Thermal decomposition kinetics. Part XI. Mechanism of thermal decomposition of calcium oxalate monohydrate from a thermogravimetric study — the effects of heating rate and sample mass on kinetic parameters from mechanistic equations

The mechanisms of the first two stages of the thermal decomposition of calcium oxalate monohydrate

have been established from non-isothermal thermogravimetric studies. For both stages, the rate-controlling processes are phase boundary reactions; the dehydration step assumes spherical symmetry whereas the decomposition step follows cylindrical symmetry. The kinetic parameters calculated from mechanistic equations show the same trend as those from mechanism-non-invoking equations. Thus, for the decomposition of CaC₂O₄ the kinetic parameters are not appreciably affected by heating rate or sample mass. For the dehydration step they show a systematic decrease with increase in either heating rate or sample mass. The best fit correlations can be expressed as follows E(or, log A) = (Constant/Heating rate) + Constant, (at fixed sample mass) E(or, log A) = (Constant) × (Mass)² ? (Constant) × (Mass) + Constant, (at fixed heating rate)     

Empirical equations for the bond energies and vibrational frequencies at chemisorptive bonds on surfaces

Empirical equations derived for bond energies and force constants of gaseous molecules are applied to chemisorptive bonds on surfaces. For two adsorbed atoms from the same family of the periodic table, A and B, the chemisorptive bond energies, E, to the same metal, M, can be approximated by E_A–M/E_B-M ≈ (E_A2/E_B2)^{$\text{1}\text{2}$}, where E_A2 and E_B2 are the bonds energies of diatomic molecules A₂ and B₂, respectively The corresponding vibrational frequencies, ν, can be approximated by ν²_A–M/ν²_B-M ≈ (m_B/m_A)(F_A2/F_B2)^{$\text{1}\text{2}$} · m_A and m_B are the masses of atoms A and B, respectively;F_A2 and F_B2 are the force constants of molecules A₂ and B₂, respectively. These relations are applied to the chemisorption of halogens on metals and showed good agreement with experiment.     

The influence of molecular weight on the degradation of poly(N-vinylcarbazole)

The methods of isothermal and dynamic thermogravimetry have been used to study the degradation of poly(_{N-vinylcarbazole}) (PNVC). The multiple heating rate method has been used, as a dynamic method, to obtain kinetic parameters. A linear relationship between the activation energy. E, and $\text{M}{}_{\mathrm{w}}{}^{\mathrm{?1}}$ ($\text{M}{}_{\mathrm{w}}$ being weight average molecular weight) was found. From isothermal experiments, a temperature was found for which E was independent of molecular weight. We could then refer to a degradation characteristic- temperature of the polymer. On the other hand, altering the heating rate leads to changes in the values of E for each molecular weight indicating two kinds of scission: one occurs in the backbone, producing mainly monomer; in the other, both side-group and backbone scissions occur producing different products.     

Study of copper-chromium oxide catalyst: I. Thermal decomposition of copper(III) chromate,CuCrO4

The kinetics, mechanism, and activation energy of the isothermal decomposition of CuCrO₄ was studied using an isothermal TG method and an X-ray high-temperature diffraction technique in either air or a flowing atmosphere of N₂. The enthalpy change ΔH of the decomposition reaction

$\text{2}\text{CuCrO}{}_4\text{→}\text{CuO}\text{+}\text{CuO}\text{+}\text{CuCr}{}_2\text{O}{}_4\text{+}\text{3}\text{2}\text{O}{}_2$

was determined by DSC analysis. The mechanism of the thermal decomposition of CuCrO₄ is well represented by the standard Avrami-Erofeev kinetic equation $\text{[?}\text{ln}\text{(1 ? α)]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= kt}$. According to this mechanism, the reaction rate is controlled by the formation and growth of nuclei on the surface of the reactant. The activation energy E_A of the process in air is E_A = (248 ± 8) kJ mole^?1, in flowing atmosphere of nitrogen E_A = (229 ± 8) kJ mole^?1. ΔH in air is 110 kJ mole^?1, in flowing nitrogen 67 kJ mole^?1. The lower values of ΔH and E_A in the flowing atmosphere of nitrogen are due to the fast elimination of O₂ from the reaction interface. However, the decay of the crystalline portion of CuCrO₄ during its thermal decomposition, studied by the X-ray diffraction, is controlled by a different reaction mechanism (first-order kinetics). The reaction mechanism is discussed in the relation to the crystal structure of the reactants.     

