 159 f 7 1.014 6 184 f 7 CeC1, 0.979 3 111 f 2 1.:359 4 166 f 2 1.974 4 51f1 1.984 10 1 4 3 f 1 2.462 3 33f4 2.957 5 112 f 2 0.501 9 184 f 2 ZnC1, 0.250 6 213 f 7 CoC1, 0.749 4 162 f 2 0.493 7 190 f 3 0.993 10 144 f 3 0.762 3 l76f3 0.816 4 174 f 2 1.494 3 114 f 2 0.515 7 212 f 5 1.017 10 164 f 4 CSCl 1.001 4 192 f 2 1.069 4 158 f 3 1.028 3 187 f 4 1.250 5 154 f 1 1.505 3 170 f 3 1.460 4 149 f 1 1.993 4 152 f 3 1.939 4 132f3 2.203 4 138 f 2 2.005 8 132422 2.517 5 132 f 3 2.959 8 108 f 2 3.002 3 119 f 2 HNO, 1.000 25 236 f 4 3.382 4 105 f 1 2.000 25 230 f 2 4.003 3 97f1 4.000 18 221 f 4 4.028 3 98 f 1 Al(NO,), 0.308 6 202 f 5 5.003 4 78f2 0.602 5 171 f 3 6.003 5 64f2 1.095 5 127 f 7 6.122 4 60 f 2 Ba(NO,), 0.158 9 222 f 3 0.497 4 192 f 2 0.298 7 207 f 4 CuCl, 0.519 3 189 f 1 Ca(NO,), 0.497 9 195 f 4 0.763 6 169 f 1 0.990 5 155 f 6 0.994 4 155 f 1 1.961 4 101 f 3 1.002 4 156 f 1 Cd(NO,), 0.551 5 194 f 5 1.499 4 122 f 1 0.740 4 181 f 3 1.517 4 124 f 1 1.548 4 133 f 2 0.500 4 186 f 3 2.046 5 110 f 3 FeC1, 1.016 1 148 f 2 Ce(NO,), 0.997 10 137 f 3 2.064 4 84f7 1.862 9 85 f 2 0.503 4 208 f 1 2.952 10 50 f 3 KCl 1.002 6 178 f 2
Pure Oxygen at Atmospheric Pressure and concn of solution, mol/dm3 CO(NO,)~ 0.502 0.753 1.002 1.487 CsNO, 0.314 0.325 0.615 0.624 0.930 Cu(NO,), 0.298 0.497 0.613 0.987 1.267 Fe(NO,), 0.498 0.739 0.999 1.037 KNO, 0.746 1.013 1.510 1.852 La(N03), 0.493 0.966 2.227 LiNO, 0.955 1.916 2.070 2.869 Mg(NOJ2 0.861 0.992 1.663 2.238 Mn(NO,), 0.506 1.011 1.482 1.936 NaN0, 0.762 1.017 1.533 2.078 ",NO, 0.998 1.991 2.050 3.120 Ni(NO,), 0.752 0.852 1.385 2.062 RbN0, 0.487 0.522 0.958 1.006 1.058 1.360 1.989 2.017 Th(NO,), 0.488 0.741 0.974 1.385 Zn(NO,), 0.499 0.756 0.995 1.239 1.506 1.651 H2S04 1.000 1.500 1.600 2.000 2.500 AI,(SO,), 0.197 0.298 0.396
~ salt ~ ~
na 5 6 4 3 2 3 3 3 3 4 3 4 4 4 6 3 4 3 4 6 4 6 3 3 4 8 4 5 4 6 4 3 3 12 9 5 8 4 8 4 4 12 11 4 11 4 7 5 6 9 8 5 2 5 6 3 6 3 3 3
3 13 13 14 5 5 9 9 10 3 15 14 8 8 8
