Anal. Chem. l982, 5 4 , 2303-2306
bulk liquid membrane transport in which the organic phase is toluene, the selectivity for Na' vs. the other alkali metal cations is lower than was previously observed with chloroform ( 3 , 5 ) . The reason for the unexpectly high transport of Li' into toluene in three of the six cases (solvent extraction using 1 and 2; bulk liquid membrane transport using 2) remains unclear at this time. However the possible errors which could arise from assuming that the selectivity order established for a given combinatifonof aqueous and organic solvents with one separation technique may be extrapolated to a different separation method are readily apparent.
LITERATURE CITED (1) Strzelbicki, J.; Bartsch, R. A. Anal. Chem. 1981, 53, 1894-1899. (2) Strzelbicki, J.; Bartsch, R. A. Anal. Chem. 1981, 53, 2247-2250. (3) Strzelbicki, J.; Bartsch, R . A. Anal. Chem. 1981, 53, 2251-2253. (4) Strzelbicki, J.; Iieo, G. 6.;Bartsch, R . A. Sep. Scl. Technol. 1982, 17, 635-643. (5) Charewicz, W. 4.; Heo, 1G. S.;Bartsch, R . A. Anal. Chem. 1982, 5 4 , 2094.
2303
Bartsch, R. A.; Heo, G. S.; Kang, S. I.; Liu, Y.; Strzelbicki, J. J . Org. Chem. 1982, 4 7 , 457-460. Strzelbicki, J.; Bartsch, R . A. J . Membr. Scl. 1982, 10, 35-47. Jensen, 8. S. "Solvent Extraction Research"; Kertes, A. S.; Marcus, V., Eds,; Wlley-Interscience: New York, 1969; pp 29-36. Rozen, A. M. "Solvent Extraction Chemistry"; Dryssen, O., Liljensen, J.-O., Rydberg, J., Eds.; Wiley: New York, 1967; pp 195-235. Schwind, R . A,; Gllligand, T. J.; Cussler, E. L. "Synthetic Multidentate Macrocyclic Compounds"; Izatt, R . M., ChriS€enSfen,J. J., Eds.; Academic Press: New York, 1978; pp 298-299. Li, N. N.; Shrier, A. L. "Recent Developments in Separation Science": Chemlcal Rubber Co.: Cleveland, OH, 1972; VoI. 1, pp 163-174. Strzelbicki, J.; Charewicz, W. J . Inorg. Nucl. Chem. 1978, 4 0 , 14 15-1421. Strzelbicki, J.; Charewicz, W. Sep. Scl. Technol. 1978, 13, 141-152. Volkel, W.; Halwachs, W.; Schugerl, K. J . Membr. Sci. 1980, 6. 19-31.
RECEIVED for review June 14,1982. Accepted August 9,1982. This research was supported by the Department of Energy (Contract DE-ASOS-80ER-10604) and the Texas Tech University Center for Energy Research.
Kinetics of Formation and Basic Decomposition of p-12-Molybdosilicate C. C. Klrcher and S. R. Crouch* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824
Stopped-flow klnetics studies of the formation of 0-12molybdosllicate (12-MSA) In HN03, H2S04,and HCIO, solutions were conducted at 25 OC and 1.0 M Ionic strength in the pH 1.2-1.8 range. The absorbance-tlme profile follows a simple exponential equation. The rate laws are ldentlcal In form for each acidlc medium tested. A possible mechanism includes an acidlc dissociatlon prlor to Mo(V1) complexatlon with slllcate and ani acid-catalyzed rate-determinlngstep wlth Mo80284-. Rate constants in the three media are compared, and experlmental considerations for reactlon-rate slllcon determlnatlons are presented. The rate equation and a proposed mechanlsm for the bask decomposition of @-12-MSA are presented. The proposed mechanism involves a rapid equlllbratlon of P-12-MSA with an intermedlate, posslbly a12-MSA, and subsequent reaction of the Intermediate wlth hydroxide.
