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J. Phys. Chem. 1980, 84, 2972-2980
Illumination accelerates the reaction. An activation energy 51 kJ/mol has been measured and a mechanism has been proposed. Of
Acknowledgment. This work was supported by the National Science Foundation MRL Program under grant NO. DMR76-80994. References and Notes (1) (a) Lautenberger, W. J.; Jones, E. N.; Miller, J. G. J. Am. Chem. Sm. 1968, 90, 1110-5. (b) Baselle, C. J.; Miller, J. 0. J. Am. Chem. Soc. 1974, 96, 3813-6. (c) Jones, E. N.; Lautenberger, W. J.; Willermet, P. A.; Miller, J. G. J. Am. Chem. SOC.1970, 92, 2946-9. (d) Willermet, P. A,; Miller, J. G. J. Phys. Chem: 1976, 80, 2473-7.
(2) Additional details are contained In the Ph.D. Dissertationof G. A. Parod, Unlversity of Pennsylvania, 1978. (3) Halpern, J. J . Electrochem. SOC.1953, 100, 421-8. (4) Kulkarni, M.; Wiles, D. R. Can. J. Chem. 1965, 43, 1978-84. (5) Duwell, E. J. J. Electrochem. SOC. 1966, 173, 763-6. (6) Jenkins, L. H. J . Electrochem. SOC. 1960, 707, 371-8. (7) Boggio, J. E. J. Chem. Phys. 1972, 57, 4738-42. (8) Grlmley, T. 8.; Trapnell, B. M. W. Proc. R . SOC.London, Ser. A 1958, 234, 405-18. (9) Mott, N. F. Trans. Faraday SOC. 1939, 35, 1175-7. (10) Frornhold, A. T.; Cook, E. L. Phys. Rev. 1987, 758, 600-12; 1987, 163, 650-64. (11) Asscher, M.; Vofsl, D. J. Chem. SOC. 1961, 2261-4. (12) Inaki, Y.; Ishiyama, M.; Takemoto, K. Angew. Makromol. Chem. 1972, 27, 175-87. (13) Marshall, R.; Mitra, S. S. J. Appl. Phys. 1965, 36, 3882-3.
Stability Constants of Complexes of Molybdate and Tungstate Ions with o-Hydroxy Aromatic Ligands Samuel Natansohn,’ Joel I. Krugler, Joseph E. Lester, Mark S. Chagnon, and Robert S. Flnocchlaro GTE Laboratories Incorporated, Wanham, Massachusetts 02154 (Recelved:June 7, 7979; In Flnal Form: January 7, 1980)
The reactions of Moo4%or WOt- with o-hydroxy aromatic ligands to form 1:l and 1:2 metal-to-ligandcomplexes have been studied. Values of the equilibrium formation constants of the complexes have been obtained from analysis of the absorbkce-concentrationdata. A statisticalmodel which accounts for the three main contributions to the data variance has been developed as well as a nonlinear technique toextract the equilibrium constants in cases where the optical properties of the complexes could not be independently determined.
1. Introduction It has been known for some time that the metal oxyanions, SnOt-, CrOt-, Moot-, and W042-,form colored complexes with nucleophilic ligands such as catechol and catechol derivatives.lP2 It is also known that both 1:l and 1:2 metal-to-ligand complexes are formed. No evidence of 1:3 complexes for Mo(V1) or W(V1) has been reported. Some measurements of the stability constants have been made,l13but, in most cases, only the 1:2 complex constants were determined as this is the complex of analytical importance. More recently, Kustin and co-workers have carefully studied the kinetics of formation of the 1:l M o o t - and W042-complexes of several catechol derivat i v e ~ In . ~these ~ ~ studies they determined both the 1:l and 1:2 complex stability constants for catechol with MOO:-. There was significant disagreement between their reported values and those of Halmek0ski.l Therefore, we undertook to reexamine those MOO^^- and W042- systems where disagreement existed and to extend the range of substituents on the aromatic ring in order to test the hypothesis that the stability constants of the complexes were linearly dependent on the pK, of the ring hydroxyl groups. We also were interested in substituent effects on the ratio of MOO^^- to W042-stability constants. A rather general nonlinear regression technique for the analysis of the absorption data was developed which enabled us to extract the values of the stability constants from the experimental data. 2. Chemical Model
The metallate ions and ligands which are the subject of this report can exist in several different states of protonation and in different configurations. Both MOO^^- and W042-are tetrahedral as free ions;5however, the addition 0022-3654/80/2084-29?2$0 1.OO/O
of a proton to MOO:- is not diffusion controlled, thus a coordination change probably accompanies protonation.6 The most likely change is from tetrahedral to pseudooctahedral geometry. One possibility is that the molybdate or tungstate ion exists in solution in kinetic equilibrium between tetrahedral and hydrated octahedral form3 and that the latter protonates rapidly. The intermediacy of this “octahedral” metallate ion would also help to explain the behavior of these anions on coordination. The overall stoichiometry of the complexation reactions can be expressed as M042-+ H2L F! HZMO4L2(1) HzM04L2- + H2L
MO2L2- + 2Hz0
(2) where H2L is the ligand in the form where both hydroxy groups are protonated. Reaction 1’with R(OH)2equivalent F!
