Pore-Size Distribution by a Rapid, Continuous FIow Method RAYMOND M. CAHEN and JOSEPH
E. M.
MARECHAL
labofina S. A. (Centre de Recherches du Groupe Petrofina), 98-7 00, chauss6e de Vilvorde, Bruxelles 72, Belgium MARC P. della FAILLE and JOSE 1. FRlPlAT laborafoire de Chimie MinBrale, Agronomic lnstitute of the University, Heverlee, louvain, Belgium
b A new method is described for the determination of nitrogen desorption isotherms. The technique involves passing a mixture of 15 to 20% nitrogen in helium over the sample cooled in liquid nitrogen at a total pressure of 4.000 to 5.000 mm. of Hg causing the nitrogen partial pressure to approach its liquefaction pressure, and nitrogen to b e adsorbed by the sample. By lowering the total pressure in a continuous and steady way the partial nitrogen pressure is also lowered, the adsorbed gas. is progressively desorbed, and the amount of nitrogen evolved is recorded as a function of pressure. The continuous recording of the desorption isotherm requires a period of time from 1 to 3 hours according to the nature of the sample.
M
for t,he pore-size determination of pulverulent substances have drawn the attention of experimentors for a number of years ( I , 5 , 7 , 10, 12, 19-21, 23, 25). The practical applications of such determinations are numerous-Le., studies of catalyst action, diffusion problems in catalysis, ceramics, geology, wood and pressed materials, cement, fertilizers, textiles, leather, etc. The conventional experimental process is based on the volumetric determination of the adsorption or desorption isotherm. The gases most frequently used are nitrogen, argon, and krypton, their corresponding isotherms being determined, respectively, a t - 196' C., -183" C., and -183' C. These methods are time-consuming and require relatively specialized operators. Attempts were made to determine the complete adsorption and desorption isotherms more rapidly. The methods of Ballou and Doolen (4, Haley ( I 5 ) , Lange ( I 6 ) , Numinco-Orr (18)) and Sandstede and Robens (22) should be considered. All of these methods except that of Lange reproduce more or less mechanically the series of operations manually done in the conventional volumetric apparatus and the isotherm plot is essentially discontinuous. As far as the spec,ific surface area deterETHODS
mination alone is concerned where only three points of the isotherm need to be measured, the technique developed by Nelsen and Eggertsen (I7 ) has become conventional and is being commercialized. On the other hand, Gregg and Stock ( I S ) , Eberly ( I I ) , and Stock (24) have shown that it is possible to determine a part of a hydrocarbon or ammonia adsorption isotherm by a continuous flow method. The method consists of transporting a known quantity of adsorbate through the outgassed adsorbent by means of an inert, nonadsorbable carrier gas. After saturation, the adsorbed material is eluted by the pure carrier gas. Attempts made here in this direction have unfortunately shown that the method is practically inoperative because of the desorption characteristics of the type IV isotherm ( 6 ) ,and because of the large dead volume correction i t requires. Another method, developed by Ritter and Drake (21))is based on the penetration of a nonwetting liquid, such as mercury, under pressure. An automatic mercury penetrometer was devised by Guyer ( 1 4 ) and commercialized. With this technique it is necessary to produce very high pressures; for pores of 150A. diameter, a pressure of 1000 kg./cm.2 is required. For this reason this method is better suited for pore-size measurement in the 150- to 150,000-A. diameter range. This paper describes the principles of a method based on the continuous and automatic determination of a desorption isotherm and reports the rapid experimental technique derived therefrom. THEORETICAL
An adsorption isotherm is a plot of the quantity of gas adsorbed per unit mass us. pressure a t one temperature. Relative pressures, P / P o , are generally used, that is, the ratio of equilibrium pressure, P , to the saturating vapor pressure, Po, a t this temperature. In sumrn,zry, there is an independent variable, P/Po, and a dependent variable, V , which is the adsorbed volume per unit weight.