Quantitative silicate determinations have been performed in many laboratories by reacting silicate with Mo(V1) in acidic solution. The product is a yellow-colored 12-molybdosilicate anion (12-MSA), which may be measured with inexpensive spectrochemical or electrochemical techniques. The experimental procedures are generally simple. Some modifications extraction of the 12-MSA complex and reinclude solv-sn~. duction to the intensely colored silicomolybdenum blue. The literature is filled with reports that characterize the chemistry
of molybdosilicate formation. Two isomers of 12-MSA have been found in silicate solutions mixed with molybdate (1). The a and /3 isomers have different spectrophotometric properties (2); the /3 isomer has the higher molar absorptivity over the wavelength range 400-440 nm. Their formation times and relative stabilities are affected by the solution p H ( 3 ) ,ionic strength (4), the solvent composition (5), and the presence of other chemical species (notably, complexing agents) (6). Reaction-rate procedures for silicate offer advantages of short analysis times and elimination of time-independent interferences such as turbidity. Rate equations for P-lB-MSA formation have been reported (7,8). A first-order dependence on the silicate concentration is verified, but the rate equations are reported in terms of analytical molybdate concentrations. Recently, the predominant Mo(V1) complexes and their relative distribution in acid solution became known (9, 10). The two limiting forms of the rate equation in Hargis' report (7) arise because a different set of Mo(V1) species predominate solutions more acidic than pH 0.9 (the Mo(V1) isoelectric pH) compared with solutions in the pH range 1.0-5.0. More importantly, Mo(V1) species concentrations can be calculated from total and analytical acid and molybdate concentrations (11). Consequently, a rate equation for P-12-MSA formation at 25 O C in HC1 solutions has been reported in terms of Mo(VI) species concentrations (12); such an equation provides more definitive information on the molybdosilicate reaction pathway and aids in the optimization of experimental conditions. In this study we report the kinetics of P-12-MSA formation a t p H 1.2-1.8 in HN03, H2S04,and HC10, solutions and of
0003-2700/82/0354-2303$01.25/00 1982 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
Table I. Rate Constants for 6-1 2-MSA Formation in Various Acidic Mediaa acidic medium b,&M s m,&M Z s rxy K,,C M - ' s - ' KVC M HCl 0.987 0.122 0.000 791 1.5 HNO 0.452 3.25 x 10-4 0.988 0.332 0.000 719 0.999 0.296 0.000 616 1.5 HClO, 0.508 3.13 x 10-4 1.5 H2SO4 0.149 3.08 x 10-4 0.996 1.01 0.002 1 0 1.8 HNO, 0.219 3.30 x 1 0 - 4 0.986 0.69 0.001 50 1.8 HClO, 0.226 3.23 x 10-4 0.972 0.67 0.001 40 1.8 HZSO, 0.114 2.79 x 10-4 0.981 1.31 0.002 4 a T = 25.0 "C, I = 1.0 M. Constants in [H,MoO,]/RATE = m / [ M 0 , 0 , , ~ - ] + b. Constants in d[p-l2-MSA]/dt = ~,[Si(OH)41[H,Mo041[Mo,0,4']/(k, -t [ M o ~ O ~where ~ ~ -d[p-12-MSA]/dt ]) = RATE/eb,, K , = ~b,[Si(OH),l/b,and K , = m/b. The molar absorptivity of 0-12-MSA ( E = 803.3 M-' cm-') was the ensemble average of values obtained in a previous Data from ref 12. study (18); observation cell path length b o = 1.87 cm. pH 1.2d
P-12-MSA decomposition in basic solutions. These investigations were carried out with stopped-flow spectrophotometric measurements at 25.0 O C and 1.0 M ionic strength. The form of the rate equation and the rate constant values are compared with the other reported results, and considerations for silicate determinations based on this study are discussed.
