109
Ind. Eng. Chem. Fundam. lQ82, 21, 109-113
f = failure rate of relief valve; f = 0.01 yr-’ is assumed B+ = safe rupture disk B- = dangerous disk has been installed F+, G+ = relief valve in an unfailed state F-, G-= relief valve failed D = total pressure demand rate, y-l (weak and strong preeaure demands) D* = strong pressure demand rate, yr-l (capable of bursting the vessel) D - D* = weak pressure demand rate, yr-l (capable of only bursting a rupture disk but not the vessel) P,,= probability of being in state n H = instantaneous hazard rate, yr-l, at t HT= instantaneous hazard rate, yr-l, at t = T, the end of the maintenance interval H = average hazard rate over a period of time, yr-’ T = maintenance interval, yr t = time, yr [I = probability at t = 0 Literature Cited
over the range of variables shown in Figures 18 and 19, the effect is quite small for c = At values of c sigdkantly greater than the effect of test and installation error in the relief valve is significant, but good maintenance control procedures should preclude such large values of C.
Conclusions The hazard rates of five different pressure protective systems, some with several different maintenance strategies, have been evaluated using Markov models. The Markov analysis is uniquely effective in describing the sequential and parallel steps that lead to failure of the pressure protective system and ultimately to a hazard. All systems, even those involving rupture disks, degenerate with time, making the maintenance interval an important factor in the average and instantaneous hazard rates. Although most systems are considered to be passive, the bursting of a rupture disk provides active insight which can be used to reduce the hazard rate. The Markov analysis is particularly effective in analyzing the benefits of interlocking maintenance strategies, as illustrated in the examples considered here. Nomenclature a = premature bursting rate of rupture disks, yr-’ b = probability that a dangerous disk is employed per installation; b = 0.001 is assumed c = probability of a relief valve being in a failed state after testing
Greene A. E.; Bourne, A. J. ”Rellabllky Technology”; Wlley: New Y a k . 1972. Greene, A. E.; Bourne, A. J. UKAEA Report No. AHSB(S) R117, Part 111, 1966. pp 377-382. Henley, E. J.; Kumamato, H. “Rellabillly Engineering and Risk Assessment”; PrentlceHall: Englewood ClWs, NJ, 1981. Kletz, T. A. "Proceedings of 1st Internatlonal Loss Prevention Symposium”; The Hague, The Netherlands, May 1974a; pp 309-315. Kletz, T. A. C h i n . procesS. a p t 1974b, 77-81. Kletz, T. A. Hydroatrbon Process. 1977, 56(5), 297. Lees, F. P. C h m . Ind. March 1976, No. 6 , 195-205.
Received for review July 21, 1981 Accepted December 28, 1981
Infinite-Dilution Activity Coefficients from Differential Ebulliometry Georgleanna M. Loblen‘ and John M. Prausnltz’ Department of Chemical Engineering, Universlty of California, Berkeley, California 94720
Using a differential ebulliometer, limiting activity coefficients were obtained for four partially miscible binary systems: 2-methoxyethanol-n -heptane, 1-butanol-water, 2,4-pentanedione-water, and methanol-cyclohexane, and for two totally miscible binary systems: pyridine-water and piperidlne-water. When experimental limtting actMty coefficients are used to fix binary parameters in a common expression for the excess Gibbs energy, prediction of solubility limb for partially miscible systems is sensitive to mathematical details of that expression. Predicted solubility limits are often poor. Conversely, when experimental solubility limits are used to fix binary parameters In an expression for the excess Gibbs energy, prediction of limiting activity coefficients Is also poor. It appears that commonly used expressions for the excess Gibbs energy are not able to represent simultaneouslyvapor-liquid and liquid-liquid equilibria in binary systems.
