Study of the Uncatalyzed Oxidation of Arsenic(ll1) by Cerium(lV) in Perchloric Acid Medium Kenneth G. Everett' and D. A. Skoog Department of Chemistry, Stanford University, Stanford, CaliJ 94305
S ectrophotometric studies have permitted the identihation and thermodynamic characterization of two complexes formed in perchloric acid solution of cerium (IV) and arsenic(ll1); the composition of these complexes i s postulated to be CeH3As03'+and CeH2AsOa3+. Rate studies, also described in this paper, suggest that these two corn lexes are important intermediates in the oxidation oParsenic(ll1) by cerium(lV). Thus, the kinetic data can be rationalized by assuming the rate-determining steps for the reaction involve the decomposition of the two intermediates, probably forming cerium(ll1) and arsenic(1V). The latter is then believed to react rapidly with an additional cerium (IV) ion.
OXIDATION OF ARSENIC(III) by cerium(1V) is of sufficient importance in analytical chemistry to warrant a detailed study of the mechanism by which the reaction takes place. To date, only two studies of the uncatalyzed reaction are reported in the literature, and these have yielded conflicting and ambiguous conclusions. Stefanovskii and Gaukhman (I) reported that the reaction in sulfuric acid was second order and that the rate could be described by the equation rate
=
-
d[Ce(IV)l ____ dt
=
k[Ce(IV)1[As(III)1
Moore and Anderson (2), however, subsequently showed that the second-order rate constant k exhibited a definite timedependent drift; their data suggested that the reaction was third order rather than second, and they proposed a mechanism involving a termolecular rate-determining step in which two cerium(1V) ions combine with one molecule of arsenious acid. Other kinetic studies of the oxidation in the presence of catalysts such as iodine, osmium, and ruthenium are also found in the literature (3). I n all of these, however, the rate was determined largely by the reaction of the catalyst with cerium(1V) or arsenic(II1). Thus, little information about the uncatalyzed reaction between the two species is to be found in these papers. Rechnitz ( 4 ) has pointed out that quite generally oxidations by cerium(1V) are so complicated by complexation steps, solvent effects, and reaction intermediates that elucidation of a detailed mechanism has seldom been possible. The cerium (1V)-arsenic(II1) reaction system is no exception to this generalization. In perchloric acid medium, hydrolytic equilibria lead to at least three cerium(1V) species while in Present address, Department of Chemistry, Stetson University, Delano, Fla. (1) V. F. Stefanovskii and M. S . Gaukhman, J. Gen. Chem. U.S.S.R.,11, 970 (1941). (2) J. W. Moore and R. C . Anderson, J. Amer. Chem. Soc., 66, 1476 (1944). (3) For example, R. D. Sauerbronn and E. B. Sandell, Michrochim. Acta, 1953, 22; C. Surasiti and E. B. Sandell, J. Phys. Chem., 63, 890 (1959); R. A. Barkley and T. G. Thompson, ANAL. CHEM.,32, 154 (1960). (4) G. A. Rechnitz, ANAL.CHEM.,36,453R (1964).
sulfuric acid solutions several sulfate complexes of the cation must also be considered (5). In addition we have found evidence for moderately stable complexes of cerium(1V) and arsenic(II1) in perchloric acid media. The most obvious manifestation of these complexes is the intense red color that appears when perchloric acid solutions of cerium(1V) are mixed with aqueous arsenious acid. At room temperature the color fades rapidly as the arsenic(II1) is oxidized, but in the range of 0 to 10 "C the oxidation-reduction process is slowed sufficiently to permit convenient investigation of the species responsible for the color. It was our view at the outset of this work that interpretation of kinetic measurements of the cerium(1V)-arsenic(II1) reaction would require a preliminary characterization of the predominant constituents of the reaction mixtures. The first part of this paper is thus devoted to a thermodynamic study of the species present initially when perchloric acid solutions of cerium(1V) are mixed with solutions of arsenic (111). The second part of this paper describes our kinetic studies which, with the aid of the thermodynamic data, are readily interpreted by postulating a relatively simple and logical reaction mechanism. It seems probable that the data reported should also be helpful in understanding the more complex systems in which sulfate and other anions are present. Work on the sulfate system is in progress in these laboratories and will be reported at a later date. EXPERIMENTAL Reagents and Solutions. The water employed throughout
this work was first deionized and then distilled from alkaline permanganate. Cerium(1V) solutions were prepared by dilution of a stock solution (obtained from G. Frederick Smith Chemical Co., Columbus, Ohio) that was analyzed as follows: the cerium (IV) content was determined by titration of aliquots with a standard iron(I1) solution; total cerium was obtained by the method of Willard and Young (6); cerium(II1) was found by difference ; the acid concentration was determined by titration with standard base after removal of both cerium(II1) and cerium(1V) as the insoluble cerium(II1) oxalate formed by the addition of an excess of Na2C204. For diluting the stock cerium(1V) reagent, solutions that were at least 0.1M in HCIOl were always employed; this precaution was necessary in order to avoid formation of colloidal hydrolysis products of the cation. When stored in the dark the stock cerium(1V) solution was found to change concentration at the rate of about 0 . 2 x per month. Diluted solutions, on the other hand, decomposed at a rate as great as 1 per day; therefore, diluted solutions were freshly prepared each time they were to be used. A standard, stock solution of arsenic(II1) was prepared by solution of a weighed quantity of primary standard Asz03 in base followed by neutralization with HC104.
