agents usually used to limit these interferences with Eriochrome Black T are equally effective with Calmagite. Although large amounts of potassium and the common anions caused no trouble, the presence of large amounts of sodium caused some difficulty, possibly owing to the formation of nonionized compounds of sodium with EDTA or the indicator. This difficulty may be avoided in most cases simply by the use of potassium hydroxide rather than sodium hydroxide
whenever large amounts of acid are to be neutralized prior to the EDTA titration. In general, Calmagite seems to possess enough advantages over Eriochrome Black T to warrant the int,roduction of a new indicator. LITERATURE CITED
W. C., Flaschka, H., Chemist-Analyst 45, 86, 111 (1956); 46,18, 76, 86 (1957).
(1) Barnard, A. J., Jr., Broad,
(2) Diehl,
H., Lindstrom, F., ASAL. CHEM.31,414 (1959). (3) Diehl, H., Ellingboe, J., Ibid., 32, 1120 1960.
(4) Diskant, E., Ibid., 24,1856 (195?). (5) Knecht, E., Hibbert, E., Xew Reduction Methods in Volumetric hnalysis,” p. 78, Longmans, Green, London, 1918. (6) Schmidt, J., Maier, W.,Ber. 64, 767 (1931). (7) Schwarxenbach, G., Biedermann, TI-., Helv. Chim. Acta 31, 678 (1948). RECEIVEDfor review April 18, 196!). Accepted June 6, 1960.
NucIe a ti o n in Precipitation Reactions from Homogeneous Solution ROBERT 6. F I X H E R 1 Gates and Crellin Laboratories, California Institute of Technology, Pasadena, Calif., and Indiana University, Bloomington, Ind.
b The nucleation process determines the ultimate size and number of crystals formed in any precipitation reaction. An internal standard method is described for the counting of precipitated particles with a light microscope. It was found that, in precipitation from homogeneous solutions, all nucleation occurs very early and only growth thereafter. It is shown by calculations from the rates of reactions that the initial stage of precipitation, during which all nucleation occurs, is not one of homogeneous precipitation but rather is one of direct mixing of reactant solutions. Analytical implications of these conclusions are discussed.
A
formed from homogeneous solution ideally should consist of large single crystals (9). This often is the case, yet it is not unusual for a precipitate formed from homogeneous solution to consist of particles which are so tiny that they run through conventional filter media For ( \ample, Gordon and Rowley reported that barium sulfate formed by the h j drolysis of sulfamic acid consists of particles too small to be retained b j a fine sintered-glass frit unless formed m the presence of a high concentration of ammonium ion ( 8 ) . The present author has verified these observations and found that the crystals formed by the hydrolysis of sulfamic PRECIPITATE
1 Present address, Department of Chemistry, Indiana University. Bloomington.
Ind.