Introduction The utility of infinite-dilution activity coefficients for representing phase-equilibria behavior has been recognized for some time (Gautreaux and Coates, 1955; Schreiber and Eckert, 1971; Nicolaides and Eckert, 1978). Schreiber and Eckert (1971) showed that, when only binary limiting activity coefficientsare used to determine the two parameters in the Wilson equation (1964), vapor-liquid equilibrium behavior for many binary systems can be represented well over the entire composition range. To illustrate, Figure Chevron Research Corporation, Richmond, CA. 0196-4313/82/1021-0109$01.25/0
1 shows that when limiting activity coefficients for acetone-benzene (Nicolaides, 1977) are used to evaluate the parameters in the Wilson equation (1964),the y x and P-x curves for the system are predicted with good accuracy. Similarly, limiting activity coefficients can be used to determine two parameters in other expressions for the excess Gibbs energy, i.e., the van Laar (1910) and UNIQUAC (Abrams and Prausnitz, 1975) equations. However, the scarcity of accurate infiite-dilution activity coefficients has prevented their full exploitation for describing liquid-phase nonidealities. This work discusses an experimental procedure for rapid and accurate measurement of activity coefficients a t infinite dilution and presents ex@ 1982 American Chemical Society
110
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982
Table I. Solubility Limits Calculated from VLE Datae Using van Laar or UNIQUAC solubility limits 100 x , ' components
temp,"C
acrylonitrile (1)-water ( 2)c
25 40 25 35 50 60 73.6 40 60 80 0 35
methyl acetate (1)-water ( 2)c
2-butanone (1)-water (2)d ethyl acetate (1)-water ( 2 ) d 2-butanol (1)-water ( 2 ) d methanol (1)-benzene ( 2)c methanol (1)-n-hexane ( 2)d
van Laar UNIQUAC 3.0 6.0 5.5 8.0 7.0 13.5 16.0 3.0 3.0 38.0 7.0
0.8 0.2 a
1.4 3.9 3.1 4.8 a a a
18.7 a
100 x;' vanLaar UNIQUAC
obsd 2.6 2.8 6.7 6.8 6.9 7.1 5.2 1.4 3.5 4.1 b 21.4
15.0
3.6 44.9
14.0 32.0 21.o 22.0 29.0 20.0 49.0 53.5 18.0 15.5
a
11.4 10.7 10.7 17.2 a a a
1.8 a
a Denotes total miscibility. Data are unavailable. LLE data from compilation by Seidell (1941). compilation by Stephen and Stephen (1963). e VLE data from compilation by Gmehling et al. (1977).
obsd 9.4 12.9 b b b b 41.3 16.7 67 .O 70.7 25.7 23.3
LLE data from
t
Experimental
A
I .o
0
0.1
0.2 0.3 0 4 0.5 XI
c y
1
I
C
02
0 4
I
06
~
08
Io 2 0 '0
XI
Figure 2. Uncertainties in graphical extrapolation of activity coefficientsto infinite dilution for the system ethanol (1)-water (2) at 55 O C . Data of Mertl et al. (1972).
Figure 1. Vapor-liquid equilibria for the system acetone (1)benzene (2) at 45 OC. Calculations based on Wilson equation using 71- = 1.65 and 72- = 1.57.
perimental results for six binary systems. Traditional methods for determining infinite-dilution activity coefficients include graphical extrapolation of finite-concentration data and fitting binary vapor-liquid equilibrium data to an expression for the excess Gibbs energy. Both of these methods give results of dubious quality. To illustrate, Figure 2 shows a plot of activity coefficient vs. mole fraction for the system ethanol-water; there is much uncertainty in determining 7 - when x = 0. Figure 3 shows how difficult it is to determine unique values for ymby fitting vapor-liquid equilibrium data to an expression for the excess Gibbs energy; data for the system propanol-water were fit to the Wilson (1964) and van Lam (1910) equations. Each equation predicts a different set of limiting activity coefficients. Similar conclusions were reported by Eckert et al. (1981). To increase our knowledge of infinite-dilution activity coefficients, we require an experimental method which is rapid; which does not depend on a particular expression for the excess Gibbs energy; which does not require extrapolation from concentrated regions to infinite dilution; and which does not require chemical analysis of mixtures in highly dilute regions. Experimental methods which meet these requirements include differential ebulliometry (Eckert et al., 1981; Nicolaides, 1977; Newman, 1977) and gas chromatography (Leroi et al., 1977; Newman, 1977). Gas-chromatographic
2.51
XI
Figure 3. Calculated activity coefficientsfor 1-propanol (l)-water (2) at 90 OC. Binary parameters determined by fitting VLE data of Ratcliff et al. (1969).
