“THEORY OF COPRECIPITATION.” T H E FORMATION AND PROPERTIES OF CRYSTALLINE PRECIPITATES

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BY I. M. KOLTHOFF

1. Introduction It has been known for a long time that crystalline precipitates separating

from a solution are not, as a rule, quite pure but usually contain imperfections of mother liquor with foreign constituents. A vast number of empirical facts pertaining to the presence of various impurities in crystalline precipitates may be found in the analytical literature. Unfortunately, these data are of not much use in the interpretation of the so-called “coprecipitation” or “carrying down,” mainly for the reason of poor description of experimental conditions. As will be shown later in this paper, the latter are of primary influence as regards the kind and amount of coprecipitation. bloreover, it has been a general custom in analytical chemistry to use the words, coprecipitation, carrying down, occlusion, inclusion and adsorption as collective names, meaning nothing else but the establishment of the fact that impurities are carrisd down with or in a precipitate. In a systematic treatment of the problem, it should be emphasized, however, that three different phenomena m a i n l y account for the presence of impuri t ies i n the precipitate and in a study of the problem, it is necessary first to find out what kind of coprecipitation we are dealing with. I n this paper, three cases are distinguished:

In this case the impurities are in- corporated in the crystal lattice and they do not change tile regular structure of the latter. The amount of mixed crystal formation depends as in case C upon adsorption phenomena during the growth of the precipitate.

In this case the impurities are not incorporated in the crystal lattice, but they are atiao,rDed during the grozth of the crystals and give rise to the formation of imperjcctl‘on.? in the crystal. (“Hohlraume or Locker- stellen” (Smekal) ; or centra of’ activity-(H. S. Taylor).) Here adsorption phenomena during the growth of the crystals are mainly responsible for the amount of occlusion. I t is especially with this kind of coprecipitation that we are concerned in this paper.

e. Surface udsorption by the precipitnte after i t has been formed or separated. This kind of coprecipitation is only of practical importance when the precipitate has a large surface,i.e. when it behaves like a flocculated colloid. If the precipi- tate has a definitely micro-crystalline character (as observed under the micro- scope) the amount of coprecipitation caused by surface adsorption is, as a rule, of no practica1 significance. Confusion is caused in the anaIytica1 literature by the fact that certain phenomena have been attributed to coprecipitation (an expression often used to indicate that a precipitate is not quite pure), but which have nothing to do with it. This may be illustrated by two examples.

a. T h e formotion of mized crystals.

b. Occlusion.

THEORY O F COPRECIPITATIOS 86 I

In most text books of analytical chemistry, it is mentioned that magnesium is coprecipitated with calcium oxalate. Although there is actually a slight co- precipitation of this element, the presence of magnesium in calcium oxalate, if the latter is precipitated from solutions containing much magnesium salt, is mainly due to the slight solubility of magnesium oxalate. If relatively much magnesium is present and an excess of oxalate is added, the solution becomes supersaturated with respect to magnesium oxalate. First of all, calcium oxalate precipitates and then on standing magnesium oxalate crys- tallizes out slowly. Therefore, we are not dealing here with a case of co- precipitation, but of l~ost-precipitation, the crystals of calcium oxalate being not a t all or only slightly contaminated by magnesium. The magnesium oxalate crystallizes out as a separate phase. A detailed investigation of co- precipitation with calcium oxalate is being made in this laboratory by E. B. Sandell ; the results will be described in his doctor’s thesis and communicated later. Another example of post-precipitation is the so-called “coprecipitation of zinc with copper sulfide.” In an extensive investigation’ it, has been shown that here again we are dealing with a case of post-precipitation. In relatively weakly acid medium a solution saturated with hydrogen sulfide is super- saturated with respect to zinc sulfide. First of all, the copper sulfide precipi- tates according to the laws of fractional precipitation; on standing zinc sulfide separates out slowly. Even in the more recent literature, this “post- precipitation” of zinc sulfide is described as a coprecipitation although it has nothing in common with it. Of course, it is quite possible that the primary precipitate has a promoting effect upon the separation of the secondary precipitate as in the copper sulfide-zinc sulfide case, the precipitation of zinc sulfide is enhanced at the surface of copper sulfide. It should be clearly understood however, that the secondary precipitate is not carried down by the primary precipitate and that we are not dealing here with a real case of coprecipitation.

d. A case which rarely occurs is that coprecipitation actually has to be at- tributed to the formation of a definite chemical compound. The so-called coprecipitation of alkali oxalate with lanthanum oxalate is caused by the formation of a double oxalate as has been shown by I. 11. Kolthoff and R. Elmquist.* From experiments of Z. Karaoglanov and B. Sargotschev,3 it appears that coprecipitation of lead bromide and lead chloride with lead oxalate is due to the formation of a double salt (PbX)*Ox. However, the formation of such definite chemical compounds is very seldom encountered in analytical work, although it should not be overlooked as a possible interpre- tation of the presence of much “impurity” in the precipitate.

In this paper an attempt is made to formulate a general theory of co- precipitation, especially of the kind specified in Sub. b. The hope is expressed that such a theory will not only contribute to the understanding of the forma- tion of impurities in precipitates formed under analytical conditions and

’ I. M. Kolthoff and E. Penrson: J. Phys. Chern., 36, j49 (1932). Kolthoff and Elmquist: J. Chem. Soc., 53, 1232 (1931). Karaoglanov and Sargotschev: Z. anorg. allgem. Chem., 199, 7 (1931).

862 I. M. KOLTHOFF

thereby the improvement of the exact precipitation procedures, but will also have a wider bearing on the problems of mineralogical formations and the properties of slightly soluble micro-crystalline precipitates.

It should already be mentioned here that in recent years various authors have tried to treat the problem of coprecipitation from a more general view point. However, no sharp distinction has been made between the various kinds of coprecipitation as is done in this paper.

In the following a short discussion will be given of the formation and properties of precipitates which is of importance with regard to the general problem. More detailed information will be given in consecutive papers which will contain the results of experimental studies being made at the present time in our laboratory.

2. The Thermodynamic Potential of Crystals An ionic lattice, according to the precipitation rule of Paneth-Fajans*

has a strong adsorbing action for ions which form a slightly soluble or slightly dissociated compound with ions of the lattice of opposite charge.

It seems advisable to distinguish between primary and secondary adsorp- tion of ions by an ionic lattice. If silver chloride, for example, is shaken with an alkali chloride solution, there is a primary adsorption of chloride ions. Owing to the fact that the system must be electrically neutral an equivalent amount of any kind of foreign cations has to be adso-hd as well (secondary adsorption). A preferential adsorption of those cations will take place, whose compounds with the primary adsorbed ions are slightly soluble or slightly dissociated. This rule should be correlated with the following: The higher the valence of the ions with a charge opposite to that of the primary adsorbed ions, the stronger they will be adsorbed. This may be inferred from measure- ments made by L. Imre4a on the adsorption of actinium, thorium B and radium by negatively charged silver iodide and could be expected already from the similarity between flocculation of colloids and adsorption of ions by a particle. If the lattice surface does not contain an excess of its own ions there may be a primary adsorption of foreign ions. These will be held by much less stronger forces than the lattice ions and as a rule will easily be replaced by the latter.