-
OH
0
-
OH
to H2L in eq 1probably better represents the molecular chemistry of the first complexation reaction. The equilibrium constants associated with these reactions are K1 = (HzM04L2-)/ (MO,’-) (HZL) (la) K2 = (MOzLz2-)/(HzM04L2-)(H2L) (24 where the parentheses denote the activity of the particular chemical species and the activity of HzO has been presumed to be unity. The fact that tris(catecho1)molybdate is unknown indicates that two of the oxygens on the metal atom are substitutionally inert. Because of the existence of several different protonated species, the complete 0 1980 American Chemical Society
Stability Constaints of Complexes of Molybdate and Tungstate Ions TABLE I : St,ability Constants of Complexes of Molybdate Ion with o-Dihydroxybenzene Derivatives at pH 8.01 P , , L/ P ~ / P , , * 1 0 ? 3 , ~ ligand-______pKaa mol L/mol L*/mol 3,4-dihydroxy9.16 1 9 i: 1300 i: 0.252 i: toluene 1 150 0.003 1,2-dihydroxy9.19 31 i: 1840 i: 0.572 i: benzene 12 680 0.073 2,3-dihydroxy9.02 33 f 1410 i: 0.459 f toluene 2 100 0.008 1,2,3-trihydroxy- 8.62 93 i: 1560 ? 1.44 i: benzene 9 160 0.054 3,4-dihydroxy8.67' 95 i: 1230 i: 1.17 f benzoic acid 6.5 85 0.042 1,2-dihydroxy-4- 8.24 117 i: 2720 i: 3.19 i: chlorobenzene 7 175 0.14 3,4-dihydroxy7.22d 141 i: 2195 i: 3.09 f benzaldehyde 12 185 0.085 1,2-dihydroxy-4- 6.73 1 6 3 i: 1790 i: 2.91 i: nitro benzene 12 195 0.30 3,4,5-trihyldroxy- 8 . 3 V 210 i: 1550 i: 3.21 i benzoic acid 20 150 0.11 2,3-dihydroxy8.77 270 i: 2800 i: 7.61 i: naphthalene 45 550 0.62 a pKa of the first ring hydroxyl group. pJp, = (MoO,L,'-}/[ {H2Mi~0,LZ-}(H,L}]. ' Y. Murakami, K. Nakamura, and M. Tokunada, Bull. Chem. SOC.Jpn., 36, 669 (1963). P. J. Antikainen and €€. Oksonen, Acta Chem. Scand., 22, 2867 (1968). e G. Ackermann, D. Hesse, and P. Volland, 2. Anorg. Allg. Chem., 311, 92 (1970).
