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CHARLES B. HURD AND HOWARD E. SHEFFER
J. Willard Gibbs, First edition, Vol. 11, P a r t 11, pp. 17-29. Longmans, Green and Company, S e w York (1928). HILDEBRAND, d . H.: Ind. Eng. Chem. 10, 96 (1918). LBWENRERZ, R.: Z.physik. Chem. 13, 459 (1894). MOREY, G . W‘.:J. Phys. Chem. 34, 1715 (1930). TEEPLE, J. E.: The Industrial Dewlopment of Searles Lake Brines, pp. 100-2. The Chemicnl Catalog Company, Inc., New York (1929). VAN’T HOFF, J. H. : Cntersuchungen uber die Bildungaverhdltnisse der ozeanischen Sakablugerungen, pp. 223-6. Akademische ~erlagsgesellschaft(1912).
(4) GIBES,J. W.: “Elements of Vect,or Algebra” in Collected Works of
(5)
(6) (7) (8)
(9)
STUDIES O X SILICIC ACID GELS. X I
THE EFFECTO F CONCENTRATION CHARLES B. HURD
OF SILICA UPON THE
AND
TIMEOF
SET
HOWARD E. SHEFFER’
Department of Chemistry, Cnzon College, Schenectady, New York Received April 1 , 1940 INTRODUCTION
Recently one of us has noted that the relation between concentration of silica and the time of set of a silicic acid gel should be studied (3). Very few data have been published bearing on this relation, although Batchelor’s (1) recent paper gives some curves for a study in which potassium silicate and mixed mineral acids were used. The present paper reports our study of this relation, using solutions of sodium silicate and acetic acid. These solutions were used both for conformity with previous studies from this laboratory and because of satisfactory control and constancy of pH in these mixturw. EXPERIMENTAL
The same technique was used as has been used in previous papers of this series (7, 6, 5, 4). The silicate solution titrated 1.21 W in sodium hydroxide equivalent. It was prepared from “E” brand sodium silicate. The time of set was found by the tilted-rod method (7). The mixtures were carefully thermostated. All pH values were measured with a quinhydrone apparatus, using electrodes of bare platinum wire (5). The silica Concentration was varied by changing the relative amount of sodium silicate solution used. 1 Present addresn: Department of Chemistry, Rensselaer Polytechnic Institute, Troy, X e w York
589
SILICIC ACID GELS. XI EXPERIMENTAL RESULTS
The results are shown by curves. In figure 1, in a condensed curve, are given results at three different temperatures for a number of mixtures
v '0
L 11s
4
JO
0
. I
3 w t i 10 wnL>nwc.cq
FIG.1. Relation of time of set tu pH for different concentrations of silica at three different teniperatures in silicic acid gels.
590
CHARLES B. HDRD AND HOWARD E. SHEFFER
at different pH values. The logarithm of the time of set is plotted against the pH. Four principal variables are present: namely,-time of set, pH, temperature, and silica concentration. From the curves of figure 1, data were taken showing the relation between the time of set and the silica concentration a t constant temperature and pH. Figure 2 shows curves for these data a t pH = 5.5. Similar curves for pH = 5.0 and 6.0 were plotted. It was found by trial that the time of set gave a practically linear curve when plotted against the reciprocal square of the concentration of silica.
CONCENT~ATION
%
s l o p @Y WCl6HT
FIG.2. Time of set as a function of silica concentration
Figure 3 shows this relation, but, to give it a proper spread, the square root of the time of set was plotted against the reciprocal concentration of silica. This is for mixtures of pH = 5.5 and a t 25%. The energy of activation was found from graphs of the logarithm of the time of set against the reciprocal absolute temperature a t different pH values and different silica concentrations, as previously described (7). The agreement was good, though the curves were not quite so straight as those obtained by Hurd and Miller (7). Table 1 gives the results over a fourfold change in silica concentration. In the first paper of our series, Hurd and Letteron (6) attempted, by
591
SILICIC ACID GELS. XI
the development of the simple equation for the rate of a reaction, to find the order of reaction involved in the setting of a silicic acid gel. We now know that this naive attempt was defeated by the simultaneous variation of the hydrogen-ion concentration with that of the silica. In the nine years since then, we have learned to control and to understand the effects of the principal variables. So far as we know, the data
FIG. 3. Relation between square root of time of set and reciprocd concentration of silica.
TABLE 1 Energy of activation of the setting of silicic acid gel miztures i n n h t i o n to the concentration of silica CONCENTRATION OF
SiOt
I
ENEBQT OF ACI'IVATION
mm-mdca per liur
0.25
0.50 0.75 1 .oo
15,000 15,700 16,600
16,;Iu)O
of this paper are the first where all of these principal variables have been controlled. We shall therefore once more attempt the calculation of n. Some investigators may feel compelled to dispute the premises, but the results are interesting. In their development, Hurd and Letteron (6) assumed that the formation of a silicic acid gel resulted from a reaction of the n t h order between
592
CHARLES B. HURD AND HOWARD E. SHEFFER
like molecules; also that the process followed the laws of an ordinary chemical reaction, so far as velocity is concerned, and that the time of set measured the time when a certain definite fraction of the silica, in whatever form, had reacted. They developed2 the equation for the rate of an nthorder reaction
-dx-- k(u - x y dt
to give the result
where t‘ is the time of set, c’ a constant depending only on the fraction 2, k a
the specific reaction rate, and a the original concentration of silica.
TABLE 2 Values of n in equation 1 CONCENTRATI~NOF
Si02
-
pH
-
pH
6.0
-
pH
6.6
1
gram-mlcs per liter
0.50 and 0.75 0.50 and 1.00 0.50 and 0.25
2.79 2.85
Average.. . . . . . . . . . . . . , ,
3.08
1
2.91
2.98
-
3.16 3.16 3.10
-I
-
6.0
2.97
2.83 3.25 3.02
From equation 2 for the times of set ti and t: for mixtures of original silica concentration al and u2, we may obtain the relation
n
-1
log t: - log 1: = 2.30 log a2 - log UI
(3)
Using the data of the present paper between our concentrations shown by table 1 for three pH values, we obtain the values of n in table 2. Since the tilted-rod method is an empirical test, demanding certain strength in the gel, we should find mixtures below a certain concentration iiever able to hold up the rod. At 38.2’C. a mixture containing 0.90 per cent of silica set in 30 hr. and one containing 0.75 per cent of silica set in 68 hr. After one month a mixture with 0.40 per cent of silica had not set, but showed a cloudy fibri!lar structure, while the 0.20 per cent mixture was clear. To compare with table 2, note that a mixture containing 3.9 per cent of silica contains about 0.65 gram-mole of silica per liter. 2
For the development reference should be made t o the paper cited.
SILICIC ACID GELS. XI
593
Possibly one of the optical methods, such as t