x
( 5 ) F. B. Baker, T. W. Newton, and M. Kahn, J. Phys. Chem.,
64, 109 (1960). (6) H. H. Willard and P. Young, J . Amer. Chem. Soc., 50, 1379 (1928).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
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Table I. Spectrophotometric Data for Solutions of Cerium (IV) in Perchloric Acid Absorbance, at HC10, concentration ofa Calculated values Temperature, "C 0.119M 0.294M 0.586M 0.878M 4 K¶ 30.8 0.290 0.372 0.426 ... 11.2 f 1.3 0.16 f 0.03 24.5 0.318 0.400 0.451 0.473 6.4f 0.4 0.12 f 0.01 0.098f 0.005 18.9 0.345 0.426 0.478 0.506 3.0 f 0.1 12.6 0.380 0.454 0.500 0.538 1.8 f 0.2 0.082f 0.014 7.6 0.413 0.484 0.531 0.586 1.2f 0.1 0.052f 0.011 #All solutions were adjusted to unit ionic strength. The total ceriurn(1V) concentration was 3.16 X lW4Mand the cerium(II1) concentration was 2.9 X 10-6M. Absorbance measurementswere made at 290 nm with a 1.00-cm cell.
Stock solutions of cerium(II1) perchlorate were prepared by reducing analyzed solutions of cerium(1V) perchlorate with an excess of unstabilized, 3 % hydrogen peroxide. The excess hydrogen peroxide was removed by boiling; after cooling the resulting solutions were diluted to known volumes. Standard solutions of arsenic(V) were prepared by dissolving carefully weighed quantities of reagent grade arsenic(V) oxide in concentrated sodium hydroxide. After dilution, the solutions were neutralized with perchloric acid. Throughout this study, the ionic strength of solutions was maintained at unity by suitable additions of a stock NaC104 solution. The reagent was prepared by careful neutralization of HC104solution with NaZCO3; COZwas removed by boiling. The concentration of the solution was determined from the weight of NaCIOa obtained by evaporation of aliquots and drying at 150 "C. Spectrophotometric Measurements. A Beckman Model DU spectrophotometer with matched, 1.00-cm silica cells was employed throughout. Temperature control to +O.l "C for solutions within the cell compartment was obtained by circulating a thermostated liquid through hollow, thermospacer plates on either side of the cell compartment. Experimental Procedure. All solutions were prepared at room temperature and then allowed to come to temperature equilibrium in the cell compartment before measurement. For both the thermodynamic and kinetic studies of the cerium(IVbarsenic(II1) complexes, appropriate volumes of the cerium(IV), HC104, and NaC104 solutions were mixed at room temperature and an exactly 3-ml aliquot of the mixture was transferred to the spectrophotometer cell. The cell and solution were then allowed to come to temperature equilibrium in the cell compartment. An appropriately diluted solution of arsenious acid was precooled in a n ice bath and exactly 0.300 ml was quickly injected by means of a calibrated, cooled syringe into the spectrophotometer cell through a hole in the cover plate of the cell compartment. A stopwatch was started at the instant of injection. The mixture was rapidly homogenized by stirring with a thin Teflon (Du Pont) disk fitted over the syringe needle. Absorbance data were taken at minute intervals for 10 to 20 minutes. The logarithm of the absorbance decreased linearly with time; thus the absorbance of the mixture at the time of mixing could be obtained by linear extrapolation of the plots. An experimental study indicated that the maximum temperature fluctuation immediately after injection of the arsenic(II1) solution was 10.5 "C and that the solution quickly returned to its equilibrium temperature. It is estimated that temperature uncertainties in the study averaged h0.2 "C. RESULTS OF THE THERMODYNAMIC STUDY
Cerium(1V) Hydrolysis. Interpretation of the data presented in later sections of this paper required quantitative information about the hydrolytic behavior of cerium(IV) at reduced temperatures. Data of this kind are sparse in the literature, and as a consequence the hydrolysis of cerium(1V) in perchloric acid in the temperature range of 7 to 30 "C was studied briefly. 1542