io4& 194 f 4 177 f 4 157 f 2 126 f 2 226 f 2 228 f 2 215 f 2 209 f 1 198 f 2 213 f 5 198 f 1 188 f 3 160f 1 144 f 1 189 f 5 169 f 1 147 f 3 147 f 1 201 f 1 191 f 3 169 i 2 161 f 6 184 f 2 141 f 2 69f2 201 f 4 169 f 4 164 f 3 140 f 3 176 f 6 162 f 2 124 f 2 99f3 198f 2 161 f 3 132 f 6 112 f 1 200 f 3 189 f 4 166 f 3 151 f 4 210 f 4 185 f 4 181 f 4 158 f 2 173 f 1 167 f 2 135 f 1 99f1 219 f 3 216 f 5 193 f 3 192 f 3 192 f 5 177 f 4 158 f 1 155 f 7 174 It 1 145 f 2 121 f 3 92f1 196 f 3 178 f 3 159 f 5 146 f 3 128 f 4 119 f 1 209 f 7 189 f 5 190 f 1 177 f 5 163 f 4 175 f 2 151 f 3 129 f 2
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
Table I (Continued) concn of solution, concn of solution, concn of solution, salt mol/dm3 no 104ab salt mol/dm3 na 104ab salt mol/dm3 CdSO, 1.012 4 132 f 2 0.998 5 132 f 3 NaHSOa 0.489 1.583 5 96f3 1.386 9 108 f 2 0.519 1.989 4 70f2 1.407 4 108 f 1 0.776 5 50f2 2.510 1.740 4 88fl 0.995 2.735 4 45 f 1 Na2S04 0.498 LO 163 f 2 1.018 5 36fl 3.026 4 136f2 0.748 1.503 14 174 f 2 0.497 CoSO, 0.883 8 120 f 2 1.574 4 150f1 0.767 0.993 7 113 f 2 1.939 5 128 f 2 1.001 1.325 3 87fl 2.628 1.494 4 96fl 1.487 1.031 3 76f 2 NH,HSO, CS2SO4 1.762 4 171 f 1 0.500 4 63f1 1.503 4 120 f 1 (NHJzS04 1.015 1.016 4 140 f 2 1.982 1.525 4 86fl 1.047 7 137 f 2 2.643 5 66f1 1.909 1.988 4 86f2 3.010 cuso, 4 177 f 1 0.496 2.007 5 82f 2 CsOH 0.890 4 168 f 4 0.591 2.498 5 66f2 2.142 a 155 f 3 0.741 2.984 2.325 4 51fl 4 139 f 1 0.959 3.499 4 4 4 f 1 KOH 0.938 7 133 f 1 NiSO, 1.000 0.499 4 176 f 2 1.030 Fe2(S04)3 0.487 4 148 f 2 0.749 4 150 f 1 1.844 0.723 4 115 f 2 1.181 2.135 6 116 f 3 0.940 5 94f2 1.489 5 95f3 2.311 K2S04 0.247 8 200 f 3 Rb2S0, 3 181 f 1 0.401 2.329 0.297 10 190 f 2 4 138 f 2 0.803 3.077 0.397 5 177 f 2 1.199 4 104 f 1 3.502 5 174 f 3 ZnSO, 0.405 0.501 a 170 f 2 4.848 0.500 12 166 f 3 0.719 6 148 f 5 4.871 0.582 6 157 f 2 1.006 1.015 6 122 f 4 LiOH Li,SO, 0.510 4 177 f 2 1.481 5 98f2 1.856 4 127 f 2 1.007 1.499 6 95f3 3.075 1.903 4 71f1 1.783 5 a2f1 4.059 MgSO4 0.497 19 174 f 3 2.151 5 66f 1 NaOH 1.000 0.750 5 148 f 4 KHSO, 0.565 4 192 f 2 1.139 4 128 f 1 0.996 4 176 f 1 0.771 2.000 1.196 4 112 f 2 1.011 4 162 f 3 2.105 1.202 4 113 f 2 1.484 4 141 f 2 2.122 1.500 5 89f2 1.522 7 137 f 3 3.035 2.003 4 66f3 1.638 4 133f2 4.071 2.013 4 66f2 1.798 4 128f 3 RbOH 1.112 MnSO, 0.503 4 179 f 2 1.805 4 127f2 2.070 0.691 9 161 f 4 2.017 5 115 f 2 3.187 a Number of oxygen measurements. bMean value of Bunsen's coefficient with standard deviation in mL/(mL atm).
