S. A. GREENBERG
196
and possibly heat transfer are much more important factors in these mixtures than in TNT-A1 and TNT-RDX-A1 mixtures. The temperature of the latter will always be in the neighborhood of the final temperature, irrespective of the fraction of explosive react.ed, but this is by no means true in fuel sensitized AN mixtures. Two other possible limiting factors besides heat transfer in the condensed phases thus arise. The limiting factor determining rate in the AN-AI mixtures thus might be either (1) mass transfer (or mixing) in the gas phase, or/and (2) heat transfer in the gas phase. In the previous examples studied these processes were apparently unimportant and the rate of reaction was limited by the upper limit of temperature and reaction rahe in the solid (the Eyring process). However, in AN-A1 mixtures the gaseous phase is apparently not in equilibrium, and factor (l),(2) or both thus limit the rate of reaction. The fact that the rate decreases rapidly with density indicates that the limiting factor is mass transfer. (Diffusion falls rapidly with increasing density or pressure in the vapor phase, but thermal conductivity does not.) This situation corresponds approximately to that occurring in granular “low” explosives such as black powder in which the burning
Vol. 61
rate decreases with increasing density. Single and double-base propellants in which the solid phase is homogeneous apparently have thermal conductivity as the rate-determining factor. That is, the rate in these explosives is probably determined by the temperature at the solid-vapor interface, but the initial process of decomposition is endothermic or much less exothermic than the over-all reaction. Most of the heat is thus generated a short distance away from solid-vapor interface and must be transferred back by thermal conduction to support the reaction. The temperature gradient away from the surface (temperature being smallest a t the solid surface) , therefore, increases with pressure, and the effective surface temperature also increases with pressure. The result is that the burning rate increases with pressure. The anomalous D ( p l ) curves observed a t d = 10 cm. in 90/10 AN-DNT are characteristic of nearly all AN-combustible mixtures in small diameter. Quantitative studies of the DID” vs. p1 curves of such mixtures should thus lead to valuable information on mass transfer in gases a t higher densities and pressures in addition to important practical and theoretical information regarding the reaction kinetics of AN-combustible mixtures.
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THERMODYNAMIC FUNCTIONS FOR THE SOLUTION OF SILICA I N WATER BY S. A. GREEN BERG^ Laboratory for Inorganic and Physical Chemistry,University of Leiden, Holland Received July 4, 1066
The thermodynamic functions connected with the equilibria between both high surface area, amorphous silica and quartz and aqueous solutions saturated with monosilicic acid (H4Si04)were calculated from data reported in the literature.
Introduction Although accurate measurements have been made of the solubility of high surface area amorphous silicas2” and quartz2v4in water a t various temperatures, the thermodynamic functions connected with these equilibria have not yet been reported. The equilibrium between solid silica and saturated aqueous solutions may be written SiOa(s)
+ mHtO(l)
H1SiO4.aq
(1)
Since the silicic acid is very weake no appreciable dissociation in neutral water would be expected. It has been established fairly conclusively that the soluble species of silica in neutral solutions of low ,~ ionic strength is monosilicic a ~ i d . ~Therefore, the equilibrium constant for the reaction K,is equal to the activity of the monosilicic acid. Because (1) Chemistry Department, Seton Hall University, South Orange, New Jersey. (2) For review see R. K. Iler, “The Colloid Cherniatry of Silica and the Silicates,” Cornel1 University Press, Ithaoa, N. Y., 1955. (3) G. B. Alexander, W. M. Heston and R. K. Iler, THISJOURNAL. 68, 453 (1954). (4) G . C. Kennedy, Econ. Ceol., 45, 629 (1950). (5) C. S. Hitohen, ibid., 40, 361 (1945). (6) 8. A. Greenberg and J. J. Hermans, J . Phys. Chem., in press.
the concentration of silicic acid in saturated solutions is small, it is possible to equate activity with concentration (moles/l.) without introducing a large error. Results Calculation of A H , AFO,,,, and AS2,,,.7-Data for the evaluation of these quantities were taken from Iler? and K e n n e d ~ . ~ I n order to calculate the heat of reaction AH for the equilibrium (eq. 1) the van’t Hoff equation was used. I n Fig. 1 the negative logarithm of the concentration of silicic acid is plotted as a function of the reciprocal of the absolute temperature. AH values were determined from the average slopes (Table I). TABLEI THERMODYNAMIC FUNCTIONS FOR SOLUTION OF SILICA Amorphous silica
+2.65 f 0.28 AH, kcal./mole +3.98 f 0.04 AFo20,,,kcal./mole AS,,,,, cal./deg. mole -2.82 f 0 . 5 0
Quartz
*
+7.34 0.37 f5.20 f 0.04 4-4.53 f 0 . 7 1
It is obvious from the deviations from the average (7) For discussion see F. H. MaoDougall, “Physical Chemistry,” The Maomillan Co., New York, N. Y., 1936.
.
