Experimental and calculation methods of studying the effect of second coordination sphere on standard rate constants of charge transfer for Cr(III)/Cr(II) redox couple in chloride melts

The cyclic voltammetry method was used to determine the standard rate constants of charge transfer (k _s) on a glassy carbon electrode for the Cr(III)/Cr(II) redox couple in the systems of NaCl-KCl-CrCl₃, KCl-CrCl₃, and CsCl-CrCl₃ in the temperature range of 973–1173 K. It was shown that k _s grows at an increase in the temperature and decreases as sodium cations are replaced by potassium and cesium cations in the second coordination sphere of chromium complexes. The calculations carried out using the PC GAMESS/Firefly quantum-chemical software by means of the DFT technique showed that the values of the charge transfer activation energy change monotonously in the series of Na-K-Cs in accordance with the ratio of reorganization energies. In its turn, this leads to monotonous variation of the charge transfer rate constants.     

Standard rate constants of charge transfer of Nb(V)/Nb(IV) redox pair in equimolar NaCl-KCl melt

Standard rate constants of charge transfer (k _s) on platinum and glassy carbon electrodes for Nb(V)/Nb(IV) redox pair in the NaCl-KCl-K₂NbF₇ melt are determined using the method of cyclic voltammetry in the temperature range of 973 to 1123 K. It is found that k _s increases with increasing temperature and when we pass from glassy carbon to platinum electrode. The “apparent” activation energies of charge transfer are determined; it is shown that the charge transfer between the Nb(V) and Nb(IV) complexes is quasi-reversible and is controlled predominantly by the diffusion.     

Standard rate constants of charge transfer for Nb(V)/Nb(IV) redox couple in chloride-fluoride melts: Experimental and calculation methods

Standard rate constants k _s of charge transfer for Nb(V)/Nb(IV) redox couple in NaCl-KCl (the equimolar mixture) -K₂NbF₇, KCl-K₂NbF₇, and CsCl-K₂NbF₇ melts are determined by using cyclic voltammetry. An unconventional series of the standard rate constants is found: k _s (KCl) < k _s (CsCl) < k _s (NaCl-KCl). Ab initio calculations carried out by using a PC Gamess/Firefly quantum-chemical program showed that the charge transfer activation energy can change not monotonically in the Na-K-Cs series, in compliance with the reorganization energy relationship. This leads, in its turn, to nonmonotonic change in the charge transfer rate constants.     

Charge-transfer kinetics in the Nb(V)/Nb(IV) couple in alkali-metal molten chlorides

Charge-transfer standard rate constants k _s for Nb(V)/Nb(IV) redox couple in KCl-NbCl₅ and CsCl-NbCl₅ chloride melts at glassy carbon and platinum electrodes are determined. The Nb(V) electro-chemical reduction process in the NaCl-KCl (equimolar mixture)-NbCl₅ melt was shown being reversible even at high polarization scan rate (v = 2.0 V s^?1); hence, the determination of k _s appeared impossible. Values of k _s in KCl-NbCl₅ melts are higher than those in CsCl-NbCl₅ melts. Quantum-chemical calculations done in nM⁺[NbCl₆]—model systems by the Discrete Fourier Transformation method showed that the calculated ratio of charge-transfer activation energies in the K⁺-Cs⁺ series corresponds to changes in the experimental charge-transfer rate constants. The charge-transfer standard rate constants increase with the increasing of temperature and with the passing from glassy carbon electrode to platinum one.     

Absolute rate constants for the reaction of O(3P) aroms with n-butane and NO(M  Ar) over the temperature range 298–439 K

Absolute rate constants for the reaction of O(³P) atoms with n-butane (k₂) and NO(M  Ar)(k₃) have been determined over the temperature range 298–439 K using a flash photolysis-NO₂ chemiluminescence technique. The Arrhenius expressions obtained were k₂ = 2.5 × 10^?11exp[-(4170 ± 300)/RT] cm³ molecule^?1 s^?1, k₃ = 1.46 × 10^?32 exp[940 ± 200)/ RT] cm⁶ molecule^?2 s^?1, with rate constants at room temperature of k₂ = (2.2 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 and k₃ = (7.04 ± 0.70)×10^?32 cm⁶ molecule^?2 s^?1. These rate constants are compared and discussed with literature values.     