n"
779
104ab
5 194 f 2 3 193 f 1 3 175 f 3 5 159 f 2 4 159 f 2 3 135 f 1 5 132 f 2 6 118f 3 4 92f2 a 176 f 3 4 153 f 2 7 135 f 2 4 116 f 1 8 108 f 2 3 174 f 1 4 108 f 3 3 100 f 1 4 169 f 1 5 164 f 2 4 122 f 1 4 108 f 2 4 102 f 1 4 100 f 1 3 79f1 4 67fl 4 42f1 4 37f1 4 175 f 1 4 135 f 1 4 95f2 4 65f4 4 164 f 1 4 155 f 2 4 114 f 1 5 104 f 1 4 106 f 1 4 74f1 4 49f1 a 157 f 2 6 109 f 3 5 76f3
Table 11. Experimental Salting-Out Parameter k,,,(dm3/mol) for Oxygen in Aqueous Solutions of Various Chlorides, Nitrates, Sulfates, Hydrogen Sulfates, and Hydroxides at 310.2 K and 1 atm (101.325 kPa) Oxygen Partial Pressure" ion chloride nitrate sulfate hydrogen sulfate hydroxide H+ 0.027f 0.001 (5)b 0.010f 0.004(3) 0.067f 0.001 (5) Li' 0.094f 0.003(6) 0.081f 0.0006 (4) 0.278f 0.003(3) 0.137 f 0.002(4) Na+ 0.131f 0.001 (7) 0.101f 0.002(4) 0.334f 0.002(7) 0.169f 0.001(7) 0.165f 0.003(9) K+ 0.124f 0.002(5) 0.098f 0.002(4) 0.331f 0.005(6) 0.158f 0.002(9) 0.160f 0.001(10) Rb+ 0.114f 0.001 (5) 0.095f 0.001 (8) 0.304f 0.001(3) 0.161f 0.003(3) Cs+ 0.099f 0.001(14) 0.090f 0.0036(4) 0.295f 0.001(4) 0.153f 0.001(3) NH4+ 0.076f 0.002(4) 0.059f 0.0006(4) 0.227f 0.002(6) 0.121 f 0.003( 5 ) Mg^+ 0.202f 0.001 (9) 0.172f 0.002 (4) 0.280f 0.002 (8) Ca2+ 0.226f 0.002(10) 0.192f 0.001(3) BaZ+ 0.265f 0.001 (3) 0.223f 0.002(2) Mn2+ 0.206f 0.002(4) 0.173f 0.001 (4) 0.252f 0.002(6) Co2+ 0.222f 0.003(4) 0.187f 0.002(4) 0.270f 0.003(4) Ni2+ 0.214f 0.004(3) 0.186f 0.002(4) 0.271f 0.001(4) Cu2+ 0.194f 0.002(7) 0.177f 0.001 ( 5 ) 0.257f 0.003(5) Zn2+ 0.211f 0.002(2) 0.181f 0.002(6) 0.268f 0.004(7) Cd2+ 0.188f 0.003(4) 0.167f 0.001 (4) 0.269f 0.003(6) AI3+ 0.301f 0.003(6) 0.252 f 0.002(3) 0.687f 0.005(3) Fe3+ 0.219f 0.004(3) 0.210f 0.002(4) 0.438f 0.003(3) La3+ 0.334f 0.004(4) 0.243 f 0.001(3) Ce3+ 0.347f 0.003(4) 0.236f 0.004(3) Th4+ 0.302f 0.003 (4)
k,,, for ZnC1, and CdC1, was calculated from the slope in the low concentration range (0-0.5 mol/dm3). Oxygen solubility in pure water: 0.0241mL/(mL atrn). * T h e figures in parentheses give the number of concentrations of the electrolyte used t o determine the salting-out parameter as calculated from the slope of the plot log ( a " / a )vs. cs by a linear regression analysis through the origin.
