The mechanism of thermal decomposition of ionic oxalates

A mechanism for the thermal decomposition of ionic oxalates has been proposed on the basis of three quantitative relationships linking the quantitiesr _c/r _i (the ratio of the Pauling covalent radius and the cation radius of the metal atom in hexacoordination) andΣI _i (the sum of the ionization potentials of the metal atom in kJ mol^?1) with the onset oxalate decomposition temperature (T _d) (Eq. 1) the average C-C bond distance (¯d) (Eq. 2), and the activation energy of oxalate decomposition (E _a) (Eq. 3): (1) $$T_d = 516 - 1.4006\frac{{r_c }}{{r_i }}(\sum I_i )^{\frac{1}{2}}$$ (2) $$\bar d = 1.527 + 5.553 \times 10^{ - 6} \left( {122 - \frac{{r_c }}{{r_i }}(\sum I_i )^{\frac{1}{2}} } \right)^2$$ (3) $$E_a = 127 + 1.4853 \times 10^{ - 6} \left( {\left( {\frac{{r_c }}{{r_i }}} \right)^2 \sum I_i - 9800} \right)^2$$ On the basis of these results it is proposed that the thermal decomposition of ionic oxalates follows a mechanism in which the C-O bond ruptures first. From Eq. 3 it is further proposed that strong mutual electronic interactions between the oxalate and the cations restrict the essential electronic reorganization leading to the products, thereby increasingE _a.     

Kinetic study of the thermal dehydration of syngenite K2Ca(SO4)2·H2O under isothermal conditions

A study of the kinetics of the thermal dehydration of syngenite was carried out using the isothermal gravimetric method. Weight changes of the samples were followed by means of a Mettler Thermoanalyzer. The applicability of nine equations commonly used to describe the thermal decomposition of solids was investigated. The experimental results can be best represented, over the whole temperature range of the change, by the Avrami equation I $$[ - \ln (1 - \alpha )]^{1/2} = Kt$$ whereα=degree of decomposition,t=time, andK=rate constant. The activation energy deduced for the process is 51.8±3.7 kcal·mole^?1 and the log of the preexponential factor is 20.5±0.1.     

Thermal studies on anisaldehyde carbohydrazone methyl trimethylammonium chloride complexes of zinc,cadmium and mercury

The kinetic parameters of the thermal decomposition of Zn, Cd and Hg(II) hydrazone complexes of the general formula [MCl₂(AGT)₂]Cl₂, where AGT=anisaldehyde carbohydrazone methyl trimethylammonium cation, $$CH_3 O - C_6 H_4 - CH = N - NH - CO - CH_2 - \mathop N\limits^ + (CH_3 )_3 ,$$ and M=Zn, Cd and Hg(II), have been determined from the corresponding thermal curves. The order of the reaction (n) and the activation energy (E _a) have been derived. The kinetic data are discussed in terms of the effect of the metal ion on the activation energy. A thermal decomposition mechanism is suggested.     

Determination of the kinetic constants of endothermic decompositions of the type Asol f Bsol + Cgas

The present work describes the endothermic decompositions of calcium carbonate and nickel carbonate, recorded on a MOM derivatograph in the non-isothermal mode at different heating rates. The possibility and advantages of determining the kinetic parametersE, Z, andn for reactions proceeding in one step, as well as the detection of simultaneous (parallel or concurrent) reactions in the decomposition process, are discussed. The results obtained permit the conclusion that the thermal decomposition of calcite occurs in one step. In this case, the kinetic equation has the following form: $$\lg \left[ {\frac{{d\alpha }}{{(1 - \alpha )^n }}} \right] = \lg \frac{Z}{q} - \frac{E}{{2.3R}} \cdot \frac{1}{T}$$ where f(α)=(1?α)ⁿ,n=0.3, andE=176.8 kJ/mol. In the case of nickel carbonate the results of treating the experimental data have been obtained only in the graphical form. From the shape of the curves obtained, it is clearly seen that the decomposition of nickel carbonate in open air proceeds in several steps (i.e. several simultaneous reactions take place), which cannot be described by the equations for a one-step reaction.     

