I n d . Eng. Chem. Res. 1988,27, 2105-2110
2105
Absorption of Carbon Monoxide with Reversible Reaction in Cuprous Chloride Solutionst R a g h u r a j V. Gholap and Raghunath V. C h a u d h a r i * Chemical Engineering Division, National Chemical Laboratory, Pune 41 1 008, India
The kinetics of absorption of carbon monoxide in an aqueous cuprous chloride solution in the presence of NH4C1 and ammonia was studied. The reaction was found to occur in fast reaction regime in the range of variables studied. The reaction was found to be second order with respect to cuprous chloride in both systems. The order with respect to CO was found to be 1.5for the CO-CuCl-aqueous NH4C1 system, whereas a change in the reaction order with temperature was observed for the CO-CuC1-aqueous NH3 system. The forward and reverse reaction rate constants for both systems have been obtained using the theory of mass transfer with reversible chemical reaction in a fast reaction regime. The rate of absorption versus temperature passed through a maximum for the CO-CuC1-aqueous NH3 system. This unique trend is a result of the reversible reaction in which the activation energy of the reverse reaction is greater than that of the forward reaction. Absorption of carbon monoxide is important in the purification of carbon monoxide in its removal from other gaseous streams. A well-known process of CO purification involves absorption of CO in ammoniacal cuprous chloride solutions (Kohl and Riesenfeld, 1985, Ledon, 1986). In this process, CO reacts reversibly with copper(1) complexes to produce carbonyl species. Generally, CO absorption is carried out at ambient temperature and high pressure, while the decomposition of the carbonyl complex occurs at lower CO pressure and higher temperature. Thus, the reversibility of this reaction has been commercially utilized in purification of carbon monoxide. The stoichiometric reaction can be described as follows:
co + CUCl Y [Cu(X),CO]+C1-
6)
where X represents NH4Cl or aqueous NH,. The literature on this reaction is very scanty, and there are only a few reports on the kinetics of this reaction. The earlier studies by Van Krevelen and Baans (1950) and Sriram and Joshi (1985) report rate data only up to 30 OC and atmospheric pressure. Sriram and Joshi have reported the kinetics of this reaction considering it as an irreversible reaction, which may not be true for this system. It is thus observed that there has been no report on the kinetics of this reaction covering higher CO partial pressures and temperatures. It was, therefore, thought desirable to study the kinetics of absorption of CO in cuprous chloride solutions in the presence of NH4Cl and aqueous ammonia under conditions of practical relevance. It was also the objective of this work to investigate the mechanism of absorption considering the complexities of mass transfer with a fast, reversible reaction. Some interesting trends on the effect of temperature on the rate of absorption have been discussed. Theory Absorption of CO in cuprous chloride solutions (as described by reaction i) is a case of gas absorption with a reversible chemical reaction of the following type:
Being a fast reaction, it is important to consider the role of mass transfer in the absorption-reaction process. Theoretical analysis for gas absorption with a fast rever-
* Author to whom correspondence should be addressed. NCL Communication 4349.
0888-5885/88/2627-2105$01.50/0
sible reaction has been reported by Onda et al. (1970),for the reaction scheme, A(g) B(1) + E(1) + F(1). They reported analytical solutions for the enhancement factor @A based on the f ilm theory. Following their analysis, the enhancement factor (@A) for the present case (reaction 1) is given by
+
(")( ); ( + )( 1
@A
=
+
+
m + l
p
rE tanh M 2 1 / 2 )
1
TM2'f2
m+l where
M2 = M [
; I n[
1
--]
+m + l T P+lrE
(3)
(4)
and
K2e?-' T=bin
The enhancement factor
(@A)
(5)
is defined as RA
@A
=
KLaA*
where RA represents the rate of absorption of CO, kmol/ (m3.s);kLu, the overall mass-transfer coefficient, l/s; and A* the concentration of dissolved CO at the gas-liquid interface, kmol/m3. The above set of equations are applicable for the fast reactions and the following condition must be satisfied: @A
2 3
(7)
Experimental Section The absorption experiments were carried out in a mechanically agitated pressure reactor of 0.6-L capacity (Parr Instruments Co., Moline, IL). This reactor was provided with automatic temperature control, variable stirrer speed, and a thermocouple. A scheme of the experimental setup used is shown in Figure 1. The absorption experiments were carried out at a constant desired pressure, and the progress of reaction was followed by observing a change in pressure in the reservoir vessel. Since the system under 0 1988 American Chemical Society
2106 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
GAS
VESSEL
GAS
REGULATOR
GbS
INLET
S A M P L I N G VALVE PRESSURE
iHDICATOR
STIRRER TEMPERbTURE
@
1L-
ul
GAS
PROBE
VENT
@
COOLING
WATER
CUT
@
COOLING
WATER
IN
a
DIP
TUBE
Figure 1. Schematic diagram of experimental setup.