The applicability of Setchenov's concept for predicting oxygen solubilities in aqueous salt solutions according to
eq l a using only two parameters-the solubility of oxygen in pure water (ao)and an experimentally determined
780
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
Table 111. Comparison of Salting-Out Parameters of Electrolytes for Oxygen at 37 "C with Literature Data molar molar k m concn k::m this k,,,, concn T . K dm3/mol ranee ref work salt 7'. K dm3/mol ranee ref salt 0-2.0 Geffcken (1904) 0.027 298.2 0.089 0-1.5 Geffcken (1904) HCl 298.2 0.031 0-2.0 McArthur 0.094 0-1.5 Bruhn et al. 323 0.088 298.2 0.100 LiCl (1916)' (1965) Geffcken (1904) Khomutov and 0-2.0 0.131 0-1.2 298.2 0.244 NaCl 298.2 0.141 Konnik (1974)a Yasunishi 0-1.5 298.2 0.398 0-4.0 McArthur 298.2 0.138 (1978) (1916)" McArthur 0-0.5 298.2 0.325 Eucken and 298.2 0.145 0-1.5 (1916)" Hertzberg (1950) Khomutov and 0-1.2 298.2 0.376 0-1.2 Khomutov and 0.136 298.2 Konnik Konnik (1974)" (1974)" Mishnina et al. Yasunishi 0-5.4 308.2 0.420 0-1.7 298.2 0.145 (1961) (1978) Mishnina et al. 298.2 0.345 Geffcken (1904) 0-0.5 0-5.4 303.2 0.139 (1961) McArthur 0.124 298.2 0.345 McArthur 0-0.5 KC1 0-4.0 298.2 0.128 ( 1916)" ( 1916)' Khomutov and 0-1.2 298.2 0.297 0-0.6 Khomutov and 298.2 0.129 Konnik Konnik (1974)' (1974)' Yasunishi 298.2 0.290 0-0.3 Khomutov and 298.2 0.095 0-3.0 Konnik (1978) (1974)' 298.2 0.225 0-0.5 Khomutov and Yasunishi 308.2 0.087 0-3.0 Konnik (1978) (1974)' Bruhn et al. 0-0.5 Khomutov and 0.114 0-3.0 RbCl 298.2 0.120 (NHJ2S0, 298.2 0.212 Konnik (1965) (1974)' Bruhn et al. 0.099 323.2 0.196 0-3.0 0.098 0-0.5 Khomutov and CsCl 298.2 (1965) Konnik (1974)" McArthur 0-1.0 0.202 298.2 0.273 0-1.7 Yasunishi MgC1, 298.2 0.258 MgS04 (1916)" (1978) McArthur Yasunishi 0.211 298.2 0.250 2-5.0 0-2.4 298.2 (1916)' (1978) 0-1.7 Yasunishi Yasunishi 308.2 0.280 0-2.5 0.200 298.2 (1978) (1978) Yasunishi Yasunishi 0.222 0-3.9 308.2 0.293 0-2.6 298.2 (1978) (1978) 2.43 McArthur 0.192 0-1.0 0.226 MnSO, 298.7 0.194 Murray et al. 298.2 CaC1, (1916)' (1968) Yasunishi Bruhn et al. 0-2.7 coso, 298 0.115 0-1.5 0.204 298.2 (1978) (1965) Yasunishi Bruhn et al. 0-4.5 323 0.128 0-1.5 0.226 298.2 (1978) (1965) McArthur Bruhn et al. 0-1.0 0.265 NiSO, 298 0.113 0-1.5 0.270 298.2 BaC1, (1965) ( 1916)" Bruhn et al. 323 0.128 Y asunishi 0-1.5 0.212 0-1.5 298.2 (1965) (1978) Bruhn et al. 0.206 cuso, 0-1.5 298 0.114 MnC1, 298.7 Murray et al. 2.69 0.202 (1965) (1968) Bruhn et al. Yasunishi 323 0.123 0-1.7 0.301 0-1.5 0.274 298.2 A1CI3 (1978) (1965) Pogrebnaya et 0-2.0 0.010 298.2 0.745 Yasunishi 0.024 0-0.8 HNO, 298.2 Al,(SO,), (1978) al. (1972) Pogrebnaya et 0.012 0-2.0 313.2 al. (1972) Khomutov and 0-0.07 0.081 LiOH 0.015-1.2 Khomutov and 0.196 LiN02 298.2 298.2 0.091 Konnik Konnik (1974)" (1974)' 0.15-1.2 Khomutov and 298.2 -0.040 Konnik (1974)" NaNO, 298.2 0.124 0-1.2 Khomutov and 0.101 NaOH 298.2 0.180 0-2.0 Geffcken (1904) Konnik (1974)" 0-5.1 Yasunishi 0-1.2 Khomutov and 298.2 0.109 298.2 0.180 Konnik (1978) (1974)'
k:za this work 0.067 0.278 0.334
0.331
0.304 0.295 0.227
0.280
0.252 0.270
0.271
0.257
0.687
0.137
0.169
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
781
Table 111 (Continued)
dm3/mol
molar concn range
323
0.110
0-1.0
298.2
0.105
0-1.2
298.2
0.102
0-2.0
R b N 0 3 298.2
0.096
0-0.5
CsN03 298.2
0.066
0-0.5
RbOH
298.2
0.168
0-0.5
CsOH
298.2
0.158
0-0.5
kscm
salt
KNO,
T,K