Theoretical considerations on the temperature and pressure dependence of the kinetics of reversible thermal decomposition processes of solids

Whereas the temperature dependence of reaction rates of reversible solid-state decomposition processes of the type A_solid ? B_solid + C_gaseous has been outlined in numerous theoretical as well as in experimental studies, its simultaneous dependence on the actual pressure of the gaseous product has not been taken into account sufficiently. Theoretical considerations elucidate, however, that specific and reproducible kinetic data, in particular umambiguous values for activation energies, can only be determined under vacuum conditions or in some cases by fulfilling the following precondition: $\text{p}{}_{\mathrm{<mtext>exp</mtext>}}\text{p}{}_{\mathrm{<mtext>equ</mtext>}}\text{= f(T) =}\text{constant}$, where p_exp is the actual pressure and p_equ the equilibrium pressure of the gaseous product.     

Influence of heating rate on kinetic quantities of solid phase thermal decomposition

Thermogravimetric analyses of thermal decomposition (pyrolysis, thermal dissociation and combustion) of 9 different samples were carried out in dynamic conditions at different heating rates. The kinetic parameters (E, A and k_m) of thermal decomposition were determined and interrelations between the parameters and heating rate q were analyzed. There were also relations between Arrhenius and Eyring equations analyzed for thermal decomposition of solid phase. It was concluded that Eyring theory is an element, which interconnects used thermokinetic equations containing Arrhenius law and suggests considering kinetic quantities in way relative to 3 kinetic constants (E, A and k_m). Analysis of quantities other than km (i.e. E, A, Δ⁺H, Δ⁺S) in relation to heating rate is an incomplete method and does not lead to unambiguous conclusions. It was ascertained that in ideal case, assuming constant values of kinetic parameters (E and A) towards heating rate and satisfying both Kissinger equations, reaction rate constant k_m should take on values intermediate between constants (k_m)₁ and (k_m)₂ determined from these equations. Whereas behavior of parameters E and A towards q were not subjected to any rule, then plotting relation k_m vs. q in the background of (k_m)₁ and (k_m)₂ made possible classification of differences between thermal decomposition processes taking place in oxidizing and oxygen-free atmosphere.     

X-ray study of Hg2Cl2Br2 and HgCl2HgBr2 reactions in solid state

The reactions (I) Hg₂Cl₂(s) + Br₂(g) and (II) HgCl₂(s) + HgBr₂(s) have been investigated by an X-ray method. Both the reactions yield two forms of the mixed halide HgClBr, designated as α-HgClBr and β-HgClBr. The cell parameters of the two are as follows:α-HgClBr: $\text{a = 6.196}\text{A}\text{?}$, $\text{b = 13.12}\text{A}\text{?}$, $\text{c = 4.37}\text{A}\text{?}$, z = 4, ? = 5.91 g/cm³. The powder pattern and cell parameters are similar to that of HgCl₂. Therefore it is probable that the chlorine atoms, in the linear halogenHghalogen molecules of HgCl₂ structure have been replaced by bromines, and since the radius of the bromine atom is larger than that of chlorine, the lattice is larger in this case.β-HgClBr: $\text{a = 6.78}\text{A}\text{?}$, $\text{b = 13.175}\text{A}\text{?}$, $\text{c = 4.17}\text{A}\text{?}$, z = 4, ? = 5.40. These parameters are the same as those reported in the literature for β-Hg(ClBr)₂, and its X-ray powder pattern is similar to HgCl₂. Therefore this phase also has linear halogenHghalogen molecules but the distribution of Cl and Br atoms is perhaps random.Heating the products (I) and (II) up to the melting point increases the amount of α phase and decreases the β phase, whereas crystallization increases the β phase. DTA study has supported the X-ray findings.     