EXPERIMENTAL SECTION Instrumentation. All kinetics measurements were made on the computer-controlled stopped-flow system designed in our laboratories (13-15). The quartz observation cell had a 1.87 & 0.02 cm optical path length and was interfaced to a grating monochromator (GCA McPherson EU-700) with tungsten light source by a quartz fiber optic light guide. A quartz rod transferred the transmitted radiation to a photomultiplier tube (RCA 1P28A). Absorbance measurements were made at 430 nm with the slit width adjusted to give a 2-nm monochromator band-pass, At 430 nm there is negligible background absorption due to silicate or Mo(V1) species compared with P-12-MSA absorption. Since the kinetics experiments were conducted in the pH range 1.2-1.8, essentially none of the a-12-MSA isomer forms and interferes with the P-12-MSA absorption (12). The stopped-flow system was interfaced to a Digital Equipment Corp. PDP 8/e minicomputer. The software for operating the stopped-flow system, for acquiring the data, and for analyzing the results has been described (15). For most of the kinetics experiments, the absorbance was measured each millisecond after a stopped-flow push and a 7-ms delay time. One hundred absorbance measurements were averaged for signal-to-noise enhancement, and an average data point was recorded every second for a 100-9 analysis time. An average absorbance at each time point was calculated for eight stopped-flow pushes and stored on floppy disk. Photocurrents were converted to voltage with a Keithley Model 427 current amplifier and digitized with a Date1 DAS-16-M12B, 12-bit analog-to-digital converter. An optointerrupter (GE H13B1) attached near the stop syringe triggered the minicomputer to initiate the data-taking sequence. Other computer peripherals include a graphics terminal and a line printer. The drive syringes, mixer, observation cell, and solution receptacles were thermostated at 25.0 f 0.1 "C with water circulated from a constant temperature bath. Reagents. The solution employed in the stopped-flow experiments were prepared from standardized stock solutions of 4.943 M HN03, 4.960 M HC104,0.01026 M Na2SiO3.9HZ0,0.500 M NazMo04.2Hz0,and 5.046 M NaOH; these were prepared from commercially available analytical reagents without further purification. The silicate solution was standardized by titration with HNOB to the bromphenol red end point immediately after preparation in order to avoid interference from COz. The ionic strength of each solution was adjusted to 1.0 M with a stock 5.00 M NaC104solution. The molybdosilicate solution was prepared by adding silicate to acidified molybdate solution. The solutions were stored in polyethylene bottles after preparation to reduce the contamination of any silicon from the volumetric glassware. The concentration of each reagent in the stopped-flow solutions required to give a particular solution pH or a particular molybdate concentration upon mixing was calculated with the ALGOL-60 program HALTAFALL (11). This program solves the equilibrium constant equations reported by Aveston et al. (IO),and the Mo(V1) and H+ mass balance equations for [H+],the predominant Mo(VI)
species concentrations, and the solution ionic strength without NaC104present. With the (3-12-MSAequilibrium constant data, HALTAFALL showed that essentially all silicate is complexed as molybdosilicate when molybdate is present in a hundred-fold excess. The maximum P-12-MSA reaction rate was determined for a given stopped-flow experiment as the maximum slope obtained from linear regressions of the 430 nm absorbance-time data over any 5-s interval. All correlation coefficients obtained were greater than 0.998. The maximum rate data were fit to various linear equations in [H+], [HzMo04], [ M O ~ O ~ and ~ ~ - ][H2M070244-] , through a program in a HP-25 pocket calculator. The ranges of silicate and molybdate concentrations and pH used in this kinetics study were 0.1-0.5 mM, 0.01-0.10 M, and 1.2-1.8, respectively. The highest silicate concentration prior to 50% dilution in the stopped-flow system was 1 mM. This low concentration and the pH range used assures that silicate is present primarily in the monomeric form (16),abbreviated here as Si(OH),. With the large excesses of molybdate relative to silicate, the solution pH and molybdate content do not change significantly as P-12-MSA forms, and the yellow complex forms in an amount that obeys Beer's law. Despite the relatively narrow acid range, maintaining the solution pH between 1.2 and 1.8 guarantees that (3-12-MSAis the only 430 nm absorbing species present ( I 7). A mixture of both a and (3 isomers would be difficult to analyze since these species have different absorptivities at 430 nm. In the basic decomposition study, the molybdosilicate, molybdate, and hydroxide concentrations employed were 0.1-0.5 mM, 0.01-0.05 M, and 0.1-0.5 M, respectively.
