d[P-12-MSA] - klkz[Si(OH)~l[HMo~+16 dt k-1[H+I5 Equation 5 is in exact agreement with the experimental rate data and Equation 6 is in very close agreement, differing only by two orders of magnitude in the hydrogen ion dependence. A reason for the disagreement is not readily apparent, but, since the hydrogen-ion order depends on the exact nature and degree of protonation of the reactive molybdate species, the assumed singly-protonated dimeric cation may not be entirely correct. In any case, it is felt that this minor lack of agreement is not a serious challange to the validity of the proposed mechanism. Rate Constants. The value for kl was calculated from the slope of the initial rate us. silicate concentration curve, the data for which was obtained under conditions where Equation 5 is valid. The value k2/k-l was obtained similarly from data obtained under conditions where Equation 2 is valid (K2 =
klk2/k-l). Since the concentration of the first silicate-molybdate intermediate was not known, individual values for k2 and k-l could not be obtained. The average values for kl and k2Ik-l were (6.12 =t0.08) x 10-l l.-mole-I-sec-l and (4.68 =t 0.31) X IOa moles2-1.-2, respectively. In order to test the general validity of these values, they were used in Equation 4, the derived rate law (modified for inverse seventh order hydrogen ion dependence), to calculate the reaction rates for varying concentrations of molybdate and perchloric acid. The results are shown graphically in Figures 1 and 2. The solid circles represent experimental points and the solid lines represent the calculated rates. The agreement is good with the average deviation of the experimental points from the calculated curve being less than 5 %.
RECEIVED for review April 7, 1970. Accepted August 7, 1970. Presented at the 159th National Meeting, American Chemical Society, Houston, Texas, February 1970.
Spectrophotometric Study of Formation and Reduction of ~~-12-Molybdosilicic Acid L. G . Hargis Department of Chemistry, Louisiana State Unicersity in New Orleans, New Orleans, La. 70122 The stoichiometry of the formation of ~ 1 2 - m o l y b d o silicic acid (a-12-MSA) in perchloric acid solution was studied using a spectrophotometric technique. Reaction coefficients were evaluated from spectrophotometric data obtained under conditions where the amount of a-12-MSA formed in the reaction was negligible compared to the initial reactant concentrations. The Mo:Si:H reaction stoichiometry was 6:l:-6 indicating six molybdate units combine with one silicate liberating six hydrogen ions. The molybdenum must exist principally as a dimer to account for the well known 12: 1 (Mo: Si) stoichiometry of the final complex. The reduction of a-12-MSA to a heteropoly blue is simplified because of the stability of the complex. The kinetics of the reduction with ascorbic acid as reductant were studied and the rate constant for the reaction was calculated.
ANALYTICAL METHODS for the determination of silicon are usually based on the formation of 12-molybdosilicic acid or the corresponding reduced complex (1, 2). A great deal of material has been published on this basic analytical method. Unfortunately, the earlier literature failed to recognize the existence of two isomers of 12-molybdosilicic acid and the importance of certain solution conditions in dictating which isomer is formed. Strickland (3) was the first to clearly demonstrate that the acid to molybdate ratio is critical in dictating which isomer is formed. P-12-Molybdosilicic acid (P-12-MSA) is formed in solutions acidified with at least 2 moles of acid per mole of molybdate while a-12-molybdosilicic (1) N. H. Furman, Ed., “Standard Methods of Chemical Analysis,’’ 6th ed., Vol. 1, Van Nostrand, Princeton, N. J., 1962. (2) F. D. Snell and C. T. Snell, “Colorimetric Methods of Analysis,” Vol. IIA, Van Nostrand, Princeton, N. J., 1959. (3) J. D. H. Strickland, J . Amer. Chern. SOC.,74, 862, 868, 873
(1952).