K. Fajans and W. Frankenburge? give a very clear picture of what occurs when a crystal lattice is in contact with a solution containing an excess of one of its own ions.6 “The crystal lattice adsorbs one of the kind of ions constituting it. The adsorption forces are here identical in nature with those holding the adsorbent together . . .’, “If we assume, for simplicity, a difficultly soluble salt, both of whose ions are equally strongly adsorbed on the

F. Paneth: Physik. Z., 15, 924 (1914); K. Horovits and F. Paneth: Z. physik. Chem., 89, 513 (1915); Wien. Ber., 123, I P , 1819 (1914); K. Fajans and P. Beer: Ber., 46,. 3486 (1913); Fajans and K. Richter: 48, 700 (1915); 0. Hahn, 0. Ersbacher and N. Feichtinger: Ber., 59, 2014 (1926); 0. Hahn: Naturwissenschaften, 14, 1196 (1926).)

(a L. Imre: Z. physik. Chem., 153 A, 127 (1931.)) SK. Fajans and W. Frankenburger: Z. physik. Chem., 105, 255 (1923). 6 Ref. 5 , page 270.

THEORY OF COPRECIPITATION 863

same crystal lattice, i.e. in contact with the saturated solution containing both ions in equal concentration, there arises no potential difference between salt and solution. If we add an excess of one of the ions, say the cations, the adsorption equilibrium of this ion on the anions of the lattice will be disturbed and consequently the cations will be deposited on the anions of the lattice covering them in part and giving the lattice a positive charge. The equilib- rium with the anions in the solution is thereby also disturbed as can easily be seen from the fact that the anions of the lattice which are covered by positive ions are removed from kinetic contact with the solution and that the surface now carrying an excess of positive charge exerts an increased attraction on anions of the solution. Fresh anions must, therefore, be deposited on the crystal lattice from the solution until a new state of equilibrium is set up with a smaller concentration of anions. This means that the solubility of the salt is lowered by an excess of cations. I t is clear that a closer investigation of the whole adsorption isotherm of both ions must give a quantitative connec- tion with the law of solubility product. Two points can clearly be seen: Since the adsorption of cations in the case considered is greater, the greater the excess added to the solution so must the amount of anion precipitated in- crease likewise and the solubility decrease corresponding entirely quantita- tively with the law of mass action.” In excellent papers J. A. V. Butler’ has already shown that there is no reason to expect that a crystal lattice will adsorb cations and anions equally well. “It may obviously happen that the tendency of one of the ions to go in solution may be greater than that of the other ion owing either to a smaller attraction by the lattice or a greater attraction of the solvent for this ion.” To this statement may be added the fact that the conditions under which the thermodynamic potential will be equal to zero will be different in different solvents, since the activities of various ions change in a different way in going from one solvent to another.

H. R. Kruyt and P. C. van der Willigens in harmony with Butler’s state- ment found that crystals of silver iodide in contact with the saturated solu- tion in water assume a negative charge, thus showing a preferential adsorp- tion of the iodide ions. Butler succeeded in showing that the expression for the solubility product holds only by considering the kinetic equilibrium be- tween solution and solid,

From the above it is evident that any crystal in equilibrhm with its solu- tion always will adsorb ions of its own kind, if they are present in excess in the solution; only under one condition, either in a saturated solution in water (if the adsorption potential of the anions equals that of the cations) or in presence of a slight excess of anions (adsorption potential of anions smaller than that of cations) or in presence of a slight excess of cations (adsorption potential of anions larger than that of cations) will the thermodynamic potential be equal to zero.

J. A. V. Butler: J. Phys. Chern., 28, 438 (1924); Trans. Faraday SOC., 19, 659, 723, 734 (1924).

8 H. R. Kruyt and P. C. van der U‘illigen: Z. physik. Chem., 139, 53 (1928).

864 1. M. KOLTHOFF

In considering the adsorption by a crystalline precipitate during its growth it will be seen that this thermodynamic potential primarily determines the amount of coprecipitation. Quantitatively there is a simple relation between the thermodynamic potential and the corresponding ion concentration in the solution as has been shown by F. Haber.g The same expression is found as the one that holds for the potential difference between an electrode and a solu- tion containing ions which the electrode can send into solution (Kernst’s equation) ;

E = - -1n alon + Const. RT n F

alon is the activity of the ion. I t is singular that no analytical application has been made of this relation

between thermodynamic potential of a crystal lattice and a solution contain- ing ions which are the building stones of the lattice. It may be expected, for example, that a barium sulfate electrode will behave as a specific electrode for barium-and sulfate ions. With the present development of the technique of measuring the electromotive force of cells with extremely high resistances, a wide field of potentiometric measurements may be anticipated.

The relation between thermodynamic potential and the amount of ions adsorbed has been determined in the case of silver iodide by E. Lange and R. Berger’O who found that the change of the thermodynamic potential is proportional to In C,,, in the solution and up to a certain limit to the con- centration of adsorbed ions on the surface.

3. Solubility and Particle Size For many years it has been known that the solubility of crystals of very

small size is larger than that of crystals of large dimensions” owing to the greater surface energy of the former. If the crystal size becomes smaller than I to z p the solubility quite generally increases with increasing surface development. The most extensive and interesting experiments in this field have been carried out by 11. L. Dundon and E. hIack,l* who also have given corrected values for the classical data of G. A. Hule tP on the solubility and crystal size of gypsum. Although the order of magnitude of the surface tension of various crystals as calculated by Dundon is probably correct no claim is made for great exactness of the figures. The particle size was approxi- mated by microscopic measurements, involving a relatively large uncertainty at’ small dimensions, and it was assumed that the crystals were quite com- pact, i.e. the presence of capillaries (inner surface) was not considered. More-

@ F. Haber: Ann. Physik, 47, 26,947 (1908); F. Haher and Z. Klemensiewicz: 2. physik. Chem., 67, 385 (1909).

E. Lange and R. Berger: 2. Elektrochemie, 36, 1 7 1 (1930). For literature review compare H. Freundlich: “Kapillarchemie,” 2nd Ed., 207-21 I

(1922); R. A. Gortner: “Outlines of Biochemistry,” I j o (1929); T. B. Smith: “Analytical Processes,” 239-278 (1929).

M. L. Dundon and E. Mack: J. Am. Chem. Soc., 45, 2479 (1923); hl. L. Dundon: 45, 2658 (1923).

I3G. A. Hulett: Z. physik. Chem., 37, 385 (1901); 47, 357 (1909).

THEORT OF COPRECIPITATIOS 865

over the following paradoxical phenomenon has not been adequately ex- plained: If coarse crystals of b:iriuni sulfate w r e added to a saturated solu- tion in equilibrium with crystals of very small size the solubility decreased gr:idually anti finally became equal to the “inacroscopic solubility” (normal solubility), although by microscopic examination a great number of particles of original small size appe:ired to he present. In order to explain this peculiar f:ict Ilundon considers one of the two altrrnntives; either that originally rii:iny particles had been present which were too small for microscopic mea- sureinent (which mould mean th:tt none of the data in the following table are correct) or that soon after a sxturated solution in equilibrium with the small p:irticlcs has been formed the solubility of the smaller particles is decreased by some adsorption effect such as the acquisition of il charge. According to Ilundon, the latter assuniption seems to be in harmony with the facts. How- ever it cannot be denied that this esp1nn:ition is far from being satisfactory. The adsorption process 1:rkes place rsther quickly and it is hard to accept the view that the particlcs do not acquire a charge until a saturated solution has been formed. JIoreover experimentnlly the influence of the charge of a particle on its solubility has never been shown although IV. C. AIcC. Lewist4 and L. F. Knapplj in more or less mathenintical papers show that the charge opposes the surface tension and hence tends to decrease the solubility. The charge increases with decreasing size and the solubility reaches a maximum a t certain dimensions, and decreases with increasing surface development. Without entering into a detailed discussion it should be realized that the solubility decreases with increasing thermodynamic potential of the particles, as has been mentioned in the preceding paragraph; experimentally however it has never been shown that the electrokinetic potential exerts a simi1:tr in- fluence; and on thermodynamic grounds this is not to be expected.

