Massenspektrometrische Untersuchungen an Azoverbindungen: I

A number of symmetrical and unsymmetrical azo compounds have been studied by electron impact mass spectrometry. In all cases (except azoisobutyronitrile) the compounds follow a two-step fragmentation mechanism \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm R}^{\rm 1} - {\rm N = N - R}^{\rm 2} } \right]_{}^{_.^ + } $\end{document} → [R¹? N₂]⁺ (+R²˙)→[R¹]⁺(+N₂).     

Oxidation of captopril by hydrogen peroxide and peroxomonosulfate ion catalyzed by a ruthenium(III) complex: kinetic and mechanistic studies

The complex [Ru^III(edta)(H₂O)]^? (edta^4? = ethylenediaminetetraacetate) catalyzes the oxidation of captopril (CapSH) using primary oxidants, hydrogen peroxide (H₂O₂) and peroxomonosulfate (\( {\text{HSO}}_{5}^{ - } \)). The kinetics of the oxidation reaction were studied as a function of both oxidant (H₂O₂, \( {\text{HSO}}_{5}^{ - } \)) and substrate (CapSH) concentrations using stopped-flow and rapid scan stopped-flow techniques. Spectral and kinetic data are suggestive of a pathway involving rapid formation of the intermediate complex [Ru^III(edta)(CapS)]^2? followed by direct attack of the oxidant (H₂O₂ or \( {\text{HSO}}_{5}^{ - } \)) at the S atom of the coordinated CapS^?. ESI–MS and HPLC analysis of the reaction products showed that captopril disulfide (CapSSCap) is the major oxidation product. A probable mechanism in agreement with the spectral and kinetic data is presented.     

Über Chalkogenolate. 171. Reaktion von N,N′-Diphenylformamidin mit Kohlenstoffdisulfid 4. Ester der N,N′-Diphenyl-N-formimidoyldithiocarbamidsäure

On Chalcogenolates. 171. Reaction of N,N′-Diphenyl Formamidine with Carbon Disulfide. 4. Esters of N,N′-Diphenyl-N-Formimidoyl Dithiocarbamic Acid Potassium N,N′-diphenyl N-formimidoyl dithiocarbamate reacts with alkyl halides to yield the corresponding esters \documentclass{article}\pagestyle{empty}\begin{document}${\rm C}_6 {\rm H}_5 {\rm N} = CH - {\rm N}({\rm C}_6 {\rm H}_5) - {\rm CR} - {\rm SR, where R = CH}_3,{\rm C}_2 {\rm H}_5,{\rm CH}_2 - {\rm C}_6 {\rm H}_5,$\end{document} \documentclass{article}\pagestyle{empty}\begin{document}${\rm and (C}_6 {\rm H}_5 {\rm N} = CH - {\rm N}({\rm C}_6 {\rm H}_5) - {\rm CS)}_{\rm 2} = {\rm CH}_2 .$\end{document} The phenyl ester (R = C₆H₅) has been synthesized by reaction of N,N′-diphenyl formamidine with the phenyl ester of chlorodithioformic acid. The prepared compounds have been characterized by means of electron absorption, infrared, nuclear magnetic resonance (¹H and ¹³C), and mass spectra.     

Loss of methyl radical from some small immonium ions: Unusual violation of the even-electron rule

Several small immonium ions of general formula \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R}^{\rm 1} {\rm R}^{\rm 2} {\rm C = }\mathop {\rm N}\limits^{\rm + } {\rm R}^{\rm 3} {\rm CH}_{\rm 3} $\end{document} (R¹, R², R³ = H or alkyl) eliminate ^.CH₃; this reaction occurs in the mass spectrometer in both fast (source) and slow (metastable) dissociations. Such behaviour violates the even-electron rule, which states that closed-shell cations usually decompose to give closed-shell daughter ions and neutral molecules. The heats of formation of the observed product ions (for example, [(CH₃)₂C?NH]^+.) can be bracketed using arguments based on energy data. Deuterium labelling results reveal that the methyl group originally bound to nitrogen is not necessarily lost in the course of dissociation. Thus, for instance, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm{(CH}}_{\rm{3}})_2 = \mathop {\rm{N}}\limits^{\rm{ + }} {\rm{HCD}}_{\rm{3}} $\end{document} eliminates both CH₃^. and CD₃^., via different mechanisms, but very little CH₂D^. or CHD₂^. loss occurs.     