Cross-conjugated biradicals: Kinetics and kinetic isotope effects in the thermal isomerizations of cis- and trans-2,3-dimethylemethylnecyclopropane,cis- and trans-3,4-dimethyl-1,2-dimethylenecyclobutane,and of 1,2,8,9-decatetraene

cis- and trans - 2,3 - Dimethylenemethylenecyclopropane ($\text{C}$ and $\text{T}$) interconvert at 160.0° with a small normal kinetic isotope effect (KIE) when the exo-methylene is deuterated, but the 1,3-shift products, 2-methylethylidenecyclopropane, show a large normal KIE, 1.35 and 1.31, when formed from $\text{C}$ and $\text{T}$, respectively. This data can be interpreted in terms of either parallel reactions or a common trimethylenemethane diradical intermediate formed with a normal KIE of 1.11 and closing to 1,3-shift product with a normal KIE of 1.29 due to the effect of deuterium in the required 90° rotation of the exo-methylene carbon.The kinetics of the thermal 1,3- and 3,3-shifts of cis- and rans-3,4-dimethyl-1,2-dimethylenecyclobutane ($\text{CB}$ and $\text{TB}$) were determined in a flow reactor. The first order rate constants are log k_CB (sec^?1) = 13.7 ? 42,200/2.3 RT and log k_TB (sec^?1) = 13.6 ? 41,900/2.3 RT (E_a in kcal/m) which compare favorably to that from the parent hydrocarbon. 1,2-dimethylenecyclobutane, after reasonable correction for dimethyl substitution.Rearrangement of $\text{TB}$ and its bis(dideuteriomethylene) derivative at 230.0° revealed a normal KIE of 1.08. This KIE could be interpreted in terms of either a methylene rotational isotope effect in a concerted reaction or formation of a bisallyl diradical with the expected normal rotational IE on closure to the 1,3-shift product of 1.12 with no IE in the ring opening when the result is corrected for return of the biradical to starting material.The kinetics of intramolecular 2 + 2 cycloaddition of 1,2,8,9-decatetraene were determined in a flow reactor. The first order rate constant is log k(sec^?1) = 9.4 ? 30,800/2.3 RT (E_a in kcal/m). These energetics are compared with those of other 2 + 2 cycloadditions. The major product is 3,4-dimethylenecyclooctene ($\text{DC}$) which is also found from the minor product, cis-7,8-dimethylenebicvyclo[4.2.0]octane ($\text{CO}$), at higher temperatures. The trans isomer, $\text{TO}$, also gives $\text{DC}$ at about the same rate as $\text{CO}$.     

Effects of the working conditions on the values of the kinetic parameters of the thermal decompositions of some complexes

The kinetic parametersn, A andE (the order of the decomposition reaction, the pre-exponential factor and the activation energy of the thermal decompositions) of some complexes of general formula [MCl₂(GTD)₂]Cl, where GTD=Girard T-diacetylmonoxime cation andM=central metal ion=Mn(II), Fe(III) and Co(II), were calculated through their TG curves. The effects of working conditions such as the sample weight and the rate of heating on the evaluated kinetic parameters are discussed.     

Etude comparative des structures type K4NiF4 et pérovskite par la méthode des invariants

The study of K₂NiF₄ and perovskite structure type by the “method of invariants” leads to the relationship: $\text{(A-X)}{}_9\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? (A-X)}{}_{12}\text{=}\text{constant}$, where (A-X)₉ and (A-X)₁₂ are the invariant values associated with cation A in coordination number 9 and 12. In the case where A = K⁺ and X = F^?, we propose the relationship:

$\text{(K}{}^{\mathrm{+}}\text{?F)}{}_{\mathrm{R}}\text{= 2.832 R}{}^{\mathrm{<mtext>1</mtext><mtext>11.4</mtext>}}$

where R is the coordination number.     

Nonstoichiometry and electronic defects in yttrium iron garnet

Results are presented of a thermogravimetrical analysis of yttrium iron garnet, Y₃Fe₅O_12?δ, in the temperature range 950–1270°C. From these measurements the oxygen vacancy concentration δ is obtained for partial oxygen pressures between 1 and 10^?5 atm. The data can be fitted with a relation $\text{δ = A}\text{exp}\text{(}\text{?E}\text{kT}\text{)}$. Values of A and E are given for different values of P_O2. The combined data from electrical conductivity measurements, measurements of Seebeck coefficients, and thermogravimetric analysis, are used to calculate the concentrations of point defects in the garnet lattice. The results are expressed in terms of equilibrium reaction constants. The model is also used to analyze diffusivity data.     