methods, however, are useful only for volatile solutes in nonvolatile solvents as discussed by Leroi et al. (19771, Newman (1977), Richon et al. (1979), and Santacesaria et al. (1979). For mixtures of volatile components, the preferred method is differential ebulliometry. The choice of binary systems studied in this work was, in part, dictated by increasing interest in accurate representation of thermodynamic properties of partidy miscible systems. Presently, no particular expression for the excess Gibbs energy accurately represents both vapor-liquid equilibria (VLE) and liquid-liquid equilibria (LLE) for binary systems; a particular expression suitable for one
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 111
Table 11. Activity Coefficients at Infinite Dilution Calculated from VLE and Solubility Data Usina van Laar or UNIQUAC UNIQUAC van Laar Y 1-
components acrylonitrile (1)-water (2)
temp,"C 25 40 73.6
2-butanone (1)-water (2) ethyl acetate (1)-water (2) 2-butanol (1)-water ( 2 )
40 60 80 35
methanol (1)-n-hexane ( 2 ) a
VLE 39.4 29.2 14.3 12.0 34.2 38.0 21.8
VLE data from compilation by Gmehling et al. (1977).
van Laor
1 .oO 45.0
Observed
1.70 58.1
Y 1-
7 2-
LLE 46.2 43.6 27.0 77.1 31.8 28.6 9.89
VLE 9.99 7.01 9.71 3.45 3.01 10.5
LLE 14.8 11.3 4.31 8.57 2.35 2.24 9.14
7 2-
VLE
LLE
VLE
LLE
39.3 42.0 23.6 12.1 34.1 43.0 30.3
19.8 17.6 14.2 30.7 259 215
17.8 4.06 7.35 0.53 3.48 3.09 13.9
9.40 7.54 3.40 5.73 3.35 3.15
LLE data sources as listed in Table I.
1.0-
RUN-JOB
0.8Mole Fraction
Uncorrected
I
0
0.004
I
I
I
C I12
0.008
Mole Fraction 2-Methoxyethonol 35-0.-
0
0.2 0.4
0.6
0.8
1.0
XI
Figure 4. Molar Gibbs energy of mixing for 1-butanol (1)-water (2) at 70 OC. Binary parameters from infinite-dilutiondata. 1c' and d' denote solubility limits.
binary may be poor for another binary. For example, when one uses VLE data for a partially miscible binary system to determine the parameters of an excess Gibbs enelgy equation, the prediction of solubility limits is often poor. Table I and Figure 4 show examples. Prediction of VLE data from LLE data is also poor. Table I1 shows that using solubility limits to determine parameters in an excess Gibbs energy equation leads to poor limiting activity coefficients. The limited evidence now available suggests that commonly used, two-parameter expressions for the excess Gibbs energy are inadequate, there appears to be a need for a new expression for the excess Gibbs energy which represents both VLE and LLE for a wide range of binary systems. Unfortunately, the development of such an expression is impeded by the lack of binary systems for which both accurate VLE and LLE data are available. Therefore, one goal of this work is to provide VLE data, in the form of infinite-dilution activity coefficients, for partially miscible systems where solubility data also are available. Only when reliable limiting-activitycoefficient data are available is it possible to test the validity of an expression for the excess Gibbs energy of partially miscible systems.
Thermodynamic Analysis Nicolaides (1977) and Newman (1977) have developed a differential ebulliometric technique to determine y", following earlier work by Gautreaux and Coates (1955). For isobaric conditions, Gautreaux and Coates (1955) derived an expression for y" in terms of pure-component properties and the limiting slope of the temperature with respect to the liquid-phase mole fraction, ( d T / d ~ ) "Null ~ (1970) improved this expression for 7-by including also terms for vapor-phase nonidealities.
Figure 5. Temperature changes for 2-methoxyethanol in heptane (To= 350.00 K). Upper line shows data corrected for vapor and liquid holdup. Lower line shows uncorrected data.
