RATE OF NUCLEATION OF SILVER CHROMATE
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T H E RATE OF NUCLEATION OF SILVER CHROMATE I N SUPERSATURATED SOLUTIONS’ ANDREW VAN HOOK
AND
J. C. AHLBORN
Department of Chemistry and Chemical Engineering, University of Idaho, Moscow, Idaho
Received July 18, 1041 INTRODUCTION
In two previous papers (7, 8) on the kinetics of the precipitation of silver chromate it was implied that the rate of nucleation thereof is h e a r in terms of the supersaturation, when this concentration is expressed aa the ion product. This present report verifies the assumption for the purpose for which it waa suggested. METHODS
Proper amounts of dilute silver nitrate solutions were poured rapidly into violently stirred solutions of potassium chromate. At definite intervals of time an aliquot portion of the reaction mixture was removed, and the reaction therein arrested by pouring into a large excms of saturated reaction medium (2). The seed density in these “killed” mixtures was then determined, without too much delay, by direct count under a Bausch and Lomb cardiod condenser mount. Since the same technic was always used, the original seed density may be taken as proportional to the actual count. By employing extreme care in the cleaning, drying, and handling of all equipment, the background count was always very small. The resolving power of the optical combination used was equivalent to a sphere of silver chromate 40 millimicrons in diameter. The determination was also effected in 3 per cent gelatin medium and in huffered medium (pH 5.8, acetic acidsodium acetate). Satisfactory results were not obtained. In the former case it waa undoubtedly the dispersing action of the protein which vitiated the anticipated results, while in the latter case coagulation was intense. RESULTS
The assumption being tested is:
-
n=A+kSt
where n is the seed density, A the initial seed density, S the supersaturation expressed as the ion product, t the time, and k the velocity constant. The solutions observed were all uninoculated and therefore A is ostensibly zero. The fundamental seed nucleus, or “grain” (l),is of a size far below that discernible in the ultramicroscope. This “grain” grows in the solution a t a rate dependent on the supersaturation in a bimolecular manner; since all the ob-
’
This paper is baaed upon a thesis submitted by J . C. Ahlborn to the Graduate Faculty of the University of Idaho in partial fulfillment of the requirements for the degree of Master of Science, June, 1941.
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ANDREW VAN HOOK AND J. C. AHLBORN
servations reported are within the induction period of the reaction, this growth velocity remains essentially constant within a given run. Hence the actual seed or grain density will be directly proportional to the observed count.
MINUTES
FIG.1. Nucleation rates in aqueous medium. X, Ho Ho = 25 X 1W”;0 ,Ho = 30 X 10-”; +, Ho = 35 X 10-l’.
=
FIG.2. Kon-stoichiometric ratios and gelatin medium.
ahg+.acro,--=
+, aqueous
20 X 10-1s; 0 ,
medium, Ho =
35 X 10-12, R = 6. 0 , 1 per cent gelatin, unbuffered, pH = 4.8, .V(Ag,CrOc) = 0.005. 3 per cent gelatin, unbuffered, p H = 4.7, .V(Ag2Cr04) = 0.005.
X,
The principal results obtained are presented in figures 1 and 2 . The individual values, composing the averages, deviate only slightly from the mean. From the lowest concentration practical to measure, to a concentration equivalent to Ho = 35 X 10-12, the rate of nucleation is seen to be fairly linear over the greater part of the induction period. Toward the end of this period the grain number falls away from linearity, and this deviation is more pronounced, and a t earlier periods, the larger the number of particles present. The cause of these devia-
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397
tions is undoubtedly aggregation of the primary particles, and the form of the curves may be accounted for by modifying our equation by the Von Smoluchowski expression for slow coagulation. The new equation is
where T is another cohstant, effectively the half-life of the aggregation. Thus when t is small the n vs. t plot remains essentially linear, while as t grows larger relative to T , the plot falls from linearity. It was attempted to eliminate or reduce the extent of aggregation by the use of a dispergator, as suggested by Von Weimarn (10). Most of the substances tried were ineffective, others prevented the appearance of crystals entirely, while only a few (starch and 0.25 per cent gelatin) acted partially to reduce aggregation. There undoubtedly exists a condition where, in the presence of a dispergator, silver chromate nuclei would be generated and grow to a visible size without aggregating. However, the exact definition of this condition is a difficult and questionable matter and its specification is hardly warranted in the light of the limiting results obtained. For non-stoichiometric ratios of reactants the observed results are the same as with equivalent amounts, if the non-equivalence ratio is not too far from 1. The result shown in figure 2 represents the extreme, and the limiting values of R (R=