ref Broden and Simonson (1974) Khomutov and Konnik (1974)O McArthur (1916)' Khomutov and Konnik (1974)" Khomutov and Konnik (1974)" Khomutov and Konnik (1974)O Khomutov and Konnik (1974)"
k:Jo this work
km, T , K dm3/mol 298.2 0.160
salt
0.098
molar concn range
k:za this work
ref
0-6.4
Yasunishi (1978)
308.2
0.167
0-6.4
Yasunishi (1978)
323
0.185
0-1.5
0.095
KOH 298.2
0.177
0-1.2
Bruhn et al. (1965) Geffcken (1904)
0.090 0.161
298.2 298.2 298.2
0.130 0.175 0.180
0-4.0 0-12 0-16
McArthur (1916)" Davis et al. (1967) Shoor et al. (1969)
0.153
298.2
0.176
0-0.8
313.2 318.2
0.168 0.160
0-16 0-10
Khomutov and Konnik (1974)" Shoor et al. (1969) Knaster and Apelbaum (1964)
0.160
" Air-saturated solutions. Table IV. Relative Salting-Out Parameters H i of Oxygen for Individual Ions = 0)" Partial Pressure (HNa+ cation H+, dm3/mol cation H+, dm3/mol cation H+ -0.200 f 0.003 Mg2+ -0.025 f 0.002 ~13+ Li+ -0.060 f 0.008 Ca2+ -0.015 f 0.001 Fe3+ fO.OOO f 0.009 Ba2+ +0.003 f 0.001 La3+ Na+ K+ -0.013 f 0.010 Mn2+ -0.029 f 0.006 Ce3+ Rb+ -0.025 f 0.005 CO" -0.021 f 0.005 Cs+ -0.041 f 0.011 Ni2+ -0.022 f 0.004 Th4+ CU" -0.030 f 0.006 NH4+ -0.098 f 0.005 Zn2+ -0.024 f 0.004 Cd2+ -0.031 f 0.004
at 310.2 K and 1 atm (101.325 kPa) Oxygen
H+, dm3/mol -0.018 f 0.001 -0.032 f 0.005 -0.014 f 0.004 -0.015 f 0.007
NO3HSOI-
H-, dm3/mol 0.257 f 0.009 0.220 f 0.010 0.340 f 0.006 0.333 f 0.004
-0.017
so:-
0.163 f 0.006
anion C1OH-
Hifor Fe3+ and A13+ is the mean calculated from the chloride and nitrate only, but not from the sulfate. salting-out parameter for the electrolyte (ksca)-was against predicted checked by a plot of experimental (aexptl) (apred) oxygen solubilities, as shown in Figure 2. The good correlation between experimental and predicted oxygen solubilities, even at low values corresponding to high salt concentrations, justified the use of Setchenov's concept. The salting-out parameter, k,,,, which represents the net effect of salting-out oxygen with respect to the electrolyte, can be correlated with the single-ion parameter, Hi, of the dissolved ionic species of which the electrolyte is composed if a suitable reference ion is chosen. From the fact that sodium salts are well dissociated in aqueous solutions, e.g., Na2S04is more dissociated than H2S04,the sodium ion was chosen as a reference ion and arbitrarily set to zero, HNa+= 0. According to eq 2 k,,, = 1/2CiHixizi2; a set of Hi parameters for each independent positive and negative ion of all studied electrolytes could be derived relative to the sodium ion (Table IV) by an iteration procedure: In a first step, with Hi values of the anions C1-, NO3-, SO:-, and OH- calculated from the experimental k,,, values of their sodium salts relative to HNa+ = 0, all Hi values for the other cations of the corresponding electrolytes could be calculated and a set of Hi values was obtained for anions and cations, averaged over Hi's of the same cation. Then, in a second step, with the set of averaged Hi's of the cations, Hi of the anion for each electrolyte could be calculated and the mean was taken for all Hi's of the chlorides, nitrates, sulfates, hydrogen sulfates, and hydroxides. With this set of averaged H i s of the anions, a new set of averaged Hi's of the cations could be derived, and the iteration was continued until the H i s of the last two sets were consistent. With such a best set of individual ion parameters, Hi, from
250 A A
chlorides chlorides
E
I
0 0
0 0
nitrates sulfotes sulfotes
I
I I
-E
. -
200
'P
/'
hydroxides
I
-EE x . n
d
G
150 150-
100 -
/
Io!