acid are smaller than those formed by direct addition of sulfate solution t o a barium chloride solution of the same concentration. The morphologies also differed, with the latter being much more dendritic than the former McNerney and Wagner reported that the large, readily filterable particles of molybdenum sulfide formed by the thioacetamide method mere aggregates of tinier crystals rather than large individual crystals (14). The present author has observed the physical form of sulfides precipitated by thioacetamide under widely varying conditions. I n no case were the crystals much larger than about 2 microns, a size which is just barely filterable without aggregation in conventional filter media. Particles of metal sulfides precipitated by direct addition of hydrogen sulfide are generally even smaller, but the ideal of large, readily filterable crystals is not reached in the precipitation of metal sulfides by the thioacetamide hydrolysis method. The coarseness of a precipitate of a metal ion as formed from homogeneous solution is very markedly dependent upon what anions are present (9, 18). I n the precipitation of metal ions by slow hydrolysis of urea to ammonia, the anions presumably enter the reaction to form basic salts. But even in other precipitations from homogeneous solutions, the presence of certain foreign ions can influence the crystal size of the precipitate. Similar phenomena are frequently encountered in direct precipitation processes (Y), but the more ideal conditions encountered in homogeneous methods could be
expected to render the prePence of foreign ions less significant. Several studies have been reported on nucleation in homogeneous precipitations. LahIer and Dinegar determined the critical supersaturation ratio for the precipitation of barium by sulfate ion generated by reacting persulfate and thiosulfate (12). Collins and Leineweber reported that the critical supersaturation ratio in this process is highly dependent upon the purity of the reagents (3’); similar phenomena are encountered in direct precipitation processes as ~ 1 1 .Collins and Leineweber assumed in the analysis of their data that all nucleation occurs in a single burst early in the process and that only growth ensues. This assumption appears reasonable, as pointed out by Klein and Gordon (IO), but no direct experimental indication of it has been reported in the literature. Takiyama has reported results of a study by electron microscopy and electron diffraction of the nucleation and growth of barium sulfate crystals precipitated by the persulfate-thiosulfate method (16). The purposes of the present investigation were to devise a mc%hod of counting particles which is particularly applicable to precipitated particles, to ascertain directly whether or not all nucleation occurs in one burst early in a process of precipitation from homogeneous solution, and to investigate the origin of thr nuclei. It was anticipated that the results might be significant in explaining why homogeneous processes often do not result in large crystals and why the VOL. 32, NO. 9, AUGUST 1960
1127
crystal size is so highly influenced by the presence of foreign ions. METHOD
OF
C O U N T I N G PARTICLES
The systems selected for study were the precipitation of cadmium and lead sulfides by the acid hydrolysis of thioacetamide because the over-all kinetics of these reactions have been elaborated by Swift and coworkers (1, 15), and the precipitation of barium sulfate by the hydrolysis of sulfamic acid because of widespread interest in this substance. Preliminary results indicated that the particles of the metal sulfides were generally of the order of 1 or 2 microns in diameter and those of the barium sulfate only slightly larger. Calculations on the assumption of a compact shape such as a cube or a sphere show that, for a fixed mass of precipitate, a tenfold difference in linear dimension corresponds to a thousandfold difference in number of particles; therefore, a direct counting method would be more sensitive in determining numbers of particles than any method based simply on size measurement. Similar calculations show that, for a fixed number of particles, a thousandfold difference in total mass signifies an inverse tenfold difference in linear dimension; so a final particle size of 2.0 microns, for example, would mean a particle size of 0.2 micron when the reaction has proceeded only 1/1000 of the way to completion. Because a light microscope can reveal the presence of particles even somewhat below its resolution limit of a few tenths of a micron, it was used in this investigation. The approximate number of particles to be encountered was calculated from the mass, density, and the approximate particle size as determined in the preliminary experiments. For example, the precipitation of lead sulfide from a solution initially 0.01M in lead ion mould result, if the particles were cubes and 2.0 microns on an edge, in 3.5 X lo7 particles per ml. Conventional methods of counting particles involve counting all particles within a specified volume of liquid (2). Uncertainty in measurement of the volume, particularly when it must be small to include only a reasonable number of particles and to be within the field of view of the microscope, is a major source of error. I n the present work an internal standard method was devised in which known volumes of the unknown and the standard suspensions are mixed and the ratio of numbers of the two types of particles are counted on random portions of the mixture under the microscope. An internal standard method with polystyrene latex spheres as the standard is used for counting virus particles in electron microscopy (6), and a light microscope method using lyco-
1 128
ANALYTICAL CHEMISTRY
podium powder as the standard has also been reported ( 2 ) . The internal standard substance must consist of particles which are uniform in size and shape, of known number per unit volume, distinctly different in morphology from those of the substance t o be counted, of approximately the same size as the particles of the unknown, and stable in aqueous suspension. The substance selected for the standard in this work was barium sulfate precipitated by direct mixing of 0.01M solutions of barium chloride and sodium sulfate; the precipitate consisted of X-shaped dendrites which were of a suitable size and uniformity and m-ere very easy to distinguish from particles of cadmium and lead sulfides and from homogeneously precipitated barium sulfate. The standard substance was centrifuged and resuspended in water twice, and the number of particles per milliliter of the h a 1 suspension was determined by counting all particles in a measured volume of a known dilution of the standard. S n y error in this calibration value would be of no consequence in comparing the results of particle counts as long as the same standard suspension were used in all counts. No doubt other standard substances could have been used just as well. It was desired to count the particles dry, both to permit localization of all particles within a plane for optimum operation of the light miscroscope and to permit retention of a mount for subsequent counting or recounting. All dissolved constituents which were present with the particles to be counted were removed by dialysis through a Parlodion film about 200 A. thick, a technique commonly employed in electron microscopy (6). Centrifugation, decantation. and resuspension in water can be used in some instances, but only B-hen experiment shows that no particles are lost during decantation.