From potentiometric measurements, Sherrill, King, and Spooner (7) concluded that at low concentrations of cerium (IV) and at perchloric acid concentrations of 0.2 to 2.4M, the hydrolysis process can be adequately described by K1 =
Kz
=
[CeOH 3+1[H+l Ice4+]
[Ce(OH)z'+l[H+l [CeOH3+]
They reported a value of 0.6 for KZat 25 "C and showed that the first hydrolysis step was essentially complete under their experimental conditions. Baker, Newton, and Kahn (5) also investigated these equilibria potentiometrically and found that at room temperature the first hydrolysis step was at least 8 5 % complete while at 1.6 "C it was greater than 70%. They reported values of 0.15 and 0.08, respectively, for Kz at the two temperatures (ionic strength = 2.0). Offner and Skoog (8), from spectrophotometric studies, obtained a value of 0.2 for KZat 25 "C and at an ionic strength of unity; in their treatment, the first hydrolysis step was assumed to be sufficiently complete so that the concentration of Ce4+ was negligible compared with the concentration of the two hydrolysis products. The present study was based upon absorbance measurements at 290 nm, a wavelength near the absorption peak for cerium(1V) solutions (see Figure lb). Cerium(II1) does not absorb significantly at this wavelength. The concentration of cerium(1V) was kept small enough so that no significant amount of dimer formation should take place. The experimental results are found in Table I. In addition to Equations 1 and 2, two further equations were employed for treatment of the data; these were
+ [CeOH3+]+ [Ce(OH)z'+I A = eo[Ce4+]+ el[CeOHS+] + ez[Ce(OH)zZ+] C1 = [Ce4+1
(3) (4)
where C1is the analytical concentration of cerium(1V) and A is the measured absorbance; €0, €1, and €2 are the molar absorptivities of the three cerium(1V) species. The four equations for the system are readily reduced to A[H+]' A[H+]Ki AKiKz - eoCi[H+]' - eiCi[H+]Kl CZCIKIKZ = 0 (5)
+
+
which was then employed in the computations of KI and KlKz as well as of eo, el, and e?. For the calculations, an iterative procedure was used in which values for €0, €1, and ez were first assumed. Substitution of the assumed values and the experimental data into Equation 5 produced a set of five (7) M. S. Sherrill, C. B. King, and R. C. Spooner, J. Amer. Chem. SOC.,79,3675 (1957). (8) H. G. Offner and D. A. Skoog, ANAL.CHEM., 38, 1520 (1966).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
Table 11. Effect of Cerium(IV) and ArsenicOII) Concentrations on Complex Formation. Absorbanceb 8.30 X 11.06 X HIASOI 2.77 X 5.53 X concn, lW4M W4M W4M 1 0 - 4 ~ ce'+ ce'+ ce'+ M x 103 ce4+ 1.865 0.805 1.372 0 0.420 1.14 0.499 1.038 1.578 2.116 2.28 0.565 1.142 1.728 2.297 0.612 1.229 1.854 3.42 2.467 4.56 0.641 1.295 1.953 2.587 2.035 2.689 5.70 0.612 1.347 All data at 7.3 OC, HCIO, concentration of 0.31M, and ionic strength of 1.00. Measured at 290 nm with 1.00-cm cells; data obtained by extrapolation to zero time. 5
Table 111. Effect of Arsenic(II1) Concentration and Acidity on Complex Formation. HClOi AS(II1) Absorbance* concn, concn M M x 103 T 4 " C 5.1 "C 8.4 "C 11.1 "C 1.365 1.309 0.127 0 1.470 1.430 1.14 1.556 1.491 1.696 1.633 2.27 1.861 1.798 1.713 1.635 3.42 1.853 1.775 2.015 1.950 4.55 2.138 2.062 1.961 1.877 5.69 2.241 2.153 2.065 1.979 1.617 1.568 1.510 1.441 0.263 0 1.848 1.795 1.14 1.713 1.633 1.961 2.27 1.872 1.790 2.009 2.161 2.107 3.42 2.015 1.928 4.55 2.273 2.209 2.119 2.025 2.367 2.301 2.208 2.118 5.69 1.690 1.638 0.433 0 1.590 1.535 1.954 1.890 1.14 1.820 1.757 2.101 2.27 2.061 1.996 1.916 2.268 2.204 3.42 2.134 2.049 2.371 4.55 2.311 2.240 2.152 2.465 2.399 5.69 2.324 2.243 0.603 0 1.757 1.712 1.644 1.606 1.14 2.019 1.959 1.884 1.834 2.27 2.195 2.137 2.066 2.004 3.42 2.276 2.340 2.207 2.136 4.55 2.378 2.439 2.310 2.237 5.69 2.464 2.524 2.411 2.337 1.800 1.760 0.773 0 1.700 1.650 1.14 2.061 2.009 1.938 1.884 2.27 2.237 2.183 2.110 2.052 3.42 2.373 2.321 2.253 2.184 4.55 2.474 2.430 2.368 2.278 5.69 2,571 2.509 2.455 2.376 All solutions were 9.22 X 10-'M in cerium(IV), 0.70 X lO-'M in cerium(III), and 1.00M in ionic