RESULTS AND DISCUSSION P-12-MSA Formation Kinetics and Mechanism. The overall kinetics profiles for P-12-MSA formation were monitored for 100 s in solutions of varying initial reagent concentrations. The absorbance-time profiles were found to follow a simple exponential equation of the form A = 8, + Oz exp(03t). This behavior indicates that there is only a single rate-determining step in the mechanism, and the maximum absorbance increase with time corresponds to the initial reaction rate. A first-order dependence on the silicate concentration was found throughout the concentration range studied. Several linear equations were used in an attempt to fit the experimental initial rate data; for the molybdate dependence, the equation that best fit the data had the form [H2Mo04]/RATE= m/[Moa0,,4-] + b. An identical equation has been found to fit similar data in HC1 solutions (12). The rate constants of Truesdale et al. (12) at pH 1.2 and the rate constants found here in HN03, H2S04,and HC104 solutions a t pH 1.5 and 1.8 are given in Table I. The values differ because of the different pH values and different acidic media used for the experiments. The HNO8 and HC104 solutions at pH 1.2 exhibited suspiciously low initial reaction rates which became independent of the total molybdate concentration at values exceeding 0.05 M. This behavior and the appearance of turbidity suggested MooBprecipitation, since pH 1.2 is close to the Mo(V1) isoelectric pH of 0.9. In HC1 solutions the C1could have complexed some Mo(V1) species to reduce the free
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982
molybdate concentration; under such conditions Truesdale et al. (12) could have studied the P-12-MSA kinetics without Moo3 precipitation. Because of the propagated errors in calculating the solution pH from HALTAFALLand experimental errors in measuring the initial reaction rate (5-10% RSD), the acid dependence for the P-12-MSA reaction was difficult to determine. Inspection of the K1 and K z values in Table I suggests inverse relationships between both conEitants and the [Hs] in HN03, HzS04, and HC104 solutions. The variation was not as large in H2S04 solutions; perhaps the buffering capacity of the HSOL-SOi2system regulated the concentration of hydrogen ions as the molybdosilicate reaction progressed. The chemical mechanism of Truesdale et al. (12),consistent with the observed rate law, contains a rapid equilibration step between silicate and HzMo04followed by a rate-determining step between the molybdosilicate intermediate and Mo802$-. To accomxpodate the acid dependence as well, this mechanism need only be modified to include an acidic deprotonation of HZSiO3or H2MoO4 and an acid-catalyzed rate-determining step with M 0 ~ 0 ~ ~ 2 -
I
I
I
I
I
09
2305
TI I
(M sec)
on each curve
200
O
400
800
600 ’
1000
I200L
I
[M080z6]( Flgure 1. Plots of the P-12-MSA formation rate as a function of Mo(V1) species concentrations in various acidic solutions at I = 1.0 M, T = 25 OC, and X = 430 nm. k
IIS~O~ +-H,MOO~2A or or k-z 112Si03 A
(2)
HMo04-
+ M080264-+ H+
kS
products
(3)
The rate equation derived from this mechanism is d[ P-12-MSAI dt
-
K,[Si(OH),] [H2Mo04][Mo80264-]
(4) KQ K ~ [ H ’ ] [ M o ~ O ~ , ~ - [] H ~ M o O[~M] O ~ O ~ G ~ - ]
+
+
where K , = kl, K2 = k-lk-2/k2k3,and K3 = k-,/kZ. When this equation is rearranged to a linear form for the molybdate dependence, an extra term is present [si(OH)41[HzM~)041 -- RATE
KZ --__ K,[MO@264-]