Counting Procedure. ,4 measmed volume (pipet) of the unknown suspension is mixed with a measured volume (pipet) of the standard suspension in a test tube. Both suspensions are vigorously shaken by hand just prior to use, and the relative volumes are such t h a t the ratio of numbers of particles in the mixture is within the range of 2 t o 1 to 1 to 2 (trial and error necessary). Water is added if trial shows the particles are too numerous for convenient counting (volume of water need not be measured). A thin film of Parlodion is formed over water by placing 1 drop of a 1% solution in amyl acetate on the surface of water filled to the top in a 600-ml. beaker and allowing a minute or so for the amyl acetate to evaporate. Tiny droplets of the suspension are placed on the Parlodion surface by a drawn-out stirring rod. After 15 minutes, during which dissolved components of the droplets diffuse through the Parlodion
film into the much larger volume of water below, the portion of the film which supports the droplets is picked up from below on a glass slide. The mount is dried in room air, preferably in sunlight. The numbers of particles, both unknown and standard, are counted in various areas under a light microscope. The ratio of numbers of unknown to standard is corrected to equal volumes of the two and is then multiplied by the number of particles of standard per milliliter to obtain the number of particles per milliliter of the unknon n suspension. Usual statistical concepts are applied to provide a measure of the reliability of each final count. The method was checked by obser\-ation of blanks involving separately each reagent to be used in subsequent precipitation reactions and of several different volume ratios of an unknown suspension to the standard suspension. A statistical evaluation of the several possible sources of error in this procedure revealed that the one major source in all of the systems studied is random variation in distribution of particles over the area covered by the residue from the droplets of the mixed suspension. There was some clumping of the standard particles and even more so of the unknown particles. The former could possibly be eliminated by seaidi for a more ideal standard, but the latter is apparently an unavoidable characteristic of the precipitates of interest. This factor simply makes necesbary the counting of large numbers of particles t o render the statistical uncP1 tninty acceptable. EXPERIMENTAL DATA
Experiments were conducted on lead and cadmium sulfides and on barium sulfate, all formed by precipitation from homogeneous solution, to ascertain directly whether or not all nucleation occurs in one burst early in the process. Each initial metal salt solution was 10-2M, so lOOyo precipitation corresponds to 1.12 mg. of cadmium per ml., 2.07 mg. of lead per ml., and 1.37 mg. of barium per ml. The two sulfide reaction media were 10-2M in hydrochloric acid, and the sulfate medium was acidic solely because of the sulfamic acid and its hydrolysis product. The temperature was 65' C. The thioacetamide solution was equally fresh for both precipitations. The per cent precipitated a t the time each aliquot was withdrawn for counting was calculated from the rate constants which, for the hydrolysis of thioacetamide, were obtained from published data (1, 15) and for the hydrolysis of sulfamic acid were estimated roughly from published data (11). The time required for complete precipitation under these conditions was nearly 6 hourq for the sulfides and nearly