There is much more reason to assume that on account of the charge or the presence of an ion atmosphere around the particle the speed of exchange of ions between surface and solution (the kinetic equilibrium between solution and deposition velocity) is materially inhibited. This may give an explana- tion of the peculiar fact that the crystals of small dimensions disappear so slowly if macroscopic crystals are added to their saturated solution. At the surface of the large crystals, the solution and deposition equilibrium is estab- lished much more quickly than at the surface of the charged particles of small size. If the large and small crystals are both present as solid bodies the state of equilibrium between the former and the solution is readily established; the small crystals very slowly send more ions into the solution, which then are deposited on the surface of the large crystals; in other words the latter grow Since the solution rate of the latter is so sniall it will require a long time before all small particles have disappeared. This explanation based on the difference between solution and deposition rate a t the surface of small and large crystals readily accounts

slozclu a t the cost of the small sized particles.

I4 JV. C. McC. Lewis: Kolloid-Z., 25, 91 (1909). L. F. Knapp: Trans. Faraday SOC., 14, 457 (1921/22).

866 I. M. KOLTHOFF

for the fact that a normal solubility is found if the small particles are present with the larger size crystals.

This interpretation is in harmony with recent experiments of P. S. Roller’G on the relative rate of solution of gypsum. Down to a diameter of z 5 p he found the rate of solution to be proportional to the specific surface, and the dissolution factor was a constant. Below z5p the rate of solution increased more rapidly than the surface exposed until a t a size of 2 . 8 ~ the dissolution factor reached a maximum. At smaller dimensions it decreased again, probably on account of acquisition of a charge.

Assuming, then, that Dundon’s data a t least give the order of surface tension of various crystals it is possible to explain with their aid some facts which so far have been more or less obscure in analytical chemistry. In the following table a summary of Dundon’s results is given.

TABLE I Surface Tension of Some Substances according to M. L. Dundon

Substance M Mol. Vol. r (p) % Increase T,emp. u Hardness

PbI2 461 6.16 74.8 0.4 2 30 130 Very Soft CaS04.aH20 172 2.32 74.2 0.2-0.5 4.4-12 30 370 1.6-2

Ag2CrO4 332 5 . 5 2 60.1 0.3 IO 26 575 Appr. 2

PbF2 245 8 . 2 4 29.7 0.3 9 2 5 900 ” 2

SrS04 184 3.96 46 .4 0.25 26 30 1400 3.0-3.5 BaS04 (Hulett) 233 4.5 5 2 0.1 80 25 1250 2 . 5 - 3 . 5

CaF2 78 3.18 24.6 0.3 18 30 2500 4 M denotes molecular, weight, E density of crystal; Mol. Vol. molecular volume: r is radius of particle expressed in microns (microscopically measured), u is surface tension of particle, Yc Increase Sol. is per centum increase of solu- bility with regard to massive crystals.

If we consider slightly soluble salts the saturated solutions of which are completely dissociated into the ions and whose activity coefficients can be put equal to I the relation between increase of solubility on the one hand and the size of crystals and their surface tension on the other, can be repre- sented bv the equation

Solubility C

(Dundon) 0.2 90 30 3000

R is the gas constant, T the absolute temperature, M the molecular weight, Sr the solubility of particles with a radius r, S the same of normal crystals, u the surface tension and 5 the density.

By means of this equation and Dundon’s data the ratio Sr/S for barium- sulfate, silver chromate and lead iodide a t a size of 0.04~ ( r= 0 . 0 2 ~ ) was calculated.

‘6P. S. Roller: J. Phys. Chem., 35, 1133 (1931).

THEORY OF COPRECIPITATION

s o . 0 2 BaS04- = 930 S Ag,CrOl = 4.0

PbI2 = 1.38

Whereas a t this small size the solubility of barium sulfate is about 1000 times larger than that of the large crystals, the solubility of silver chromate under the same condition has increased only 4 times and that of lead iodide only 1.4 times.

These differences explain the fact that substances of about the same solubility and precipitated under analogous conditions behave in an entirely different way. Silver chloride and barium sulfate have a solubility product of the same order of magnitude; in spite of this, silver chloride is always precipitated as a flocculated colloid, barium sulfate as microcrystals under analytical conditions. It is easy now to account for this difference. Suppose a barium solution is added to a sulfate solution and silver ions are added to a chloride solution under such conditions that the “macroscopic supersatu- ration” of barium sulfate and silver chloride are the same. The silver halides form soft crystals’’ and their solubility is more or less independent of the crystal size: in other words, the solubility of the particles first formed in the solution (nuclei) is about the same as that of large size crystals. For barium sulfate (strontium sulfate, lead sulfate, etc.) the case is quite different. The solubility of the primary particles is much larger than that of the large crystals: therefore the solution is much less supersaturated with respect to the small particles of barium sulfate than of silver chloride. The velocity of formations of nuclei and growth of the latter to large crystals increases with increasing supersaturation. Therefore the formation of nuclei is much more spontaneous in the case of silver chloride than of barium sulfate; by the rapid formation of so many nuclei the solution is soon exhausted and no ions are left in solution to contribute to a growth of the small particles; the silver chloride precipitates as a flocculated colloid. In the case of barium sulfate much less nuclei are formed, which grow at the cost of the ions left in the solution; the slightly soluble substance finally settles as a micro- crystalline precipitate. From the above it is evident that Bottger’sl* relation between sensitivity of a precipitation reaction and solubility:

E = L + S in which E represents the sensitivity, L, the solubility and S the visibility of the particles has no general validity. I t will only holdig if the “micro” and “macro” solubilities of the substance are approximately the same as in the case of silver halides. But if this condition is not fulfilled, which is very often the case (barium sulfate, strontium sulfate, calcium oxalate) there is no simple relation between solubility and sensitivity of the reaction.

I’ Comp. A. Rei8 and L. Zirnrnerrnann: 2. physik. Chern., 102, 299 (1902). 18Comp. W. Bottger: Chern. Ztg., 33, 1003 (1909); M. Gorski: 2. anorg. allgem. Chem.,

81, 315 (1913); W. Bottger: Chem. Ztg., 36, 1097 (1912); 2. angew. Chern., 25, 1992 (1912). IQ I. M. Kolthoff: Bottger Festschrift, 2. anal. Chem., 86, 34 (1931).

868 I. ni. KOLTHOFF

The velocity of recrystallization of finely divided precipitates is also determined by the relation between solubility and surface tension. I t is well known that finely divided precipitates of barium sulfate, calcium oxalate, etc., which are formed in not too dilute solution on standing crystallize to large crystals; with silver chloride, such a recrystallization does not take place, because the difference in solubility between the small and large size crystal is too small. Only if the supersaturation is made very slight is i t possible to obtain large crystals of silver chloride (recrystallization from ammonia).