acid (a-12-MSA) is formed in solutions acidified with less than 1.5 moles of acid per mole of molybdate. The p isomer, once formed, is less stable and spontaneously converts to the a isomer (3). Since the absorption properties of the two isomers are somewhat different, there has been considerable confusion in the earlier literature regarding solution stability, optimum time for absorbance measurements, optimum acidity, and so forth. This paper represents a two-fold effort: first, to establish the exact stoichiometry for the formation of the a complex and, second, to investigate the reduction of this complex to a heteropoly blue. Similar studies have been made on 12molybdophosphoric acid ( 4 ) and dimeric 18-molybdobismuthophosphoric acid (5) and have been generally successful in their stated aims. The method employed to study the stoichiometry of the formation of the a complex requires solution conditions where the total amount of complex formed is small with respect to the initial reactant concentrations. In previous studies of other heteropoly complexes, this condition was accomplished by controlling the solution acidity. Herein lies a problem not encountered in the previous studies. The direct formation of a-12-MSA requires that the acid to molybdate mole ratio be less than 1.5. The inability to vary the acidity to larger ratios prevented one from using this parameter to achieve the desired high degree of dissociation. Indeed, there is evidence that, once formed, a-12-MSA is quite stable in strongly acidic solutions (3). Interestingly, this problem can apparently be overcome. Acidities which provided an acid to molybdate mole ratio of greater than 2 were used which resulted in the (4) S. R. Crouch and H. V. Malmstadt, ANAL.CHEM.,39, 1084
(1967).
(5) H. D. Goldman and L. G. Hargis, ibid., 41,490 (1969). ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
1497
Table I. Reaction Coefficients in Perchloric Acid Solutions Varied Csi, M C M ~M, CHClOa, M 0.12 1.1 x 10-5-1.1 x 10-4 2 . 0 x 10-3 Si(OH)4 0.12 1.0 x 10-3-2.2 x 10-3 1.1 x 10-4 Na2Mo04 0.12-0.18 2.0 x 10-3 1.1 x 10-4 HClOi confidence level. a Range given is the confidence limits of the regression coefficients at the 95
direct formation of the p isomer, but only in small amounts compared to the initial reactant concentrations. The solutions were allowed to stand to permit the p isomer to convert to the thermodynamically stable a isomer. Strickland has shown that this p to a conversion is spontaneous and he was unable to stop or reverse the reaction (3). Strickland further states that the reaction has characteristics of an irreversible reaction, a statement which conflicts with results of this work. The approach used in this study basically depends on the final product, a-12-MSA, being in equilibrium with the silicate and molybdate reactants. The reaction between silicate and molybdate may be represented as
+
+
K1
Si(0H)a MO(VI)~ e P-12-MSA H+ where Mo(VI), refers to the total amount of unreacted molybdate and K, is the equilibrium constant. But the p isomer spontaneously converts to the a isomer 0-12-MSA
Kz
+ a-12-MSA slow
If this reaction is reversible the p isomer may be viewed as simply an unstable intermediate whose lifetime is extended due to a slow rate of equilibration. In order for the method used to work properly, Kzmust be much larger than K1. This ensures that the equilibrium concentration of p-12-MSA is always much smaller than that of a-12-MSA. The equilibrium constants are not known and they will not be easily obtained because of the similarity of the a and isomers and uncertainty concerning the exact nature and concentration of the reactive Mo(V1) species. There is indirect evidence indicating that K z is much larger than K l . Strickland (3) prepared solutions of p-12-MSA from the reaction of silicate and molybdate. After standing 25-30 hours, their absorption spectra and the absorption spectra of the reduced products were very similar to those of corresponding solutions of the a complex. Since p-12-MSA has a larger molar absorptivity than a-12-MSA, it must have been present only in negligible amounts.