scheme for reaction 1 following Kustin3 should be expressed as -
HL +-
It
3-
C M03(0H)L
It
11 H2L
MO(OH),L
with the vertical arrows denoting the appropriate protonation-deprotonation reactions. A similar reaction manifold can be written for the formation of the 2:l complex. To take all of these possible reaction pathways and protonation products into account would unnecessarily complicate thle ana1:ysis of the systems. If one operates in a relatively narrow pH range and if the pK, of neither the reactant nor the product falls in that range, then the system may be treat,ed as if described by eq 1 and 2. One can test for tlhe existence of significant concentrations of different degrees of protonation by examining either the titration curve of an insoluble component or the behavior of the extinction coefficient of one of the complexes. The protonation pKa's of MOO^^- and WO2- lie below the pH range of interest in these experiments. The hydroxy pKa values for the ligands are given in Table I. Even in the case where a ligand or a complex exists in more than one protonation ritate in the pH range of interest, one can adopt an operational definition for the stability constants derived from eq 1 and 2. Thus (H2M04L2-] (3) 131 = (M04")(H&] (4)
The Journal of Physical Chem/stty, Vol. 84, No. 22, 1980 2973
where the braces denote the sum of the concentrations of all species related by protonation or deprotonation to the one indicated. Obviously, PI and pzwill be pH dependent and are equal to the true equilibrium constants only in the pH region where the indicated species are the predominant species. (Activity coefficients have been neglected in all of these arguments.) Such an operational definition was adopted in the evaluation of the experiments presented below. 3. Experimental Section 3.1. Materials. Reagent grade chemicals were used whenever available. Thus Fisher reagent grade sodium molybdate, sodium tungstate, sodium metabisulfite, catechol, pyrogallol, and gallic acid were used without further purification, 2,3-Dihydroxynaphthalene(Aldrich), 2,3dihydroxy-4-nitrobenzene(Aldrich), and 3,4-dihydroxybenzoic acid (Aldrich) were also used as received, although several techniques were tried, unsuccessfully, to purify the latter compound. 2,3-Dihydroxytoluene (K&K Laboratories), 3,bdihydroxytoluene (Pfaltz and Bauer), and 2,3-dihydroxy-4-chlorobenzene(Pfaltz and Bauer) were purified by sublimation between 55 and 60 "C at a pressure of 0.07-0.1 torr while 3,4-dihydroxybenzaldehyde was sublimed at 70-75 "C. The integrity of the sublimed reagents was confirmed by infrared spectroscopy and differential thermal analysis. 3.2. Instruments. The spectroscopic data were obtained either with a Perkin-Elmer Model 575 or with a GCA/ McPherson Series Eu-700 spectrophotometer. The solutions were measured in matched quartz cells of either 1-cm or 1-mm pathlength as appropriate. Measurements at specific temperatures were made on the Perkin-Elmer instrument by use of a thermostated cell holder which maintained the desired temperature to 10.1 "C. The pH was determined by using an Instrumentation Model 245 or Orion Research Model 701A pH meter. 3.3. Procedure. The solutions used in the determination of the stability constants of complexes with all ligands except catechol were made in a buffer of pH of 8.0 which and 0.08 M NazS2O5and has an consists of 0.1 M ",OH ionic strength of 0.575 M. The Na2S205is added to prevent the oxidation of the ligand. The catechol complexation experiments were conducted in a NH40H-(NH4)2S04 buffer of an ionic strength of 0.1 M and a NazSz05concentration of 0.015 M. Determination of the stability constants of the tungstate-catechol complexes in both buffers showed them to be within the experimental error of each determination. This buffer was used in the experiments with catechol because it allowed for a wider pH range within the same buffer system. The deionized water used for the preparation of the buffers was purged with argon overnight, and the buffer was stored under a positive pressure of argon. The pH of all solutions was checked routinely before and after the absorbance measurements and it stayed at 8.0 1 0.05. The solutions were prepared by dispensing the requisite amounts of components, molybdate or tungstate solution, ligand solution, and buffer, with precision pipets. A stock solution of 1M sodium tungstate or molybdate was used, which was diluted with buffer to the appropriate molarity for each experimental set. A fresh solution of ligand in buffer was made daily. The components of the samples were added in fixed order: buffer first, then the metal solution, and finally the ligand solution. The sample solutions had a volume of 20 cm3;the concentration of the metal ion was usually in the range of 0.001-0.1 mol/L while that of the ligand was limited because of low ligand solubility to the range of 0.001-0.02 mol/L. A typical exper-
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TABLE I1 : Stability Constants of Complexes of Tungstate Ion with o-Dihydroxybenzene Derivatives at pH 8.0
30 28
ligand
L/mol
P,/P,P L/mol
1o-*P,, L2/mo12
3,4-dihydroxytoluene 1,2-dihydroxybenzene 2,3-dihydroxytoluene 1,2,3-trihydroxybenzene 3,4-dihydroxybenzoic acid 1,2-dihydroxy-4chlorobenzene 3,4-dihydroxybenzaldehyde 1,2-dihydroxy-4nitrobenzene 3,4,5-trihydroxybenzoic acid 2,3-dihydroxynaphthalene
265i 17 395f 24 1660 i: 400 950 f 85 1700f 150 1800 f 200 1265f 105 2060 f 170 2200 t 175 3700f 1100
5800f 365 9650f 930 4000 i: 670 1630 f 120 1520f 90 2600 f 21 0 2510f 160 1420 f 90 2450 f 185 2930i 580
1.54.1 0.16 3.82f 0.53 6.63 i: 0.86 1.55 f 0.11 2.59i 0.31 4.7 i: 0.8 3.17i: 0.33 2.92 f 0.32 5.83 I 0.68 11.1t 4.4
P i ,
Natansohn et al.