I t is not very easy to find suitable examples for the demonstration of validity of the mass law expression. A “saturated solution’’ of silver chloride or lead iodide gives almost instantaneously a precipitate with excess of one of the two ions; the experiment does not succeed with lead sulfate, strontium sulfate, calcium oxalate, etc. V. Chlopinzo reports that he was able to prepare stable lead sulfate solutions which were more than 1000 times supersaturated. The explanation is simple again, the solution is supersaturated only if inocu- lated with large crystals, but it is not necessarily supersaturated with respect to the primary particles formed at the beginning of crystallization.

Considering then crystallization from a solution it may quite generally be said that supeysatura‘tion is a relatiz’e conception: the supersaturation can- not be expressed in an absolute figure unless crystals of the normal solubility are present as solid body.

4. Filterability of Precipitates

I t is the usual practice in analytical chemistry to heat precipitates and mother liquor after precipitation for some time in order to obtain a more readily filterable precipitate by recryst,allization.21

In the preceding chapter however we have seen that the process of recrys- tallization of very small particles is extremely slow. DundonlZ for example boiled a suspension of barium sulfate (size 0.2 to 0 . 3 ~ ) under a reflux con- densor for a week with no visible change of particle size even when seeded with large crystals. From experiments made by Professor Bigelow, H. M. Trimblezz expected that the rate a t which larger crystals of a nearly insoluble substance grow at the expense of smaller ones in contact with the saturated solution must be very low, probably too low to account for coalescence of the precipitate as it occurs in analytical chemistry. Experimentally this was shown to be true. Finely divided barium sulfate digested for a few hours in the presence of some hydrochloric acid at 100’ was readily filterable if not stirred during digestion, Microscopic examination showed that the average size of the small particles (between I and 4p) remained unchanged during digestion. If the mixture was stirred during the digestion, no clear filtrate was obtained even after three to four days.

2 o V. Chlopin: Naturwissenschaften, 17, 959 (1929). 21 Cornp. Wi. Ostwald: “Grundlagen der analytischen Chemie,” 14, 22 (1894). rzH. M. Trirnble: J. Phys. Chem., 31, 601 (192;).

THEORY O F COPRECIPITATIOS 869

From these and analogous experiments Trimble inferred that the “co- alescence” of an unfilterable precipitate to give a filterable one, cannot be explained in terms of growth of the larger particles at the expense of the smaller ones. During the digestion without stirring the particles come into close contact with one another and form aggregates which adhere firmly. As digestion proceeds, barium sulfate either from supersaturated solutions or from dissolution of very small particles, deposits upon these aggregates and cements them together. This effect is enhanced when the solution is allowed to cool. On the other hand, when digestion is accompanied by stirring, all crystals grow alike at the expense of any material which may be separating from solution; there is no opportunity for cemented aggregates to form. With E. B. Sandell, the writer has made various experiments with

B C. A . f l o v a b / a D o u b i a L a y e r F i o c L u J a t c d F l a c c o l a t a d

( c o l l o i d ) ( X / n I A t t l C . ) ( P r o b a b f . c a s e )

FIG. I

suspensions of barium sulfate, calcidm oxalate monohydrate, silver chloride, etc. I t was observed that after digestion with or without stirring for one to two days, a distinct growth of crystals took place. Even in a silver-chloride suspension it was possible to observe small crystals under the microscope after heating for a day. Still it is true that’ in any case, after prolonged heating, a vast amount of the small particles is present with the original size. In the preceding chapter it has been shown that’ recrystallization of charged particles is a slow pro~ess.2~ On t’he other hand it is also true that suspensions which originally did not yield filterable precipitates gave clear filtrates after digestion. Under the microscope one gets the impression that’ the small particles of the precipitate are held together in a film after digestion. The problem of filterability then is reduced to the question, why the particles of a flocculated sol glue together. In textbooks on colloid chemistry this problem is not discussed. A priori it is not to be expected that small particles will grow t,ogether. If a flocculated particle possessed a pure crystal surface one could accept the view of K. Fajans and von Beckerat,h2‘ that the small particles will grow together with loss of energy, the negative ions in the surface of one lattice being attracted by those of opposite sign of the other lattice. However, it is hard to assume that the picture is as simple as this. Suppose in Fig. I “A” represents a particle of silver chloride, which is kept in colloidal solution by an excess of chloride ions. After destruction of the diffuse electrical double layer the picture is that represented by B or C. I t is

23 Many examples may be found in P. P. von Weimam’s monograph: “Die Allgemeinheit des Kolloideustandes. Kolloides und kristalloides Losen von Niederschliigen” (1925).

24 K. Fajans and von Beckerath: Z. physik. Chem., 97, 478 (1921).

870 I. M. KOLTHOFF

not to be expected that every kind of flocculating ion (X) can be incorporated in the crystal lattice (C), in other words forms mixed crystals and therefore C represents the most usual case after the flocculation. The surface of the other flocculated particles will have a similar appearance and there is no direct reason why the flocculated particles will lay their surfaces together (cement together). I t is much more reasonable to assume that a t the moment of flocculation the particles will repel each other; an impression which is actually obtained in observations under the ultramicroscope. This problem will be studied more extensively in Professor Gortner’s laboratory. The flocculating ions X (Fig. I ) which are adsorbed a t the surface of the floccu- lated particle are still able to exert a polarizing effect upon the solvent, in this case water, which means that they are more or less hydrated. It is a well known fact that a flocculated colloid contains large amounts of water. If the hydration is great enough a water layer will be formed around the particle, which, on account of its high curvature will have a tendency to decrease its surface. This may be accomplished by aggregation of various particles which in this way share their water jacket, thus giving the impres- sion of a film formation. In this manner it is also possible to explain why the rate of solution and of deposition of ions from the solution on the surface is so strongly inhibited, for the surface of the flocculated particles is more or less isolated.

Before drawing further conclusions, an experimental study is necessary to show whether the view offered here gives a true account of the facts. In a quantitative treatment, the orientation (polarization) of the water molecules around the particles should be considered.

5. The Formation of Precipitates. Amorphous and Crystalline Precipitates An exhaustive treatment a t this place of the speed of formation of nuclei

and of growth of small crystals would require more space than is allowable. There is a specisl lack of exact data in the literature on the speed of formation of nuclei from supersaturated solutions; it may be expected that this speed will be proportional to the degree of supersaturation if the latter is expressed with regard to the solubility of the nuclei (v. i.). More is known of the speed of growth of crystals, especially from studies made by p h y s i ~ i s t s . ~ ~

The speed of growth of crystals decreases on going from the corners to the edges and from thence to the planes. The speed of growth is not deter- mined by the rate of diffusion but by the speed with which the ions are adsorbed a t the crystal surface. Constituents which change the adsorption equilibrium may have a tremendous influence on the speed of growth of various pla6es and the crystal habit finally obtained. Special reference is

25 Comp. M. Volmer and I. Estermann: Z. Physik, 7, 13 (1921); 9, 193 (1922); Volmer and A. Weber: Z. physik. Chem., 119, 277 (1925); Volmer: Z. Elektrochemie, 35, 555 (1929); Volmer and M. Marder: Z. physik. Chem., 154 A, 97 (1931); K. S angenberg: Z. Krist., 59, 403 (1924); H. Brandes: Z. physik. Chem., 126, 196 (1926); W. %ossel: Natur- wisaenschaften, 18, 901 (1930); I. Stransky: Z. physik. Chem., 136, 259 (1928); I lB, 342 (1930); D. Balarew: Kolloidchem. Beihefte, 30, 249 (1930); 32, 205 (1931); for eneral dls- cussion comp. A. E. von Arkel and J. H. de Boer: “Chemische Binding als Eleftrostatiach Verschynsel,” 248-286 (1930).

