REACTION OF VITREOUS SILICA WITH HYDROFLUORIC ACID
July, 1959
transition. Wilson1’ has shown that this is to be expected on the basis of the selection rules for molecules of Czv symmetry. For CHzF2the measurements gave a value of tan 6 = 1.3 x low4a t 1 atm. This is an appreciable loss, although it is less than that observed for any of the other gases. Significantly, the pressure dependence of the loss tangent is different from that observed for the other gases, the variation of loss tangent with pressure being much smaller. This is the type of effect that would be expected if the loss were due to a nearby rotational line rather than to the non-resonant absorption connected with inversion. The evidence for CH,F!, is not conclusive. but it is probable that the observed ~ S isS due td nearby rotational transitions rather than to inversion. (11) E. B. Wilson, Jr., Tms JOURNAL, 63, Aug. (1959).
1129
Conclusions The absorption of microwave energy by CHC12F is of the typical non-resonant type, giving a linear plot of p2/tan 6 against p 2 . This, in addition to the correlation between the value of (tan G/p)max calculated from the absorption data and that computed from the dielectric constant measurements, gives strong support to the contention that the dielectric dispersion in this gas is of the same inversion type studied previously in symmetric top molecules. The absorption studies correlate also with dielectric constant measurements in indicating no measurable effects of inversion in molecules of Czv symmetry. Acknowledgments.-The authors wish to express their thanks to Mr. Andrew p. Deam and to Dr. Donald C. Thorn for valuable assistance in the design and construction of the equipment.
DIFFERENTIAL THERMAL -4NALYSIS AND HETEROGENEOUS KINETICS : THE REACTION OF VITREOUS SILICA WITH HYDROFLUORIC ACID BY AVROM A. BLUMBERG’ Mellon Institute, Pittsburgh 13, Pennsylvania Received November 66, 1068
The method of Borchardt and Daniels, using differential thermal analysis to study the kinetics of reactions, has been extended to solid-liquid heterogeneous reactions. A simple method of determining the necessary thermal constants has been suggested. The heat of reaction was determined to be 33 i2 kcal. The rate of solution of vitreous silica can be described by the rate law dM/dt = - (koe-*E/RT)S(HF) where the frequency factor ko is 0,120 i 0.022 (9. Si02/sec. cm.2 H F molarity), and the activation energy is 9 i 1 kcal.
Introduction The reaction between vitreous silica and hydrofluoric acid2 6HF
+ SiOz +2Hz0 + H2SiFe
will be discussed in more detail in another paper. For the present, it is sufficient to know the stoichiometric coefficients of hydrofluoric acid and silica and something of the equilibria of the acid. Acidfluoride systems are described by the equilibria
+
HF ++ H f FHF F-+-+ HFZ-
+
K~ (250) = 7
x
10-4
IC2 (25’) = 5
where the numerical values are averaged from those of several ~ o r k e r s . At ~ high acidity it is possible to suppress the first reaction and to have virtually all the fluoride as the undissociated hydrofluoric acid. The work here does not employ hydrofluoric acid concentrations greater than 2.5 molal because there is evidence of polymer formation a t higher concentrations. The earliest application of DTA t o the study of kinetics is the work of Borchardt and Daniels6 who developed the method for single phase liquid systems and we have used an adaptation of their pro(1) Pittsburgh Plate Glass Company Fellowship. (‘2) N. V. Sidgwick, “The Chemical Elements and Their Compounds,” Vol. I , Oxford University Press, Oxford, England, 1950, p. 615. (3) Ref. 2 , Val. 11, p. 1105. (4) R. P. Bell, K . N. Bascombe and J. C. McCoubrey, J . Chem. Soe., 1286 (1956). ( 5 ) H. J. Borchardt and F. Daniels, J . Ana. Chem. Soc., T 9 , 4 1 (1957).