V
,
50
100
150
200
io
1 0 ' a q ' ~ ~ r n l / i mal t m i
Figure 2. Comparison between experimental and predicted oxygen Solubilities calculated by eq l a due to Setchenov: apred = aO1O-ksc=cs.
Table IV, the salting-out parameter, k,,,, of an electrolyte could be calculated. The usefulness of the concept was checked by comparison of the predicted and experimental Setchenov parameters, k,,,, of the studied electrolytes. As can be seen from Figure 3, the correlation was satisfactory and the mean relative deviation between predicted and experimental k,,, values was of the order of *3.5%.
782
Ind. Eng. Chem. Fundam., Vol. 25, No. 4 , 1986
0
0.1
0.2
03
OL
k p r e d ,dm3 /mol SCa
Figure 3. Comparison between experimental and predicted salting-out parameter k , , , calculated by eq 2 due to Schumpe et al. T h i s e x t e n s i v e s t u d y has s h o w n that f o r practical p u r p o s e s the S e t c h e n o v c o n c e p t is a p p l i c a b l e t o m o s t of t h e i n v e s t i g a t e d a q u e o u s electrolyte s y s t e m s i n w h i c h oxygen w a s d i s s o l v e d and o v e r a w i d e c o n c e n t r a t i o n r a n g e , and that the S e t c h e n o v p a r a m e t e r , k,,,, f o r an electrolyte c a n be c a l c u l a t e d f r o m a s e t of relative i n d e p e n d e n t single-ion p a r a m e t e r s , H,, d u e t o t h e S c h u m p e m o d e l .
Nomenclature a', u = Bunsen coefficient of oxygen solubility in p u r e water a n d in a q u e o u s salt solution, m L / ( m L a t m ) cs, c, = molar concentration of salt a n d of ionic species i in solution, m o l / d m 3 h = salting-out p a r a m e t e r defined by e q Ib, d m 3 / m o l h,, h-, hc = c o n t r i b u t i o n s t o h of positive ion, negative ion, a n d dissolved gas, d m 3 / m o l H , = contribution of salting-out p a r a m e t e r for oxygen of individual ions, d m 3 / m o l I = total ionic strength of electrolyte defined by I = 1 / ~ ~ l c , z , 2 . mol/dm3 I , = ionic s t r e n g t h of ionic species i in solution defined by I , = 1/2cIz!2. m o l / d m 3 h,,,, = salting-out p a r a m e t e r for single electrolyte defined by e q la, d m 3 / m o l x, = n u m b e r of ions of t y p e i in t h e electrolyte z, = charge n u m b e r
Subscripts exptl = e x p e r i m e n t a l p r e d = predicted sca = (s) salting-out p a r a m e t e r , (c) molar concentration, ( a ) B u n s e n solubility coefficient
Registry No. HC1, 7647-01-0; AlCl,, 7446-70-0; BaC12, 10361-37-2;CaC12,10043-52-4;CdC12,10108-64-2;CeCl,, 7790-86-5; CoClz, 7646-79-9; CsC1, 7647-17-8; CuC12, 7447-39-4; FeCl,, 7705-08-0; KC1, 7447-40-7; LaCl,, 10099-58-8; LiCl, 7447-41-8; MgC12, 7786-30-3; MnCl,, 7773-01-5; NaC1, 7647-14-5; NH,Cl, 12125-02-9; NiC12, 7718-54-9; RbCl, 7791-11-9; ZnCl,, 7646-85-7; HNO,, 7697-37-2; A1(N03),, 13473-90-0; Ba(NO,),, 10022-31-8; Ca(N03)2,10124-37-5;Cd(N03)2,10325-94-7;Ce(N03)s,10108-73-3; Co(NO3)2, 10141-05-6; &NO3, 7789-18-6; C U ( N O , ) ~3251-23-8; , Fe(N03),, 10421-48-4; KNOB,7757-79-1; La(N03),, 10099-59-9; LiNO,, 7790-69-4; Mg(NO3I2,10377-60-3;MII(NO,)~,10377-66-9; NaNO,, 7631-99-4; ",NO3, 6484-52-2; N i ( N 0 J 2 , 13138-45-9; RbNO,, 13126-12-0;Th(N03),, 13823-29-5; Zn(N03)z,7779-88-6; HZSO,, 7664-93-9; Al,(SO,),, 10043-01-3; CdSO,, 10124-36-4; CoSO,, 10124-43-3; Cs2S04, 10294-54-9; C u S 0 4 , 7758-98-7; Fez(SO,),, 10028-22-5; KzSO4,7778-80-5;Li2S0,, 10377-48-7;MgSO,, 7487-88-9; MnSO,, 7785-87-7; N a 2 S 0 4 , 7757-82-6; ( N H 4 ) 2 S 0 4 , 7783-20-2;NiS04, 7786-81-4;Rb2S04,7488-54-2;ZnSO,, 7733-02-0; KHSO,, 7646-93-7; NaHSO,, 7681-38-1; N H 4 H S 0 4 , 7803-63-6; CsOH, 21351-79-1; KOH, 1310-58-3; LiOH, 1310-65-2; NaOH, 1310-73-2; RbOH, 1310-82-3; 0 2 , 7782-44-7.
