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ANDREW VAN HOOK
(3) (4) (5) (6)
International Critical Tables. McGraw-Hill Book Company, Inc., New York. KELLEY: U. S.Bur. Mines, Bull. No. 394 (1935). KELLEY:U. S. Bur. Mines, Bull. No. 407 (1935). LANDOLT-B~RNSTEIN: Physikalisch-chemische Tabellen. J. Springer, Berlin (1923). (7) LEWIS AND RANDALL: Thermodynamics and the Free Energy of Chemical Substances. McGraw-Hill Book Company, Inc., N e w York (1923). ( 8 ) PARKS:Chem. Rev. 18, 325 (1936). (9) PARKSAND HUFFMAN: Free Energies of Some Organic Compounds. The Chemical Catalog Company, Inc., New York (1932). (10) RICEAND GREENBERQ: J . Am. Chem. SOC.66, 2268 (1934).
THE PRECIPITATION OF SILVER CHROMATE. I11 GELATINMEDIUM’ ANDREW VAN HOOK Department of Chemistry and Chemical Engineering, University of Idaho, Moscow,
Idaho Received June g9, 1940 INTRODUCTION
For the complete quantitative description of the Liesegang ring phenomenon, on the basis of a supersaturation theory, it is necessary to know the kinetics of the precipitation of the substance forming the bands. Silver chromate has been investigated in this way, in spite of expected difficulties in the kinetic interpretations of its rate of precipitation, because it is the best-known example of a material forming rhythmic bands. It has already (8) been found possible to represent the rate of precipitation of silver chromate from aqueous medium in not too complex a manner. It was then desirable to have this same information for the precipitation from gelatin medium, since quantitative data on the Liesegang phenomenon are difficult to obtain in a mobile, fluid medium, such as water. However, it is known (9) that various ions are sequestered to a greater or less extent by gelatin, and therefore it was necessary to have some information on the effective activities of the silver and chromate ions in this medium. With these data available (9), it is possible to apply successfully the analysis previously found valid for water medium to the rate of precipitation of silver ohromate in gelatin medium. 1 Presented in part at the Seattle Meeting of the American Association for the Advancement of Science, June, 1940.
PRECIPITATION OF SILVER CHROMATE.
I11
1195
METHODS AND MATERIALS
Methods and materials used were the same as previously described (8, 9). The 3 per cent gelatin solution was selected because it gives an excellent medium in which to generate Liesegang rings, and it is intended to apply the results of these kinetic investigations to the quantitative explanation of that phenomenon (7). The environment was maintained a t a constant pH of 5.9-6.0 and a total ionic strength of 0.20-0.25. Sodium acetateacetic acid buffers, 0.20 M or less, were generally used. Even with extreme values of molecular weight and valence (6), the maximum contribution of the gelatin to the ionic strength at the highest concentration employed is only 4 per cent of the total. At more reasonable values the contribution is still less, and generally it may be ignored entirely, especially since the value of 1 does not enter a t all into the kinetic calculations. The 3 per cent gelatin medium employed is a firm gel a t 25OC., requiring several hours or less to set to this condition, according to the treatment applied. Since it is inexpedient to mix gels thoroughly, the initial mixing of the reacting silver nitrate and potassium chromate was conducted while the individual samples were still fluid a t 25OC. The mixture could then be caused to gel during M e r e n t periods of time, according to the temperature and the rate of cooling. The standard procedure adopted was to add the required amount of gelatin to the individual solutions of proper strength, and allow it to soak for 3-4 hr. or overnight. This mixture was heated momentarily to 60-7OoC. (3); then it was cooled to 25OC., and the solutions were mixed. With this treatment the mixture remained fluid during most of the runs conducted. Numerous runs in which the gelation was accelerated and accomplished during the measurements were not appreciably Werent (when due allowance for the drastic treatments is made) from the unaccelerated ones, especially during the early and significant parts of the runs. It is recognized that the history of a sample of gelatin determines its properties (4),but no radical differences in the growth curve8 were observed with slight modifications in this standard procedure. As before, all reaction mixtures were stirred at a rate well above the critical. The initial concentrations of reactants were always such that equal volumes of solutions were employed. Any great deviation from this ratio caused variations in results, owing to localized excessive concentration gradients. In order to eliminate irregularities from this same cause, stirring during the first few seconds had to be more violent than during the remainder of the reaction. RESULTS AND DISCUSSION
When silver chromate precipitates in the presence of gelatin (3, 5), the course of reaction is entirely similar to that observed in aqueous medium
1.196
ANDREW VAN KOOK
@),-namely, a flat induction period (associated with nuclei generation), followed by a diminishing growth period. These two parts of the curves are considered separately, and in order, in the following presentation. T h e nuclei generation period Within limited concentrations of reactants the induction period may be specified quite closely either from inspection of the data or by backward extrapolation of the growth curves. It is experimentally impossible, under the circumstances employed, to ascertain the termination of the induction period accurately when it is less than 1 min. For periods over 1 hr., a welldefined induction period loses significance. The time of initial, relatively slow adjustment may be shortened in all cases by the addition of extraneous crystal seeds. TABLE 1 Summary of values for induction period . AgCrO,
J
N
ninuies
0.0070 0.0065 0.0060 0.0055 0,0050 0.0045 0.0040 0.0035 0.0030 0.0025
0 0.1 0.25 1.17 2.8 7.3 12.0 37 (160) (1500)
Ho X
I
1010
44 38 19 19 12.4 7.6 6.8 5.7 0.7 0.4
-
Y 6 x 10-S) X J X 10'0
3.3 3.5 16.4 20.6 19.1 21.6 26
The values of the induction period, J , when the reactants are brought together in equivalent amounts and no extra seeds added, are given in table 1. The observed initial activities of silver ion compare favorably with those interpolated from the previous recorded results for silver nitrate (8). The activities of chromate ion have been calculated from the effective activity coefficients of this ion, and no easy, direct experimental comparison is available. If, as anticipated, ( H - K ) J = constant, K may be evaluated as the dope on an H J versus J plot. In this way a value of K = 5.0 X 10-lo, i n s t d of 0.12 X 10-lo, which is the solubility product for the system in the medium used (8), is realized. The former value makes the previous nwmption agreeable in spite of the fact that the ultimate concentration in all Iuns tends to the latter value. Kinetically, it might mean that there is some impediment to the release of "bound" silver ions (or chromate), so
PRECIPITATION OF SILVER CHROMATE.
1197
111
that the proper equilibrium activities are not realized immediately as silver chromate is removed from solution. Since the enhanced value makes possible a simple description of the duration of the induction period, it will be used as an empirical representation of the data. The average value of the constant, excluding the first two values, is 20.7 X 10-lo, which comobserved in aqueous medium, pares closely with the value 10.5 x TABLE 2 Values o f J when non-equivalent ratios of reactants are used
minutes
5.7
x
33
10-10 10: 1 1:1 1:6 1:28
6.8
x
HO
R
J
12.4 x 10-10
20:1
10: 1
ca. 4 3.0
1:I
2.8
R
HO
l0-lo
37 42
1
minutes
/I
I
1:15 1:80
ca. 45
16:l 9:l 1.9:1
15 12 I 13 12 11.5 5 6.3 19
1:l
1:5.8 1:11 1:27 1:161
25
x
10-lo
ea.
2.5 1
15: I 5: I 1:I 1:10