Mass spectrometry of organic compounds of the group V Elements: VI—A new type of amine fragmentation under electron impact

A new type of amine fragmentation under electron impact is elucidated for proline, sarcosine and aspartic acid derivatives and aminomethylphosphines of the general formula R₂NCH₂X. Ordinary α-cleavage affording the \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R}_2 \mathop {\rm N}\limits^{\rm + } {\rm = CH}_{\rm 2} $\end{document} ion is suppressed by elimination of a neutral HX particle and [M - HX]⁺ ion formation, or M-HX neutral particle ejection and generation of an [HX]⁺ ion from [M]⁺˙. Such fragmentation is ensured by the presence of an α-heteroatom (N, O, P, S) in one substituent (X) and a CO₂R type delocalizing group in the α-position of the other substituent (R₂N).     

Dynamics of magnesium-bicarbonate interactions

The complexation kinetics of Mg²⁺ with CO ₃ ⁼ and HCO ₃ ^? has been studied in methanol and water by means of the stopped-flow and temperature-jump methods. Kinetic parameters were obtained in methanol by coupling the magnesium-carbonato reactions with the metal-ion indicator Murexide. Relatively high stability constants were found in methanol (K=1.0×10⁵ liters-mole^?1 for Mg²⁺-Murexide,K=7.0×10⁴ liters-mole^?1 for Mg²⁺?HCO ₃ ^? , andK=2.0×10⁵ for Mg²⁺?CO ₃ ⁼ liters-mole^?1). The corresponding, observed formation rate constants were determined to be $$\begin{gathered} k_f = 4.0 \times 10^6 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - Murexide) \hfill \\ k_f = 5.0 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - HCO_3^ - ) \hfill \\ k_f = 6.8 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - CO_3^ = ) \hfill \\ \end{gathered} $$ The relaxation times were found to be much shorter (τ≈5–20 μsec) in aqueous solutions, primarily due to the relatively high dissociation rate constants. The data could be interpreted on the basis of a coupled reaction scheme in which the protolytic equilibria are established relatively rapidly, followed by a single relaxation process due to the formation of MgHCO ₃ ⁺ and MgCO₃ between pH 8.7 and 9.3. The observed formation rate constants were determined to be $$\begin{gathered} k_f = 5.0 \times 10^5 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - HCO_3^ - ) \hfill \\ k_f = 1.5 \times 10^6 M^{ - 1} - sec^{ - 1} (Mg^{2 + } - CO_3^ = ) \hfill \\ \end{gathered} $$ These results, in conjunction with NMR solvent exchange rate constants, are analyzed in terms of a dissociative (S _N1) mechanism for the rate of complex formation. The significance of these kinetic parameters in understanding the excess sound absorption in seawater is discussed.     

Potential energy profiles for unimolecular reactions of organic ions: [C3H8N]+ and [C3H7O]+

The unimolecular decompositions of two isomers of [C₃H₈N]⁺, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} {\rm CH} = \mathop {\rm N}\limits^ + {\rm H}_2 $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H = CH}_{\rm 2} $\end{document}, are discussed in terms of the potential energy profile over which reaction may be considered to occur. The energy needed to promote slow (metastable) dissociations of either ion is found to be less than that required to cause isomerization to the other structure. This finding is supported by the observation of different decomposition pathways, different metastable peak shapes for C₂H₄ loss, the results of ²H labelling studies, and energy measurements on the two ions. The corresponding potential energy profile for decomposition of the oxygen analogues, \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 3} {\rm CH}_{\rm 2} {\rm CH =\!= }\mathop {\rm O}\limits^ + {\rm H} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm O}\limits^ + {\rm = CH}_{\rm 2} $\end{document}, is compared and contrasted with that proposed for the [C₃H₈N]⁺ isomers. This analysis indicates that for the oxygen analogues, the energy needed to decompose either ion is very similar to that required to cause isomerization to the other structure. Consequently, dissociation of either ion is finely balanced with rearrangement to the other and similar reactions are observed. Detailed mechanisms are proposed for loss of H₂O and C₂H₄ from each ion and it is shown that these mechanisms are consistent with ²H and ¹³C labelling studies, the kinetic energy release associated with each decomposition channel, the relative competition between H₂O and C₂H₄ loss and energy measurements.     