The study of redox reactions of bisarenechromium complexes by the rotating disk and the rotating ring disk electrode techniques: III. Cathodic reduction of chromium(0) π-complexes and the corresponding arenes in dimethyl sulfoxide solutions

The rotating disk (RDE) and the rotating ring-disk (RRDE) electrode techniques have been employed to study the cathodic behavior of eight bisarenechromium complexes and seven corresponding arenes in DMSO solutions. In the first electrochemical step of the process reversible addition of one electron results in anion-radicals, whose formation has been demonstrated for certain arenes and chromium π-complexes by oxidation of these particles on the ring electrode.Substituents on different ligands of bisarenechromium complexes were found to exert pronounced mutual influences. The role of the chromium atom in transfer of electronic effects from one ligand to another is discussed.It was found that a linear correlation exists between the variations in the free energy of the equilibrium “initial compound

anion-radical” (due to coordination of free arene with chromium which is displayed as a shift of the cathodic process half-wave potential ΔE_{$\text{1}\text{2}$}^CL) and the half-wave potential of the oxidation of the corresponding Cr⁰ π-complex to a cation E_{$\text{1}\text{2}$}^X ΔE_{$\text{1}\text{2}$}^CL = a + αE_{$\text{1}\text{2}$}^X At E_{$\text{1}\text{2}$}^X < ?0.3 V, complex formation slows down the cathodic process and at E_{$\text{1}\text{2}$}^X > ?0.3 V the process is facilitated.     

Molecular beam chemiluminescence XI: kinetic and internal energy dependence of the NO + O3 → NO2*,→ NO23 reaction

Seeded supersonic NO beams were used to study the kinetic energy dependence of both the electronic (NO₂^*) and vibrational (NO₂³) chemiluminescence of the NO + O₃ reaction. In addition the electronic CL is found to be enhanced by raising the NO internal temperature. This is shown to be due to enhanced reactivity of the NO(²Π,_{$\text{3}\text{2}$}) fine structure component. By difference NO(²Π_{$\text{1}\text{2}$}) is concluded to yield predominantly groundstate NO₂³. The excitation function for NO₂^* formation from NO(²Π_{$\text{3}\text{2}$}) is of the form σ_{$\text{3}\text{2}$}(E) = C(E/E₀ - 1)ⁿ over the 3–6 kcal energy range where n = 2.4 ± 0.15, C = 0.163 Ų and E₀ = 3.2 ± 0.3 kcal/mole. Vibrational IR emission from NO₂³ has an energy dependence different from electronic NO₂^* emission, confirming that emitters are formed predominantly in distinct reaction channels rather than via a common precursor (either NO₂^* or NO₂³). The short wavelength cutoff of the CL spectra recorded at elevated collision energies E ? 15 kcal/mole corresponds to the total available energy. These and literature results are discussed in the light of general properties of the (generally unknown) ONO₃ potential energy surfaces. The formation of electronically excited NO₂^* rather than energetically preferred O₂ (¹ Δg) (Gauthier and Snelling) can be rationalized in terms of surface hopping near a known intersection of potential energy surfaces more easily than by vibronic interaction in the asymptotic NO₂ product.     

Unusual rearrangement of σ-vinylpalladium complexes into η2-olefin complexes. The structure of (η2-1-triphenylphosphonium-2-carbomethoxyethylene)(triphenylphosphine)iodopalladate

β-Substituted σ-vinylpalladium complexes [Pd(σ-CHCHCOOR)(PPh₃)₂(X)] (I) (X = Cl, I; R = Me, Et) have been obtained by interaction of the E- and Z-β-halogen acrylates with tetrakis(triphenylphosphine)palladium. On heating complexes I rearrange into isomeric η²-olefin-ylidepalladium complexes [$\text{P}$$\text{dCH(COOR)-C}$HPPh₃(PPh₃)(X)] (II). The structure of these com X-ray study of the compound with X = I, R = Me.     