consideration involves a very fast reaction, a pressure transducer with high sensitivity was used to record the pressure in the reservoir vessel. In a typical experiment, a known amount of solution with desired concentrations of CuCl and NH4C1or aqueous NH3 was charged into the reactor, already flushed with nitrogen. The contents were then heated to a required temperature. After the required temperature was attained, the gas phase in the reactor was carefully flushed with CO. During this operation, the stirrer was put off so that absorption of CO was negligible. The reactor was then pressurized with CO, and the experiment was started by switching the stirrer on. The progress of the reaction was followed by observing the pressure change with time in the reservoir vessel. It was observed that before the stirrer was put on, virtually no absorption of CO occurred. Following this procedure, several experiments were carried out in which pressure (in the reservoir) versus time data were obtained. During an experiment, the pressure in the reactor was kept constant. The initial rates were calculated from the observed data on consumption of CO as a function of time. Analysis of copper(1) in the initial solution was carried out by using a volumetric method described by Vogel (1975). The materials used, such as cuprous chloride, NH4C1,and aqueous ammonia, were of more than 99% purity. The purity of CO used was greater than 99.7% as tested by gas chromatography. Physicochemical Properties and Mass-Transfer Parameters Physicochemical properties such as diffusivities and solubilities are required in the analysis of the rate data using eq 2-6. The solubility of CO in water, A*, is expressed by Henry's law as A* = Pi/He' (8) The values of He' for the CO-water system were obtained from the data reported by Dake and Chaudhari (1985). The data on the CO-water system were corrected for the presence of ions, using the following relationship suggested earlier by Van Krevelen and Hoftijzer (1948): log [ H e / H e ' ] = hlIl + hzIz + etc. (9) The corrected values of solubilities using the above equation were used in the calculations and are presented in Tables I and 11. The diffusion coefficients of CO in water were calculated by using the Wilke-Chang (1955) equation, while the diffusi5ties for the CuCl-water system were obtained from the data reported by Tamhankar and Chaudhari (1979). The values were corrected for change in viscosities at different concentrations of ions. The mass-transfer parameters, kLa and a , were determined by a chemical method using catalytic oxidation of the sodium sulfite system described by Linek and Vacek
Table I. Experimental Data on the Absorption of CO in CuCl-NHdClSolutions" partial pressure 103~*, of c o , 103~*, IOBO, kmol/ run atm kmol/m3 kmol/m3 (m3*s) $A 283 K Data 2.07 5.27 1 6.8 4.520 0.86 2.40 6.11 2 6.8 4.507 1.00 3.40 8.70 4.490 1.35 3 6.8 4.11 10.56 4.475 1.60 4 6.8 5.30 13.67 4.454 2.00 5 6.8 6.30 16.32 4.436 2.30 6 6.8 2.45 12.62 2.23 2.00 7 3.4 13.06 7.60 6.68 2.00 10.2 8 12.38 9.60 8.91 2.00 13.6 9 10 11 12 13 14 15 16
6.8 6.8 6.8 6.8 4.08 9.52 12.25
4.70 4.66 4.63 4.59 2.78 6.47 8.34
303 K Data 0.7 1.5 1.9 2.7 1.9 1.9 1.9
1.25 3.05 4.10 6.45 2.34 5.73 7.13
17 18 19 20 21 22
6.8 6.8 6.8 6.8 4.08 12.25
4.96 4.94 4.92 4.88 2.95 8.85
333 K Data 1.10 1.35 1.6 2.40 1.6 1.60
1.276 1.62 1.95 2.28 1.05 3.80
a
2.94 7.27 9.84 15.61 9.36 9.84 9.50 2.74 3.50 4.22 7.15 3.80 4.56
Concentration of NH,Cl, 2 kmol/m3; agitation speed, 15 Hz.