cedure, extending it to the reaction of a solid with a liquid phase. If we have in a bath, a t temperature Tb which increases with time, two similar containers, one, designated by the subscript “1,” with a reacting mixture, the other, designated by “2,” with an inert mixture, then in a time interval dt, the temperature changes in the flask are described by Ci dT1 = dH 4-Kl (Tb - TI) dt Cz dTz = Kz (Tb - Tz) df
(1) (2)
where Ci is the heat capacity, Ki the thermal conductivity, Ti the temperature of each flask, and dH is the heat evolved during that time interval. By adjustment, we can make C1 = C2 = C and K1 = K Z = K ; by subtracting equation 2 from equation 1, and defining AT = T I - T z d H = C dAT
+ KAT dt
(3)
Integrating of equation 3 between t = 0 and t = m and defining A as the total area under the AT vs. t curve, the total heat of evolution is A H = KA
(4)
In the heterogeneous reaction ZL(so1ution)
+ mM(so1id) +product
where 1 and m are the usual stoichiometric coefficients, we assume the rate of disappearance of either solid or soluble reactant to follow a law such as k’=
- s (3“
(5)
AVROM A. BLUMBERG
1130
VOl. 63
Equation 6 may be written
- dL/dt
=
kLxMz/~
or
-2.0
$- -3.0
From the known values of K , C, Loand w, the atoichiometric coefficients m and 1 (which are 6 and 1, respectively, in the case of silica and hydrofluoric acid) and the experimentally determined AT, dAT/dt, A and a, the rate constant k may be determined as a function of x as the only unknown parameter, for any temperature for which measurements are available. Only for one value of 2 will a plot of log k us. 1/T produce a straight line, according to the Arrhenius law
ul
0
u
+ -4.0
.-
Y
01
-5.0
-6.0
k = koe-AE/RT
This x is the order of the reaction with respect to the soluble reactant. Reaction orders commonly 3.45 350 3.55 360 3S5 encountered are 0, 1/2, 1, 3/2 and 2. Such plots Io ~ / T . from one experiment are shown in Fig. 1. The Fig. 1.-The logarithms of calculated rate constants, as- slope of the straight line gives the energy of activasuming certain orders of reaction, plotted against reciprocal tion. temperature. Case 11. An Excess of Soluble Reactant.-Here M [KAT C dAT/dt] where L/V is now the concentration of the soluble dM/dt = (12) reactant, (L moles in V kg. of water), S is the M exposed area of the solid, and x is the order with M = ",[K(A - a ) - CAT] (13) KA respect to the soluble reactant. If we assume that (a) the mass change of the Gater is negligible 1 Mo ( K a CAT) L = Lo - (14) during the course of reaction, so V is constant, and mw KA (b) the solid is consumed in a uniform manner with Case 111. An Excess of Neither Reactant.-Here no significant change in shape, so
L
-7.0 I 3.35 3.40
I
I
I
I
I
+
+
Lc/l = Mojmw
+so M% MO%
(15)
and equations 10 and 13 become identical, as do where M is the mass of the solid phase, and SO (9) and (14). Experimental and M Oare the initial area and mass, then equation I. Preparation of the Reaction Flasks and Thermo5 may be rewritten k = L"J!l%
(6)
The assumption that the glass is attacked uniformly, so that the surface varies as the 2/3 power of the mass, was judged to be a valid one; microscope examination of powder samples before and after considerable attack revealed no changes in the general shape of the particles. Case I. An Excess of Solid Reactant.-Suppose we start with Lo moles of soluble reactant and Mo grams of solid reactant (whose formula weight is w),and suppose further that there is an excess of solid reactant, ie., Jfo/mw > Lo/l. At time t d f = 1cfo
- mu(Lo - L ) 1
(7)
grams of solid reactant remain. Also
- dL/dt
=
Lo [KAT + C dAT/dt] ~2
(8)
And L = LO
KA [K(A
sot
- a ) - CAT]
(9)
where a = AT dt, is the area under the AT - t curve up to time t. From equations 7 and 9 LO M = M o - mw [Ka f CAT] 1 KA
(10)
couples.-Both flsskA were polyethylene pint bottles with tightly fitting screw caps. Thirty gauge copper-constantan thermocouples in two concentric polyethylene tubes (0.075" and 0.128" 0.d.) were passed through the flask walls so that the junctions (treated with molten polyethylene to have them in contact with and completely surrounded by polyethylene) were immersed in the contained liquids. The differential thermocouples from the flasks were passed to a microvolt amplifier and then the signal to a recorder so that AT = T I - T I could be read to 2.56 X lod3. On the same recorder the bath temperature, Tb, was printed directly to the nearest this was checked contjnually by a calibrated thermometer read to the nearest 0.1 . If the bath temperature increases linearly with time Tb = m nt (16) equations 1 (with d H = 0, in the case of a suitable inert liquid) and (2) have the non-transient solutions Ti = m nt - n Ci/Ki (17) or Ti T b f TIS, (18) Here Tiagis the amount by which each flask temperature lags behind the bath temperature, due to the finite heat transfer rate from bath to flask. From equation 17
+
+
AT = n
[g E] -
When the two flasks are not balanced and are in a bath whose temperature is defined by equation 16, AT will reach a steady value represented by equation 19. here Tb is non-linear with respect to time t , no steady value will be reached, but the drift will be slow for small coefficients of t2 and higher terms.
