8th Annual Summer Symposium--Mole of Reaction Rates
Kinetics and Mechanism in Formation of Slightly Soh ble Ionic Precipitates JAMES
D. O'ROURKE
Department of Chemistry, University o f Michigan, Ann Arbor, M i c h .
RALPH A. JOHNSON' Department o f Chemistry, University o f Illinois, Urbana,
111.
I t is believed that precipitation occurs in two stages: the first involves nucleation and growth, the second involves only the growth process. The formation of priniary particles is effectively terminated early in the precipitation process when the existing particles have reached a size such that their surface contribution to the growth rate in combination with the higher solubility of srnall particles reduces the effective rate of nucleation to a reluli\elg small value. Chronometric integrals derived on the basis of the above concepts are shown to describe the precipitation process using barium sulfate as an experinicntni model.
T"";'-'
,uietics of the precipitation process occupies an important place in the fundamentals iipon which precipitLition technnlogy rests. For analytical chemistry, this technology has special importance. Within recent years, new concepts have been developed concerning the mechanism and kinetics of forniation of slightly soluble ionic precipit:itcs. Because the liternt u r e in this area is somexliat abstruse and scattered, an attempt ii. made here to present a simplc interpretation of its content and a n explanation of its m:iin itleas. From the standpoint of nieclianiwi, precipitation is regarded Iirocecdiny as follow: as a series of stepwise reacti
+ .Y 1-+ 3-.. s, s+ zY,$ X + X p - l -+7Xp X +X, X
cluster Iiuiid-up = nionomer Xz, ctc., clusters
-+
X
s:j +
S
+ Xi
-+
S i+
50
MINUTES
Figure 1.
Variation of [Ba++]= [SOa--] with time
1,:irwiniental points, measured conductometrically ( 1 4 ) . Ciirve riilct?lated froni empirical g r o x t h rate expression, Equaiiun D
I)
L-
nucaleation step S,; = nucleus p = number of monomers in nucleus first growth s t q ) crystallite growth Xi = cr?-stallite of i mononiers
5
Present address, Shell Development Co., Emeryville, Calif.
15 b i ,
.\l! i)olynicrs smaller than the nucleus arc c:rllcd clusters. 'Y!ie>, are a pnrt of the mother phase and arc in a quwi-equilibrium state with each other. K i t h increasing size, the cheniical pot e n t i d of clusters prcsum:tbly increases, and their equili:,riuni concentrntion decreases. Polymers excceding the nucieiis &e are termed crystallites, or particles. They are in n separate phase and their chemical potentials, or solubilities, decrease Tyith increasing size in a manner generally indicated by the Thonison equation. Standing between the clusters and the crystallites in size and ut a maximum x i t h respect to chemical poten nucleus. Addition of a monomer to the nucleus iriitiat of spontaneous further monomer additions, which is the growth reaction. The reactions within the cluster equilibrium leading t o replacement, of the growth-removed nuclei constitute the nuclention reaction, Experimentally, the systems most useful to nucleation and growth studies are those in which the contributions of the sepa1
60
40
(1)
-+ s 2
+
20
0
-1
"- ii
Figure 2. Induction period and Frowth surge of barium sulfate 0 a = a/# a, 0 = 112
r,ite reactions are n-ell sepnrnted with respect to the timing :tiid the magnitude of their contribution. For these conditions a prototype system is one in which a loug induction period iy possible a t high supersntiirations. Certain supcrsntiirations of bnrium sulfate admiralily fit this prototype, and conseqi:entl~-this salt has been the Pi:l,jec*t of considerably more !cinetic investigation than any other salt of its type. A t>-pic:il precipitation curve is shoirn in Figure 1 and a close-up of the induction period is given in Figure 2. It is profitable to begin our study by examining separately the natures of the nucleation and growth reactions and proceed then t,o consideration of the interplay of the two processes in the course of :in actual precipitation.