(1981). For this system, it is observed that, for a certain range of catalyst (Co2+)concentration, oxygen absorption rate is independent of catalyst concentration and hence gas-liquid mass transfer is a major controlling resistance. The rate data in this region can be used for determination of kLa. Similarly, at higher concentration of the catalyst, the rate shows half-order dependence on the catalyst concentration, and this represents a fast reaction regime, allowing us to determine the interfacial area, a. This approach was used to experimentally determine kLa and a for the equipment used in this work. The data are shown in Table I11 for 30 "C. The values of izlL calculated by dividing kLa by a are also given in Table 111. The values of kLa and kL for other temperatures were corrected for changes in diffusivity. Results and Discussion Experimental data on the rate of absorption of CO in cuprous chloride solutions were obtained both in the presence of NH4Cl and aqueous NH3. The rates were calculated from the observed data on consumption of CO as a function of time. Some examples of the experimental results are shown in Figures 2 and 3, as plots of CO consumed versus time. The initial rates of absorption were calculated from the slope of such plots in the initial region. Several experiments were carried out at different partial pressures of CO, concentrations of cuprous chloride, agitation speeds, and temperatures. The ranges of variables covered are given in Table IV. The analysis of the results is discussed below. Absorption of CO in Aqueous CuCl Solutions Containing NH4Cl. The experimental rate data for this system are presented in Table I. Also, Figures 4-6 present the effect of agitation speed, partial pressure of CO, and concentration of cuprous chloride on the rate of absorption at different temperatures. The rate of absorption was found to increase with increases in CO partial pressures and cuprous chloride concentrations but decreases with
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2107 Table 11. Experimental Data on the Absorption of CO CuCl-NH., Solutions" partial pressure 103~*, 103~*, 10Bm kmol/ of co, run atm kmol/m kmol/m3 (m34 283 K Data 1 4.08 1.525 2.7 3.25 2 4.08 1.505 3.8 4.50 3 4.08 1.493 4.5 5.42 4 4.08 1.484 5.0 6.20 5 4.08 1.462 6.2 7.50 6 4.08 1.450 6.9 8.20 7 4.08 1.431 8.0 9.60 8 6.80 2.488 4.5 6.70 9.52 3.483 4.5 7.72 9 10.88 3.981 4.5 8.18 10 13.60 4.976 4.5 8.98 11
in
+A
24.53 34.36 41.56 48.02 58.96 65.08 77.11 30.97 25.47 23.64 20.74
0
a0
40
120
TIME,S
12 13 14 15 16 17 18 19 20 21 22 23 24 25
4.08 4.08 4.08 4.08 4.08 4.08 4.08 4.08 2.72 6.80 9.52 12.24 13.60 16.33
298 K Data 1.600 1.7 1.565 3.1 1.545 4.0 1.540 4.5 1.510 5.65 1.500 6.00 1.480 7.30 1.470 8.20 1.026 4.50 2.566 4.50 3.593 4.50 4.620 4.50 5.130 4.50 6.160 4.50
2.19 4.20 5.35 6.15 7.70 8.20 9.95 11.20 4.90 8.10 9.50 10.80 11.40 12.50
15.38 30.15 38.90 44.87 57.30 61.41 75.54 85.62 53.65 35.46 29.70 26.26 24.97 22.80
26 27 28 29 30 31 32
4.08 4.08 4.08 4.08 2.72 8.16 13.60
333 K Data 1.682 2.6 1.635 4.8 1.605 6.5 1.576 8.0 1.090 4.8 3.270 4.8 5.450 4.8
1.42 3.30 4.95 6.47 2.25 6.13 9.34
9.00 21.50 32.78 43.67 21.93 19.93 18.23
33 34 35 36 31 38 39 40 41 42
4.08 4.08 4.08 4.08 4.08 4.08 6.80 8.16 10.88 13.60
373 K Data 1.813 2.3 1.791 3.3 1.770 4.3 1.760 4.7 1.748 5.3 1.714 7.0 2.933 4.7 3.520 4.7 4.693 4.7 5.867 4.7
0.89 1.54 2.23 2.56 3.05 4.66 4.04 4.80 6.10 7.45
4.91 8.60 12.58 14.54 17.48 27.19 13.76 13.65 12.98 12.70
"Concentration of NH3, 4 kmol/m3; agitation speed, 15 Hz.