REACTION OF T‘ITREOUS SILICA WITH HYDROFLUORIC ACID
July, 1959
Although exact matching is not essential since the steady value for AT can be taken as the base line ( i n lieu of A T = 0) from which AT readings are t.aken during reaction, IC values can be adjusted by wrapping waterproof tape around the flask with the higher thermal conductivity. Heat capacities are adjusted by varying the amount of liquid in either flask. 11. Evaluation of the Terms K I and Cl.-From equation 1 in the special case where flask “1” is filled with a suitable i,nert liquid ( L e . , d H = 0 ) , and heated to some temperature f l , o > Tb, then replaced in the bath (at Tb), where 2’2 = Tb, TI will approach T b = Tz ( L e . , A T 0) according to the relation In AT = In
1131
2.1
- Tz) - K -I 1
c1
Thus from the slope K1/C1 and the known value C1, K I may be calculated for the flask. The nature of CI must be discussed. Both the fluid within and the flask itself cool to T b . Since the flask has a heat capacity, its effect must be considered in the cooling (and in the regular reaction). The term Ki includes the thermal conductivity of the flask material and also the two film coefficients on either side of the flask.6 If the flasks are shaken so that the liquids within and without are similarly agitated, the temperature will be very nearly the average (TI Tb). As will be apparent, the smaller the specific heat of the flask as compared to that of the solution within, the less serious is any error arising from the mean-wall temperature assumption. The heat capacity of the wall, C,, will be taken to be that of the flask material alone ( L e . , the heat capacities of the films are neglected); Cf deRignates the heat capacity of the fluid. Then when the fluid temperature drops by dT1, the mean-wall temperature drops by l/z dT1; the total loss of heat is CfdTl Cd’/zdTl) = CldT1 or Cl = Cf l/eCw (21) The steps involved in determining K1 and C1 are: (a) with a suitable fluid in flask “1,” cooling according to equation 20, and with CI defined by equation 21, the slope KI/C1 is obtained and from it the value K1 for the flask; (b) with the reaction solution in flask “1,” again cooling according to equation 21, and with the slope KI/CI and K , from (a) above, C, for the reaction solution and flask 18 obtained. Heat capacities of polyethylene were taken from literature values.7 A typical set of curves is shown in Fig. 2. In practice the plot of In A T us. t can be repeated several times by following the cooling on several sensitivities of the recording instrument. Also, K1 and CI were evaluated both before and after each reaction. This scheme is experimentally quicker and analytically Nimpler than that originally proposed.6 From inspection of, for example, equations 8, 9 and 10 it is apparent that the ratio K / C is sufficient to determine both the order of reaction and activation energy. The heat of reaction (vide rquation 4) depends on K and in this method ultimately on C. But the assumptions leading t o equation 21 introduce error8 in K less than those arising in measuring A . 111. Preparation of Materials.-Powdered vitreous silica was prepared by passing Corning fused silica 7940 lump cullet (analysis: less than 100 p.p.m. impurities) through a jaw crusher and a hammer mill and screening to sort the powder in five ranges between 100 and 270 mesh. This was followed by repeated washing with aqua regia (to remove iron, as indicated by thiocyanate test), and repeated sedimentation along a four-foot column of water (to remove fines, as indicated by the Tyndall effect and confirmed by microscopic examination). Impurities, determined by emission spectroscopy, were less than 88 p.p.m. after this processing. Surface areas were determined by krypton adsorption. Hydrochloric acid wa8 prepared from reagent grade stock and standardized against primary standard sodium carbon-
I
c 0 C 6 v)
I.
0
0
c
c
4
C
+
I.(
+
+
_____
(0) W. L. Badger and W. L. MoCabe, “Elements of Chemical Enginepring.” McGraw-Hill Book C o . , Ino.. New York, N. Y.,1936, p . 128-13 1. (7) M. Dole, W. P. Hettinger, Jr., N. R . Larson and J. A. Wethington, Jr., J . Chem. Pliys., 20, 781 (1952).
A I 5OC for 250.0 groms of woter and 65.0 groms of polyethylene, the heat copacity (using equation 23)
C
= 250.0 x 1.0048 i 6 5 . 0 x 112 x 0.492
= 251.2 = 15.8
-
267.0
t (sed
I
2
Fig. 2.-Evaluation of K1 and C1 from the rate of cooling of a warmed flask, according to the equation in AT = -K/Ct constant.
+
ate. Hydrofluoric acid was prepared from reagent grade stock and standardized against sodium hydroxide solution (which, in turn, was Standardized against the hydrochloric acid). The reaction solution was prepared from these by weighing out the proper amounts of each and enough distilled water to make a total of 300 g. for each run. IV. Conducting the Reaction.-The flasks were filled with equal masses of water, suspended from a wrist action shaker, shaken, immersed in and allowed to come to thermal equilibrium with the bath at constant temperature T b . The thermal conductivities were adjusted, while Tb was increased linearly with time, according to equation 19. Then, with T b constant and near the freezing point, K I was determined according to the procedure (IIa) of this section. Water was replaced with the reaction solution (water-hydrochloric- and hydrofluoric acids),, and C1 similarly was determined (IIb). Finally, with T b increasing linearly with time, CZwas adjusted to C I by adding to or removing from flask “2” an amount of water calculated by equation 19. After these adjustments, the bath temperature was lowered to about the freezing point and one of two silica samples of equal mass (to the nearest milligram) was added to the inert flask. After T1 = TZ = Tb, the other silica sample was added to flask “1,” the bath heater was turned on, shaking resumed, and both A T and T b were recorded. At the end of the reaction, which here is complete in about four hours, the heater was turned off (the bath by this time is usually a t 30-35’), and KI/C1 determined for the spent reaction mixture-flask system a t this higher temperature. Then, with water in the flask, K1 is obtained.