26
P,lP, = {WO,L,* 1 I [ CH,W0,L2- XH,L)].
300
250
imental set consisted of 24 solutions; in 12 of these, the concentration of the ligand was held fixed while the concentration of the metal ion was increased, thus tending to favor the formation of the complex with a molar ratio of metal to ligand of 1:l. Conversely, in the other 12 solutions, the metal concentration was held constant while the ligand concentration was increased. This favors the formation of the 1:2 metal-to-ligand complex. The stability constants and extinction coefficients reported in Tables 1-111, respectively, were calculated from absorbance measurements made on no fewer than four such sets representing 90-160 individual solutions. The data reported in Table IV are based on at least 50 individual solutions. The selection of the wavelengths at which absorbance measurements were to be made was based on the preliminary evaluation of spectra of solutions with a preponderance of metal and ligand. The absorbance was measured, whenever possible, at the wavelength of a charac-
350
400
450
500
WAVELENGTH (nml
Flgure 1. Absorbance of (a) 0.02 M Moot-, (b) 0.02 M 1,2,3-trlhydroxybenzene (PG), (c) 0.1 M Moot- 4- 0.004 M PG, (d) 0.004 M MOO,*- 4- 0.016 M PG. Solutions measured In 1-mm cells at pH 8.0.
teristic spectral feature such as maximum of an absorption band or where the difference between the spectrum of the solutions with predominantly the 1:l complex as compared to the one with the 1:2 metal-to-ligand complex was most pronounced. The absorbance spectra of the MOO:-1,2,34rihydroxybenzene system depicted in Figure 1provide an illustration of the criteria governing the selection of wavelengths for the absorbance measurements. One of the wavelengths used was 340 nm, close to the maximum of the absorbance of the 1:l complex (curve c) but in a region where the contribution of the ligand (curve b) to the total absorbance was small. The other wavelength was 390 nm, at the top of the absorption band of the 1:2 metal-to-ligand complex. Absorbances measured at two
TABLE 111: Extinction Coefficients of Complexes of Molybdate or Tungstate Ions with Derivatives of o-Dihydroxybenzene at pH 8.0 Moo,'w0,zligand 1,8-dihydroxybenzene 2,3-dihydroxytoluene 3,4-dihydroxy toluene
A, nm
330 4 50 305 400 340 41 -- 0-
450 500 3,4-dihydroxybenzoicacid 390 440 1,2-dihydroxy-4-chlorobenzene 330 430 1,2-dihydroxy-4-nitrobenzene 500 520 1,2,34rihydroxybenzene 350 390 3,4,5-trihydroxybenzoic acid 4 20 500 2,3-dihydroxynaphthalene 420 500
3,4-dihydroxybenzaldehyde
E,," 2940 f 380 0 2 1 5 0 t 35 0 3240f 90 510 _ - _ c 90 __
0 0
1 O O O i 55 280 f 60 3210 f 95 0 2070f 35 885 i: 20 2330f 40 1 2 6 0 f 55 8 3 0 f 75 230 f 30 740 i: 270 98 f 41
A , nm
2320 i: 70 3640i: 70 3810i 12 5640f 20 3440f 11 4960 f . 1. 5 _._ 4 2 4 0 i 20 1370 * 6 6 0 3 0 i 65 4 8 0 0 f 55 4 2 0 0 f 55 5060f 10 2600f 25 950t 9 4 6 2 0 f 55 5040 i: 60 5290i: 55 1 9 3 0 f 20 6690 i: 75 975 f 11
a E,, is the extinction coefficient of the 1:1 metal-to-ligand complex. to-ligand complex.