Laser-induced chemical kinetics: Absolute rate constants for the reactions Ċ2F2 + Br2 → C2F5Br + Ḃr and n-Ċ3F7 + Br2 → n-C3F7Br + Ḃr

Absolute rate constants at room temperature for the metathesis reaction have been measured under VLPP conditions: k₁ = (2.0 ± 0.5) × 10⁸M^?1·s^?1, k₂ = (3.0 ± 0.7) × 10⁸M^?1·s^?1. The radicals were generated through collisionless infrared-multiphoton decomposition of the corresponding iodides by irradiation from a high-power CO₂-TEA laser. The reaction of ?₂F₅ and ?₃F₇ with \documentclass{article}\pagestyle{empty}\begin{document}$$\mathop {\rm N}\limits^{\rm .} {\rm O}_{\rm 2} $$\end{document} are briefly discussed in relation to the reaction of ?₃ with \documentclass{article}\pagestyle{empty}\begin{document}$$\mathop {\rm N}\limits^{\rm .} {\rm O}_{\rm 2} $$\end{document}, which had been measured previously.     

Quantum-Chemical Study of Anisole Molecule

The potential functions of internal rotation around the C -O bond in the C₆H₅OCH₃ molecule were obtained by HF/6-31G(d), MP2(f)/6-31G(d), and B3LYP/6-31(d) calculations. Hartree-Fock calculations reveal a fourfold barrier to internal rotation around the C -O bond. The MP2 and B3LYP calculations reveal a twofold barrier with a height of 7.78 and 10.70 kJ mol^{- 1}, respectively (corrected for the zero vibration energy). The molecular geometries, first Koopmans ionization potentials, and dipole moments are reported. Calculations for liquid anisole in the self-consistent reactive field (SCRF) continual model give the results that only slightly differ from the results obtained for the isolated molecule in a vacuum. Within the framework of the Natural Bond Orbitals formalism, the following parameters were determined: energy, degree of hybridization, and population of oxygen lone electron pairs and energy of their interaction with antibonding ^* orbitals of the aromatic ring.     

Zum Einfluß der Alkylsubstitution auf die Kupfer(II)-Extraktion mit 1-Alkyl-2(2-hydroxyphenyl)-Δ2-imidazolinen

The Influence of the Alkyl Substituents on Copper(II) Extraction by 1-Alkyl-2(2-hydroxyphenyl)-Δ²-imidazolines In acid solution (pH ≤ 4) 1-alkyl-2(2-hydroxyphenyl)-Δ²-imidazolines (RLH) form cations RLH₂⁺ and copper(II) chelates of the type Cu(RNNO)₂. Therefore in the course of the copper(II) extraction the addition of two ligands RLH and the elimination of four protons are expected. For systems with BuLH as an extractant this prediction is confirmed by slope-analysis (lg D_Cu vs. lg c_o,BuLH and lg D_Cu vs. pH). But in extraction systems of OcLH and DodLH, depending on the concentration of RLH, the slope of lg D_Cu vs. lg c_o,RLH is not higher than 1 or even 0. The reason is that the copper(II) extraction is preceded by the formation of the complexes \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm Cu}\left[{\left({{\rm R}\mathop {\rm N}\limits^ \oplus {\rm HNOH}} \right){\rm X}^ \ominus } \right]^{2 \oplus } $\end{document} ( III ) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm Cu}\left[{\left({{\rm R}\mathop {\rm N}\limits^ \oplus {\rm HNOH}} \right){\rm X}^ \ominus } \right]_2 ^{2 \oplus } $\end{document} ( IV ) in the aqueous phase. Among other reasons the concentration of III and IV depends on the tendency of RLH₂^⊕ to form ion pairs \documentclass{article}\pagestyle{empty}\begin{document}$ \left({{\rm R}\mathop {\rm N}\limits^ \oplus {\rm HNOH}} \right){\rm X}^ \ominus $\end{document} ( I ). This tendency increases with the length of the alkyl chains and for the anions in the order SO₄^2? ≤ NO₃^? ≤ ClO₄^?. Such quantities of III and IV which are essential for the course of the extraction are formed only with the extractants OcLH and DodLH, but not with BuLH. In general a variation of peripheric alkyl chains in metal extractants changes only the distribution coefficients of the corresponding metal chelates. But in the series BuLH, OcLH, DodLH both the distribution coefficients and the extraction process as a whole are changed. Some influence of the partial deprotonation of III and IV on the extraction curves is observed.     