1699
1700
ANALYTICAL CHEMISTRY
One of the objectives of the studies is to find a chronometric integral (chronomal) which describes the experimental precipitation curve in terms of the nucleation and growth processes and which corresponds to a reasonable physical picture and reaction mechanism.
by chemical generation of the precipitating solute or one of the reactants-Le., homogeneous precipitation. If the nucleation reaction is higher order, as is probably the case for sulfur hydrosol formation ( 2 4 ) , it may be expected that a myriad of nuclei are formed almost instantaneously upon attainment of a certain critical supersaturation and that this reaction easily reduces the supersaturation belorv the limits in which nucleation occurs. As a consequence, further nucleation does not occur and a monodisperge sol is formed. Jn contrast, for a low order nucleation the gradually increasing supersaturation brings about, over a considerable concentration range, a steadily increasing flow of nuclei into the gron th reaction. The complication of the variable nucleation rate probably affords more difficulties in interpretation than the uncertainties due to mixing fluctuations. Direct mixing is accordingly preferred for studies on crvqtnlline precipitates.
NUCLEATION
If the intermediates leading to nucleation (Equation 1) are in the same phase and in a quasi-equilibrium state, the nucleation reaction may be represented as p X -+ X p and the nucleation rate as
where v is the number of nuclei, K is the rate constant, and C is the concentration of monomers, or, for a salt of 1 to 1 configuration, c =
~''m.
It is assumed that the supersaturation is large enough that the dissociation of the nucleus does not take place and that monomei addition to the nucleus is a relatively rapid reaction. From a steady state treatment of the above nucleation process, Christiansen ( 4 ) found an indication in available experimental data that the steady state for nucleation is reached instantaneously. He derived the above rate expression with the aid of steady state assumptions. The incipient crystallites are relatively soluble. Correspondingly, the back reaction for nucleation is undoubtedly greater than that for growth. As a consequence, as precipitation progressively depletes the supersaturation, the nucleation rate must be curtailed more sharply than the growth rate. The magnitude of p is the index of rate of change of nucleation rate with change in monomer concentration. A comparison of the nucleation of water droplets and of barium sulfate serves to illustrate this point. Water nuclei are estimated to consist of approximately 100 molecules (19). Correspondingly, the appearance of nuclei is found experimentally to be critically dependent upon supersaturation. The range between the supersaturation above which nucleation occurs instantaneously and below which nucleation does not occur is a narrow one. I n contrast, for barium sulfate, the supersaturation limit at which turbidity appears immediately (1'7) is four or five times greater than the limit below which autonucleation is practically nonexistent (18). This comparison between lvater and barium sulfate indicates a lower dependence of nucleation rate on concentration for the latter, Kinetic treatments by Christianseii ( 6 )and by Johnson and O'Rourke ( 1 4 ) of experimental data bear out this indication. The probability of a low order for the nucleation of crystalline ionic substances has fundamental implications to problems related to the methods of bringing about the initial supersaturation. If the reactants are brought together by direct mixing, there arises the question of the number of nuclei generated from momentary higher supersaturations occurring in the mixing process in comparison to those formed after homogenization. Because the differential of nucleation rate with respect to concentration is of a low order, the extra amount of nuclei due to mixing fluctuations is not expected to be great relative to those arising after homogenizaticn. This expectation is confirmed for the barium sulfate system as shown by the data in Table I, which reveal that the number of particles formed is nearly independent of concentration and, thus, rejects the mixing fluctuation hypothesis for this system. This conclusion is further confirmed by the experiments and theory of Duke and Brown ( 9 ) ,discussed in a section belorv, which clearly relates the number of particles to kinetic properties of the precipitation reaction. Accordingly, the hypothesis of homogeneous nucleation taking place throughout the induction period and for a period thereafter is expected t o prevail for the slightly soluble salts in concentrations presenting an induction period. In some experiments (13, 1 7 ) the mixing fluctuations are avoided
Table I.