Polyèdre de coordination de l'etain(II) dans SnC2O4: Relations structurales entre SnC2O4, Na2C2O4 et Na2Sn(C2O4)2

The crystal structure of SnC₂O₄ has been determined by X-ray single-crystal techniques and refined to R = 0,018 for 1139 reflections. The cell is monoclinic, space group $\text{C2}\text{c}$ with Z = 4 formula units, the parameters being a = 10,375(3)Å. b = 5,504(2)Å, c = 8,234(3)Å, β = 125,11(2)°. The oxalato groups, located on symmetry centers, are chelated to two Sn atoms through one oxygen on each carbon atom, giving rise to an infinite string (SnC₂O₄)_n. The Sn(II) atom is one-side bonded to four oxygen atoms with two SnO bonds of 2,232(2) Å and two of 2,393(2) Å. The tin atom is in a distorted trigonal bipyramid SnO₄E, the lone pair E occupying one of the apices of the equatorial trigonal base of the polyhedron. Crystal structure comparison with disodium bisoxalatostannate(II), Na₂Sn(C₂O₄)₂, permits one to deduce SnC₂O₄ by crystallographic shear operation $\text{1}\text{8}\text{[34}\text{2}\text{](001)}$ of $\text{c}\text{2}$ periodicity. Na₂Sn(C₂O₄)₂ can be described as an intergrowth of SnC₂O₄ and Na₂C₂O₄ structures and consldered as the first member of a new series Na₂Sn_1+n(C₂O₄)_2+n with n integer ? 0.     

Palladium-catalyzed asymmetric cyclization of methyl (E)-oxo-9-phenoxy-7-nonenoate and its analogs

Asymmetric cyclizations of methyl (E)-3-oxo-9-phenoxy-7-nonenoate ($\text{1}$) or methyl (E)-3-oxo-9-(methoxycarbonyl)oxy-7-nonenoate ($\text{4}$) without added base were carried out in the presence of a catalytic amount of palladium(II) acetate and chiral diphosphine as ligands. Allylic carbonate $\text{4}$ reacted by use of Pd(OAC)₂-(S)-(R)-BPPFA at room temperature to give (R)-3-vinylcyclohexanone ($\text{3}$), after decarboxylation, in up to 48% e. e.     

Thermal decomposition of aqueous manganese nitrate solutions and anhydrous manganese nitrate. Part 3. Isothermal kinetics

The kinetics of the thermal decomposition of aqueous manganese nitrate solutions and anhydrous manganese nitrate in air were established from isothermal experiments. By heating the solution, first most of the water evaporates to a composition of equimolar amounts of water and manganese nitrate; this concentrated solution then decomposes to γ-Mn(NO₂, NO₂ and water, usually in two steps. The first step can be described best by the model [?ln(1 ? α)]^{$\text{1}\text{2}$} = 8.9 × 10¹¹ exp(?121000/RT)t, whereas the second step is described equally well by several models. The kinetic parameters of these models are quite similar, the average activation energy being 141 kJ mole^?1.The decomposition of anhydrous Mn(NO₃)₂, which proceeds in a single step, can also be described with several similar models. In this case the average activation energy is about 92 kJ mole^?1.     

Über Ordnungs-Unordnungsphänomene bei Sauerstoff perowskiten vom Typ A2+3B2+M5+2O9

Perovskites of the type A²⁺₃B²⁺M⁵⁺₂O₉, where A²⁺ = Ba, Sr; B²⁺ = Mn, Co, Ni, Zn; M⁵⁺ = Nb, Ta, show order-disorder phenomena. At lower temperatures a thermodynamically unstable disordered cubic perovskite is formed ($\text{1}\text{3}$ formula unit—$\text{AB}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{M}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{O}{}_3$—in the cell), which transforms irreversibly into a 1: 2 ordered high-temperature form with 3L structure (sequence (c)₃). For A²⁺ = Ba this lattice is hexagonal (space group $\text{P}\text{3}\text{m1}$; one formula unit in the cell); with A²⁺ = Sr a triclinic distortion is observed. For Ba₃CoNb₂O₉ a second transformation into a cubic disordered perovskite takes place at 1500°C. This transition is reversible and of the order-disorder type. The vibrational and diffuse reflectance spectra are discussed.