Standard charge transfer rate constants for Nb(V)/Nb(IV) redox pairs in fluoride melts

Standard charge transfer rate constants (k _s) were defined for Nb(V)/Nb(IV) redox couples in NaF-KF (eutectic)-K₂NbF₇, KF-K₂NbF₇, and CsF-K₂NbF₇ melts using the cyclic voltammetry technique. It was established that in fluoride melts, the k _s values change in the following order depending on the composition of the second coordination sphere: k _s (CsF) < k _s (KF) < k _s (NaF-KF).     

Cadmium ion reduction at mercury electrode in aqueous KCl solution in presence of adsorbed polyvinyl alcohol

The influence of polyvinyl alcohol on the kinetics of cadmium ion reduction in 1M aqueous KCl solution at the dropping mercury electrode was investigated using the impedance method. It was found that small additions of PVA did not change the diffusion coefficient much, but affected only the rate of charge transfer process. The electroreduction of cadmium in the presence of PVA became less reversible. The standard rate constant dependence on coverage degree is described by the following equation: k_s=k_s0(1?ν)ⁿ, where n=2.     

Polymer films on electrodes: Part XVIII. Determination of heterogeneous electron transfer kinetics at poly(vinylferrocene) and nafion/Ru(bpy)2+3 polymer-modified electrodes by convolution voltammetry

Convolution voltammetry was used to evaluate the rates of heterogeneous charge transfer to ferrocene groups in poly(vinylferrocene) and to Ru(bpy)²⁺₃ in Nafion-modified electrodes under semi-infinite conditions. This technique allows correction for uncompensated resistance and double layer capacitance, as well as detrmination of the diffusion coefficient, D, transfer coefficient, α, and half-wave potential, E_1/2, from a single cyclic voltammogram. Vinylferrocene in solution and a bound copolymer of vinylferrocene and styrene in a ratio of 58:42 were also examined. For the polymer films, the heterogeneous charge transfer rate constants, k°, are 10^?4 ≥ k° ≥ 10^?5 cm/s; these values are about two order of magnitude smaller than those for the similar species in homogeneous solution. The values of k°/D^1/2, however, are comparable to those in soluton; 10 > (k°/D^1/2) > 0.1 s^?1/2.     

Electrochemical investigation of the redox couple Sm(III)/Sm(II) on a tungsten electrode in molten LiF–CaF2–SmF3

This article is focused on the electrochemical investigation (cyclic voltammetry and related studies) of the redox couple Sm(III)/Sm(II) in an eutectic LiF–CaF₂ melt containing SmF₃. The first step of reduction for Sm(III) ions involving one electron exchange in soluble/soluble Sm(III)/Sm(II) system was found on a tungsten electrode. The study of the Sm(II)/Sm(0) electrode reaction was not feasible, due to insufficient electrochemical stability of LiF–CaF₂. The first step was found reversible at temperatures 1,075 and 1,125 K up to polarization rate 1 V/s and at temperature 1,175 K the process was reversible at all sweep rates applied in this study. The diffusion coefficients (D) of Sm(II) and Sm(III) ions were determined by cyclic voltammetry, showing that D decreases when oxidation state increase, while the activation energy of diffusion (E _a) increases. The standard rate constants of charge transfer (k _s) were calculated for the redox couple Sm(III)/Sm(II) at 1,075 and 1,125 K based on the data of cyclic voltammetry.     