The desorption isotherm determination implies that the sample will be saturated a t a relative pressure close to unity and that, by decrements, the pressure will be progressively brought toward zero. The corresponding volumes of the gas desorbed are simultaneously measured. I n practice, however, for the calculation of pore-size dist'ribution, it is not necessary to lower PIP0 below 0.15, a t least when nitrogen is used as adsorbate gas. The V = j ( P l P o ) functions generally group themselves into five types as classified by Brunauer (6), of which types I1 and IV are the most frequent. Considering the relative pressure region where the decrease is being made, the isotherms show that the desorbed volumes can vary considerably. The higher the derivative, d V / d (PIPo), the greater the volume of gas desorbed in the interval, d ( P l P o ) . I n other words, the relative pressure range corresponding to the steepest part of the isotherm is also relative to a maximum of probability in the pore-size distribution spectrum. The desorption isotherm can theoret:cally be obtained continuously, either by a progressive elution of the adsorbed gas using a physically unadsorbed carrier gas, or, by gradually lowering the partial pressure of the adsorbate gas contained in constant concentration in the carrier sweeping the sample. The first procedure is very difficult to apply, whereas the second one has been entirely successful. The principle is very simple. A helium-nitrogen mixture of nitrogen mole fraction, y, close to 0.15, sweeps a given mass of sample cooled to - 196" C. The total gas pressure, Pt, over the sample is raised until the relative pressure, Pt y/Po, approaches unity. The helium-nitrogen mixture is continuously monitored by a conventional system, such as a katharometer. When equilibrium is attained throughout the system as indicated by a constant base line of the recording bridge, the sample is assumed to be saturated by nitrogen a t a relative pressure close to unity. The relative pressure, P / P o , is then progressively lowered to 0.15 by bringVOL. 37, NO. 1, JANUARY 1965
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133
F------,
REFERENCE LINE
EXPERIMENTAL
-
CALIBRATION LINE
Figure 1 .
Desorption apparatus
A : PzOb or cold-trap; B: high precision pressure regulator; C: needle valves; D: 3-way valves; E : pressure recorder; F : ballast reservoirs; G: sample tubes; H: filter containing nttings; I : dual 4 - w a y rotary switch valve; J: thermal conductivity detector bloc; K : gas sampling valve; I: bubbler; M: measurement cell; M1 and M 2 : nitrogen-helium gas mixture reservoirs; N: nitrogen gas reservoir; 0,P: capillary flowmeter,; Q: manostat; R: reference cell; S: relay; T: 2-way salenoid valve; V :
2-way valves
ing the total pressure, Pt, to atmospheric. The function, V , desorbed in f (time) is thus recorded. It can easily be converted into the wanted function V = f (P/Po) provided that the law of decrease of the total pressure, Pt in f (time), is simultaneously known and recorded. Although the principle of this method seems simple a t first sight, its practical realization encounters a number of difficulties. The principal ones are caused by diffusion phenomena in the sample mass. The gradual decrease of the total pressure must be slow enough that the volume of gas desorbed be small with respect to the desorption time interval. Thus the critical part of the isotherm is where the slope of the function V = f (PIPo) is the steepest. I n an interesting study by a conventional automated method Ballou (2) recently noted that valid data on catalysts of median pore radius greater than 100 A. can be obtained by filling or emptying less than 0.7% of the pore volume per minute. Data on catalysts of smaller pore size can be obtained a t higher rates. With the type of apparatus described here, the continuous recording of the desorption isotherm requires a period of from 1 to 3 hours according to the nature of the sample. If this period of time is compared to that required by the conventional units requiring from one to several days, the improvement is considerable. Furthermore, the very simple apparatus does not present any of the difficulties encountered by the attempts to automatize the conventional method. I n order to compute the desorption isotherm from the recorded diagram it is 134