Zum Einfluß der Zusammensetzung gemischter Lösungsmittel auf die Stabilitäts- und Bildungskonstanten von Kupfer(II)- und Nickel(II)-Komplexen substituierter 1,2-Dioxime

Influence of the Composition of Mixed Solvents on the Stability and Formation Constants of Copper (II) and Nickel(II) Complexes of Substituted 1,2-Dioximes The stability constants ^cK₁, ^cK₂, and _cβ₂ of the complexes which are formed in the systems M²⁺/DH₂, M²⁺/Ac? DH₂, and M²⁺/Et, Me\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm N}\limits^ \oplus $\end{document}? DH₂ (M²⁺ ? Cu²⁺, Ni²⁺; DH₂, Ac? DH₂, Et₂Me\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm N}\limits^ \oplus $\end{document}? DH₂ = 1,2-dioximes) are determined in water and in water-dioxane mixtures (25, 50 and 75 per cent). Because of the stabilisation of the l,2-complexes by intramolecular hydrogen bonds ^cK₂, is always higher than ^cK₁. On account of the decrease of the dielectricity constant the constants ^cK₁, ^cK₂, and ^cβ₂, rise with increasing contents of dioxane in the mixtures. The influence of the dielectricity constant may be eliminated by considering the formation constants ^cK_1(B), ^cK_2(B), and ^cβ_2(B). The individual formation constants ^cK_1(B) of the 1,l-complexes investigated are independent of the composition of the solvent, but among the overall formation constants ^cβ_2(B) this comes true only for the complexes Ni(Ac? DH)₂, Ni(Et₂Me\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm N}\limits^ \oplus $\end{document}? DH)₂, and Cu(Et₂Me\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm N}\limits^ \oplus $\end{document}? DH)₂. With Cu(DH₂) and Cu(Ac? DH)₂ a linear relation between log ^cβ_2(B) and the molar fraction of water is stated. This effect is attributed to a specific solvatation of the chelates Cu(DH)₂ and Cu(Ac? DH)₂ by water.     

Removal of Nitrogen and Organic Matter in a Radial-Flow Aerobic-Anoxic Immobilized Biomass Reactor Used in the Posttreatment of Anaerobically Treated Effluent

This work reports on the removal of organic matter and nitrogen in a radial-flow aerobic-anoxic immobilized biomass (RAIB) reactor fed with domestic sewage pretreated in a horizontal-flow anaerobic immobilized biomass (HAIB) reactor. Polyurethane foam was used as support material for biomass attachment in both reactors. In batch experiments, a first-order kinetic model with residual concentration represented the organic matter removal rate, whereas nitrogen conversion followed a pseudo-first-order reaction in series model, with kinetic constants k ₁ (ammonium to nitrite) and k ₂ (nitrite to nitrate) of 0.25 and 6.62 h⁻¹, respectively. The RAIB reactor was operated in continuous-flow mode and changes in the airflow rate and hydraulic retention time were found to interfere in the apparent kinetic constants to the nitritation (k ₁) and nitratation (k ₂). Nitrification and denitrification were achieved in the partially aerated RAIB reactor operating with hydraulic retention times of 3.3 h and 2.7 h in the aerobic and anoxic zones, respectively. Ethanol was added in the anoxic zone of the reactor to promote denitrification. The effluent flow of the RAIB reactor presented a COD of 52 mg l⁻¹, and concentrations of 2 mg , 1.24 mg and 3.46 mg .     

