AVROMA. BLUMBERG AND STAVROS G. STAVRINOU
1438
Yol. 64
ratio to increase with intensity (to 2.2 a t 7 X lo8 rads/hr.) was observed and may be due to underlying reactions which produce “dimer” product by other processes. The second type of experiment involved the use of iodine to scavenge the free radicals produced initially. Unfortunately because of the sensitivity limits presently imposed by chromatographic methods such studies must be carried out a t relatively high iodine concentrations (-0.003 M ) and are accordingly plagued by unresolved questions concerning the use of scavengers a t these concentration~.~ The results, however, appear to be in complete agreement with the conclusions reached above. It is seen in Fig. 3 that the yields found for the inCEH9 C i ” --+ CIOHI~ (4) dividual radicals in the scavenging experiments are CsH9. CsHii, --+ CnHzo (5) directly proportional to the electron fraction of the CsHii, CaIIii. --+ CizHzz (6) l f combination is purely statistical, ie., k4:kS: ks = parent material present. This is expected since 1:2 : 1 then the product ratio [CIIHzo]/[CloH~sl’/~secondary chemical processes should not interfere [C13H22:1~2 should be equal to 2. A ratio as they do in the absence of scavenger. Energy between 1.8 and 1.9 was found for all the transfer between cyclopentane and cyclohexane apexperiments of Fig. 2. This shows that parently does not occur and we observe ideal bedifferentiation does not occur as a result havior. This result also substantiates the assumpof a favored combination reaction, a possibility tions on energy absorption made in the initial parasince a fraction of the radicals are lost in dispro- graph of the discussion. portionation processes. A slight tendency of this (4) R. H. Sohuler, THISJOURXAL, 61, 1472 (1957).
stants of 1 and 2 be very slightly different in order to explain the present observations. Change in the identity of radicals a t the low intensities of most y-ray experiments can be expected to be even more pronounced in cases where easily abstractable hydrogen atoms are present. The change of product composition with intensity shows that chemical processes other than those of first order are involved. This rules out reactions of ions or excited species with solvent molecules as the sole source of these “dimer” products. Presumably these products result to a considerable extent from the combination of cyclopentyl and cyclohexyl r:idicals according to the competing reactions
+ + +
TABXJLA’I’ED FUKCTIOSS FOR HETEROGENEOUS REACTIOS liATES : THE ATTACK OF VITREOUS SILICA BY HYDROFLUORIC ACID BY AVROMA. BLUMBERG’ AND STAVROS C. STAVRINOU] Mellon Institute, Pittsburgh 13, Pennsylvania Received March 81 1960 ~
The ra,te equ3tion describing the reaction between a solid and liquid has been integrated in tabular form for the cases where the partial order with respect to the solute (liquid) reactant, n = 1/2, 1, S/Z and 2, and has also been integrated in functional form for 15 = 1 . The reaction between powdered vitreous silica and aqueous hydrofluoric acid in strongly acidic media is very closely first order with respect to hydrofluoric acid concentration, and the order and rate constant obtained here agree with those calculated from the results of a different method.
Introduction The reaction between hydrofluoric acid and silica was prlobably discovered by Scheele a t the time he first prepared the acid in 1771.2 Berzelius jdent’ified the products as silicon tetrafluoride and water,3 and later the combination of the tetrafluoride with hydrofluoric acid to form the stable fluorosilicic acid was ~ b s e r v e d . ~This last is a strong acid, comparable to sulfuric acid, and does not etch glass or attack silica. Early studies on the rate of attack include the work of Gnutiers who compared the degree of attack on glass, fused silica and two faces of crystalline quartz; of Lebrun6 who measured the velocities of dissolutdon of quartz, along four different faces; (1) Pittsburgh Plate Glass Company Research Project. (2) A. :B. Burg, “Fluorine Chemistry,” Vol. I (J. H. Simons, Mitor). Academic Press, Ino.. New York, N. Y.. 1950, p. 180. ( 3 ) J. J. Berselrus, Pogg. Ann., I, 169 (1824). (4) N. V. Sidmvick, “The Chemical Elements and their Compounds,” Vol. 1, (Oxford University Press, Oxford, England, 1950, p. 615. ( 5 ) 4 . IGautier and P. Clausmann, Compf. rend., 167, 176 (1913). ( 6 ) J. Lebrun, R d 1 . Classe Sci. Aeod. Roy. Belg., 953 (1913).
and of Schwarz? who exposed, in turn, quartz, tridymite, cristobalite and amorphous (vitreous) silica to hydrofluoric acid and found the amount dissolved to increase in the order given. More recently, Palmers found the rate of attack of “Vitreosil” to be related not to hydrofluoric acid concentration but to bifluoride concentration. At low ionic strength the rate increased with this property, too. Hydrogen ion had a catalytic effect. Nevertheless, reaction has been observed using hydrogen fluoride gasgand in some aqueous systems of high acidity,s in neither case of which is there much bifluoride ion. It seems worthwhile to resolve this point by studying systems in which conipeting reactions are ruled out; and t,he present study, limiting the attacking species t o hydrofluoric acid alone, was undertaken. (7) R. Schwarz, 2. onorg. Chem., 7 6 , 422 (1912). ( 8 ) W. G. Palmer, J. Chcm. Soc., 1656 (1930). (9) W. K. Van Hagen and E. F. Smith, J. A W k . Chen. Yoc., SS, 1504 (1911).