320 400 350 410 305 400 380 420
370 410 340 410 500 520 350 390 380 4 20 360 400
E ,la 1 9 7 0 f 160 0 1440i: 60 275 f 1 5 6460i: 60 0 2640i 10 48f 3 345 f 20 77 f 4 1190i: 40 95f 6 1020 f 7 360 f 1 1000 f 20 330f 9 335 f 1 2 76t 3 810f 50 100 f 6
5730 f 85 1120i: 20 4460 i: 20 915f 4 7080f 50 1710 f 11 4730 i: 30 435f 3 3820 f 30 860 f 6 7220f 45 985 * 6 0 0 4 9 7 0 i 25 2080i: 11 2810 t 35 640 i: 8 7850+ 190 1060i:25
E,, is the extinction coefficient of the 1:2 metal-
Stability Constaints of Complexes of Molybdate and Tungstate Ions TABLE IV: Effect of pH on the Stability Constants of Complexes of 1,2-DiIhydroxybenzene with Molybdate or Tungstate Ions
Moo4’-
-__-
pH P I , L/mol K , , L/mol
7.5 8.0 8.5 9.0 9.5
34+ 31 i 29 i 25 f 14 i
11 12 7 5 6
34 33 34 41 42 a 9 34 i 4
7.5 8.0 8.5 9.0 9.5
10-4~,~,, LZ/molz 7.6 6.5 7.8 8.9 10.1 av 8.2i 1.3
wo,2-
~-
DH
10-4p2, L2/mola 7.3 i 1 . 5 5.7 i 0.7 5.5 i 0.8 3.3 f 0.4 1.1 i 0.3
PI, LII mol
10-6pz, 10-6KK,K,, K.. Llmol Lz/mo12 L2/molz 760 14.’7 f 0.9 15.3 7 5 0 i !220 4.3 4 20 3.13 i 0.5 395 2 24 7.7 500 5.4 t 0.8 4 2 0 5 44 1.13 i 0.3 4.8 3 5 5 + 30 580 6.4 900 0.7 f 0.1 300 i :32 av 630 i 200 av 7.7 i 2.2
a Error estimates on K , and K,K, averages are the standard deviation of calculated values.
different wavelengths (using buffer solution as the reference) were wed in the computations of the stability constants, but frequently data were taken at several wavelengths of which the two giving the smallest errors were selected. In general, it was sought, whenever possible, to determine the stability constants of the complexes with a precision of at least &lo%. The absorbance of the solutions was monitored at periodic intervals up to 24 h and it was found to be time dependent. At very short times, the changes are probably due to temperature equilibration and/or complex formation kinetics. In the molybdate system the absorbance of the solutions became essentially constant within minutes of their preparation so that the data wed in the calculation of stability constants for most of the molybdenum complexes were those obtained at 2 min after the reagents were mixed. In the tungstate system this time interval was considerablylonger, namely 2 h. In a few cases, the average values of the &ability constants after a longer time interval were essentially the mme as those obtained at the standard time intervals but the errors were smaller. The values with the narrower error bars were then reported in Tables I or 11, All data used in calculating the Stability constants of complexes of a particular metal-ligand system were measured after identical time intervals. The acid dissociation constants of the ligands were determined by standard titration techniques. Solutions of 0.01 M ligand and standardized NaOH were prepared by using deoxygenated water. The titrations were performed in a cell which was flushed with nitrogen to reduce the possibility of ligand oxidation at higher pH. As the ligands are polyprotic and have pK, values approaching that of water, the analysis of the titration curves must be done carefully. A ]procedure described by Fleck7 was used to extract pK viilues from the titration data. Results are given in Table I. 4. Data Analysis
4.1. Mathematical Model. Absorbance data collected a t two wavelengths are presumed, in the absence of experimental error, to fit the model 4
Ai, = C eipCpn i = 1, 2; n = 1,N p=l
(5)
The Journal of Physical Chemistty, Vol. 84, No. 22,
1980 2075
where Ai, is the absorbance of sample n at wavelength Xi, C,, is the concentration of species p in sample n, eip is the molar absorptivity of species p at Xi,and p = 1, 2, 3, 4, corresponds to M, L, ML, and ML2, respectively. It is further assumed that W-4 (MLl PlPZ = = (MIILJ M(L12 Defining Mln as the initial metal concentration and Mzn as that of the ligand one obtains the mass balance equations M z n = Czn + C3n + 2C4n (6) M1n = C1n + Can + C4n in which polynuclear metal species and ligand degradation species are neglected. The equilibria conditions are then expressed as