THEORY O F COPRECIPITATIOS 87 1

made to the work of R. Marc and collaboratorsz6 and more particularly to that of W. G. France and his studentsz7 on the influence of dyestuffs on the habit of various growing crystals. The problem of crystal growth is of ex- treme importance for that of coprecipitation because the amount of copre- cipitated substance is greatly dependent upon the speed of formation of the crystals. This will be shortly discussed in the following chapter.

The form, shape, and size of a precipitate depends upon the experimental conditions. From all that has been said above, it is evident that a simple relation between supersaturation on the one hand, and the speed of growth and form of crystals on the other, as has been advocated by P. P. von Wei- marnz8 cannot exist.

Although it cannot be denied that interesting statements and experiments of qualitative nature may be found in von Weimarn’s numerous publications, his general equations are too simple and cannot be accepted. The velocity of formation of nuclei (condensation) during the first stage of the precipi- tation is formulated thus:

in which W is the initial rate of precipitation; Q the total concentration of the substance that is to precipitate, S the solubility of coarse crystals of the substance; Q - S = P the amount of supersaturation and U the percentage supersaturation a t the moment precipitation begins. Von Weimarn recog- nized that the velocity W of the first stage of precipitation could not be measured in actual practice and therefore, he introduced a specific coefficient called the “precipitate form coefficient” or “dispersity coefficient X,” which is given by the expression:

S = P S K,I, Kad K b d K,, Z

in which Z is the viscosity, and Knb Kcd etc. represent the “physical and chemical association” of the substances AB, CD etc., which enter into the reaction AB (in solution) + CD (in solution) = AC (precipitate + BD (in solution). H. B. WeiserZ9 remarks: “The significance of ‘physical asso- ciation’ is known, but it is not clear what von Weimarn means by ‘chemical association.’ ”

The growth of the nuclei depends not only on the degree of supersatura- tion, a t a given moment, but also according to von Weimarn upon the diffu- sion coefficient :

V = D / d 0 (C-S) z e R . Marc and Wenk: Z. physik. Chem., 61, 385 (1908); 68, 104 (1910); 73, 685 (1910);

75, 710 (1911); 79, 71 (1912). 4 7 T. S. Eckert and W. G. France: J. Phys. Chem., 34, 72 (1930); F. G. Foote, F. C .

Blake and W. G. France: 34, 2236 (1930); W. G. France: Col?oid Symp. Ann., 59 (1930); especially C. H. Saylor: J. Phys. Chem., 32, 1441 (1928).

2u P. P. von Weimarn: “Zur Lehre von den Zustknden der Materiel’ Bd I Text, Bd I1 (1913); “Die Allgemeinheit des kolloiden Zustandes” (192 j).

2 8 H. B. Weiser: “The Colloidal Salts” (1928); for a discussion of von Weimam’s theory see also T. B. Smith: “Analytical Processes,” 263 (1930).

872 I. M. KOLTHOFF

in which D is the diffusion coefficient, d the thickness of the adherent film, 0 the surface, C the concentration of the solution and S the solubility of the disperse phase.

Without entering too much into details, it is evident that von Weimarn’s equations have no general quantitative bearing:

(a). In the equations of the speed of formation of the nuclei S represents the solubility of coarse crystals. In a preceding chapter we have seen that S is a function of the size of the crystals, and even the order of its magnitude may be quite different for nuclei and for larger crystals; the percentage supersaturation has no definite value.

The equation for the speed of growth of the crystals cannot be accepted, since this rate does not depend upon the speed of diffusion but upon the speed of adsorption. All factors which influence the speed of adsorption of the ions during the growth may materially change the speed of growth and the habit of the crystals obtained.

I t is to be expected that the speed of formation of nuclei will be dependent not only upon the relative supersaturation but also upon the actual concentration of the reacting ions. The formation of nuclei in a solu- tion ten times supersaturated with regard to calcium sulfate is much more rapid than in that of barium sulfate of the same supersaturation. That the actual concentration of the reacting ions is of primary significance may also be inferred from the studies of Sven OdBnzg8 on the formation of precipitates. I t should be mentioned that in most studies on the speed of precipitation the supersaturation was calculated on the basis of the solubility of the sub- stance in pure water. Even if the difference between “micro” and “macro solubility” could be neglected the repression of the solubility by the common ion effect should be considered. On account of this omission most of these studies have no quantitative significance.

Of much more importance are the views of F. H a b e P on the formation of precipitates. He considers primarily the following two factors: aggregatzon eeloczty, (called by Haber Hdufungsgeschwindigkeit) and orientatzon neloczty, (Ordnungsgeschwindigkeit). If the solubility limit is exceeded, the molecules or aggregates of molecules, will have a tendency to lay themselves together and to accumulate to give larger aggregates. This aggregation velocity is a function of the supersaturation; the larger the latter, the less regular the separated aggregates will be. Besides the supersaturation the absolute concentration of the reacting ions will also be of significance. The aggregates formed, in which the molecules are mixed in a more or less arbitrary manner, are not stable. By loss of energy they tend to reach a state of equilibrium, in which the mass is ordered in a regular way in a crystal lattice. The speed with which this process takes place is called the orientation ve- locity. I t is evident that the form in which a precipitate separates depends upon the competition between the aggregation and orientation velocity.

(b).

(c).

z9* Sven O d h : Ark. Kemi Mineral. Geol., 7, No. 26 (1920); 9, No. 23 (1925); No. 32 (1926).

3 O F. Haber: Ber., 55, 1717 (1922).

THEORY O F COPRECIPITATION 873

If the supersaturation is extremely large the aggregation velocity will domi- nate and the separated particles do not show an X-ray spectrum, in other words they are amorphous. On standing, (aging) the amorphous precipitate will slowly transform into a crystalline modification. The phenomena de- scribed can be observed in the precipitation of various extremely slightly soluble hydrous metal oxides and metal sulfide^.^'

Strongly polar substances, such as silver chloride, for example, will have a high orien- tation velocity, comparable with the crystallization velocity of this kind of molecule from the vapor state. The more completely the central ion of a molecule is surrounded by the ions of opposite charge the weaker the electric field outside the molecule will be, because its electric effect is mostly com- pensated by the surrounding ions. Such molecules will show a small orienta- tion velocity. From this point of view it is clear why precipitated cadmium hydroxide, for example, is never obtained in an amorphous form; hydrous ferric oxide, on the other hand, if precipitated from cold solutions is amor- phous, but is transformed on aging, especially on heating into a crystalline product. Hydrous oxides of the quadrivalent cations, like those of thorium, cerium, zirconium, in which the central ion is more or less completely sur- rounded by the anions, always precipitate in an amorphous form and show on aging very little or no tendency toward crystallization.

In the slow preparation of colloidal suspensions according to the conden- sation method, crystalline sols are obtained; if the precipitation takes place quickly as under analytical conditions, amorphous precipitates may be formed. In the older literature, a sol was usually considered as an intermediate state in the process of formation and growth of Precipitates, this appears not to be true; the sols are crystalline whereas it is quite possible to obtain many slightly soluble substances in an amorphous form.