Kinetics and mechanism of diels-alder additions of tetracyanoethylene to anthracene derivatives-III : Effect of substituents on rates and intermediate complex formation

In Diels-Alder additions of tetracyanoethylene to 1,2-, and 9-substituted anthracenes, formation constants (K) for the intermediate complexes have been separated from the global rate constant (k₂^obs). The relatively small range of values of K indicates a very small charge transfer in the complexes. The transition state for conversion of complex into adduct showed a marked degree of charge development, particularly for the 9-substituted derivatives (p = -7). Substituents in the outer rings gave good rate correlations with composite constants (σ_m⁺+σ_p⁺) with a p value of - 3. The substituent effects are discussed in terms of these and other parameters. Values for equilibrium constants for the overall addition (K_cq) are reported.     

Absolute Rate constants for O + No + N2 → NO2 + N2 from 217–500 K

Flash photolysis of NO coupled with time resolved detection of O via resonance fluorescence has been used to obtain rate constants for the reaction O + NO + N₂ → NO₂ + N₂ at temperatures from 217 to 500 K. The measured rate constants obey the Arrhenius equation k = (15.5 ± 2.0) × 10^?33 exp(1160 ± 70)/1.987 T] cm⁶ molecule^?2 s^?1. An equally acceptable equation describing the temperature dependence of k is k = 3.80 × 10^?27/T^1.82 cm⁶ molecule^?2 s^?1. These results are discussed and compared with previous work.     

Evaluation of unimolecular rate constants for some outer-sphere electrochemical reactions

Unimolecular rate constants, k_et (s^?1), and transfer coefficients, α_cet, for the outer-sphere electroreduction of several Co(III) ammine and ethylenediamine complexes have been evaluated by electrostatically adsorbing the reactants at silver electrodes coated with chloride or bromide monolayers. Sufficiently strong diffuse-layer adsorption is thereby produced so to enable k_cet and α_cet to be determined by means of linear sweep voltammetry, employing sufficiently fast sweep rates (10–100 V s^?1) and dilute reactant concentrations (≤ 50 μM) so that the bulk solution reactant contributes negligibly to the observed faradaic transients. Comparison with corresponding rate constants and transfer coefficients for the solution reactants enables the influence of precursor-state stability upon the latter rate parameters to be assessed.     

Theoretical and experimental study of the catalytic cathodic stripping square-wave voltammetry of chromium species

The electrocatalytic mechanism of Cr(III) reduction in the presence of diethylenetriaminepentaacetic acid (DTPA) and nitrate ions is studied theoretically and experimentally by using stripping square-wave voltammetry (SWV). Experimental curves are in excellent agreement with theoretical profiles corresponding to a catalytic reaction of second kind. This type of mechanism is equivalent to a CE mechanism, where the chemical reaction produces the electroactive species. Accordingly, the reaction of Cr(III)–H₂O–DTPA and \( {\mathrm{NO}}_3^{-} \) would produce the electroactive species Cr(III)–NO₃–DTPA and this last species would release \( {\mathrm{NO}}_2^{-} \) to the solution during the electrochemical step. In this regard, the complex of Cr(III)–DTPA would work as the catalyzer that allows the reduction of \( {\mathrm{NO}}_3^{-} \) to \( {\mathrm{NO}}_2^{-} \). Furthermore, it was found that the electrochemical reaction is quite irreversible, with a constant of k _s?=?9.4?×?10^?5 cm s^?1, while the constant for the chemical step has been estimated to be k _chem?=?1.3?×?10⁴ s^?1. Considering that the equilibrium constant is K?=?0.01, it is possible to estimate the kinetic constants of the chemical reaction as k ₁?=?1?×?10² s^?1 and k _?1?=?1.29?×?10⁴ s^?1. These values of k ₁ and k _?1 indicate that the exchange of water molecules by nitrate is fast and that the equilibrium favors the complex with water. Also, a value for the formal potential E°’?≈??1.1 V was obtained. The model used for simulating experimental curves does not consider the adsorption of reactants yet. Accordingly, weak adsorption of reagents should be expected.     