According to Null (1970), the infinite-dilution activity coefficient is given by
Pl8)~,/RT1I (1) The pure-component vapor pressure, Pi",and liquid molar volume, ui, are readily available for most liquids. Empirical equations for the temperature dependence of Pi" and uiare given elsewhere (Lobien, 1980). Fugacity coefficients, #J~, and their derivatives with respect to pressure, (d4?/dP),, are determined using the virial equation of state, with virial coefficients estimated by the method of Hayden and O'Connell (1975). The limiting slope of the temperature with respect to the liquid-phase composition, ( d T / d ~ ) ~is ~measured , by differential ebulliometry. As pointed out by Nicolaides (1977), the derivation of eq 1requires no assumption concerning the dependence of the activity coefficient on composition. Further, eq 1 does not rely on extrapolation of experimental activity coefficients to infinite dilution. Rather, eq 1 uses the limiting slope of T-x curves, whose slope at low compositions is essentially linear and whose end point is fixed at x = 0, A T = 0 (see Figure 5). Experimental Apparatus In this work, the quantity (dT/dx)p" was determined by measuring isobaric changes in the boiling point of a solvent which result when small, known amounts of solute are added. Measurements were made in a differential ebulliometer which consists of two, glass, boiling chambers connected, through condensers, to a common manifold. The change in boiling point is measured as the difference
112
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982
molecular sieves (type 3A) and batch-distilled, under dry nitrogen, at a pressure of approximately 2/3 bar. The distillation column used was a 15-tray Oldershaw column, run at a reflux ratio of at least 10 to 1. The top 10% and bottom 15% of the batch were discarded. The middle 75% was analyzed by NMR and/or gas chromatography to detect any impurities. Purified water was obtained by running standard distilled water through a Culligan SR Cartridge Water Treatment System with an organic trap, deionizer, and microfilter to remove any residual organics or ions. Analysis of Data Equation 1was used to determine the infinite-dilution activity coefficients. Table IV gives Pi" and uifor each of the pure fluids used in this study. Since the solute and solvent have different volatilities, they are distributed in the vapor in a proportion different from that in the liquid. Therefore, the vapor and condensate above the liquid in the boiling chamber have a different composition than that of the boiling liquid. Hence, when calculating the limiting slope of temperature with respect to liquid mole fraction, the liquid composition
Table 111. Suppliers and Grades of Chemicals chemical supplier grade 1-butanol
Aldrich
cyclohexane n-heptane methanol
Aldrich Aldrich Mallinckrodt
2-methoxyethanol 2,4-pentanedione piperidine pyridine
Aldrich
9 9 t %, spectrophotometric grade 99+ % 99+ % anhydrous (absolute) (acetone free) 99t%
Aldrich
99+%
Aldrich Mallinc kro dt
98% analytical reagent
between the boiling point of the pure solvent (in one chamber) and the boiling point of the solute plus solvent (second chamber). The apparatus and experimental procedure used are similar to those used by Eckert et al. (1981). Chemicals Grades and sources of chemicals are shown in Table 111. Except for water, all the chemicals were dried over Linde
Table IV. Measured Activity Coefficients at Infinite Dilution ; Pure-Component Liquid Molar Volume, cm3/mole; and Vapor Pressure, torr, for Six Binary Systems components n-heptane (1)-2-methoxyethanol ( 2 )
2,4-pentanedione (1)-water ( 2 )
temp, "C 47 63 67 77 90 105 70 81 90
100 1-butanol (1)-water ( 2 )
70 80 90 99 110 35 45 60 70 90 100 70 90 100
methanol (1)-cyclohexane ( 2 ) pyridine (1)-water ( 2 ) piperidine (1)-water ( 2)
a
Y 216.1
-a
-
6.10
-
12.7 11.5 9.95
5.16 4.37 3.40 28.6 26.1 23.9 22.0 67.8 46.5
-
4.60 3.36 1.89 3.27 3.12 3.07 2.97 2.90 18.9 17.4 16.6 2.87 2.80 2.80 3.00 3.23 3.61
-
27.1
-
54.2 38.0 27.5 24.6 20.0 17.0 6.62 6.89 7.24
VI IP,S
V,IP,S
151.851129.46 155.041233.94 155.931271.07 158.241384.93 161.431586.77 165.411914.63 108.01/79.62 109.48/120.31 110.741165.26 112.191231.26 97.80198.99 99.141160.54 100.5512 51.49 101.88/366.61 103.591562.87 39.651205.40 40.291327.43 41.311621.70 84.91/163.00 86.331337.78 81.841469.68 104.421223.80 106.911451.58 108.241619.67
81.50133.43 83.09170.39 83.53184.70 84.671131.48 86.231222.45 88.171384.92 18.211232.59 18.431367.98 18.621522.94 18.841755.54 18.211232.59 18.41 1353.43 18.621522.94 18.811728.98 19.06/1067.94 110.09/147.62 111.441220.59 113.571382.16 18.211232.59 18.621522.94 18.841755.54 18.211232.59 18.621522.94 18.841755.54
A dash (-) indicates that no measurement was made.