It is of practical importance to consider the solubility of amorphous precipitates somewhat more fully. I t does not seem justifiable to speak of an “amorphous rnod?fication” if by some wild growth an amorphous precipi- tate is obtained; at least if a. “modification” is considered as a chemically homogeneous individual. The amorphous form consists of aggregates which :ire grown together in a more or less arbitrary manner; it is not stable but is undergoing continuous transformation into a more stable crystalline state. The soliibility of the amorphous form therefore, will not only be quite different from that of the crystalline phase, but what is more important, the solubility will no longer be constant but depend upon the state in which the amorphous form happens to be at a certain moment. This inference is quite important because in analytical problems, such as the precipitation of slightly soluble hydrous oxides and metal sulfides, the mass action law as a rule is applied. The latter, however, holds only for stable modifications when there is equilib-

The orientation velocity will vary for various substances.

For esampies comp. F. Haber: (ref. 27); J. Bbhm and H. Siclassen: 2. anorg. allgem. Chem., 132, I (1923); G. F. Huttig and collaborators: 187, I ; 190, 353, 364; 191, 161; 192, 1 x 7 , 2.25; 193, 81, 93, I O O irggo). Kolloidchem. Beihefte, 31, 347 (1930); and especially R. Fricke: 2. anorg. allgem. Chem., 166, 244 (1927); Kolloid-2. 49, 229 (1929).

874 I. M. KOLTHOFF

rium between solution and solid phase. The amorphous form is not in internal equilibrium and, therefore, neither with the solution. If an amor- phous hydrous oxide is precipitated under various conditions, the same solubility product can hardly be expected. The water present in the amor- phous precipitate will also have a great influence upon the solubility. Sup- pose for example, that a hydrous aluminum oxide is precipitated by mixing aquo aluminum ions Al(HB06)+++ with hydroxyl ions. With the large aggregation velocity, the aluminum ions will carry part of their water into the amorphous precipitate, and the hydroxyl ions probably will keep part of the water molecules oriented by polarization. The water is a powerful dielectric, and by its presence in the precipitate, will diminish the force by which the aluminum and hydroxyl ions attract each other in the solid. Therefore] owing to the presence of water between the ions, the solubility of the amorphous hydrous aluminum oxide must be much greater than that of the crystalline modification. It cannot be expected that the solubility will remain a constant during the transformation of the amorphous into the crystalline form; i t will gradually decrease until the entire precipitate is present as the crystalline modification. Neglect of these considerations has caused some unfortunate confusion in the literature.

In the rapid formation of precipitates, another point must be considered. If various crystalline modifications of a substance exist, there is always a possibility that a metastable form will separate out first. On standing the labile form will be transformed more or less rapidly into the stable modifi- cation thus causing an entire change of the internal structure. B e r t h e l ~ t , ~ ~ for example, claimed that freshly precipitated silver iodide undergoes a trans- formation on standing, a fact not confirmed by the experiments of J. W. A. van Henge1.33 In agreement with Berthelot, the latter found however, that freshly precipitated barium carbonate undergoes a structural change on aging. E. B. Sandell, in experiments carried out in this laboratory found that calcium oxalate di or tri hydrate was separated under conditions under which only the monohydrate is stable. In the interpretation of the change of the amount of coprecipitated substance with the time of standing, such allotropic changes must be considered.

6. The Theory of Coprecipitation In the introduction i t was emphasized that the expression “carrying

down” used as a collective term to indicate that a precipitate contains foreign constituents is misleading, and that first of all i t should be decided whether the impurities are incorporated in the crystal lattice or form imperfections in the interior of the crystals or finally are adsorbed a t the surface of the precipitate. The second group in which the impurities are present as imper- fections in the crystals is the most common one and will be defined as “real coprecipitation.”

r2 Berthelot Ann. Chim. Phys. 151 4, 181 (1875); 29, 242 (1883). 33 J. W. A. van Hengel. De metastabiliteit der stof. Praecipitatie-reacties, Thesis Utrecht

(1931). On theory see espec.ally C. H. Saylor (ref. 27).

THEORY OF COPRECIPITATION 875

Mixed crystal formation: Although the phenomena of isomorphism and mixed crystal formation have been known for almost a century, it is only of relatively recent date that more general relations have been discovered between size of ions and mixed crystal formation. H. G. Grimm and collabo- rators34 formulated three conditions which must be fulfilled for the formation of mixed crystals of polar compounds:

( I ) , The chemical building type must be the same. ( 2 ) . The lattice types must be similar. (3). The lattice constants must be of the same order of magnitude.

Grimm already showed that the following systems form mixed crys- tals: SrSOl + KMn04; BaSeO, + KMnO,; BaCrO, + KMn0,; BaS04 + KBF4; KBF, + KMn0,. Grimm’s studies are supplemented by the beau- tiful investigations of V. M. Goldschmidt35 on the relation between crystal structure and lattice properties on the one hand and chemical constitution on the other. The laws of isomorphism and mixed crystal formation are laid down, especially in his seventh Isomorphism he defines as the phenomenon that substances of analogous chemical formula show analogous crystal structure. Analogy of chemical formula means analogous “brutto formula” in respect to total number of ions and to the number of positive and negative building stones (ions). Analogy of crystal structure means that both substances possess a geometrically symmetrical elementary paral- lelopiped, in which a same number of atoms is arranged in a geometrically similar fashion in such a manner, that the kind of charge (positive or nega- tive) of the individual crystal building stones correspond with one another in both structures. Isomorphism occurs if the relative size of the crystal building stones and the relative strength of their polarizability within certain limits are identical, assuming of course that the brutto formulas of both substances are the same. If not only the relative size, but also the absolute size of the building stones are the same, the conditions of mixed crystal formation are created, other conditions being the same. There is a certain tolerance with regard to similar size; it seems that mixed crystal formation is still possible if the radii of the ions does not differ more than 157,. With these rules it is understandable why BaS04 - KMnO,; BaSOl - PbS04; CaC03 - NaN03 can form mixed crystals, Relatively little is known of the properties‘of mixed crystals, which are formed in analytical processes; especially of their stability. From studies of 0. Ruff and E. A ~ c h e r ~ ~ one would infer that mixed crystals are very unstable if one of the constituents is slightly soluble and the other readily soluble. Thus in the case of CaC03 - NaN03 Ruff and Ascher found practically no sodium nitrate in the crystals,

34 H. G. Grimm and G. Wagner: Z. physik Chem., 132, 131 ( ~ 6 ) ; H. G. Grimm: 98, istall., 57, 574 (1922); 353 (1921); Z. Elektrochemie, 28, 75 (1922); 30, 467 (1924); Z.

Handb. Physik, 24, 581 (1927). 35 V. M. Goldschmidt: esp. Geornetrische Verteilun sgesetee der Elemente VI1 Die

Gesetze der Kristallochernie, Videnskapssel Skrifter I &fat. Naturw. Klasse Det Norske Videnskaps Akad. i Oslo I 1926; No. 2 ; Utgitt for Fridtjof Nansens Fond.

3E 0. Ruff and E. Ascher: 2. anorg. allgem. Chern., 185, 369 (1929).