decomposition kinetics of P-12-MSA in basic solution. Acidic solutions containing P-12-MSA were mixed with excess hydroxide in the stopped-flow system, and the decrease in the absorbance was measured at 430 nm. Refractive index changes caused by temperature changes in the stopped-flow system were negligible, as evidenced by an absorbance change of less HI N 0 3 was mixed with 1.0 M NaOH. than 0.002 when 0.1 & The decomposition kinetics were found to follow the rate law
--d--[P- 12-MSAI - K1[P-12-MSAI [OH-] Kz
dt
+ [OH-]
(6)
with K1 = 20.7 f 0.5 s-l (HNOJ and 20.1 f 0.5 s-, (HC104) and K2 = 0.192 f 0.015 M (HN03)and 0.176 f 0.014 (HC104). Here [OH-] in eq 6 represents the excess hydroxide after all acid has been neutralized ([OH-] = COH- - C,+). A possible mechanism for the basic hydrolysis is k
P-SiMo12& I
K3[Hs1 + [HzMo041 (5)
+-
Kl
K1
Under most experimental conditions, however, the last term is less than 1 % of the values of the other two terms. Of course, other Mo(V1) species may be represented in the empirical rate equation, such as HMo04- in place of HzMo04, HzMo7O2:” in place of M080264-,and different [H+] dependencies. However, in the pH range 1.2-1.8, H2Mo04is the predominant mollybdato monomer, and Mo80264-is more prevalent than any of the heptameric species. The rate equation given in eq 4 and the experimental kinetics data were supplied as inputs to a general curve fitting program KINFIT (Is)to adjust the constants K1, K z , and K3 to give the best regression. The rate equation coverage during execution; however, the final values for the adjusted parameters had large standard deviations associated with them. Many of the problems encountered originated from the nonlinearity of the [HzMoO,]/RATE vs. 1/[Mo8OZ,4-]plots as shown in Figure 1. The linearities obtained from other equations with isopolymolybdates were considerably worse, h6wever. 8-12-MS A Decomposition Kinetics. To complete our characterization of the molybdosilicate sygtem, we studied the
I
+ OH-
k2
k-I
products
(7) (8)
If intermediate I is assumed to be a steady-state intermediate, the rate law in eq 6 is reproduced, with K , = k l and Kz = k-,/kz. Furthermore, within experimental error, the rate constants do not change values with different acidic media. The experimental errors associated with measuring the spectrophotometric transmittances and calculating the rate constants are small because of the large decreases in absorption observed as 0-12-MSA decomposes. However, several model errors arise since the reaction rate was observed to increase slightly for a few milliseconds before decaying exponentially thereafter. This observation could result from an initial lag period for the decomposition to begin, but the delay time between the stopped-flow push and the start of the data-taking sequence should have covered such a lag period. Nevertheless, this potential error source limits the reaction speed that can be observed accurately. On the other hand, if the intermediate I also absorbs 430 nm radiation, the apparent increqse in the reaction rate results as the steady state in I is established. The error in the initial rate measured is expected to be less than 5% since steady state is attained quickly.
2306
ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1’’t ?
Table 11. p-12-MSA Formation Rates at Different Solution Ionic Strengthsa ionic initial rate, ionic initial rate, strength, abs/s strength, absls M (h=430nm) M (h=430nm) 0.00257 1.50 0.00180 0.50 2.00 0.00147 1.00 0.00219 a Csi = 0.1 mM, C R . = ~ 0.02 ~ M, pH 1.5 (HC10, solutions), T = 25.0 “C.