The influence of uncompensated solution resistance on the determination of standard electrochemical rate constants by cyclic voltammetry,and some comparisons with a.c. voltammetry

a digital simulation analysis is presented of the deleterious effects of uncompensated solution resistance, R_us, on the evaluation of standard rate constant, k^s_ob, by cyclic voltammetry. The results are expressed in terms of systematic deviations of “apparent measured” rate constants, k^s_ob(app), evaluated in the conventional manner without regard for R_us, from the corresponding actual values, k^s_ob(true), as a function of R_us and other experimental parameters. Attention is focused on the effects of altering the electrode area and the double-layer capacitance on the extent of the deviations between k^s_ob(app) and k^s_ob(true), and on comparisons with corresponding simulated results obtained from phase-selective a.c. impedance data. The extent to which k^s_ob(app) <k^s_ob(true) for small R_us values was found to be similar for the cyclic and a.c. voltammetric techniques. The latter method is, however, regarded as being preferable under most circumstances in view of the greater ease of minimising, as well as evaluating, R_us for a.c. impedance measurements. The influence of solution resistance on k^s_ob measurements with microelectrodes and without iR compensation is also considered.     

Determination of the population,depopulation and the anisotropic spin lattice relaxation rates in the photoexcited triplet state of phenazine. A light modulation-EPR study

The photoexcited triplet state of phenazine in toluene glasses at 35 K is investigated by light modulation-EPR spectroscopy. From the transient EPR spectra and the kinetics in the three canonical orientations (p = x, y, z) the rate parameters are determined. Thus, the depopulation rate constants k_p, the anisotropic spin lattice relaxation rate constants W_p, and the ratios between the population constants A_p are calculated: k_x = (2.2 ± 0.3) × 10² s^?1, k_y = (0.21 ± 0.04) × 10² s^?1, k_z = (0.06 ± 0.03) × 10² s^?1, W_x = (8.6 ± 0.9) × 10³ s^?1, W_y = (11.0 ± 1.0) × 10³ s^?1, W_z = (14.0 ± 1.4) × 10³ s^?1, and A_x: _Ay:A_z ≈ 1:0.04:0.02. It is concluded therefore that the in-plane spin state |τ_x > is the active one.     

Electrode kinetics of the metal complexes with aminopolycarboxylic acids: Part II. Cadmium-ethylenediamine-N,N,N′,N′-tetraacetate (EDTA) complexes

The d.c. polarographic current-potential curves of Cd(II)-EDTA complexes were examined in the pH range 0.5–10.0, to elucidate the mechanism of their electrode processes and to determine the relevant electrochemical kinetic parameters. It was shown that the first wave observed below pH 3 at ?0.58 to ?0.65 V vs. SCE is the reversible reduction wave of Cd(II) aquo-ion with kinetically-controlled limiting current, and the second wave observed above pH 1.5 at ?0.75 to ?1.21 V vs. SCE corresponds to the simultaneous irreversible reduction of four complex species, CdH₃L⁺, CdH₂L, CdHL^? and CdL^2?, where CdH_pL^(p?2)+ and L^4? denote the protonated complex species with p protons and the unprotonated EDTA ion, respectively. Analysis of the dependence of limiting current on the hydrogen ion concentration led to the conclusion that the preceding reaction determining the behaviour of limiting current is CdH₃L⁺?Cd²⁺+H₃L^? with k₃^d=6.3×10² s^?1 and k₃^f=3.3×10⁶ s^?1M^?1, where k₃^d and k₃^f are the dissociation and formation rate constants, respectively. On the other hand, from analysis of the dependence of half-wave potentials of the second wave on the hydrogen ion concentration, the kinetic parameters of the four complex species were evaluated, and are given in Table 1. Further, it was shown that the cathodic rate constants of these four charge transfer processes at some reference potential together with those of Cd(II)-HEDTA complexes fulfil the linear free energy relationship.     

Determinations of the rate constants of the reactions Cl + N3Cl and N3 + NO at 295 K

The kinetics of reactions involving the ground-state azide radical, N₃ (X²Π_g, have been investigated in a discharge-flow system using mass spectrometric detection with molecular-beam sampling. The following rate constants have been determined at 295 K: Cl + N₃Cl → Cl₂ + N₃,k₂₉₅ = (1.78 ± 0.26) × 10^?12 cm³ s^?1 (1σ): N₃ + NO → N₂O + N₂, k₂₉₅ = (1.19 ± 0.31) × 10.^?12 cm³ s^?1 (1σ). A method for determining absolute N₃ radical concentration is reported.     