strength. Measured at 290 nm with 1.00-cm cells; data obtained by extrapolation to zero time. equations at each temperature (four in one instance) which were linear in K l and KlK2. Tentative values for Kl and K1K2 at each temperature were then determined by means of a computer-based least squares procedure. Substitution of the approximations for K1 and K2 into Equation 5 yielded a set of 19 equations that were linear in €0, el, and ez; these equations were then solved with the same program to yield improved values for eo, el, and e2. After three iterations, the data converged satisfactorily giving the values for Kl and K Z shown in Table 11. The computation procedure was facilitated by the fact that reasonably good approximations for the three molar absorbances could be obtained a t the outset by the following pro-
0.80
0.60
\
T
d
f
0.40
U
0.20
0
220
260
300 340 300 Wavelength, nm
420
Figure 1. Absorption spectra (a) Mixture of arsenic(II1) and cerium(IV); (b) cerium(1V) solution; (c) spectrum of complex
cedure. It was assumed that at 30.8 "C, the first hydrolysis step was sufficiently complete so that the presence of Ce4+ could be neglected. By employing the data at this ternperature and the method described earlier (4), values for el and e2 of about 500 and 1500 were calculated. From the absorbances of the solutions containing significant concentrations of Ce4+ (those at low temperature and with high acidities) it was apparent that €0 was greater than either el or € 2 ; thus a value of 2000 was assumed. The values for the three constants after the iterative procedure were: E O = 2280(*25); €1 = 1550(*6); and €2 = 451(IfII14). Here, as in Table I, the figures in parenthesis are standard deviations of the individual coefficients from the best straight line fit of the data. Plots of the logarithm of Kl and K2 against the inverse of the absolute temperature yielded good straight lines. The slopes of the lines, obtained by a least squares analysis, gave values of 16.1(+1.3) kcal/mol and 7.5(11.0) kcal/mol for AH for the first and second hydrolysis steps, respectively. Formation and Characteristics of Cerium(1V)-Arsenic(II1) Complexes. At room temperature, the intense red color observed when arsenious acid is added to perchloric acid solutions of cerium(1V) faded rapidly and disappeared after 20 to 30 seconds. Below 12 "C and in the presence of excess arsenicUII), however, fading was sufficiently retarded to make spectrophotometric studies of the solutions feasible and convenient; here decreases in absorbance of 5 to 20 during the first ten minutes after preparation were typical. In this period, a perfectly linear relationship between log A and time was always observed, and by extrapolation, zero-time absorbances could be obtained. Such data were employed for characterizing the complexes responsible for the color. Figure 1 shows absorption spectra for solutions of cerium
ANALYTICAL CHEMISTRY, VOL. 43, NO. 12, OCTOBER 1971
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240
[H+]j 0.773 200
450
-
160
400
-
350
-
300
-
250
-
2.8
200
-
Figure 2. Effect of cerium(1V) and arsenic(II1) concentrations on complex formation. Data from Table I1
150
'
80
40
0
0.4
0.8
1.2
1.6
2.0
2.4
Absorbance, A
Cerium(1V) concentration: (a) 2.77 X (c) 8.30 X 10-'M; ( d )11.06 X lO-'M
=
[P]/[CeOH3+][H3As031n
Additional equations describing the model are
+ [CeOH3+l + [Ce(OH)2*+1+ [PI
(7)
+ tz[CeOH+] + e3[Ce(OH)22+]+ €'[PI
(8)
C1 = [Ce4+l
and A = c,[Ce'+]
where t' is the molar absorbancy of the assumed complex P. Equations 1, 2, 6, 7, and 8 are readily reduced to the relationship AN1 - CiNz = -AKr[H3As03]"
+ e'Kt[H3As03]"C1
(9)
where N 1and Nz are acid dependent constants related to the hydrolysis of cerium(1V). That is,
1544
I
I
2.0
2.2
2.4
2.6
Figure 3. Effect of acidity on complex formation. Data from Table I11 at 2.4 "C and
Letting A. be the absorbance when [H3As03]= 0, Equation 9 becomes AoNi
=
CiN2
(10)
Substituting Equation 10 into Equation 9 and rearranging yields (A - Ao)Ni [H3As031n
=
-K'A
f e'K'C1
In those instances in which P