The a-isomer of 12-MSA is an attractive possibility for the intermediate since a-12-MSA absorbs 430-nm radiation, though considerably less than the @ isomer. Also, the a isomer predominates in solutions more basic (pH 3.8-4.8) than those that favor the @ isomer (pH 1.2-1.8). In addition, the equilibration between @ and a isomers does not consume any OH- equivalents or change the stoichiometry of Mo atoms and Si atoms in the polyanions. As experimental support, the decomposition rate is independent of the free molybdate concentration and appears to be nonlinearly dependent upon the excess hydroxide concentration. If the P-12-MSA equilibrium had involved a deprotonation, then a linear or firstorder hydroxide dependence would have been indicated. The reversibility of the @-isomerto a-isomer conversion has not been reported, however, though the constants in eq 6 give no clue as to what the “equilibrium constant” k l / k - l might be. 8-12-MSA Formation at Different Ionic Strengths. Because the formation constants for the anionic isopolymolybdates were determined in 1.0 M ionic strength (IO),the studies reported above were carried out at I = 1.0 M. In this way the relationship between measured reaction rates and Mo(V1) species concentrations could be deduced. Although no extrathermodynamic assumptions such as the DebyeHuckel equation are generally applicable to high ionic strength solutions, the variation of heteropolymolybdate reaction rates with ionic strength was studied for two purposes. The initial @-12-MSAformation rate was found to decrease with increasing ionic strength. These measured rates are given as a function of ionic strength in Table 11. The plots of In ( A , - A,) vs. t revealed no changes as the ionic strength was changed; the formation of p-12-MSA formation followed a simple exponential equation regardless of the solution ionic strength. The formation of P-12-MSA does not appear to be as sensitive to ionic strength variations as the P-12-MSA
conversion to a-12-MSA (20). Analytical Implications. Because of both acid and molybdate dependence in the P-12-MSA rate law, reproducible analytical acid and molybdate concentrations between samples and silicon standards are essential to ensure the integrity and accuracy of determinations. Not only are both the solution pH and isopolymolybdate concentrations affected, but the analytical concentrations also determine which isomer of 12-MSA forms. For any given molybdate concentration, the K1 value for sulfuric acid solutions was significantly greater than for any other acid solution over the pH range 1.2-1.8. Thus, a reagent molybdate solution acidified with H2S04 would provide the best sensitivity in a reaction-rate determination of silicate. In addition, variations of the reaction rate with ionic strength are significant enough to emphasize the control of ionic strength among samples and standards.
LITERATURE CITED Strickland, J. D. H. J . A m . Chem. Sac. 1952,74, 872-876. Strickland, J. D. H. J . A m . Chem. Sac. 1952,74, 868-871. Grasshoff, K. Deep-sea Res. 1964, 1 1 , 597-604. Kato, K.; Kitano, Y. J . Earth Sci., Nagoya Univ. 1966, 14, 151-158. Chalmers, R. A.: Sinclair, A. G. Anal. Chim. Acta 1965,3 3 , 384-390. Chalmers, R. A.; Sinclair, A. G. Anal. Chim. Acta 1966,3 4 , 412-418. Hargis, L. G. Anal. Chem. 1970, 4 2 , 1494-1497. Gall, R. S.Ph.D. Thesis, Michigan State University, East Lansing, MI, 1978. Cruywagen, J. J.; Heyns, J. B. B.: Rohwer, E. F. C. H. J . Inorg. Nucl. Chem. 1978,4 0 , 53-59. Aveston, J.; Anacker, E. W.; Johnson, J. S. Inorg. Chem. 1964,3 , 735-746. Ingri, N.;Kakolowicz, W.; Sillen, L. G.; Warnquist, B. Talanta 1967, 14; 1261-1286. Truesdale, V. W.; Smith, P. J.; Smith, C. J. Analyst (London) 1979, 104 - , 897-91s. -- . -
Beckwith, P. M.: Crouch, S.R. Anal. Chem. 1972, 44, 221-227. Crouch, S.R.; Holler, F. J.; Notz, P. K.; Beckwith, P. M. Appl. Spectrosc. Rev. 1977, 13, 165-259. Balciunas, R. Ph.D. Dissertation, Michigan State University, East Lansing, MI, 1981. Her, R. K. “The Chemistry of Sillca: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry”; Wiley-Interscience: New York, 1979; pp 10-15. Truesdale, V. W.; Smith, C. J. Ana/yst (London) 1976, 101, 19-31. Kircher, C. C.; Crouch, S. R. Anal. Chem. 1982, 5 4 , 1219-1221. Dye, J. L.; Nicely, V. A. J . Chem. Educ. 1971,4 8 , 443-448. Truesdale, V. W.; Smith, C. J.; Smith, P. J. Analyst (London) 1977, 73-85.
RECEIVED for review May 10,1982. Accepted August 12,1982. The authors gratefully acknowledge the financial support of the National Science Foundation through a Graduate Fellowship (C.C.K.) and through NSF Grant No. CHE 79-26490.