1132
AVROM A. BLITMBERG DATAFOR
Initial niass of silica
Ma (e.)
20.130 20.015 20.154 46.742 48.224 39.399 31.435 36.263
THE
Initial area of sample SO(om.)*
28,000 27,800 28,000 38,300 39,600 32,300 43,700 50,400
Vol. 63
TABLE I ATTACKOF VITREOUSSILICA BY HYDROFLUORIC ACID, OBTAINED BY DTA Moles of HF
Moles of HC1
Heat of reaction kcal. AH( -2)
0.600 .600 .600 ,600
1.200 1,200 1.200 1,206 1.200 1.200 0.900 0.900
32.14 30.29 35.82 34.10 31.89 30.63 36.10 36.93
I n 300 g. of reaction soln.
.600
.600 .450 .450
The KI and CI used in calculations are the average of the low and high temperature values. The actual reaction temperature a t any time can be calculated from Tb, AT and TI, = TZ - Tb (184 so
TI = Tb t Tlag f A T (22) But ?lag will be negligible for small values of nC2/Kz (equation 19).
Results The data for eight runs are presented in Table I. Two different samples of vitreous silica were used, 140-170 and 200-230 mesh with areas 820 and 1390 cm.2/g., respectively. The maximum temperature difference AT developed during the reaction ranged from 0.36' for samples with smaller areas, to 0.67", for those with larger areas. In all runs the assumption of a first-order reaction with respect to hydrofluoric acid concentration gave a straight line in the log k vs. 1/T plot (Fig. 1). Discussion The method of studying the kinetics of a reaction by differential thermal analysis has been extended to a heterogeneous system, vitreous silica and hydrofluoric acid, by including with the original procedure of Borchardt and Daniels the assumption that the surface of a powder sample varies as the 2/3 power of the mass. I n the case of isotropic substances (which include glasses but not crystalline quartz) where the rate of attack is uniform over the surface, linear ratios between dimensions can be expected to remain fairly constant for spheres, cubes and other solids whose surface-to-mass ratio is low, but not for rods and plates. The former class, which may be designated as pykna (from the Greek word for compact) is assumed to include the pulverized glass used in these experiments, since crushing has the general effect of making nonpyknic solids more nearly pyknic. Further, any errors arising from this assumption are less sig-
Activation energy A E (kcal.)
mole-
Frequency factor g. Si02
ko (sec. cm.' HF molarity)
9.13 10.5 6.82 7.28 8.55 11.3 7.66 7.22
0.132 ,151 .I10 .132 .138 ,135 .085 .081
nificant the less the solid is reduced in mass. For this reason the experiments here reported all used an excess of silica, with only from 12 to 30% of the solid consumed a t completion of the reaction. I n addition, in order to have temperature differences large enough to measure with precision, it was necessary to use both an excess of silica (to provide a large area) and a high concentration of hydrofluoric acid. The latter was restricted to no greater than 2.5 molal for reasons discussed in the Introduetion. I n the temperature range 0-35" the reaction can be described satisfactorily by a first-order kinetics law, with respect to the hydrofluoric acid concentration dM _ - - (k,e-AE/fiT)S(HF) dt
where the frequency factor
and the activation energy AE = 9 i 1 kcal.
The activation energy is of a magnitude expected either for a diffusion process or a heterogeneous reaction,8 and so no decision can be made between these two processes on the basis of this work. The heat of reaction was determined by this method to be 33 f 2 kcal./mole of SiOz. This agrees reasonably well with the literature values of 38 kcal./mole of Si02.9 Acknowledgments.-The author thanks the Messrs. Jay C. Fries and Edward R. Shuster of the Department of Research in Chemical Physics a t Mellon Institute for their work in determining surface areas and impurities in the silica samples. (8) S. Glasstone, K. J. Laidler and H. Eyring, "The Theory of Rate Processes," McGraw-Hill Book C o . , Ino., New York, N. Y.,1941, p. 391,525. (9) K. S. Evstrop'ev and M . M. Skornyakov, A k a d . Nauk S. S.S. R . 182 (1949); (see also C'. A , , 46, 10831 f, h (1952)).