Table 111. Results on Overall Mass-Transfer Coefficient, kr.a,and Interfacial Area, a agitation kr.a,"s-l 10-2a,am-l 1o4kr.,*m/s speed, Hz 15.00 0.09 2.8 3.20 11.66 0.054 1.75 3.08 8.33 0.024 0.76 3.15 5.00 0.015 0.47 3.19
" Values obtained by using oxidation of sodium sulfite method. Values obtained by dividing kLa by a. increasing temperature. A decrease in the rate with an increase in temperature can be due to higher rates for the reverse reaction compared to the rates of the forward reaction as the temperature increases. This important aspect is observed for the first time and has been discussed later. The strong dependence of the rate on agitation speed indicates the importance of gas-liquid mass transfer. In order to interpret the regime of absorption, the enhance-
Figure 2. CO consumed versus time plots for CO-CuC1-aqueous NH4Clsystem (partial pressure of CO, 6.8 atm; temperature, 303 K; agitation speed, 15 Hz; concentration of NH4Cl, 2 kmol/m3; liquid volume, 2 x 10"' m3).
S o , kmol/m3 X-0.31 0-0.45
0-0.60 A-0.02
TIME,S
Figure 3. CO consumed versus time plots for CO-CuC1-aqueous NH3 system (partial pressure of CO, 4.08 atm; temperature, 298 K, agitation speed, 15 Hz; concentration of NH3, 4 kmol/m3; liquid volume, 2 x io4 m3). Table IV. Range of Variables Covered in the Absorption Experiments system co-CUClCO-CuCINHACl NH, partial pressure of CO, atm 3.4-13.6 2.72-16.3 CuCl concn, kmol/m3 0.07-0.27 0.17-0.82 NH4Cl concn, kmol/m3 2 NH3 concn, kmol/m3 4 stirrer speed, Hz 5-15 5-15
ment factor, @*,was calculated by using eq 6. These data are also presented in Table I. I t can be seen from these data that the enhancement factor, @*,is greater than 3 in all the cases, indicating that the absorption occurs in the fast reaction regime. Therefore, eq 2-6 can be used to represent the rate data. The values of the forward and reverse reaction rate constants were determined from the experimental rates of absorption by fitting the data to eq 2. The experimental data were fitted by using an optimization program (Marquadt method). It was found that, for m = 1.5 and n = 2.0, the rate data were best repre-
2108 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 10 BO,kmol/m3
i
0-303 K
,
0.15
-333 K
,
0.16
X
u)
E
\ 4 0
*E c)
0 X
4
lY
1
j
0
1
I
5
1
15
10 A G I T A T I O N SPEED,Hz
Figure 4. Effect of agitation speed on the rate of absorption for CO-CuC1-aqueous NH,Cl system (concentration of NH4C1, 2 kmol/m3; partial pressure of CO, 6.8 atm). I
I
1
I
I
l
l
-PREDICTED 0-283K 0-303K X-333K n
0
I
I
I
I
4
I I I I I 10
A* x 10s k m o l / m3
Figure 5. Effect of CO concentration on the rate of absorption for CO-CuC1-aqueous NH,Cl system (concentration of NH,Cl, 2 kmol/m3; agitation speed, 15 Hz).
sented by eq 2. The values of the forward and reverse respectively, were reaction rate constants, kl and kl, evaluated for different temperatures, and these are presented in Figure 7 as an Arrhenius plot. The activation energies for the forward and reverse reactions calculated from the Arrhenius plot were 22.80 and 62.94 kJ/mol, respectively. Here, it is interesting to note that the activation energy of the reverse reaction is higher than that of the forward reaction. In such a case, the rate of absorption is expected to decrease with an increase in temperature, as observed in the present work (see Figure 6). This aspect of the reversible reaction cannot be realized if a simplified irreversible reaction model is considered as proposed in an earlier work (Sriram and Joshi, 1985).
I
I
1
-
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 2109 7
1 I I
-PREDICTED 0-283 K 0-298 K X-333 K
6
In
"E
5
1 E
r
UI
m -
m
E
\ 0
0
4
X
a (L
E
x
m
0
3
x
a
a.