Komplexe zwischen Eisen(II)- und Tartrat-Ion

The formation of complexes between iron(II) and tartrate ion (L) has been studied at 25° C in 1m-NaClO₄, by using a glass electrode. The e.m.f. data are explained with the following equilibria: $$\begin{gathered} Fe^{2 + } + L \rightleftarrows FeL log \beta _1 = 1,43 \pm 0,05 \hfill \\ Fe^{2 + } + 2L \rightleftarrows FeL_2 log \beta _2 = 2,50 \pm 0,05 \hfill \\\end{gathered} $$ The protonation constants of the tartaric acid have been determinated: $$\begin{gathered} H^ + + L \rightleftarrows HL logk_1 = 3,84 \pm 0,03 \hfill \\ 2H^ + + L \rightleftarrows H_2 L logk_2 = 6,43 \pm 0,02 \hfill \\\end{gathered}$$ .     

Effects of washing conditions on the thermal decomposition behaviour of gelled UO3 microspheres

DTA, TG and DTG curves obtained in various atmospheres using different heating rates were used together with X-ray examinations to study the thermal decomposition mechanisms of two types of gelled UO₃ microspheres: ammonia-washed (UN) and hot water-washed (UH) microspheres. The kinetics of the thermal decompositions were studied. The specific reaction rate constantk _r for the decomposition of UO₃ to U₃O₈ could be expressed in terms of the activation energy and the pre-exponential factor by the expressions: $$\begin{gathered} K_r (s^{ - 1} ) = 1.277 \times 10^{18} \exp \frac{{ - 295.4}}{{RT}}for the UN spheres, \hfill \\ K_r (s^{ - 1} ) = 8.406 \times 10^{19} \exp \frac{{ - 263.2}}{{RT}}for the UH spheres. \hfill \\ \end{gathered} $$      

Thermochemische und kinetische Untersuchungen der endothermen Umbildungsreaktionen des Epsomits (MgSO4 · 7H2O)

Heterogeneous decompositions of MgSO₄ · 7H₂O (Epsomite) monocrystals were studied with thermal (DTA, DSC, TG) and thermo-optical methods. The polythermal reaction is controlled by nucleation of the reactant. This process has been considered by the Avrami-Erofe'ev equation: $$kt = [ - \ln (1 - \alpha )]^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$3$}}} $$ The plots and the slope which give the activation energyE+=23.5 kcal/mole (760 Torr N₂, 50–100°), are obtained from the Freeman-Carroll equation. The DSC technique was used to determine the heat of decomposition (ΔH=42.3 kcal/mole, 760 Torr N₂, 50–100°). The heat of transformation for the reaction 39–47° $$MgSO_4 \cdot 7H_2 O\xrightarrow{{39 - 47^ \circ }}MgSO_4 \cdot 6H_2 O + H_2 O$$ wasΔH=2.8 kcal/mole. The isothermal reaction (20°, 10^?6 Torr) is controlled by first-order kinetic.     

Beziehungen zwischen Bindungslängen und Bindungsstärken in Oxidstrukturen

The vond valencev, which is a measure for bond strengths, was estimated byPauling, 1929¹, as the ratio of charge to coordination number of the cation. For non-regular coordination polyhedra, the bond valence depends strongly on the bond lengthL. Good results are obtained for the following relations ofv vs.L: $$\upsilon = \left( {\frac{{L(1)}}{L}} \right)^N $$ with exponentsN between 4.0 and 6.0 or $$L(\upsilon ) = L(1) - 2k log \upsilon $$ with most 2k-values between 0.75 and 1.1 Å. The bond valence sums are not very sensitive to the values ofN or 2k, resp., but very much to theL (1)-values (length for unit bond valence). Therefore theL (1)-values should be adapted to each structure. Some values ofL (1),N, 2k andL _max are listed. The increase of mean bond lengths with increasing distortion of a coordination polyhedron can be estimated by $$\bar L = L(\bar \upsilon ) + 2k \log \upsilon /{}^n\sqrt {\upsilon _1 \cdot \upsilon _2 \cdots \upsilon _n \cdot } $$      