Kinetic studies on pH controlled partial dechelation of the trans-imidazole-[Cr(His)2]+ cation

Partial dechelation of one tridentate N,N??,O-histidine in trans-imidazole-[Cr(His)₂]⁺ (where N and N?? are amine and imidazole nitrogen atoms, respectively, and O is carboxylate oxygen) has been studied. The aquation process is both acid and base catalyzed and the product with didentate His is converted back into the substrate at pH 4?C7. Kinetics of the chelate ring opening were studied spectrophotometrically within the 0.01?C1.0?M HClO₄ and 0.1?C1.0?M NaOH ranges under first-order conditions. The following dependences of k _obs on [H⁺] and [OH^?] were determined: $$ \left( {k_{\text{obs}} } \right)_{\text{H}} = a + b\left[ {{\text{H}}^{ + } } \right] + c/\left[ {{\text{H}}^{ + } } \right] $$ $$ \left( {k_{\text{obs}} } \right)_{\text{OH}} = a^{\prime } + b^{\prime } \left[ {{\text{OH}}^{ - } } \right]. $$ Mechanisms of the chelate ring opening in acidic and alkaline media are proposed, and activation parameters for the process in acidic solution have been determined. Additionally, kinetic studies were performed on the second dechelation stage in acidic media, which is ca. 15 times slower than the first one.     

Zum Einfluß der Alkylkette auf Protolyse,Komplexbildung und Extraktionseigenschaften N-substituierter 2-(o-Hydroxyphenyl)-Δ2-imidazoline

Influence of the Alkyl Chain on Protolysis, Complex Formation, and Extraction Properties of N-Substituted 2-(Δ²-Imidazolin-2-yl)-phenols N-substituted 2-(Δ²-imidazolin-2-yl)-phenols RNNOH may be used as extractants of copper(II) from acidic solutions. In an aqueous phase they are existent as betains \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R}\mathop {\rm N}\limits^ \oplus {\rm HNO}^ \ominus $\end{document} ( IIa ). Solvents with lower dielectricity constants (dioxane-water-mixtures) favour the neutral acid RNNOH ( IIb ) a tautomer of IIa . The protonation of IIa or IIb proceeds in a weakly acidic solution. Therefore, at 3 ≤ pH ≤ 4 which is favourable for copper(II) extraction, the extractants exist as the cations [RNHNOH]⁺. The octyl compound OcNNOH from such a solution is extracted by chloroform, less effective by toluene, as an ion pair \documentclass{article}\pagestyle{empty}\begin{document}$ [{\rm Oc}\mathop {\rm N}\limits^ \oplus {\rm HNOH]X} $\end{document}. The distribution coefficient increases in the order HSO₄^? < NO₃^? < ClO₄^? which is well-known for quaternary ammonium salts. The affinity of the ion pairs, which are derived from the butyl compound BuNNOH, to organic solvents is very weak independently of the anion. For solubility reasons a study of the formation of the trans-planar copper(II) chelates Cu(RNNO)₂ is possible only in dioxane-water mixtures. Because of lg K₁ ≥ lg k₂ + 2 the stability regions of Cu(RNNO)⁺ and CU(RNNO)₂ are clearly separated. The distribution coefficients of Cu(RNNO)₂ increase with the length of R exceeding that of the free ligand by one power of ten and more.     