Oct., 1960
T H E ATTACK ON VITREOUS SILICA BY
The equilibria, of the hydrofluoric acid in water, described by HF ++ H + HF F-
+
+ F-, K~ (250) = 7 x 10-4 HFa-, Kz (25") = 5
have been investigated by several workers and their values ha,ve been collected by Sidgwick.io At high acidity .the first dissociation is suppressed, thus reducing the fluoride and bifluoride ion concentrations to negligibly low values. For example in a solut,ion, one molal in each of hydrofluoric and hydrochloric acids, the bifluoride ion concentration is ;bout 3.5 X molal; and the fluoride ion is about 7 X:lop4molal. The work here does not involve hydrofluoric acid conc&rations above two molal because there is evidence'l that a t higher concentrations hydrofluoric acid becomes a strong acid through the formation of polymers. Experimentation Hydrochloric acid was prepared from reagent grade stock and standardized .against primary standard sodium carbonate, aTith methyl orange and carmine indigo mixed indicator, using a coinparison standard buffered at pH 3.8. The precision was within two parts per thousand. Hydrofluoric acid was prepared from reagent grade stock and standardized against sodium hydroxide solution (which, in turn, ws,s standardized against the hydrochloric acid), using phenolphth,dein indicator. Precision was within four parts per thousand. 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 sifting 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). Impurities, determined by emission spectroscopy, were less than 88 p.p.m. after this processing (e.g., Al, 30 p.p.m.; Na, 20; Fe, 10; Ck, 9; Mg, 7 ; Ca, 4; also Cu, Li). Surface areas were debermined by krypton adsorption. Reagent grade ammonium chloride was used without further purification . All reactions were carried out in polyethylene containers, suspended from a wrist-action shaker, and immersed in a thermostat bath ,st, 32.1 f 0.1". Weighed samples of powdered silica were added to known amounts of reactant solution (maintained a t the bath temperature) and shaken for suitable time intervals. The reactions were quenched t)y titration with :ammonia water to the vicinity of pH 7 . .ill quenchings were completed in about 30 seconds. Excess base was avoided to prevent alkaline hydrolysis of fluorosilicate2 with re-formation of silica. The unreacted silica was collected on a platinum Gooch crucible, washed, dried overnight, ignited t o volatilize any remaining ammonium fluoride, chloride or fluorosilicate, and then weighed to determine the mass of iinreact,ed silica. 911 solutions were prepared by weighing out the necessary amounts of dock solutions. Ionic strengths were adjusted by the addition of ammonium chloride, so that '(HCl) (?H,Cl) = 4.00 molal, unless otherwise stated. All runs involved about one g. of vitreous silica and solutions containing exart,ly 200 g. of water. assumption was made that Treatment of Data.-The (he solution of silica. follows the rat,e law dll/dt = - kS(HF)n (1) where M is the mass of tjhe vitreous silica powdpr, S is its siirfacse, anti n is the appropriat,eexponent. It. has been poin1.e.d oitt,12that, in the case of hpt,progeneous
HYDROFLUORIC hCID
1439
reactions the order of a reaction determined by comparing initial rates of separate runs does not always agree with the order determined by following the progress of a reaction throughout a run. For this reason an expression was obtained to describe the amount of vitreous silica consumed as a function of time. If the reaction between a solid (M) and a solute (Lj is represented by the stoichiometric relationship mM ZL +products
+
if M Oand M are the mass of the solid at initial and any tinic, respectively, w is the formula weight of the solid, and L o and L the moles of solute reactant a t initial and any time, then when ( M o- M)/w formula weights of solid are consumed, Lo - L moles of solute are also consumed, and
Mo-M
m
= - (Lo - L )
1
W
or
L = L o - - 1- M o + - M 1 mw mw Then (HF) = L / V , where Vis the mass of the solvelit. The assumption is made that as the solid powder is coltsumed, the surface area varies as the two-thirds power of the remaining mass of solid
s
=S~M'/J/M~~/~
This is valid for isotropic solids with low surface-to-mass ratios; such solids, designated as pykna, have been discussed elsewherel3and the 2/3 power assumption confirmed. Also, since surface area is an extensive property, initially SO= CMO,and
s=c~,,'/~~a/a
where, here, c has the dimensions cm.2/g. Introducing the last few expressions into equation 1 d M = -kcM;la M2I3(A M)n (2) dt mwV where
(-")"
-
+
is a measure of the excess of solute over solid reactant, expressed in grams of solid. Two cases may be distinguished, where A is or is not zero. I n the former, equation 2, upon integration, becomes M(1-3n)/3
- Mo(1-3n)/a
=
In the latter case, where z = (M/A)'/3, zo = ( M o / A ) ' / ~ equation 2 may be written
For the particular case TI = 1, upon integration, this becomes
+
(10) N. V. Sidgnivk, "The Chemical Elements and their Coniimnnds," Vol. 1 I, Oxford University Press, Oxford, England, 19.50, p. 1105. (11) R. P. Bell, I