2 0.1
/
Figure 10. Effect of CuCl concentration on the rate of absorption for CO-CuC1-aqueous NHS system (concentration of NH3, 4 kmol/m3; agitation speed, 15 Hz; partial pressure of CO, 4.08 atm).
01
1
I
I
-0
5
10
15
20
14
I
I
BO , k m o l l m 3
SPEED, H z
AGITATION
1
0.4 B o , kmol /m3
Figure 8. Effect of agitation speed on the rate of absorption for CO-CuC1-aqueous NH3 system (concentration of NH3, 4 kmol/m3; partial pressure of CO, 4.08 atm, CuCl concentration, 0.45 kmol/ms).
12
0-0.45 0-0.80
-
C O Pressure, atm.
, ,
4.08 4.08
- PREDICTED
' /AL
I/
11
-
B o , k mol/m3
0-283K, 0-298 K-, X-333K, 6-373K, I
I
I
I
273
0.45 0.45 0.48 0.47 I
I
39 3
Figure 11. Effect of temperature on the rate of absorption of CO for CO-CuC1-aqueous NH3 system. I
4
1
313 35 3 TEMPERATURE, K
I
10
A* x lo3,kmol/m3
Figure 9. Effect of CO concentration on the rate of absorption for CO-CuC1-aqueous NH, system (concentration of NH3, 4 kmol/m3; agitation speed, 15 Hz). Table V. Reaction Orders and Forward and Reverse Reaction Rate Constants for CO-CuCl-NHI System no. 1 2 3 4
temp, K 283 298 333 373
m 0 0.3 1 1
n 2 2 2 2
k,, (kmol/ ms)l-m-n/s 4.65 X lo2 5.52 X lo3 6.00 X lo6 9.00 x 106
k+ s-l 5.17 X 10' 1.41 X lo2 3.33 X lo3 1.00 x 104
sented by eq 2. In order to evaluate the rate parameters for the forward and reverse reactions, eq 2 was used. The optimized values of the reaction orders and the forward and reverse reaction rate constants were evaluated for different temperatures by the method described in the earlier section. The rate parameters are presented in Table V. The effect of temperature on rate constants is shown
1
I 10'I 2.6
2.8
3.0
VT x
3.2
3.4
110' 3.6
io3
Figure 12. Arrhenius plots for CO-CuC1-aqueous NH3 system.
in Figure 12 as an Arrhenius plot from which the activation
energies of the forward and reverse reactions were evalu-
2110 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988
ated as 11.53 and 51.27 kJ/mol, respectively. It is also interesting to note that there is a change in the reaction order with respect to CO partial pressure with temperature (see Figure 9). This could be explained on the basis of a possible change in the rate-determining step in the reaction mechanism. In order to explain this fact, the following reaction scheme is proposed:
+ + CO F= Cu(NH3)3Co+Cl-
CU(NH,)~CI NH, + CU(NH,)~+C~- (loa) Cu(NH,),+Cl-
(lob)
The formation of the complexes of the type Cu(NH,),+Cland Cu(NH3),CO+C1- have been reported in the literature (Clark et al., 1981; Van Krevelen and Baans, 1950). The zero order with respect to CO pressure a t lower temperature is interesting. It probably suggests that the first step (formation of Cu(NH3),+C1- complex) is rate determining under these conditions. On the other hand, the first order with respect to CO pressure at high temperatures indicates that the Cu(NH3)3+C1-complex formation is very fast and the second step, i.e., eq lob, is rate controlling.