Particle Count and Initial Concentration of Barium Sulfate
Solutions used.
,
Barium chloride. aged 1250 hours, and sodium sulfate, aged 1400 hours Procedure. Equal volumes of reagents were rapidly mixed to give the concentration indicated. Particles were counced microscopically when precipitation was complete. [ B a + + ] = [SO1--] Particles/Liter (.Moles/Liter) X 104 x 10-9 2.5 1.2 5.0 1.1 10.0 1.2 lL0 1.2 20.0 1.0 25.0 1 8' a Precipitation began immediately on mixing.
The possibility of induced nucleation is present in any nucleating system. Probably seeding is the most important and also the best understood of the induced nucleations. The effectiveness of seeds in inducing precipitation is closely related t o the similarity between the lattices of the seed and of the precipitating substance ( 2 2 ) . This limitation makes accidental seeding on foreign nuclei a much smaller consideration for nucleation of ctystals than for nucleation of liquid droplets. With regard to the induction of nucleation by stirring, little evidence is available from systematic expeiimentation to indicate the effectiveness of this mechanism. . I special effect may be mentioned as induced nucleation. Fischer (11) has shoTvn that, if freshly prepared solutions of barium chloride are used for the formation of barium sulfate, the particle size (and thereby the number of particle. formed) is a function of the age of the solution. The number of particles decreases with increasing age of the reagent qolution and the variability tends toward a constant. Tests carried out in these laboratories are summarized in Table I1 to illustrate the effect. The effect has not been satisfactorily explained and may account for certain contradictory results i n the literature of t)ar;uni wlfate formation.
Table 11. Variation of Particle Count with Age of Barium Chloride Solution (Equal volumes of 2 X 10-3.V reagents, barium chloride and sodium sulfate, were rapidly mixed. Particles were counted microscopically when precipitation was complete) Age of BaCh Particles/Li ter Solution, Hours x 109 16.4 0 4 0 3.0 3 5 4,s 10 1.9 22 1 3 1 2 34 1 1 72 0 7 166 1 2 1248
1701
V O L U M E 2 7 , NO. 1 1 , N O V E M B E R 1 9 5 5 I n general, the great number of nuclei formed and the reproducibility of their concent,ration in experiments with barium sulfate and other ionic precipitates indicate t h a t processes bringing about nucleation in a n accidental or random way are probably of minor importance for this type of sj-stem. From this and other considerations summarized, the following picture emerges for the nucleation process in slightly soluble ionic salt systems in which an induction period occ~lrs. .Ifter the reagents are mixed (homogenization can be assumed to be instantaneous) nucleation takes place at, a uniform rate. With the depletion of supersaturation a t the end of the induction period, the nucleation rate, because of the relatively low stability of nuclei and incipient crystallites, decreases rapidly and its effective cont,ribution to the precipitation rate is eliminated a t a concentration substantially greater than the macro solubility. Iccordingly, growth is the sole precipitation reaction beyond a certain intermediate stage in the process. GROWTH
I n general, the rate of crystal growth is a function of two variables, the surface available for grovth and the concentration of the precipitating solute; hence,
dC/df
-B
X f(S)X
f(c)
(3)
n-heref(C) is a function of the concentration of the precipitating solute a n d j ( S ) is-a function of the available surface. ( S o t e that C = [ABJ = .\/(L4+1 [E-] or C = [A’] = [B-I.) DEPESDENCE O F GROWTH RATE 0 . Y CONCESTRATI0.V PRECIPITATING SOLUTE
OF
I n a numericid integration of the portions of the barium SUIfate precipitation curves attributable solely to growth, Johnson and O’Rourke (1.4) found the function of concentration, .f(C), t o be ( C - C,)c. Davies and Jones (6,Y) and Kobaj-ashi (15)found the groffth rate of silver chloride upon seed crystals t o be dcpendent upon (C - Cs)2. Because diffusion control predicts t h a t the concentration function be first order, this mechanism is ruled out for these systems. Also it has been shown by Turnbull ($1)that, for very small particles, surface control rather than diffusion control is indicate11 for the groxth process. Growth 1);v random accretion of ions, or ion pairs, on plane crystal surfaces is not generally held to be a probable mechanism for crystal growth hecause of the low energy release involved and the corresponding Ion- stability of the added ion?. A more probably hypothesis has been developed, notably by Volmer ( 8 3 ) and by Becker and Doering ( 1 ) which involves the formation of “two-dimensional growth nuclei” followed by t x o dimensional growth over the respective planes. Growth in the third dimension takes place by successive repetitions of two-(iimensional nucleations followed by respective spreading reaction.. The mechanism and kinetics of two-dimensional nucleation are expected to follow along lines discussed in the preceding section. The reaction may be expressed as follom:
in n-hich q represents the number of monomers in the growth nucleus. If gionth over the plane spreads rapidly after each nucleation, the gron t h rate assumes the dependence on precipitant concentration characteristic of the niicleation reactioni.e., the growth rate is expected to be p-order. Thus, the results cited indicate a growth nucleus of two ion pairs for harium sulfate and of a single ion pair for silver chloride. -4h j pothesis for gron t h which does not require the poqtulation of groir t h nuclei has arisen from consideration of imperfections, or dislocations, in the lattice of the developing crystallite (12). Dislocations in the form of molecular terraces serve t o stabilize entering growth units. Certain dislocations perpetuate themselves throughout the crystallite’s development, thus permitting
continuous groii t h n ithout the high energy requirement imposed by the formation of two-dimensional nuclei. The prevalence of dislocations in crystal lattices is Fell established and surface structures have been microscopically observed which lend support t o this hypothesis. Addition t o the dislocations is expected to take place i n the smallest neutral units. Accordingly, the growth rate is predicted to be second order for silver chloride or barium sulfate. -1lthough the experimental growth order for silver chloride, second order, meets this prediction, that for barium sulfate, fourth order, is not in agreement with the dislocation theory. The solubility term, C,, enters the experimental rate expressions cited above by modifying the precipitant concentration term to be a supersaturation term-Le., the rate is dependent upon ( C - C,Y, not C4. Davies and Jones ( 7 ) explain this for silver chloride by assuming that growth occurs only from a surface film in M hich an equilibrium concentration of silver ions and of chloride ions, C,, is maintained in an intact absorbed monolayer. Only concentrations in excess of C3~-i,e,, ( C - C,)-are then available for growth. SURFACE FUNCTION AND GROWTH RATE
The surface function is probably the resultant of several effects taking place during groTYth. Although it is not possible t o resolve these effects experimentally especially for rapidly growing, incipient particles, the contributions of certain of the effects can be predicted. Perhaps then a first approximation of the mechanisms in play can be made. For ionic crystals n i t h the sodium chloride structure, Stranski (80) has cilculated the energy involved in adding an ion t o various sites on a crystal surface. The calculations indicate that the inception of new layers is more likely t o occur a t edges or corners than in the face. Observations of gron-ing crystals made under the microscope by Bunn and Emmett (3)revealed layera growing as a general rule from points on faces. The groLvth nucleation rate is independent of particle size if confined t o corners. If nueleation takes place on edges only, the rate is proportional to i l ’ 3 ; for surface nucleation the corresponding exponential is i 2 ’ 3 (i is the number of monomers in the growing particle). These considerations are valid if the crystal form does not change in the process. However as high index face:: are eliminated in the particle’s development, simpler forms evolve with relatively fen-er corners and edge and snrface devehpnient. These changes, if averaged into the growth nucleation rate, have the effect of adding a negative component to the exponentials de,xribed-e.g., for surface nucleation, i1’2 might represent the nucleation function averaged over a peries of form simplifications. Upon conversion of the nucleation rate to growth rate, a poPitiT-e component is added. If growth spreads immedintely over the face, or contiguous faces, from the nucleation site, the g m v t h interval resulting from each micleus expands with increasing particle size; t h w ,
dC =
- i”3dn
(5)