Table V. Solubility Limits Calculated from Activity Coefficients at Infinite Dilution Using van Laar, UNIQUAC, NRTLe solubility limits components n-heptane (l)-2-methoxyethanol(2) . .
*
2,4-pentanedione (1)water (2)' 1-butanol (1)-water (2)' methanol (1)-cyclohexane ( 2 ) c
loox,' 1oox z' ' NRTL temp, "C van Laar UNIQUAC NRTL obsd van Laar UNIQUAC NRTL obsd optimum c y d 47 67 77 70 80 90 70 80 100 35 45.1 60
27.0 40.0 50.0 4.5 5.5 6.0 1.0 2.5 5.0 2.0 3.0 5.0
a a
26.0
a
a
7.5 8.5 10.0 2.0 3.0 6.0 16.0 23.0 3.0
19.2 a
5.5 7.5
6.3 8.5
1.5 2.5
a 1.7 1.8
3.5 5.5
2.4 16.1 37.7 a
11.0
16.0 25.0 30.5 39.5 51.5 45.0 49.0 58.5 7.0 8.0 9.0
a a a
11.0
53.0 59.0 67.5 58.0 63.0 70.5 18.0 23.0 26.0
47.6 59.3
26.2
0.10
a a
58.0 59.5 21.5 38.5
48.0 59.9 a 58.1 59.7 67.0 22.2 39.6 a
0.38 0.43 0.45 0.41 0.41 0.43
' Denotes total miscibility. LLE data from Landauer et al. (1980). LLE data from compilation by Stephen and Stephen (1963). The optimum cy was determined using the solubility limit in the (") phase, e Renon and F'rausnitz (1968).
Ind. Eng. Chem. Fundam., Vol. 21, No. 2, 1982 113 Table VI. Activity Coefficients at Infinite Dilution Calculated from Solubility Data" Using van Laar or UNIQUAC Y *-
Y1-
components n-heDtane I1 )-2-methoxiethhol(2) 2,4-pentanedione(1)water ( 2 ) 1-butanol (1)-water ( 2 )
methanol ( 1)-cyclohexane ( 2 ) a
temp,"C
vanhar
UNIQUAC
47
10.9
17.8
70 80 70 80 35 45.1
23.9 20.2 52.6 50.9 12.0 7.86
30.6 25.6 76.6 74.6 75.8 44.1
obsd 7.32 28.6 26.1 67.8 46.5 54.2 38.0
vanLaar
UNIQUAC
obsd
8.21
25.9
16.1
3.83 3.20 2.54 2.47 8.97 7.45
5.63 4.44 3.24 3.09 17.8 15.3
5.47 4.60 3.27 3.12 18.9 17.4
LLE data sources as listed in Table V.
cannot be calculated directly from the weighed amounts charged to the ebulliometer. The true liquid composition was calculated by correcting for the vapor and liquid holdup above the boiling chamber. Figure 5 shows that this correction is not negligible and must be taken into account when determining the limiting slope. Details on holdup calculations are given elsewhere (Lobien, 1980). Results and Discussion Table IV gives infinite-dilution activity coefficients for six binary systems. For each binary system studied, a set of infinite-dilution activity coefficients was measured for at least three temperatures. For the four partially miscible binary systems (first four binary systems in Table IV), at least one of the sets of infirnibdilution activity coefficients was measured at a temperature below the upper consolute temperature for that binary. As expected, the infinite-dilution activity coefficients for the four partially miscible systems are large, reflecting large nonidealities in these systems. The two miscible binary systems, reflecting moderate nonideal behavior, yield smaller infinite-dilution activity coefficients. The infinite-dilution activity coefficients measured in this study were used to evaluate the ability of several expressions for the excess Gibbs energy to represent both VLE and LLE data. Table V show that, even when accurately measured infinite-dilution activity coefficients are used, the prediction of solubility limits is poor. Table VI shows that the prediction of infinite-dilution activity coefficients from solubility data is also poor. Even when accurate infite-dilution activity coefficients are available, for a variety of binary systems, the van Laar, NRTL, and UNIQUAC equations do not accurately predict solubility limits and, vice versa, given solubility limits, the infinite-dilution activity coefficients are not accurately predicted. In some cases, the NRTL equation more accurateIy predicts solubility limits, but this is achieved only by adjusting the third parameter, a. Our results indicate that a different a must be calculated at each temperature. Since some of the LLE data used are old and their accuracy is not known, some of the error in prediction may be attributed to error in the LLE data. Conclusion When infinite-dilution activity coefficients are used to determine the binary parameters in an exceas Gibbs energy equation, poor prediction of LLE data is not only a consequence of the inaccuracy of the infinite-dilution activity coefficients. Even when accurately known infinitedilution activity coefficients are used with common expressions for the excess Gibbs energy, prediction of liquid-liquid solubilities is often poor for many partially miscible binary systems.