k , = forward reaction rate constant [ k m ~ l / m ~ ] ' s-l -~-~ k-, = reverse reaction rate constant, s-l K = equilibrium constant, k l / k _ , K , = (A*)P-m-n/ K k L = liquid film mass-transfer coefficient, m/s kLa = overall gas-liquid mass-transfer coefficient, s-l M = parameter defined by eq 4 M2 = parameter defined by eq 3 m, n, p , q = reaction orders with respect to A, B, E, and F
Pi = partial pressure of CO at the gas-liquid interface, atm q B = &/A* R A = rate of
absorption of CO, kmol/(m3.s) r~ = D E / D A T = parameter defined by eq 5 Greek Symbol c$A
= enhancement factor defined by eq 6
Subscripts i = gas-liquid interface 0 = liquid bulk Registry No. CO, 630-08-0; CuC1, 7758-89-6; NH,CI, 1212502-9;
Conclusions Absorption of carbon monoxide in cuprous chloride solutions, which is a useful system in CO purification/or its removal processes, was studied. It has been observed that the absorption was followed by a fast, reversible reaction in the presence of NH4C1and aqueous NH,. The reaction was found to be second order with respect to CuCl concentration in both systems. The order with respect to CO was found to be 1.5, in the presence of NH4C1,but a change in the order with respect to CO pressure with temperature was found for the ammoniacal CuCl solution. It was interesting to observe a decrease in the rate of absorption with an increase in temperature in a certain range. This observation was made for the first time and is a result of reversible reaction with higher activation energy for the reverse step. The forward and reverse reaction rate constants for both of these systems have been determined using a theoretical model for mass transfer with fast, reversible chemical reaction. Nomenclature A = concentration of gaseous species A (CO), kmol/m3 A* = concentration of A at the gas-liquid interface, kmol/m3 B = concentration of reactant B (Cu'), kmol/m3 b = B/A* D A = diffusivity of A, mz/s DE = diffusivity of E, mz/s E = concentration of reaction product E, [CU(NH,)~CO+C~-] or [Cu(NH,C1)3CO+C1-],kmol/m3 e = E/A* F = concentration of reaction product F, kmol/m3 He = Henry's law constant for solution, atm.m3/kmol He' = Henry's law constant for water, atmm3/kmol hl, h, = solubility factor for ionic species, L/kg I,, I2 = ionic strength, kg/L
NH3, 7664-41-7.
Literature Cited Clark, D. T.; Sgamellotti, A.; Tarantelli, F. "A Theoretical Investigation of the Ground and Core Hole States of [CU(NH~)~CO]+ and [Cu(NH3)&O]+. Models for the Reversible Binding of CO to Cu(1) Complexes". Inorg. Chem. 1981, 20, 2602-2607. Dake, S.B.; Chaudhari, R. V. "Solubility of CO in Aqueous Mixtures of Methanol, Acetic Acid, Ethanol and Propionic Acid." J. Chem. Eng. Data 1985, 30, 400. Kohl, A. L.; Riesenfeld, F. C. Gas Purification, 4th ed.; Gulf Houston, 1985. Ledon, H. Ullmann's Encyclopedia of Industrial Chemistry; Gerhartz, W., Ed.; VCH: Weinheim, F. R. Germany, 1986; Part A5, pp 203-216. Linek, V.; Vacek, V. "Chemical Engineering Use of Catalyzed Sulfite Oxidation Kinetics for the Determination of Mass Transfer Characteristics of Gas-Liquid Contactors". Chem. Eng. Sci. 1981, 36(11), 1747-17.
Onda, K.; Sada, E.; Kobayashi, T.; Fujine, M. "Gas Absorption Accompanied by Complex Chemical Reactions. I. Reversible Chemical Reactions". Chem. Eng. Sci. 1970, 25, 753-760. Sriram, R.; Joshi, J. B., "Kinetics of Carbon Monoxide Absorption in Cuprous Ammoniacal Chloride Solutions". Curr. Sci. 1985, 54(15), 715-719.
Tamhankar, S.S.; Chaudhari, R. V. "Absorption and Reaction of Acetylene in Aqueous Cuprous Chloride Slurries". Ind. Eng. Chem. Fundam. 1979,18(4), 406-412. Van Krevelen, D. W.; Baans, C. M. E. "Elimination of Carbon Monoxide from Synthesis Gases by Absorption in Cuprous Salt Solutions". J. Phys. Chem. 1950, 54, 37@390. Van Krevelen, D. W.; Hoftijzer, P. J. Int. Congr. Chim. Ind., 21st 1948, 168.
Vogel, I. Quantitative Inorganic Analysis, 3rd ed.; Longmans, Green: New York, 1975. Wilke, C. R.; Chang, P. "Correlation of Diffusion Coefficients in Dilute Solutions". AIChE J. 1955, 1, 264-270.
Received for review December 29, 1987 Revised manuscript received June 3, 1988 Accepted July 1, 1988