Literature Cited McArthur, C. G. J . Phys. Chem. 1916, 20, 495-502. Battino, R. I n Oxygen and Ozone; Pergamon: Oxford, 1981; IUPAC Solubility Data Ser. Vol. 7, pp 1-38, 56-182. Broden, A.; Simonson, R. Sven. Papperstidn. 1978, 87,541-544. Broden. A,; Simonson, R. Sven. Papperstidn. 1979, 82, 487-491. Bruhn, G.; Gerlach, J.; Pawlek, F. Z. Anorg. A/@. Chem. 1965, 337, 68-79. Clever, H. L. J . Chem. Eng. Data 1983, 28, 340-343. Cotton, F. A.; Wilkinson, G. Anorganische Chemie, 2nd ed.; Verlag Chemie: Weinheim, 1970; pp 567, 802. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970; pp 18-20. Davis, R. E.; Horvath, G. L.; Tobias, C. W. Electrochim. Acta 1967, 12, 287-297. Eucken, A.; Hertzberg, G. 2 . Phys. Chem. (Leipzig) 1950, 195, 1-23. Geffcken, G. Z . Phys. Chem. Stoechiom. Verwandtschaftsl. 1904, 49, 257-302. -. . ..-. Khomutov, N. E.; Konnik, E. I.Russ. J . Phys. Chem. (Engl. Transi.) 1974, 48(31. 359-362. Knaster,"M. B.; Apelbaum, L. A. Zh. Fiz. Khim. 1964, 38, 223-225. Lang. W.; Wolf, H. U.; Zander, R. Anal. Biochem. 1979, 92,255-264. Linek, V.; Mayrhoferova, J. J . Chem. Eng. Sci. 1970, 25, 787-800. Mishnina, T. A.; Avdeeva, 0. I.; Bozhovakaya, T. K. Mater. Vses. NauchnoIssled. Geol. Inst. 1961, 46, 93-110. Murray, C. N.; Riley, J. P.; Wilson, T. R. S. Deep-sea Res. 1968, 15, 237-238. Onda, K.; Sada, E.; Kabayashi, T.; Kito, S.; Ito, K. J . Chem. Eng. Jpn. 1970, 3 , 18-24. Onda, K.; Sada. E.; Kobayashi, T.; Kito, S.: Ito, K. J . Chem. Eng. Jpn. 1970, 3, 137-142. Pogrebnaya, V. L.;Usov, A. P.; Baranov, A. V.; Machigin, A. A. I s v . Vyssh. Uchebn. Zaved., Khim. Khim. Tekhnol. 1972. 15, 16-20, Setchenov, J. Z . Phys. Chem., Stoechiom. Verwandtschaftsl. 1889, 4 , 117-125. Schumpe, A.; Adler, I.; Deckwer, W. D. Biotechnol. Bioeng. 1978, 2 0 , 145-150. Shoor, S. K.; Walker, R. D.; Gubbins, K. E. J , Phys. Chem. 1969, 73, 312-31 7. van Krevelen, D. W.; Hoftijzer, P. J. Chimie et Industrie: Numero Speciale du XXI' Congres Internationale de Chimie IndustrieNe , Bruxelles , 1948: pp 168-173. Yasunishi, A. J . Chem. Eng. Jpn. 1977, 70,89-94. Zander, R.; Euler, R . I n Measufement of Oxygen; Degn, H., Balslev, I., Brook, R., Eds.; Elsevier: Amsterdam, 1976; pp 271-276.
Received for review March 15, 1985 Accepted January 21, 1986