THERMODYNAMIC FUNCTIONS FOR THE SOLUTION OF SILICA IN WATER
Feb., 1957
slopes and the differences between the measured and average values of the concentrations that the AH quantities for both the amorphous and the crystalline silica are essentially constant over the temperature range investigated. From the usual relationships between AFo and K,, and between A S and A H , AF" and T , the values a t 200" for AF" and AS were obtained. I n Table I these quantities are listed for amorphous silica and quartz. The free energy change for the crystallization of amorphous silica into quartz may be found at 200" from the difference in the free energy relationships for each substance AF'Q
- AFOAS = RT In KASIKQ
(2)
where the subscripts refer to amorphous silica and quartz. It readily may be observed that because of the lower free energy state of quartz the solubility of the amorphous silica is greater than that of quartz by the above equation. The free energy change a t 200" on going from amorphous silica to quartz is - 1.22 kcal./mole which compares fairly well with the -1.5 kcal./mole of the 25" transition of silica glass to quartz.8 Moreover, the AH on going from hydrated amorphous silica t o quartz as found in the present study is -4.69 and from reported data,* -4.4 kcal./mole was calculated for this change. Ramsbergghas evaluated the heat of formation of silicic acid from quartz and reports it to be f2.8 kcal./mole. If the heat of solution AH of quartz (Table I) is +7.34 kcal./mole then the heat of solution of solid silicic acid must be approximately $4.5 kcal./mole. Discussion The silicas, as has been pointed out previously,2.10 are condensation polymers of silicic acid, H4Si04, and, therefore, to form a silicic acid solution a depolymerization reaction must proceed by hydrolysis. Tourky'l estimates the heat of polymerization a t -8.0 kcal./mole. Therefore, the heat of depolymerization would be approximately of this order of magnitude. The heats of solution for quartz and amorphous silica found in the present study are +7.34 and +2.65 kcal./mole, respectively. Since the product obtained by Tourky on the polymerization of silicic acid most closely resembles amorphous silica, the value of 8.0 kcal. reported by him is probably much too high. An amorphous silica with a surface area of 250 sq. m./g. contains approximately 3 g. of water per
c
100 g. Si02 in Si
groups.'O Therefore, such an
amorphous silica is about 5% hydrolyzed, whereas quartz because of its small surface area has a negligible amount of SiOH water. The negative value of AS,,,, of -2.82 found for (8) E. L. Brady, T H I a JOURNAL, 57, 706 (1953); National Bureau of Standards, Circular 500, "Selected Values of Thermodynamic Properties," U. 9. Govt. Printing Office, 1952, p. 148. (9) H. Ramsberg, J . GeoZ., 62, 388 (1954). (10) S. A. Greenberg, THISJOURNAL, 60, 325 (1956). (11) A. R. Tourky, Chemistry and Industry, 254 (1942).
197
1.9 2.1
2.3 2.5 2.7 2.9 3.1 3.3 I/T x 103. Fig. 1.-Solubility of amorphous silica ( 1 ) and quartz (2) expressed in log [H4Si04]vs. 1/T plots (0, ref. 2; 0 , ref. 4).
amorphous silica is not surprising. First, because the silica is already in an amorphous state, and, secondly, because of the reduction in entropy of the water bound to silicic acid SiOH groups by hydrogen bonds.12 The estimated heat of solution of solid silicic acid of f 4 . 5 kcal./mole is to be expected. Although silicic acid possesses four OH groups to interact with water, which would lead to a more stable state and a negative change in the heat content, there is probably a large amount of energy necessary to separate the silicic acid molecules in the formation of a solution. The higher AH, AF",,,, and AS,,,, values found for quartz are reasonable. Certainly, quartz is a t a lower free energy state than amorphous silica. A greater amount of energy would also be necessary to hydrolyze the Si-OSi bond in quartz than in amorphous silica which would lead to a higher AH change. However, the difference in entropy of 7.35 cal./deg. mole between amorphous silica and quartz for this process appears to be quite high. From the results of this discussion it appears that the treatment of the solubility data as an equilibrium is reasonable. Although theoretically the solubility of crystals is a function of particle size and surface area, according to Alexander and Johnson1*experimentally this has not been found to be the case. Apparently, small amounts of impurities can change the character of the surface to such a degree that the theoretical relationships do not hold. Since particle size seems to have no influence on solubility,a it can perhaps be assumed that a t equilibrium the amorphous silicas exhibit the same surface energies. Acknowledgements.-The author wishes to thank Professor J. J. Hermans for helpful suggestions on the manuscript and the Foundation for Fundamental Research of Matter (FOM) supported by the Netherlands Organization for Pure Research (ZWO) under whose auspices this research was performed. (12) G. H. Haggis. J. B. Hasted and T. B. Buchanen, J . Chem. PhQ8., 20, 1452 (1952). (13) For review see A. E. Alexander and P. Johnson, "Colloid
Science," Oxford Univ. Press, London, 1949.