I n the apparatus, shown schematically in Figure 1, M l and M2 are reservoirs containing nitrogen-helium mixtures, respectively, of about 5% and 20% nitrogen. ,ill the gases used are of 99.993, purity and their water content is less then 5 p.p.m. I t is essential that all traces of water be eliminated from the gas stream (8). Either the Ml or the A12 mixture is directed by the 3-way valve, D1, into the system. Passing through either a glass-bead packed coldtrap or a P206packed tube, A, the gas stream is split and monitored, on the reference side, by a high precision pressure regulator, B, from which it goes through the reference cell, R , of a Gow-Mac, type TR-11-B, thermal conductivity detector bloc, J , maintained a t room temperature. On the measurement side, the gas flow is controlled by needle valves, C1 or C2, and the pressure is recorded b y an absolute pressure recorder, E. Different lengths of tubing, F 1 , F2, and F 3 ,
ANALYTICAL CHEMISTRY
necessary to calibrate the ordinate, that is, to determine the correlation between the recorder-pen deflection and the desorbed gas volume at S.T.P. This is done by introducing known volumes of nitrogen into the carrier gas according to methods universally applied in gas chromatography, and by integrating the corresponding peak surfaces. A recording manometer simultaneously gives the abscissa data, that is the variation of the total pressure, Pt, with time. From the isotherm plot, pore-size distribution is calculated by one of the conventional methods (6, 10, 20, 96). At this stage, data from the isotherm can be transferred to punch cards for pore-size distribution calculation by a digital computer (3); but a simple examination of the recorded diagram already gives an approximate idea of the most probable maxima which will be found in the pore spectrum. As a matter of fact, these correspond to maximal gas volumes desorbed per time unit. By the use of a second gas mixture, it is possible to cross-check and to extend the desorption isotherm down to a relative pressure of 0.050; the specific surface area of the sample can then be calculated by the conventional BET method. Whatever the final relative pressure will be, it is always necessary to determine the quantity of gas remaining adsorbed a t this pressure. Therefore, as soon as the recorder pen has returned to its equilibrium base line, the liquid nitrogen bath is removed from the sample tube and the remaining gas volume is computed from the corresponding desorption p e a k
liquid nitrogen bath removed
16i I
7
b
start Figure 2.
Desorption diagram
connected by 2-way valves, V1 and V 2 , form a reservoir of variable volume which allows the gas mixture to flow through the measurement line when 3way valve, 0 2 , is closed. The sample is placed in a U tube, G, joined to' the system by means of fittings, H , which contain fine-mesh metal gauze to prevent the sample from being accidentally projected into the apparatus. A dual 4-way rotary switch calve, I , monitors the flow either through one of the 2 sample tubes, GI or G2, or through the calibration line and the gas sampling valve, K . From the sample tube, the gas passes through a solenoid valve, T, and needle-valve, C 2 , to the measurement cell, M ,of the detector bloc, J . The gas flow is measured by means of tR-o identical, dibutylphthalate-filled capillary flow-meters, 0 and P. h manostat, &, similar to the one described by Coulson and Herington (9) activates the relay, S,and the 2-way solenoid ialve, T , thus maintaining the gas flow automatically constant in the meaiureinent cell when the pressure changes in the system. Keedle valve, C2, dampens any pressure shocks and regulates the flow when solenoid valve contro! is not needed. Tubing is of l/4-inch 0.d. except for the lines leaving the sample up to the measurement cell, *If, which are of or inch 0.d. in order to reduce dead space. Procedure.
IVI U
Figure 3. graph.
Alternate apparatus by modification of a commercial gas-chromato-
PZOSor cold trap; 6 : precision pressure regulotors; C: needle valve; D : 3-way valve; E: transmitting manometer; F: ballast reservoir; G: sample tube; H: filter containing fittings; J : gas chromatograph; K: gas sampling valve; M: measurement cell; M1, M 2 : nitrogen-helium gas mixture reservoirs; N: nitrogen gas reservoir; R: reference cell; U: flowmeter; V : 2-way valve; X : soapfilm flowmeter A:
SAMPLE PREPAR.4TIOX.