in which n refers t o growth nuclei. The corresponding surface functions of groir-th rate, d C / d f : for corner, edge, and surface nucleation are then, respectively, i2’3, i! and 2’4’3, other effects, such as form simplifications, being neglected. The foregoing are primary considerations arising from the surface nucleation theory of growth. Similar considerations are derivable for the dislocation theory. Although they can si!pgest mechanisms, their present status does not permit conclusions t o be dran-n from existing experimental evidence. Experimentally, the surface function for barium snlfate is i2’3. This was determined by Johnson and O’Rourke ( 1 4 )in two ways: by numerical integration of the last part of the precipitation curve (Figure l), assuming a homodisperse set of particles and by analysis of the curvature a t the termination of the induction
1702
ANALYTICAL CHEMISTRY
period as described in the next section. For silver chloride, Kobayashi (15) has found the surface function to be i 1 / 3 from growth measurements made on seeded systems. The surface function brings to the growth rate its autoinduction character. The abrupt termination of the induction period ie largely dependent upon this function. The curvature following this terminating surge is controlled largely by the order of the growt,h reaction, q. A summary of the cited experimental evidence yields for a homodisperse set of growing barium sulfate particles -dC/dt
= kv1’3(C0
- C)213(C- C,)4
precipitate formed by each group of particles from the time of their inception, 7 , to time t is given by Equation 10 with dv replacing Y and ( t 7) replacing t . Upon combining this relationship with the nucleation rate equation (Equation 2) and integrating from the moment of mixing to time t with C” +p held constant, an expression indicating fourth-order time dependence is obtained for the over-all reaction:
-
(6)
=
The corresponding equation for silver c-hlorideis -dC/dt = W.13(C0- C)1’3(C
- C,)*
(7)
INDUCTION PERIOD AND GROWTH SURGE TERMINATING IT
Phenomenologically, the striking features of the induction period are the absence of any detectable change throughout its lifetime and its abrupt termination as evidenced by the appearance of turbidity and decrease in reagent concentration. The two empirical relationships pertinent to these features are, respectively, the reciprocity relationship of the induction period
Corti = constant
(8)
in which t i is the length of the induction period, and x is a constant, and the chronomal for the growth surge terminating the induction period is (Co - C) = btU
Co -
c = k3VC3ft3
y
(108~)
= --
k
t4
-a
(12)
Hence, the particle count data in Table I, obtained using a hemocytometer, indicate that p and q are equal for barium sulfate. This conclusion is in agreement with the evaluation obtained by another route described below. Christiansen ( 4 , 6) has approached the kinetics of precipitate formation via steady state assumptions and treatment. (Notations below follow the notations already established in this paper.) The growth process is represented by a flow sheet in which polymers made up of successively greater numbers of monomers are represented as follows. S
6
xi --+ x? s -L
s -t
s .-+
9,
-
-x,:
- x* S
.It the stead\ state. the rates of monomer addition within respective clawes of polymers are all the same-Le., s. At any time t in the proces-, the concentrations of polymers of n or fener monomers are steady, Tvhereas the concentration of the polymer X,+l and the polymers containing more than n+l monomers do not euist. The steady state rate, s, is subject to change with advancement of the value of n. The concentration of each i-mer, cz, is shown to be ci =
S -
ki‘Cq
in which i is andogous to the clurface function discussed in the preceding section. The “concentration” of monomers bound in C), is each i-mer, (C,
-
(C, -
(10)
Third-order time dependence for the growth surge chronomal-y = 3-is thus indicated. -4 fourth-order time dependence is obtained for the barium sulfate system if nucleation is assumed t o make a considerable contribution parallel to the growth reaction during the induction period. R‘jthin any period t after mixing the reactants, there are infinitesimal intervals, d r , (Ostem yield z = 4, ( 1 5 ) . When this value is combined with q = 2 and u = 1/3 experimental growth constants for this system, the nucleation order found is 7 . Phenomenologically, the scheme which appears to fit the procew during the growth surge is the following. The particles nucleated in the first moments of the induction period reach a stage of surface development at which their growth becomes rela-
Figure 3.