5 hours for the sulfate. Results are listed in Table I. Additional experiments were conducted to determine the influence of certain other factors upon the number of particles obtained. At 99" and 25" C., the numbers of particles of cadmium sulfide per milliliter were 0.90 X lo6and 1.13 X lo6, respectively; the uncertainties at 50% confidence limits expressed as per cent of the number of particles were 6 and 129", respectively. The rates of precipitation a t these temperatures should differ about 300-fold. In Table I1 are results on precipitations in which the reaction medium was filtered through Nillipore VF filters (pore size of 100 4.) immediately after bringing all of its ingredients together. The reproducibility within each set of three illustrates the overall precision of the precipitation and counting procedures. The average of the three trials with T'F filtering is only 6470 of that without this filtering. A similar comparison on cadmium sulfide with precipitation at 25" C. revealed a decrease to 63%. -1 similar experimmt on barium sulfate precipitated by the sulfamic acid method revealed that the VF filtering cut the number of final particles to 30Y0 of the number otherwise obtained. Corresponding changes in size were noted. DISCUSSION
It is evident from the data of Table I that nucleation of additioiial crystals does not occur beyond the first few thousandths of the total precipitation time-that is, during the precipitation of the first few micrograms of material in each niillilitcr of the reactioii niedium. In the cadmium sulfide precipitation, there appears to he a decrease in the number of particles, especially between the first and the last aliquots counted, but this trend is not confirmed by the other two precipitates. A decrease could result if several crystals were t o coalesce or if some of the crystals were to redissolve during the growth period, but further work with the greater resolution of the electron microscope and a t still shorter time intervals would be required to elucidate this possibility. It is not possible from these experiments to narrow the nucleation time down any further than to within the first few thousandths of the reaction time. However, it is possible to calculate certain aspects of the conditions existing earlier in the process. From the rate constant for the hydrolysis of thioacetamide a t 25" C., calculated by extrapolation from values published for higher temperatures ( I , 15), and from accepted values of the ionization constants of hydrogen sulfide, it is possible t o calculate the
about 0.2 second. If the p H is higher, even less hydrolysis time is required to provide enough sulfide ion to exceed the solubility product of cadmium sulfide, although the amount of hydrogen sulfide available for further dissociation to sulfide ion is less. The solubility product of lead sulfide is approximately the same as that of cadmium sulfide. The solubility product constants may not be directly applicable to the freshly formed precipitates, but it is not felt that this consideration would invalidate any of these conclusions.
Table I. Numbers of Particles at Several Stages of Precipitation
KO. C'
c'
Precipitated
Uncertainty a t 50y0 Confidence Limits
of
(as % of
Particles per Mi. ( X 10-7)
No. of
Particles)
Cadmium Sulfide 0 227 0.118 0.136 0.114 0.110 33.0 0.149 100.0 0 062 0.3 1.0 2.0 5.0 10.0
0.3
1.0 2.0 5.0 10.0 33.0 100.0 0.3
0.9 1.8
6.5
15 13
13
17
20 8
6
Lead Sulfide 6.21
20 15 10 10 3 14
8 80 6.80
5.60 10.0 5 24 7.78 Barium Sulfate 1.88 1.20 1.32
Uncertainty a t
S o . of Particles
Limits (as yo of No. of Particles)
Kot Filtered 0 92 1 02 1 16
i
17 6
14
1.58
!joy0Confidence
per M1. ( X 10-6)
17
1.i0
90.0
Table II. Effect of Millipore VF Filtration upon Number of Particles of Cadmium Sulfide at 65" C.
11
5
5 9
Filtered 0 74
6
0.63
In some published procedures for sulfide precipitations from homogeneous solutions, the reagent solution of thioacetamide is many minutes, even days, old ( I S ) . The conclusion appears inevitable that the nucleation step is not one of homogeneous precipitation, but rather is one of direct mixing of reagents. I n other published procedures, solid thioacetamide is added to the reaction medium (14). The hydrolysis is so rapid with respect to the amount of sulfide needed to exceed the solubility product of the metal sulfide that the first stage of precipitation again must
Calculated Molar Concentrations of HJ and Sm2 in Thioacetamide Solution One Minute Old at 25" C.
