Systematic Approach to the Quantitative Voltammetric Analysis of the Fe^III/Fe^IIComponent of the [α₂-Fe(OH₂)P₂W₁₇O₆₁]^7-/8-Reduction Process in Buffered and Unbuffered Aqueous Media

Abstract

The one-electron reduction of [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-) at a glassy carbon electrode was investigated using cyclic and rotating-disk-electrode voltammetry in buffered and unbuffered aqueous solutions over the pH range 3.45-7.50 with an ionic strength of approximately 0.6 M maintained. The behavior is well-described by a square-scheme mechanism P + e(-) <--> Q (E(1)(0/) = -0.275 V, k(1)(0/) = 0.008 cm s(-1), and alpha(1) = 1/2), PH(+) + e(-) <--> QH(+) (E(2)(0/) = -0.036 V, k(2)(0/) = 0.014 cm s(-1), and alpha(2) = 1/2), PH(+) <--> P + H(+) (K(P) = 3.02 x 10(-6) M), and QH(+) <--> Q + H(+) (K(Q) = 2.35 x 10(-10) M), where P, Q, PH(+), and QH(+) correspond to [alpha(2)-Fe(III)(OH)P(2)W(17)O(61)](8-), [alpha(2)-Fe(II)(OH)P(2)W(17)O(61)](9-), [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-), and [alpha(2)-Fe(II)(OH(2))P(2)W(17)O(61)](8-), respectively; E(1)(0)' and E(2)(0)' are the formal potentials, k(1)(0)' and k(2)(0)' are the formal (standard) rate constants, and K(P) and K(Q) are the acid dissociation constants for the relevant reactions. The analysis for the buffered media is based on the approach of Laviron who demonstrated that a square scheme with fully reversible protonations, reversible or quasi reversible electron transfers with the assumption that alpha(1) = alpha(2), can be well-described by the behavior of a simple redox couple, ox + e(-) <--> red, whose formal potential, E(app)(0)', and standard rate constant, k(app)(0)', are straightforwardly derived functions of pH, as are the values of E(1)(0)', k(1)(0)', E(2)(0)', k(2)(0)', and K(P) (only three of the four thermodynamic parameters in a square scheme can be specified). It was assumed that alpha(app) = 1/2, and the simulation program DigiSim was used to determine the values of E(app)(0)' and k(app)(0)', which are required to describe the cyclic voltammograms obtained in buffered media in the pH range from 3.45 to 7.52 (buffer-related reactions which effect general acid-base catalysis are included in the simulations). DigiSim simulations of cyclic voltammograms obtained in unbuffered media yielded the values of E(1)(0)' and k(1)(0)'; K(Q) was then directly computed from thermodynamic constraints. These simulations included additional reactions between the redox species and H(2)O. The value of the diffusion coefficient of the [alpha(2)-Fe(III)(OH(2))P(2)W(17)O(61)](7-), 2.92 x 10(-6) cm(2) s(-1), was determined using DigiSim simulations of voltammograms at a rotating disk electrode in buffered and unbuffered media at pH 3.45. The diffusion coefficients of all redox species were assumed to be identical. When the pH is greater than 6, instability of P (i.e., [alpha(2)-Fe(III)(OH)P(2)W(17)O(61)](8-)) led to the loss of the reactant and precluded lengthy experimentation.

A Systematic approach to the simulation of the voltammetric reduction of [α-SiW12O40]4− in buffered aqueous electrolyte media and acetonitrile

“…However, an accurate value of I L could be achieved by inclusion of the contributions from all processes in the simulation [8]. Consequently, the scheme A + e À B, B + e À P, P + 2e À R was simulated with all processes assumed to be quasi-reversible with apparent reversible potentials E 0 app and heterogeneous charge transfer rate constants k 0 app .…”

“…(7) indicates that the difference in the numbers of protons transferred when Ox is converted to Red (m) can be calculated by plotting E 00 (V) vs. pH and obtaining the slope = À2.303mRT/nF. However, under kinetically rather than thermodynamically controlled conditions that actually apply in voltammetry, rigorous descriptions of an electrode process involving extensive acid-base chemistry are complex [8]. Coupled electron and proton transfer steps are involved which requires consideration of the heterogeneous kinetics and thermodynamics of the individual electron transfer steps, as well as the homogeneous kinetics and thermodynamics of the protonation processes.…”

“…A constant activity of H + was used in the simulations as an alternative to use of the generic buffer reactions [8]. This approximate approach mimics a buffer system but simplifies the simulations without losing physical significance.…”

“…Also, ion-pairing with K + from electrolyte (0.1 M KCl) and buffer cations was neglected. This implies that the proposed mechanism may not be fully complete and that, in particular, general acid-base catalysis needs to be introduced into the mechanism as does ion-pairing with K + to provide a more complete simulation [8]. However, since Scheme 2 is already very complex, these terms are not included in the present work, nor are the plethora of cross redox reactions that available.…”

“…In addition, results of brief studies on [Bu 4 N] 4 [a-SiW 12 O 40 ] and [Bu 4 N] 3 [a-PW 12 O 40 ] in the aprotic solvent acetonitrile are used to probe the solvent dependence. The work draws upon recent advances in the simulation of complex reaction schemes [8,9] 12 O 40 ] were synthesized according to the literature procedures [10,11]. Prior to use, Bu 4 NPF 6 (Aldrich; 98%) was recrystallized twice from ethanol [12], and acetonitrile (Ajax FineChem; UV anhydrous, 99.9%) was purified according to a literature procedure [4].…”