Biphasic oxidation of diaquadichloro(1,10-phenanthroline)chromium(III) by N-bromosuccinimide and the formation of chromium(IV) and chromium(V)

The kinetics of oxidation of diaquadichloro(1,10-phenanthroline)chromium(III) complex, [Cr^III(phen)(H₂O)₂Cl₂]⁺, by N-bromosuccinimide (NBS) is biphasic. The first faster step involves the oxidation of Cr(III) to Cr(IV). The second slower step is due to the oxidation of Cr(IV) to Cr(V). The reaction product is isolated and characterized by electron spin resonance (ESR), IR, and elemental analysis. The chromium(V) product is consistent with the formula [Cr^V(phen)Cl₂(O)]Br. The rate constants k_f and k_s, for the faster and the slower steps respectively, were obtained using an Origin 9.0 software program. Values of both k_f and k_s, varied linearly with [NBS] at constant reaction conditions. The effect of pH on the reaction rate is investigated over the pH (4.11–6.01) range at 25.0°C. The rate constants k_f and k_s increased with increasing pH. This is consistent with hydroxo forms of the chromium species being more reactive than the aqua forms. Chromium(III) complexes, more often than not, are inert. The oxidation of the Cr(III) complex to Cr(IV), most likely, proceeds by an outer sphere mechanism. Since chromium(IV) is labile the mechanism of its oxidation to chromium(V) is not certain.     

A flash photolysis study of the elimination of dinitrogen from trans-(N2)2W(dppe)2; dppe = 1,2-bis-diphenylphosphinoethane

Flash photolysis of trans-(N2)2W(dppe)2 (1) at ?60, ?30, ?10°C, and room temperature indicates that loss of dinitrogen occurs stepwise via the following proposed intermediates. Photodissociation of 1 gives the transient A decaying with k1 ～ 4450 s?1 to the doubly coordinatively unsaturated species [W(dppe)2], B. Further reactions of B are dependent on the type of gas used to saturate the solutions. In N2-saturated media, B is efficiently reconverted into the starting complex 1 via (N2)W(dppe)2], C(N2), kN22 = 450 s?1, which in turn takes up a second molecule of N2, kN23 = 3.7 s?1. In CO-saturated solutions, trans-(CO)2W(dppe)2 is produced as the final product and the corresponding rate constants are kCO2 1500 s?1 for B → C(CO) and kCO3 = 1.14 s?1 for C(CO) → product. In Ar-saturated solvents, B is transformed, again in two steps; kAr2 = 1 s?1 and kAr3 = 0.1 s1?, to products of unknown structure.The different rate constants kN22, kCO2, kAr2 and kN23, kCO3 and kAr3, together the common activation energy of ca. 11 kcal/mol?1 for the three processes A → B, B → C(N2) and C(N2) → 1 suggest that the reactions of B and C occur by SN2-type displacement of coordinated solvent molecules by the incoming ligands.     

Zur thermischen Zersetzung von Ammoniumfluorochromaten

On the Thermal Decomposition of Ammonium Fluoro Chromates The thermal decomposition of the ammonium fluoro chromates (NH₄)₂[CrF₅(H₂O)], (NH₄)₃CrF₆, and (NH₄)₂[Cr(H₂O)₆]F₅ has been investigated by thermoanalytical and X-ray investigations. Steps of decomposition are the formation of (NH₄)₃CrF₆ und NH₄CrF₄. Further the formation of a chromium fluoride ammoniate CrF₃ · xNH₃ (x ≥ 1) has been detected. The end product of decomposition is the rhomboedrical CrF₃. The hydrolysis reactions have been suppressed by using quasi-isobaric conditions. As by-reaction a partial reduction of CrF₃ has been detected leading to the formation of Cr₂F₅.