The new experimental results show that the inability of common, two-constant expressions for the excess Gibbs energy to represent both VLE and LLE data is fundamental and not due to uncertainties in the VLE data. However, some of this inaccuracy may be attributed to the uncertainties in the LLE data. More LLE data are needed to evaluate further the available excess Gibbs energy equations. Acknowledgment The authors are grateful to the National Science Foundation for financial support and to Mr. Gunther Schulze for performing measurements for the systems pyridine-water and piperidine-water. Nomenclature P = total pressure, bar Pi'= vapor pressure of component i, bar R = gas constant T = absolute temperature, K ui = liquid molar volume of component i, cm3/mol x i = liquid mole fraction of component i y, = activity coefficient of component i y,* = activity coefficient of component i at infinite dilution 4i = fugacity coefficient of component i 4; = fugacity coefficient of pure component i at its saturation pressure Literature Cited Abrams, D. S.; Prausnk, J. M. A I C W J . 1975, 27, 116. Eckert, C. A.; Newman, B. A.; Nlcolaides, G. L.; Long, T. C. A I C E J . 1981, 27, 33. Gautreaw. M. F.; Coates, J. A X E J . 1955, 1 , 496. Gmehllng, J.; Onken, U. "Vapor-Uquid Equlilbrium Data Coilectlon";MCHEMA, Frankfurt, 1977; Vol. 1, Parts 1-7. Hayden, J. G.; O'Connell, J. P. Ind. Eng. Chem. 1975, 74, 209. Landauer, A.; Uchtenthaler, R. N.; Prausnltz, J. M. J . Chem. Eng. Cbte 1980, 25, 152. Leroi, J. C.; Masson, J. C.; Renon, H.;Fabrles, J. F.; Sannier, H. Ind. Eng. Chem. Process Des. Dev. 1977, 16. 139. Lobien, 0. Ph.D. Dissertation, Unhrersity of California, Berkeley, 1980. MI, I.C o k t . Czech. Chem. Commun. 1972, 37, 366. Newman, 8. A. Ph.D. Dissertation, Unhrersity of Illlnob, Urbana, 1977. Nlcolaldes, 0. L.; Eckert. C. A. Ind. Eng. Chem. F-m. 1078. 17, 331. Nlcolaides, G. L. Ph.D. Dlssertatlon, Unhrersity of Illinois, Urbana, 1977. Null, H. R. "Phase Equlllbrlum in Process Design"; WHey: New York. 1970 Chapter 5. Ratcliff, G. A.; Chao. K. C. Can. J . Chem. Eng. 1989. 4 7 , 148. Renon, H.;Prausnltz, J. M. A I C M J . 1966. 74. 135. Rlchon, D.; Antolne, P.; Renon, H.; Ecole des Mines, Paris. France; prhrate communlcation, 1979. Santacesarla, E.; Berlendls, D.; Cava, S. Flu& phase Equuib. 1979, 3, 167. Schrelber, L. B.; Eckert, C. A. Ind. fng. Chem. pra'ess Des. Dev. 1971. 70, 572. Seldell, A. "Solubilittes of Organic Compounds", 3 rd ed.; D. Van Nostrand Company, Inc.: New York, 1941, Vol. 2. Stephen, H.;Stephen, T. "Soiublbs of Inorganic and Organlc Compounds"; Macrnlllan: New York, 1983; Vol. 1. van Laar, J. J. 2.phvs. Chem. 1910, 7 2 , 723. Wilson, 0 . M. J . Am. Chem. SOC.1964, 86. 127
Received for review February 2, 1981 Accepted November 2,1981