Can = PlClnCzn C4n = PZCznC3n (7) Note that the system of eq 5-7 is nonlinear. In modeling the various sources of error we have found it convenient to assume linear error propagation (anapproximation only valid for small errors). Insofar as we are only interested in reasonably precise error estimates when the errors are, in fact, small, this is not a serious limitation. 4.2. Statistical Model. All sources of error will be treated as if contained within the absorption measurements represented by eq 5. The mass balance and chemical equilibrium in eq 6 and 7 will be considered as error-free. This omission will be (approximately) accounted for by inclusion of a “chemical component” of the absorption error, to be described below. Within this approximation, eq 6 and 7 can be solved for the 4N equilibrium concentrations as functions of the known total metal and ligand concentrations and the unknown equilibrium constants K l , K2 This requires solution of cubic equations such as
It then follows that
C4n = PZCZnC3n (84 The absorption equations, including an “error term”, can be written as 4
Ai,
C fipCpn + ei,
p=l
i = 1, 2; n = 1, ...,N (9)
The error term, ein,is a random variable with zero mean. Modeling of ei, (Le., decomposing it into independent normally distributed components which adequately describe the true sources of experimental noise) is the essence of the statistical approach. The complete error model used considered three types of experimental error: chemical, dispersion, and residual. The first is associated with the error in the total metal or ligand concentration in solution n;the second with the variation of Pifrom data set to data set; while the third is associated with the absorbance measurement (see Appendix A for a fuller explanation). If &, &, and the covariance matrix of einwere known, a straightforward least-squares approach would yield “best” (minimum variance) estimates of the eiP. This
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The Journal of Physical Chemistry, Vol. 84, No. 22, 1980
least-squares problem requires minimization of a bilinear form in the eight unknown ci,ts; i.e., minimizing a function of the form nm
(10) where the Uinjm,derived from the covariance matrix of ein, are chosen so that minimizing A2 yields a minimum variance estimate of the tip's. Since PI, P2, and e,, are not known a priori, we shall use an iterative procedure to minimize A2 with respect to eip and Pl, Pz. The steps are outlined as follows: (a) Model the error matrix ein, using initial guesses8for a zeroth-order determination of Uym. (b) Set up a two-dimensional grid in (pl, P2) space. For each pair of values (PI, P 2 ) , calculate the corresponding concentrations from eq 6. (c) Using these concentrations, minimize the A2 of eq 8 with respect to qp This yields a set of values Am2 (PI, P2).
(d) Perform a two-dimensional search in (pl, p2) space [repeating steps b and c ] , to minimize Am2 (&, p2) with respect to P1 and P2. (e) Using the values of (P1, P2) and tiP determined in step d, estimate the parameters of the error model from the calculated residual error distribution. (f) Using the new estimate of ei, determined in step e, determine the next order approximation to Uiim. (g) Repeat steps b-f, recycling until the error parameter estimates converge. (h) Using the final values of all parameters, and assuming linear propagation of error, estimate standard errors of all parameters. The details of this process are discussed more fully in Appendix B. 4.3. Experimental Design. Having made one or more initial experimental runs on a specific metal-ligand system, the experimenter will typically wish to sharpen the estimates of P1 and P2 by efficient selection of new concentration ranges. It is not uncommon in our experience to find that the result of these first runs will be standard errors in the equilibrium constants which are of the order of 30% or more. The objective is normally to reduce these uncertainties to