876 I. M. KOLTHOFF

if the precipitate was kept under the mother liquor until no further change took place. On the other hand, if both compounds are slightly soluble, as in the case of BaS04 - PbSO, both cations are always present in the pre- cipitate. From the analytical point of view, it is highly desirable to obtain more information regarding the ratio in which the two constituents occur in mixed crystals if precipitated under various conditions, and also of the stability of the crystals if kept under the mother liquor. Such studies are being made in our laboratory. I t seems that mixed crystal formation is not materially dependent upon the manner of precipitation; i. e. whether an excess of cations or anions is present during the precipitation. This is in striking contrast to what occurs in “real coprecipitation,” where the amount of coprecipitated foreign ions is highly dependent upon the conditions of pre- cipitation.

Otto Hahn”’ formulates his precipitation rule in the following way; “An ion precipitates from any dilution with a precipitate crystallizing out, if it is incorporated in the crystal lattice; i.e. if it forms mixed crystals with ions of the crystalline precipitate. If it does not form mixed crystals, the ion remains in the filtrate even if its compound with ions of opposite charge in the precipitate is slightly soluble.” According to 0. Hahn3* mixed crystal formation is possible even if it does not occur under normal conditions. This phenomenon is called “isodimorphism” and occurs for example accord- ing to Hahn39 in the cases BaCla + RaB(ThB) or RaD(ThD); PbS04 (ThB) + K2S04; T12S04 + ThBS04; PbCr04(ThB) + Ag2Cr04. Although Hahn worked under unusual conditions (the concentration of the radioactive constituent always was extremely small) it seems to the author that Hahn has not proved definitely the ex’stence of such isodimorphism. Hahn as we will see later, does not make a distinction between mixed crystal formation and real coprecipitation, and there are reasons to assume that his cases of isodimorphism actually are examples of true coprecipitation. However, more experimental work must be done before a decision can be reached. From the above short discussion, it follows that in all cases of coprecipitation, the possibility of mixed crystal formation should be considered.

Adsorpt ion a n d “Rea l Coprecipitation”: In a study of the purity of precipitates, a distinction must, be made between adsorption and real coprecipitation. If a precipitate separates as a flocculated colloid, it has a layer of flocculating ions rigidly adsorbed at its surface. These adsorbed ions can be partly removed by washing out or replaced by washing with suitable electrolyte solutions which do not interfere later in the analytical process (in gravimetric analysis : ammonium salts, acids and other electro- lytes which volatilize on gentle ignition may be used.) If a real coprecipita- tion takes place, the impurities are present in the interior of the crystal and cannot be removed by a washing procedure. If a precipitate separates

3 i Otto Hahn: 0. Erzhacher and N. Feichtinger: Ber., 59, 2014 (1926); 0. Hahn: Natur- nissenschaften, 14, I 196 (1926).

31 0. Hahn: Z. angew. Chem., 43, 871 (1930). 3 0 0. Hahn: Sitsungsber. preuss. Akad. Wiss., Physik. Math. Abt., 30, 547 (1930).

THEORY OF COPRECIPITATION 877

in a micro crystalline form, such a coprecipit'ation always seems to occur even if there is no trace of mixed crystal formation. From scant data in the literature, and our own experience, one would infer that colloidal precipitates always are contaminated by adsorbed ions but neuer contain the fore ign ions in the interior of the particles. In order to explain this, one has to realize that as long as the particle is in a colloidal state, the adsorbed foreign ions are present on the mobile side of the electrical double layer around the particle; they are not fixed at' the surface. Therefore, as long as t,he particles are in the colloidal state, there is no reason why these ions which have retained their mobility should be incorporated during the growth of the particles (unless mixed crystal formation occurs). Here the electrokinetic potential of the particles is the governing factor. After the colloidal state has been passed, the thermodynamic potential is the main factor in the occlusion during the growth. As has been discussed in the first chapter, a crystal surface of a slightly soluble compound adsorbs that one of its own ions which happens to be in excess in the solution. A growing barium sulfate crystal for example, in the presence of a large excess of barium chloride in solution, will adsorb barium ions at its surface. Owing to the electroneutrality of both phases, the other ions of the electrolyte (here chloride ions) must be dragged along with the barium ions to the surface of the growing particle, where they will be more or less fixed. If the condi- tions are such that the crystals will grow very slowly, the chloride ions will be replaced more or less by sulfate ions, which fit in the crystal lattice and the coprecipitation will be relatively small. If the crystals grow much faster, there is no time available for a complete exchange between contami- nating ions and those belonging to the crystal and a large coprecipitation will result. If finally, the conditions are such that owing to an extremely large supersaturation the particles are not given a chance to grow to bigger crystals, a flocculent colloid will separate and the coprecipitat'ion will be extremely or negligibly small. Various studies made in our laboratory, which will be discussed in subsequent papers, yield results in complete har- mony with the postulates of t,he developed theory. In t,he cases of calcium oxalate (E. B. Sandell) and barium sulfate, the largest coprecipitation is observed if t'he crystals are allowed to form under such conditions that they have a relatively large size. If the supersaturation is made so large that a flocculated colloid settles out, no coprecipitation should be observed but the impurities should be kept in an adsorbed state at the surface. If these small particles are allowed to recrystallize, a very slow growth takes place and a practically pure precipitate is obtained. If, finally, the conditions of precipi- tation are such that the crystals acquire an intermediate size, a real copre- cipitation takes place. We therefore, arrive at the interesting conclusion that the largest crystals are the least pure if formed under analytical conditions. This is not in harmony with the general rules of analytical chemistry, where the directions usually are based on the assumption that larger crystals are purer than small crystals. In a recent publication, 0. Hahn38 expresses this rule in the following way:

878 I. M. KomnoFF

“Fur die analytische Chemie ergibt sich auch aus diesen Versuchen das ja schon in der Praxis verwendete Verfahren, Niederschlage in moglichst oberflachenarmer, gut kristallisierender und daher gut filtrierbarer Form ahszufiihren. Al le Adsorptionsvorgange werden dadurch stark zuriickgedrangt. Je mehr man von diesem Grundsatz abgeht, destomehr entfernt man sich von der Arbeitsweise des Analytikers; man kommt in das Gebiet des Kolloid- chemikers; die Vorgange an die Grenzflachen werden ausschlaggebend.”

The contradiction between Hahn’s and our views is explained by the fact that Hahn considers only the adsorption at the surface after the crystals have been formed, but not the adsorption during the growth. For the s tudy of copre- cipitation the adsorption during the growth however i s the predominating factor. It is of interest to discuss a few other consequences of our picture of copre- cipitation, although a more detailed discussion will be given later in connec- tion with reports of practical work. The thermodynamic potential is deter- minative for the kind of adsorption taking place during the growth. If barium sulfate is precipitated from a solution containing an excess of sulfate ions, the latter will be adsorbed during the growth of the precipitate and drag foreign cations like H30+; K+, Na+, Caff etc. to the surface; if on the other hand, barium ions are in excess during the growth, foreign anions like chloride, nitrate, etc. will be adsorbed and will coprecipitate with barium sulfate. Depending u p o n the conditions of precipitation, a cation or anion occlusion will be predominant. Experimentally, this has been shown to be true in the cases of barium sulfate and calcium oxalate monohydrate, although it should be mentioned that on account of incomplete dissociation of binary and ternary electrolytes, an apparent cation precipitation may be found where only anion coprecipitation is expected and also the reverse. However, in its general form, the rule derived seems to be of general applicability. Of special interest is the coprecipitation of ferric iron with barium sulfate. If the precipitation is carried out in a solution containing an excess of sulfate, a large coprecipitation of ferric iron-either as ferric ions or more probably as positive colloidal hydrous ferric oxide which is formed by hydrolysis- takes place. If the acidity of the solution is increased, the concentration of positive ferric oxide part’icles decreases and therefore, the amount copre- cipitated also. On the other hand, if barium sulfate is precipitated from a solution containing an excess of barium ions, there is no coprecipitation of ferric iron a t all.