EXPERIMENTAL Spectrophotometric Measurement. Spectrophotometric measurements on the formation of a-12-MSA were made with a Beckman DU-2 spectrophotometer. Kinetic measurements were made with a Cary 15 recording spectrophotometer with a thermostated cell compartment. Whenever possible the 0-0.1 absorbance slidewire was used to take advantage of the greater sensitivity available. The usual procedure for making absorption measurements for the stoichiometry study was to prepare the desired solutions in volumetric flasks and allow them to stand until conversion of the @ isomer to the a isomer reached a stable equilibrium. The time required for this conversion depended on the amount of acid in excess of the molybdate (3). The progress of the conversion is easily checked by measuring the absorbance at either 350 or 400 nm over a time interval. At these wavelengths the @ isomer has the larger molar absorptivity. The conversion times were necessarily quite long, from a few hours to as much as two days in some cases. 1498
Reaction Coeffa 0.95 + 0.03 5.89 Z!Z 0.25 6.05 + 0.41
The procedure for making kinetic measurements was to prepare the desired solutions without the reductant in a suitable volumetric flask and equilibrate in a constant temperature bath at 26.0 f 0.05 “C. After thermal equilibration, a 2-ml aliquot was transferred to the 1-cm absorption cell and the reductant was added uia a 100-pl hypodermic syringe. Hand mixing and placement in the spectrophotometer cell compartment required only a few seconds and left ample time to record the initial absorbance us. time curves. Measurements relating to the formation a-12-MSA were made at 350 nm where it is known that Beer’s law is obeyed (3). Measurements relating to the formation of reduced a-12-MSA were made at 725 nm. All absorbance measurements were made against distilled water as the reference. Reagent blanks were always prepared and measured separately. The blanks were then subtracted arithmetically. This procedure was deemed desirable because the reagent blanks occasionally exhibited somewhat more than minimum absorption and if they were subtracted instrumentally, it would be at the expense of an increased slit width and lower resolution and sensitivity. Reagents. Stock silicate solutions were prepared from reagent grade sodium silicate, Na2Si03.9H20, that was evaporated with excess sodium hydroxide in a platinum crucible. Freshly distilled water was used for dilutions and the final diluted stock solutions were adjusted to pH 3 with perchloric acid. Stock solutions were standardized using a conventional gravimetric procedure (6). Stock solutions of sodium molybdate were prepared from reagent grade Na2MoOa.2Hz0 and were allowed to age for at least 24 hours prior to their first use (4). Ascorbic acid solutions were prepared fresh daily. All water was freshly distilled and solutions were stored in polyethylene bottles to prevent any possibility of silicon contamination.
RESULTS Quantitative Description of Method of Data Treatment. The stoichiometry study is based on the measurement of the amount of a-12-MSA complex formed when various amounts of reactants are mixed. The solution conditions are adjusted such that only small amounts of reactants are actually consumed in the reaction. The detailed mathematical approach has been described previously ( 4 ) and will be repeated only briefly here. The formation of a-12-MSA may be represented by the reaction a Si(OH)4
+ b MO(VI)~e a-12-MSA + c H+
where Mo(VI), refers to the total amount of unreacted molybdate and a, b, and c refer to the number of moles of each constituent that react with or are formed with 1 mole of a-12MSA. The fact that Si(OH)4 reacts with Mo(VI), initially to give p-12-MSA is of no special consequence since it may be treated as an unstable intermediate which ultimately produces a-12MSA. There are undoubtedly many intermediates formed. (6) “A.S.T.M. Methods for Chemical Analysis of Metals,” American Society for Testing and Materials, Philadelphia, Pa., 1956.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 13, NOVEMBER 1970
Figure 1. Effect of a-12-MSA concentration on reaction rate CHClOh = 7.0
x
e
10-'M;
CAscorbic nold
Experimental points - Best straight line
= 2.0
x
These intermediates differ only in that they equilibrate rapidly with other species whereas 8-12-MSA equilibrates very slowly. One simple experiment was performed to add further justification for the assumption that the amount of 0-12-MSA present after reaching a stable equilibrium is very small compared to the amount of a-12-MSA. T o a solution of a-12MSA prepared from, and thus presumably in equilibrium with, @-12-MSA,was added a known amount of a-12-MSA prepared from the solid. The absorbance of the mixture between 350 and 400 nm remained constant with time and was additive within experimental error. Since the molar absorptivity of the 8 isomer is twice that of the a isomer, any appreciable shift in the equilibrium toward the p isomer would have resulted in non-additive absorbances. The concentration of a-12-MSA was obtained from absorbance measurements at 350 nm. Since the extent of reaction is purposely maintained small (