Dynamics of ternary complex formation in the reaction of diaquoanthranilato-N,N-diacetatonickelate(II) with 2,2′-bipyridine and 1,10-phenanthroline

Dynamics of ternary complex formation in the reaction of diaquoanthranilato-N, N-diacetatonickelate(II) with 2,2′-bipyridine and 1,10-phenanthroline. $\rm Ni(ada)(H_2O)_2^{-}$ $+$ $L\rightleftharpoons Ni(ada)(L)^{-}$ $+$ $2 H_20;$ $- {{d[Ni(ada)^{-}]}\over{dt}}$ $=$ $k_f[Ni(ada)^{-}][L]+k_d\ [Ni(ada)(L)];$ $\ ada^{3-}=$anthranilate-N, N-diacetate; and L=bipy or phen. The kinetics of formation of ternary complexes by diaquoanthranilato-N, N-diacetatonickelate(II). [Ni(ada)(H₂O)]⁻ with 2,2′-bipyridine (bipy) and 1,10-phenanthroline (phen) have been studied under pseudo-first-order conditions containing excess bipy or phen by stopped-flow spectrophotometry in the pH range 7.1–7.8 at 25°C and λ = 0.1 mol dm⁻³. In each case, the reaction is first-order with respect to both Ni(ada)⁻ and the entering ligand (ie., bipy, phen). The reactions are reversible. The forward rate constants are: $k^{\rm Ni(ada)}_{\rm Ni(ada)(bipy)}=0.87\times10^3{\rm dm}^3 {\rm mol}^{-1}{\rm s}^{-1}$, . $k^{\rm Ni(ada)}_{\rm Ni(ada)(phen)}=1.87\times10^3{\rm dm}^3 {\rm mol}^{-1}{\rm s}^{-1}$; and the reverse rate constants are: $k^{\rm Ni(ada)(bipy)}_{\rm Ni(ada)}=1.0{\rm s}^{-1}$ and $k^{\rm Ni(ada)(phen)}_{\rm Ni(ada)}=2.0{\rm s}^{-1}$. The corresponding stability constants of ternary complex formation are: and , . The observed rate constants and huge drops in stability constants in ternary complex formation agree well with the mechanism in which dissociation of an acetate arm of the coordinated ada³⁻ prior to chelation by the aromatic ligand occurs. The observations have been compared with the kinetics of ternary complex formation in the reaction Ni(ada)⁻ - glycine in which the kinetics involves a singly bonded intermediate, N(ada)((SINGLE BOND)O(SINGLE BOND)N)²⁻ in rapid equilibrium with the reactants followed by a sluggish ring closure step. The reaction with the aromatic ligands conforms to a steady-state mechanism, while for glycine it gets shifted to an equilibrium mechanism. The cause of this difference in mechanistic pathways has been explained. © 1996 John Wiley & Sons, Inc.     

Zur Kenntnis der Organophosphorverbindungen. XV. Darstellung und Reaktionen von Trimethylsilylestern der Phosphinsäuren

On Organophosphorus Compounds. XV. Preparation and Reactions of Trimethylsilyl Esters of Phosphinic Acids Trimethylsilylesters of Phosphinic acids R₂P(X)YSi(CH₃)₃ (R ? CH₃, C₂H₅, C₃H₇, t?C₄H₉, C₆H₅; X, Y ? O, S) were prepared by 7 different methods as in some cases easily hydrolysable but thermally remarkably stable compounds. The properties and some reactions of these substances are reported, their structures confirmed by IR? as well as ¹H- and ³¹P-NMR-spectroscopy. Dimethylsilylen-bis(phosphinic acid esters) were obtained according to \documentclass{article}\pagestyle{empty}\begin{document}$ 2{\rm R}_{2} {\rm P(\rm X)\rm ONH}_{4} + {\rm R}_{\rm 2} {\rm SiCl}_{2} \to 2{\rm E NH}_{4} {\rm Cl + R}_{2} {\rm P(X) - O - SiR}_{2} - {\rm O - P(X)R}_{2} ({\rm R = CH}_{3};{\rm X = O,S}) $\end{document}.     