[H+l 10-2
[CHZCSSHz] 10" 10-1 10- 2
10-7
a
2
0.60
molar concentration of hydrogen sulfide ion in thioacetamide solutions which are, for example, just 1 minute old. Typical data are listed in Table 111. If the solubility product of cadmium sulfide is 3.6 X (published values vary), a lO-*iM cadmium solution becomes saturated with respect t o cadmium sulfide when the sulfide ion concentration is 3.6 X lO-*'M. Table 111 reveals that a thioacetamide solution at room temperature just 1 minute old has enough sulfide ion t o exceed the solubility product of cadmium sulfide manyfold. A 10-lLTf thioacetamide solution at pH 2 hydrolyzes sufficiently to sulfide ion t o equal the solubility of cadmium sulfide in a 10-2M cadmium solution in just 2.8 X l o + minute, or
Table 111.
8
[H2S]in 1 minute [S--2]in 1 minute
[HzSI" 1 . 3 x 10-5 1 3 x 10-6 1 . 3 x 10-7
1 3 x 10-10 1.3 X 1 3 x 10-12
10"
10-1 10-2 = =
- d [CH,CSKHz] ~~
-
dt
[S--2lL
1 3 x 10-23 I 3 x 10-24 1 3 x 10-25 3 3 x 10-18 1 3 x 10-19 1 3
x
10-20
1.3 x 10-3 x [CH,CSXHz] X [H+].
lo-** X [HzS] [H+]2
'
VOL. 32, NO. 9, AUGUST 1960
1129
be one of direct mixing; in addition, the use of a solid reagent generally enhances nucleation in precipitation processes (4). The rate constant for the hydrolysis of sulfamic acid is known only approximately (11). Calculations from the approximate rate data lead again to the conclusion that hydrolysis of sulfamic acid at room temperature yields, in only a second or so, sufficient sulfate ion to equal the solubility product of barium sulfate with a 10-2M solution of a barium salt. Of more direct significance, however, are the facts that reagent grade sulfamic acid may contain up to o.05070 sulfate ion and that it probably does come close to this limit in most cases. A 1% solution of sulfamic acid, as used in the common procedure for the homogeneous precipitation of barium sulfate by the sulfamic acid method ( I 7 ) , may contain up to 5 X 10-jM sulfate ion without any hydrolysis-5000 times as much sulfate as is needed to saturate a 10-2M barium chloride solution with barium sulfate. This substantiates the earlier conclusion that the initial stage of precipitation is one of direct mixing of reagents. It is possible to extend this conclusion to other precipitations from homogeneous solutions. No separation by precipitation can be quantitative to an extent greater than that fraction of the total mass which is soluble. Assuming that a solubility of one part per thousand parts of the substance to be precipitated is acceptable and that the reagent is generated at a uniform rate, the solubility product of the precipitate is equalled in the first one thousandth of the total time of reaction. For example, if a total reaction time of 100 minutes is required for quantitative precipitation, nucleation would occur in 0.1 minute or possibly 0.2 or 0.3 minute if the critical supersaturation value permits. In practical situations, solubilities are generally much less than one part per thousand parts of the final precipitate, the rate of hydrolysis or other homogeneous reaction decreases as the reaction proceeds and the
1 130
ANALYTICAL CHEMISTRY