T h e sample of material t o be examined i q crushed a n d sieved to a particle size of 40- to 100-mesh. If the material i- too finely powdered it is advisable to agglomerate it b y means of a laboratory press, a n d to crush and sieve it afterward. hgglomeration sometimes changes t h e pore spectrum of certain solids. I n this case the sample can be maintained in the tube by packing it with glasswool pads. Coarser samples and even little fragments of porous minerals can also be treated, but the diameter of the sample tube should then be changed accordingly. The weight of the sample is chosen so that the maximum amount of nitrogen desorbed from the sample per unit time is not greater than the volume of nitrogen introduced during the same time period from the largest calibration tube of the gas sampling valve. OUTGASSING. The main advantage of the static, volumetric method is that outgassing is carried out under vacuum. Here this is not the case, the samples are heated at atmospheric pressure under gas flow. The temperature and the duration of heating must be established according to the nature of the sample. For silica, alumina, and silica-alumina a pretreatment in a muffle oven a t 450" to 500" C. for 1 hour prior to the outgassing at 350' C. under gas flow for 1 hour in the apparatus seems to be sufficient. The outgassing can be followed directly on the recording potentiometer, or better, on an electrolytic hygrometer branched a t the outlet of the apparatus. By means of valve, C1, and regulator,
. RELATIVE
PRESSURE p i p ,
Figure 4. Nitrogen desorption isotherms a t -196" C. as determined by the conventional static method and the new dynamic method Plain liner: conventional static method Dashed lines: new dynamic method Dotted lines: dynamic method, alternate apparatus A: Alumina base desulfurization catalyst 6: Silica-alumina cracking catalyst C: Chrysotile asbestos 4T30JM D: Sahara Shale (core fragments)
VOL. 37, NO. 1, JANUARY 1965
135
B, a steady flow is established a t near atmospheric pressure in the system and the simple is outgassed under the preestablished conditions. ADSORPTION.By closing valve, C2, high pressure (about 4.000 mm. of H g for a 207, nitrogen concentration in the gas mixture) is established in the sample tube. Steady and identical flows (30 to 50 ml./minute) as indicated by the flowmeters, 0 and P , are reestablished by regulator, B, and valve, C2. The sample tube is cooled in a liquid nitrogen bath and shortly thereafter the adsorption of nitrogen from the gas mixture is indicated by a peak on the recorder chart. I t is essential for the recorder pen to return to its initial base line which must remain steady; only then is adsorption complete. DESORPTION.The solenoid valve control is switched on, and valve, 0 2 , is turned toward regulator, C1; a t the same time, the chart power of pressure recorder, E , is turned on. For very slow pressure-drop rates, valves, V1 and V 2 , remain open; for faster rates, either, V1 or V 2 , can be closed. As valve, C1, has previously been set to monitor the flow a t near atmospheric pressure, practically no gas will enter the measurement line through it at this moment. The pressure therefore steadily drops between valves, C1 and C2, and nitrogen is evolved from the sample causing the appearance of a wide desorption peak on the recorder chart. From time to time, valve, C 2 , has to be readjusted to maintain a steady flow. At the end of the desorption step, when pressure is near atmospheric, valve, C2, is completely open and, C1, again monitors the flow in the measurement branch. When the recorder pen has returned to its base line, the liquid nitrogen bath is removed from the sample tube causing the desorption of the remaining nitrogen and the appearance of a nearly symmetrical desorption peak. CALIBRATION.Calibration by means of gas-sampling valve, K , is standard procedure. Dead volume retention time ( D V ) must be measured and the necessary correction is made on the recorded diagram as shown in Figure 2. GAS-STIXTURE ~ A L Y S I S . The nitrogen fraction, y, of the gas mixtures is determined on the same apparatus by injecting identical volumes of the gas mixtures and pure nitrogen into pure helium carrier. Adsorption Isotherm Determination. Aidsorption isotherms have been determined on the same apparatus by slowly raising the total pressure over the sample via valves, C1 and C 2 . Satisfactory results have been obtained in some cases. For type I1 and 111 adsorption isotherms ( 6 ) , however, where the volume of gas adsorbed a t high relative pressures rises asymptotically with pressure, the static and the dynamic iqotherms do not coincide as well. h s satisfactory pore-size distribution data are obtained from the desorption isotherm, the adsorption technique has not been further investigated. 136
ANALYTICAL CHEMISTRY
g100
:w:
E 80 9
3
z
3 60 40
20
0
Figure 5.