Equivalents of AgN03 Equivalents of K2Cr04
which give concurring plots may be set a t about 5/1 and 1/5. These limits are much less than those reported from the electrometric precipitation curves (7, 8) -namely, 10/1 and 1/100-and the differencemay be ascribed to the coagulating effect of the excess electrolyte. The deviations of the curves were always in this direction. The same behavior is observed when neutral electrolytes are added to the medium. Satisfactory results could not be obtained in the usual buffered gelatin medium. In a few cases the antagonizing coagulating and dispersing effects were minimized by using dilute unbuffered gelatin and more concentrated reactants, so that free crystal growth occurred for a measurable time. These results are displayed in figure 2, and are sufficient to indicate the probable linearity of nucleation in the presence of gelatin. DISCUSSION
The results may be taken as approving the original implication of a linear rate of nucleation of silver chromate in aqueous and gelatin medium. In view of the success of this assumption in explaining the course of the precipitation in the previous analytical determinations (7, 8), it is also not unlikely that the same situation is realized in the presence of excess electrolyte. This would also mean that the young aggregated particle acts more like a collection of nuclei or grains than like a single center of crystal growth. This harmonizes well with our present concept of crystal building (5, 9).
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ANDREW VAN HOOK AND J . C. AHLBORN
15'
3 t
3
10-
b
B
4
=.
If one replaces the foregoing classical analysis by one recognizing the eatablished existence of germ nuclei preexisting in the metastable solution (1, 3), the same result is obtained. For then, the rate a t which these latent nuclei become active nuclei is proportional to their number, or
d" = nN dt where N' is the number of activated nuclei, N the number of latent nuclei, and n the probability of their activation. If n remainsconstant with respect to time and concentration, and if we ignore the ingestion and deactivation of germ nuclei by the active ones, - d=N ' nN - -dN -_ dt dt
which becomea N o d , or the same as our previous equation, when (nt) is s m d .
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There is some question about the constancy of the probability factor n (I, 3, 4), and it is suggested that more complete data of the type presented here may indicate its dependence on time and concentration. I t is planned to collect such data on systems in which some of the complications encountered with silver chromate are not present. SUMMARY AND CONCLUSIONS
A previously implied equation for the rate of nucleation of silver chromate in its precipitation from solution (n = A kSt) is experimentally justified. For the purpose of explaining the Liesegang ring phenomenon of rhythmic precipitation this equation may be taken as valid. Methods for the study of the number of latent nuclei preexisting in solution we suggested.
+
REFERENCES
AVRAMI, M.: J . Chem. Phys. 7, 1103 (1939); 8, 212 (1940); 9, 177 (1941). Boussu, R. G.: Compt. rend. 176, 93 (1923). J.: J. Chem. Phys. 7, 538 (1939). FRENKEL, LANDAU, L., AND LIFSHITZ: Statistical Physics, p . 226. Oxford (1938). STRANSKI, I. N . : Physik. Z . 36, 393 (1935). TAMMANN, G . : In Eucken-Jacob's Der Chemie Ingenieur, Vol. I, Part 3, p. 170. Leipsig (1933). (7) VANHOOK,A.: J. Phys. Chem. 44, 751 (1940). (8) VANHOOK, A.: J. Phys. Chem. 46, 1194 (1941). (9) VOLMER, M.: Kinetik der Phuserhildung. Steinkopff, Dresden (1939). (IO) VONWEIMARN, P. P.: Chem. Rev. 2, 216 (1925). (1) (2) (3) (4) (5) (6)
HEATS OF MIXIKG IT\' THE TERNARY SYSTEM ETHANOL-ACETIC ACID-ETHYL ACETATE BY A RAPID APPROXIMATE METHOD BRUCE LONGTIX
Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois Received September 96, 1941
In order to test adequately various theories of the thermodynamics of nonaqueous solutions, it is necessary to have available heat-of-mixing data on a wide variety of solutions. Such data have been accumulated only slowly by the more precise methods of calorimetry. A need was felt for a method employing simple apparatus, which could be used to give a rapid survey of the behavior of nonaqueous solutions with a precision of a few per cent. Such a method would be of value in selecting systems for further, more precise, study. At the same time the data obtained would be of sufficient accuracy for all engineering purposes and for rough quantitative tests of solution theories.