Growth surge of barium sulfate
For barium sulfate, the effect of temperature on the concentration-induction period relationship, Equations 8 and 20, was studied by O'Rourke (18). The concentration exponent, x = 3q ___P
+
4 7 was found to be invariant, indicating that the precipitation mechanism is not affected by temperature. The constant term shoned a slight decrease n ith increasing temperature. Since the rate constants appear in the denominator of the constantviz., as Kk3-the slight positive temperature dependence is indicated. Honever, the effect of temperature on the rate constants is small in approximate agreement with the results of Davies and Nancollas. CO~CLUSIONS
For the analysis of the kinetics and mechanism of precipitation, systems presenting an induction period terminated by appearance of precipitate and a surge of reaction are particularly useful. Nucleation takes place a t a regular rate throughout the induction period, probably according to dv/dt = KCP. The rapid depletion of supersaturation after the induction period sharply curtails nucleation; hence, beyond a certain point precipitation occurs solely through growth.
1704
ANALYTICAL CHEMISTRY
Growth is a function of the available precipitate surface and of the supersaturation-viz., dC/dt = k ( C , - C)"(C - Co)qthe surface exponent, u, represents, approximately, a complicated set of surface functions and is expected t o be a simple fraction. The supersaturation exponent indicates the size of the two dimensional growth nuclei ( 1 , 23). For q = 2, the dislocation theory of growth is also possible. A general chronometric integral (chronomal), derived by two independent methods on the basis of simultaneous nucleation and growth reactions, relates the experimental concentration to the constants and functions of those reactions. The chronoinal is limited to the induction period and the growth surge which terminates it. The curvature of the concentration-time curve a t the termination of the induction period is determined solely by the surface function of the growth reaction and is useful for determining this function. The effect of initial concentration on the length of the induction period is given by C,"t, = constant, in which x = mp
-
( 2 ) Bransom. S. H.. and Dunning. 1%'. J.. Discussions Faradau Sac.. 5 , 96 (1949). I
Bunn, C. W., and Emmett, H., Ibid., 5, 119 (1949). Christianson, J. A , Acta Chem. Scund., 8 , 909 (1954). Ibid., p. 1665. Davies, C. W., and Jones, --I.L.. Discussions Faraday Soc.. 5, 103 (1949).
Davies, C. W., and Jones, h. L., Trans. Faraday Soc., 51, 812 (1985).
Davies, C. W., and Sancollas, G. H., Ibid., 51, 823 (1955). Duke, F. R., and Brown, L. lf,,J . Am. Chem. SOC.,76, 1443 (1954).
Dunning, W. J., Discussions Faraday SOC.,5 , 195 (1949) Fischer, R. B., and Rhinehammer, T. B., ANAL.CHEX.,25, 15.14 (1963).
Frank, F. C., Discussions Faraday Soc., 5 , 48 (1949). Frisch, H. L., and Collins, F. C., J . Chem. Phys., 21,2158 (1953). Johnson, R. A., and O'Rourke, J. D., J . Am. Chem. SOC., 76, 2124 (1954).
Kobayashi, K., J . Chem. Soc. Japan, 70, 125 (1949); Science Repts. TGhoku Unz'z'., 37, 125 (1953).