original reactant is gradually depleted, and the total precipitation time even including extra time for digestion is often less than 100 minutes. All three factors tend to make the time required t o initiate precipitation even shorter. It hardly seems possible to use reagent solutions that are so fresh that direct mixing of reagents to start precipitation is avoided. In view of these considerations, it is not surprising that practical homogeneous precipitation processes frequently result in particles far smaller than those which would ideally be expected in a completely homogeneous process. It is similarly not surprising that the presence of other ions can markedly influence the particle size. as is also found with regular precipitations by direct mixing of reagent solutions. even though the mechanism of nucleation in the usual type of precipitation is still controversial ( 5 ) . Although nucleation occurs by direct mixing in the homogeneous precipitations, the concentration of a t least one reactant at the time of mixing is lower than it is in the usual direct mixing methods, so the ideal conditions are more nearly approached in the homogeneous procedures. Analytical procedures should be so designed that the reagents are brought together initially as quickly as possible after the reagent which is to react homogeneously is brought into solution. Fulfilling this desideratum is difficult, as the use of a solid reagent or of a recently dissolved reagent tends to enhance nucleation (4). Speeding up the growth stage in analytical procedures can do little harm with respect to ultimate particle size once the nucleation occurs, as is indicated by the comparative data at 25” and 99” C. The numbers of particles are not significantly different a t the tn.0 temperatures, because all nucleation is by direct mixing and is virtually instantaneous regardless of the temperature. Yet the overall precipitation is about 300 times quicker a t 99’ than a t 25” C. The data of Table I1 and the addi-
tional data referred to with it show that the reaction medium must include particles greater than 100 A. as soon after mixing as the filtration can be performed and that these particles are not replaced by further nucleation. It would be of interest t o see if further nucleation could be forced after most or all of the crystals exceeded 100 A. but while much metal ion remained to be precipitated. LITERATURE CITED
F.. Swift. E. H.. ANAL. CHEM.30, i 2 8 8 (1958). (2) Chamot, E. M ., Mason, C. W., “Handbook of Chemical Microscopy,” 3rd ed., Vol. 1 ,. -DD. - 473-83, Wiley, New York, 1958. 13) Collins. F. C.. Leineweber. J. P., 1) Bowersox. D.
3. Phys. Chem. 60; 389 (1956). ’ (4) Fischer, R. B., Anal. Chim. Acta, in press. (5) Zbid., in press. ( 6 ) Fischer, R. B., “Applied Electrcin ~
Microscopy,” Indiana University Preas, Bloomington, 1953. i’1Fischer. R. B.. Rhinehammer.’ T. 13.. h N A L . CHEM. 261 244 (1954). (8) Gordon, L., Rowley, L., Zbid., 29, 34 (1957). ( 9 ) Gordon, L., Salutsky, M ,L., Willard,
H. H., “Precipitation from Homogeneous Solution,” \Gley, N e x York, 19!59. (10) Klein, D. H., Gordon, L., Talanfu 1, 334 (1958).
Korchmarek, J. A,, Khan, 0. A., Izvest. Akad. Nauk Kazakh. S.S.R., 6kr. Khim. 1955. No. 8, 6 0 : Chem. Abstr. 49, 12931 (1955). (12) LaMer, V. K., Dinegar, R. H.. J . A m Chem. SOC.73, 380 (1951). (13) McCurdy, W. H., Jr., Vanden Heuvel, W. J. A., Casazza, .4. R.. ANAL. CHEM.31, 1413 (1959). (14) McNerney, W.N., Wagner, W. F., Zbid., 29, 1177 (1957). 115) Swift. E. H.. Butler. E. A., ZIid., ‘ 28. 146 ~~- (1956’1. - -, ( 1 6 ) Takiyama, K., Bull. Chem. SOC. Japan 32,387 (1959). (17) Wagner, W. F., Wuellner, J. -L, ANAL.CHEM.24,1031 (1952). (18) Willard. H. H.. Tang, N . K.. J . A m . &em. S O C . ’ 1160 ~ ~ , (1937). (11)
I
\
~
RECEIVED for review December 24, 1953. Accepted April 1, 1960. Division of Analytical Chemistry, l3ith Meeting, ACS, Cleveland, Ohio, April 196& Contribution No. 2533, Gates an$ Crellin Laboratories, California Institute of Technology, Pasadena Calif., and No. 932 from Department of dhernistr Indicna TJniversity. Bloomington, In$