50
100
150
200
Pore-size distributions calculated from the isotherms of Figure
4
Plain lines: conventlonal statlc method Dashed lines: new dynamic method Dotted lines: new dynamic method, alternate apparatus A: Alumlna base desulfurization catalyst B : Silica-alumina cracking catalyst C: Chrysotile asbestos 4 T 3 0 J.M. D: Sahara Shale (core fragments)
Alternate Apparatus. I n the apparatus described above, constant pressure is maintained in the thermal conductivity detector since for certain katharometer designs, pressure changes have an effect on the output signal. However, for some conductivity cells this effect is very small and can be accounted for by suitable calibration. This was the case for the apparatus, schematically shown in Figure 3, which was constructed by slight modification of a commercial gas chromatograph. U p to trap, d, the flowsheet is the same as for the first apparatus. Gas coming from one of the reservoirs, M1 or M 2 , is directed by 3-way valve, D1, toward pressure regulators, C1, and C2, through 2-way valve, V , reservoir, F , and into the gas chromatograph, J , (DAM, type UGIXE M T 60) where the sample contained in tube, G, is placed between the two detection cells, R and Ji. At the exit of the chromatograph, gas pressure is constantly measured by a transmitting manameter, E ; the gas passes then through needle valve, C , a ROTA flowmeter, C , and leaves through soapfilm flow-meter, X . A double channel recorder simultaneously records the pressure drop and the chromatograph bridge potential. A special peak area calibration factor has only to be determined a t different pressures as the conductivity response varies with pressure in this case. The
description of this apparatus shows t h a t conventional pressure-insensitive gas chromatographs can easily be adapted to pore-size distribution measurement. CALCULATION OF THE DESORPTION ISOTHERM
A typical dessrption diagram is shown in Figure 2, where the wide peak corresponds to pressure-drop desorption and the narrow one to temperature-rise desorption a t atmospheric pressure. Making allowance for D V , the pressure-drop peak is divided into time intervals of 2 or 3 minutes. Each interval corresponding to a given pressure as recorded by manometer, E , is integrated and the area of each interval is converted into nitrogen volume by means of the calibration data. The narrow peak is also integrated and the volume of nitrogen it represents corresponds to the amount desorbed at atmospheric pressure. A very interesting improvement is a printing integrator connected to the potentiometric recorder. A timing slstem automatically commands a print impulse so that the 2 or 3 minutes integrals are immediately available. RESULTS
Figure 4 represents isotherms obtained by the static and flow methods. Figure 5 shows the corresponding pore distribution curves as calculated by tha
Cranston and Inkley method (10). The time required to establish the isotherms in Figure 4 was from 50 to 75 minutes. The method described is not restricted to surface area and pore size distribution determinations. It should also provide a convenient means of comparing adsorption capacities and even adsorption rates of various solids and adsorbates. ACKNOWLEDGMENl
The authors acknowledge the work of
G. Saerens, who built the first prot’otype of the instrument and collected some of the original data. LITERATURE CITED
(1) Andenon, J. S., Z. Physik. Chem. (Lezpzzg) 88, 191 (1914). ( 2 ) Ballou, E. V., ASAL. CHEV.34, 233 (1962). ( 3 ) Ballou, E. I-., Barth, R. T., ildzlances
A-0. 33, p. 133 ACS, Washington (1961). (4) Ballou, E. V., Doolen, 0. K., AKAL. CHEV.32, 532 (1960). (5) Barrett, E. P., Joyner, L. G., Halenda, P. P., J . A m . Chem. SOC.73, 373, (1951). (6) Brunauer, S., “The Adsorption of Gases and Vapors”, Vol. I, p. 150, Princet,on University Press, Princeton, N . J., 1943. ( 7 ) Burdine, N. T., Gournay, L. S., Reichertz, P. P., Trans. Am. Inst. Jfining Met. Engrs. 189, 196 (1950). (8) Cahen, R. hI., >\lar&chal, J., ANAL. CHEM.35, 259 (1963). (9!, Coulson, E. A,, Herington, E. F. G., Laboratory Distillation Practice” p. 37, Interscience, S e w York, 1958. (10) Cranston, R. W., Inkley, F. A., “Advances in Catalysis,” IX, p. 143 Academic Press, Sew York, 1957. (11) Eberly, P. E., Jr., J . Phys. Chem. 6 5 , 1261 (1961). (12) Gilchrist, J. D., Taylor, R., J . Inst. Fuel 24, 207 (1951). (13) Gregg, S. J., Stock, R., “Gas Chromatography 1958’’ D. H. Desty, ed., p. 90, Butterworths, London, 1958. (14) Guyer, A , , Jr., Bohlen, B., Guyer, A., Helv. Chim. Acta 4 2 , 2103 (1959).
in Chem. Ser.