+
1
LaMer, V. K., and Barnes, M. D., J . Colloid Sci., 1, 71 (1946). LaAler, V. K., and Dinegar, R . H., 6.Am. Chem. Soc., 73, 380
m)p, rn being -. After the growth terms have been 2-u determined, the nucleation rate terms can be estimated from this relationship. The variation of particle count with initial supersaturation iq proportional t o the difference between the nucleation and growth order-i.e., ( p - q ) . Since p =p for barium sulfate the number of particles formed is independent of the initial concentration, lo9 particles per liter are formed if an induction period precede8 nilpearance of precipitation. (1
(1951).
O'Rourke, J. D., Ph.D. thesis. Giiiversity of Illinois, Urbana, Ill,, 1953.
Rodebush, W H., Proc. .\-atl. &ad. Sci., U . S., 40, 739 (1954); Ind. Eng. Chem., 44, 1289 (19.52).
Stranski, I. K., J . p h y s i k C'hevt. 1.. 155, 466 (1928) Turnbull, D., Acta N e t . , 1, 684 (1953). Turnbull, D., and Tonnegut. €3.. Ind. Eng. Chem., 44, 1292 (1952).
Volmer, AI., "KineLik der Phasenbildung," T. Steinkopf, Dresden and Leipzig, 1939. Zaiser, E. hl., and LalIer, V. K.. .J. C'olloid Sci., 3, 371 (1948).
LITERATURE CITED
(1) Becker, 11 , and Doering, W , Ann. Physik, 24, 719 (1935)
H E C E ~ for ~ Ereview D .kuanst 8, 105.5.
AccFPTED
Seutember 2 , 19%.
8th Annual Summer Symposium-Role of Reaction Rates
Slow Precipitation Processes Application of Precipitation from Homogeneous Solution to liquid-Solid Distribution Studies LOUIS GORDON Department
o f Chemistry,
Syracuse University, Syracuse
The direct addition of a precipitant to a solution results temporarily in a heterogeneity of conditions. In the vicinity where the precipitant has been introduced the formation of the solid phase takes place under conditions such that the solution concentrations vary between very wide limits. Therefore, results of coprecipitation studies obtained with conventional precipitation procedures may also vary markedly. Precipitation from homogeneous solution offers an ideal technique for controlling the rate and mode of addition of a precipitant. I t permits a slow precipitation process, which allows near equilibrium to be established between the surface of the solid and the solution. It is thereby possible to determine the nature and extent of coprecipitation. Applications of this technique are described in which Doerner-Hoskins' distribution coefficients have been obtained for systems containing barium-radium mixtures. Other coprecipitation studies are also described, particularly some which have revealed that the extent of coprecipitation is negligible except during the initial and final stages of the precipitation process.
IO, N. Y.
I
N 1937, Willard (45, 4 6 ) published the results of an investigation illustrating the use of urea in a slow precipitation process. This study, in which the aluminum ion was slowly precipitated :is a basic salt, served as the stimulus for many subsequent papers describing applications of the technique now referred to as precipitation from homogeneous solution. The virtue of precipitation tiom homogeneous solution lies in the production of a very dense precipitate which minimizes coprecipitation. The principles of this technique and its merits have been reviewed in two papers ( Q ,38).
Either an anion or a cation can be generated homogeneously \+ithin a solution to serve as a precipitant. Urea (39, 41. 42. 14-46), hexamethylenetetiamine ( 2 5 ) , and acetamide (10, 38) have been used to release h v d r o u 1 ion. The sulfate ion can be produced from sulfamic acid ( 8 , 34) and either dimethyl ( 5 , 6) or diethyl sulfate ( 3 8 ) . Oxalate from dimethyl (11, 80, 4 1 ) or diethyl oxlate ( 1 , 4, 1 8 ) ; phosphate from metaphosphoric deid (43) or trimethyl or triethyl phosphate ( 4 0 ) ; carbonate from the trichloroacetate ion ( 3 0 ) : sulfide from thioacetamide ( 7 ) ; iodate from periodate (18); periodate from iodate ( 3 3 ) ; and chromate from dichromate ( I S ) are other examples. The generation of a cation in a solution may be effected bj one