Exact transient solutions of kinetics of first‐order reactions with end effects

The finite set of rate equations C _m,n ^' =α _n,n-1 C _m,n-1 (t)+α _n,n C _m,n (t)+α _n,n+1 C _m,n+1 (t), $$0 \leqslant m \leqslant N,0 \leqslant n \leqslant N,$$ where $$\alpha _{i,j}$$ are $\alpha _{j,j - 1} = A,\alpha _{j,j} = - \left( {A + B} \right),\alpha _{j,j + 1} = B$ , with $\alpha _{0,0} = - \alpha _{1,0} = - \alpha$ and $\alpha _{N,N} = - \alpha _{N - 1,N} = - b,\alpha _{0, - 1} = \alpha _{N,N + 1} = 0$ , subject to the initial condition $C_{m,n} \left( 0 \right) = \delta _{n,m}$ (Kronecker delta) for some $m$ , arises in a number of applications of mathematics and mathematical physics. We show that there are five sets of values of $a$ and $b$ for which the above system admits exact transient solutions.     

Kinetics and mechanism of oxidation of cis-diaquabis(glycinato)chromium(III) by periodate ion in aqueous solutions

The kinetics of oxidation of cis-[Cr^III(gly)₂(H₂O)₂]⁺ (gly = glycinate) by $ {\text{IO}}_{ 4}^{ - } $ has been studied in aqueous solutions. The reaction is first order in the chromium(III) complex concentration. The pseudo-first-order rate constant, k _obs, showed a small change with increasing $ \left[ {{\text{IO}}_{ 4}^{ - } } \right] $ . The pseudo-first-order rate constant, k _obs, increased with increasing pH, indicating that the hydroxo form of the chromium(III) complex is the reactive species. The reaction has been found to obey the following rate law: $ {\text{Rate}} = 2k^{\text{et}} K_{ 3} K_{ 4} \left[ {{\text{Cr}}\left( {\text{III}} \right)} \right]_{t} \left[ {{\text{IO}}_{ 4}^{ - } } \right]/\left\{ {\left[ {{\text{H}}^{ + } } \right] + K_{ 3} + K_{ 3} K_{ 4} \left[ {{\text{IO}}_{ 4}^{ - } } \right]} \right\} $ . Values of the intramolecular electron transfer constant, k ^et, the first deprotonation constant of cis-[Cr^III(gly)₂(H₂O)₂]⁺, K ₃ and the equilibrium formation constant between cis-[Cr^III(gly)₂(H₂O)(OH)] and $ {\text{IO}}_{ 4}^{ - } $ , K ₄, have been determined. An inner-sphere mechanism has been proposed for the oxidation process. The thermodynamic activation parameters of the processes involved are reported.     

Preparation and electrochemical properties of {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} cathode materials for intermediate-temperature solid oxide fuel cells

Cathodic materials $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ (x?=?0.5, 0.6, 0.8, 1.0) with K₂NiF₄-type structure, for use in intermediate-temperature solid oxide fuel cells (IT-SOFCs), have been prepared by the glycine?Cnitrate process and characterized by XRD, SEM, AC impedance spectroscopy, and DC polarization measurements. The results have shown that no reaction occurs between an $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ electrode and an Sm_0.2Gd_0.8O_1.9 electrolyte at 1,200?°C, and that the electrode forms a good contact with the electrolyte after sintering at 1,000?°C for 2?h. In the series $ {\hbox{N}}{{\hbox{d}}_{{{2} - x}}}{\hbox{S}}{{\hbox{r}}_x}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ (x?=?0.5, 0.6, 0.8, 1.0), the composition $ {\hbox{N}}{{\hbox{d}}_{{{1}.0}}}{\hbox{S}}{{\hbox{r}}_{{{1}.0}}}{\hbox{Fe}}{{\hbox{O}}_{{{4} + \delta }}} $ shows the lowest polarization resistance and cathodic overpotential, 2.75????cm² at 700?°C and 68?mV at a current density of 24.3?mA?cm^?2 at 700?°C, respectively. It has also been found that the electrochemical properties are remarkably improved the increasing Sr content in the experimental range.