(15) Haley, A . J., J . A p p l . Chem. ( L o n d o n ) 13, 392 (1963). (16) Lange, K. R., J . Colloid Sci. 18, 65 (19g2). (17) Selsen, F. >I., Eggertsen, F. T., ANAL.CHEM.30, 1387 (1958). (18) Numinco-Orr, “Surface .4rea--Pore Volume Analyser,” Numec Instruments and Controls Corp., Apollo, Pa. (19) Oulton, T. D., J . Phys. Colloid. Chem. 52, 1206 (1948). (20) Pierce, C., J . Phys. Chem. 57, 149 (1953). (21) Ritter, H. L., Drake, L. C., IND. ENG.CHEM.,ANAL.ED. 17, 782 (1945). (22) Sandstede, G., Robens, E., Chem. Ing. Tech. 32, 413 (1960). (23) Shull, C. G., J . A m . Chem. SOC. 70, 1405 (1948). (24) Stock, R., ANAL. CHEM.33, 966 (1961). (25) Wheeler, A., “Catalysis”, Vol. 11, p. 105, Reinhold, New York, 1955. RECEIVEDfor review June 8, 1964. Accepted August 28, 1964. Permission to publish this paper was granted by LABOFINA directors. ETERNIT S. A . contributed to part of this study.
Spectrofluorometric Determination of Submicrogram Amounts of Aluminum and Beryllium with 2 - Hy d roxy- 3- na pht ho ic Ac id GORDON
F.
KIRKBRIGHT, T. S. WEST, and COLIN W O O D W A R D
Department o f Chemistry, lmperial College, London, S. W. 7, England
Measurement of the fluorescence intensity a t 460 mk of the blue fluorescent aluminum and beryllium comof 2-hydroxy-3-naphthoic plexes acid provides a rapid method for the determination of aluminum and beryllium down to the 2- and 0.2-p.p.b. levels, respectively. The optimum conditions of pH, reagent concentration, and development time are established; and a study of the effect of a large number of cations and anions is presented. Aluminum and other metal ions may b e prevented from interfering in the beryllium determination by masking with the calcium complex of CDTA (frans-1 ,2diaminocyclohexane tetraacetic acid). Continuous variations, mole-ratio, and slope-ratio studies indicate the formation of a l to l complex between the reagent and aluminum or beryllium. The conditional stability constants for the complexes are evaluated.
M
o m spectrophotometric methods for the determination of aluminurn depend on reaction with 8quinolinol and its derivatives ( 6 ) or the formation of lakes with reagents
such as aurintricarboxylic acid or Eriochrome Cyanine R ( 1 1 ) . White (15, 17, 18) has recently reviewed fluorometric methods. Several sensitive fluorometric methods utilize morin (3,5,7,2’,4‘-pentahydroxyflavone)(16), Pontachrome Blue Black R (sodium salt of 4-sulfo-2-hydroxy-1-naphthylazo2’-naphthol) ( 1 4 ) , S-quinolinol ( 7 ) , salicylaldehyde condensation products ( 9 ) , and various hydroxyazo dyes. Colorimetric and fluorometric methods for the determination of beryllium have been reviewed by Sandell ( 1 1 ) . The fluorometric determination of beryllium with morin has been described by several workers, most recently by Sill etal. (12, I S ) . Cherkesov (2-4) has described the use of 2-hydroxy-3-naphthoic acid for the detection of aluminum and beryllium. He reported that 0.01 p g . of aluminum or beryllium may be detected by formation of blue fluorescent complexes a t p H 3 and above; the reagent itself exhibits a green fluorescence. This paper reports the spectrofluorometric investigation of the reaction for the determination of traces of aluminum and beryllium.
EXPERIMENTAL
Apparatus. Fluorescence measurements were made with a double monochromator spectrofluorometer (Farrand Optical Co., Catalog NO. 104244) fitted with a 150-watt xenon arc lamp (Hanovia Division, Catalog S o . 901 C-1) and R C h IP 28 multiplier phototube, and equipped with a Honeywell - Brown recorder. Fused quartz cells (10 X 20 X 50 mm.) were used throughout. To obtain the maximum sensitivity compatible with good definition of maxima, 5- and 20-mp band width slits were used in the exciting and analyzing monochromators, respectively. A 7-54 filter (transmittance >75?4 over the range 275 to 375 mp) was used for the exciting radiation and a 3-73 filter (transmittance >75% above 455 niw) for the emission. To increase the sensitivity for beryllium, the 7-54 filter \%-as omitted. pH measurements were made with a Vibron pH meter, Model 39A (Electronic Instruments, Ltd., Richmond, Surrey, England). Reagents. Standard aluminum solution was made by dissolving 0.4744 gram of potassium aluminum sulfate, Al,(SO,),~KsS04 24H20 (anVOL. 37, N O . 1 , JANUARY 1965
* 137