According to the above views contaminating ions are not present in the crystal lattice, but as imperfections of the crystal lattice. They may be identified with the “Lockerstellen” or Hohlraume” in real crystals according to A. Smeka140 or “centra of activity,” according to H. S. Taylor.41

I t should be remembered that coprecipitat’ed foreign ions are not fixed by the lattice and therefore, keep more or less of their water of hydration. In this way the presence of the solvent (mother liquor) is explained and it

4 o A. Smekal: Z. angew. Chem., 42, 489 (1929), where also other literature is given; comp. also W. Jost: Z. physik. Chem., 6B, 88 (1929); 7, 234 (1930).

4L H. S. Taylor: Proc. Roy. SOC., 108, IOj (1925).

THEORY O F COPRECIPITATION 879

is a problem of interest to determine whether there is a simple relation be- tween the size of coprecipitated ions (which determines with the charge, the polarizing effect upon the solvent) on the one hand, and the ratio of amounts of coprecipitated ions and solvent on the other.

I t is a well known fact that “real crystals” are far from ideal (Smekal);40 they seem to have a porous structure. The more they are contaminated, the more pronounced the porous structure will be and vice versa. This may explain the peculiar fact that if a freshly formed precipitate is kept under the mother liquor, under such conditions that no recrystallization can take place, the amount of coprecipitated impurities decreases on aging and reaches a minimum after a day or so standing. This phenomenon seems to be quite general and has been noticed in the case of barium sulfate, lead sulfate, calcium oxalate, etc. The crystals seem to exert an action tending to perfect their own lattice which can be done only by expelling the impurities. In the interpretation of the peculiar aging effect, i t should not be overlooked that in various cases a possibility of the primary formation of a metastable modi- fication of the precipitate exists, which on standing may change into the stable modification thus yielding a radical internal change.

Summarizing then, i t seems that real coprecipitation must be attributed to and is governed by adsorption phenomena during the growth of the crystals. A purely chemical interpretation based on the formation of definite chemical compounds between ions belonging to the lattice and contaminating ions of opposite sign, as is still done by 2. Karaoglanow42 must be rejected.

D. Balarew43 in his extensive studies on purity of precipitates, attributes any kind of coprecipitation to inner adsorption by crystalline salts. In so far as true coprecipitation is concerned, Balarew’s views approach those developed in this paper; however, his picture and many of his statements are vague and he does not mention any connection between thermodynamic potential and kind of ion coprecipitation. As a result of coprecipitation “polar adsorption compounds” like BaS04, KzS04, HzO are formed according to Balarew. According to his opinion the occluded water still has solvent properties, but only for one special salt. If, for example, potassium sulfate and water are occluded by barium sulfate, no sodium or lithium sulfate can be coprecipitated, because the occluded water has solvent properties only for potassium sulfate. This view cannot be accepted as true, and is contrary to experimental evidence available a t the present time. Although Balarew’s papers contain many interesting data, his picture of coprecipitation is not of wide bearing and general applicability.

on fractional precipitation, formation of mixed crystals and adsorption compounds is very important and stimulating, but again no

Ruff’s

4*Z . Karaoglanow: Ber., 63, 597 (1930); Karaoglanow and B. Sargotschev: Z. anal. Chem., 187, 273 (1930); 81, 275 (1930); 2. anorg. allgem. Chem., 194, I j I (1930); 195, Ioj (1011).

~ .” I

4J Comp. summary of his work Kolloidchem. Beihefte, 30, 249 (1930). 440. Ruff and B. Hirsch: 2. anorg. allgem. Chem., 146, 388; 150, 8j (192j); 151, 81

(1926); 0. Ruff and E. Ascher: 185, 369 (1929); 0. Ruff: 185, 387 (1929).

880 I. M. KOLTHOFF

clear picture is developed for the case of true coprecipitation; especially adsorption during the growth of the crystals is not considered. For a quan- titative treatment of the problem, the change of adsorption with time has to be studied more closely. Interesting and promising investigations of this subject are being carried out in 0. Hahn’s laboratory, especially by L. Imre.4;

Moreover, the change in internal structure of a fresh precipitate in con- tact with its mother liquor has to be considered with regard to decrease of coprecipitated impurities on standing.

summary

(I). Impurities in crystalline precipitates are due to coprecipitation or post precipitation. Three cases of coprecipitation are to be distinguished : Mixed crystal formation, in which the impurity is incorporated in the crystal lattice; real coprecipitation, in which impurities form imperfections in the crystal and surface adsorption by the precipitate after it is formed. In all these cases the presence of impurit’ies is attributed to adsorption, either during the growth of the crystals or after their separation.

In the case of real coprecipitation, the adsorption of foreign ions during the growth of the particles is of primary importance. Depending upon the thermodynamic potential of the precipitate during the growth, a cation or anion coprecipitation may be expected. If, for example, during the precipitation of barium sulfate, an excess of barium ions is present, a coprecipitation of anions may be expected, in the reverse case a coprecipi- tation of foreign cations.

(3): Up to a certain limit, coprecipitation with a slightly soluble substance increases with crystal size; a statement which is contrary to the general rules of analytical chemistry.

The Paneth-Fajans precipitation rule should be extended in the following way: The higher the valence of an ion the more preferential it will be adsorbed by an ionic lattice which contains an excess of lattice ions of the sign opposite to that of the secondary adsorbed ions.

A precipitate which does not exceed the colloidal dimensions con- tains impurities in an adsorbed but not in a coprecipitated state (provided there is no mixed crystal formation). As long as the particles are in colloidal solution, the foreign ions are present on the mobile side of the double layer and are not occluded.

(6). The analytical significance of the relation between particle size and solubility has been discussed. The concept of supersaturation with regard to speed of formation of precipitates has no exact significance; it depends upon size and surface tension of the tiny particles. Also for this reason von Weimarn’s expression of the relation between the speed of formation of precipitates and supersaturation has no general validity.

( 2 ) .

(4).

( 5 ) .

46 L. Imre: 2. angew. Chem., 43, 875 (1930); 2. physik. Chem., 153A, 127, 262 (1931).

THEORY O F COPRECIPITATION 881

( 7 ) . A discussion is given of filterability and properties of a flocculated colloid.

(8). An explanation is given of the fact observed by Dundon, that a mixture of very small and large crystals shows the normal solubility.

(9). The expression “amorphous modification” has no exact significance. The properties of an amorphous substance are more of less accidental; the mass action law cannot be applied when amorphous precipitates are dealt with.

( I O ) . A freshly formed precipitate is not in equilibrium with its mother liquor. On standing, a change of the internal structure of the crystal takes place. Under any conditions, the amount of coprecipitated ions decreases with time of standing before filtration.

School of Chemistry of The Cniuersity of Mznnesota, Minneapol is , September. 1931.