Vacuum sublimation kinetics of urea nitrate

Urea nitrate completely sublimes in a continuously pumped vacuum at a rate dependent upon the extent of the surface area. The fraction sublimed (α) vs. time (t) curve is sigmoidal in shape with an inflection point fluctuating between 5.3 and 8.1 % weight loss in the temperature range 56 to 97°. The experimental data fit the grain burning model $$\begin{gathered} 1 - (1 - \beta )^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} = k_s (t - t_0 ) \hfill \\ \beta = \alpha - \beta _0 ,\beta = 0 at inf{\text{lection}} {\text{point}} \hfill \\ \end{gathered} $$ where k_s is a sublimation rate constant, and the constantsβ ₀ andt ₀ are the respective values ofα andt at the inflection point. This equation yielded an activation enthalpy of sublimation of 79±5.4kJ/mole.     

Thermal analysis kinetics of thermal decomposition of nickel–viscose composite fiber

In this study, the thermal decompositions of nickel composite fibers (NCF) under different atmospheres of flowing nitrogen and air were investigated by XRD, SEM–EDS, and TG–DTG techniques. Non-isothermal studies indicated that only one mass loss stage occurred over the temperature regions of 298–1,073 K in nitrogen. The mass loss was from the decomposition. But after this decomposition, nickel was oxidized in air, when the temperature was high enough. In nitrogen media, the model-free kinetic analysis method was applied to calculate the apparent activation energy (E _a) and pre-exponential factor (A). The method combining Satava–?esták equation with one TG curve was used to select the suitable mechanism functions from 30 typical kinetic models. Furthermore, the Coats–Redfern method was used to study the NCF decomposition kinetics. The study results showed that the decomposition of NCF in nitrogen media was controlled by three-dimension diffusion; mechanism function was the anti-Jander equation, the apparent activation energy (E _a) and the pre-exponential factor (A) were 172.3 kJ mol^?1 and 2.16 × 10⁹ s^?1, respectively. The kinetic equation could be expressed as following: $$ \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{{ 2. 1 6\times 1 0^{ 9} }}{\beta }{ \exp }\left( {\frac{ - 2 0 7 2 4. 1}{T}} \right)\left\{ {\frac{ 3}{ 2}(1 + \alpha )^{2/3} [(1 + \alpha )^{1/3} - 1]^{ - 1} } \right\}. $$      

0-aminophenol and 8-hydroxyquinoline as ligands of Cu(II) in 1M-Na(ClO4) at 25°C

The complex formation between Cu(II) and 8-hydroxyquinolinat (Ox) was studied with the liquid-liquid distribution method, between 1M-Na(ClO₄) and CHCl₃ at 25°C. The experimental data were explained by the equilibria: $$\begin{gathered} \operatorname{Cu} ^{2 + } + Ox \rightleftharpoons \operatorname{Cu} Ox \log \beta _1 = 12.38 \pm 0.13 \hfill \\ \operatorname{Cu} ^{2 + } + 2 Ox \rightleftharpoons \operatorname{Cu} Ox_2 \log \beta _2 = 23.80 \pm 0.10 \hfill \\ \operatorname{Cu} Ox_{2aq} \rightleftharpoons \operatorname{Cu} Ox_{2\operatorname{org} } \log \lambda = 2.06 \pm 0.08 \hfill \\ \end{gathered} $$ The equilibria between Cu(II) and o-aminophenolate (AF) were studied potentiometrically with a glass electrode at 25°C and in 1M-Na(ClO₄). The experimental data were explained by the equilibria: $$\begin{gathered} \operatorname{Cu} ^{2 + } + AF \rightleftharpoons \operatorname{Cu} AF \log \beta _1 = 8.08 \pm 0.08 \hfill \\ \operatorname{Cu} ^{2 + } + 2AF \rightleftharpoons \operatorname{Cu} AF_2 \log \beta _2 = 14.60 \pm 0.06 \hfill \\ \end{gathered} $$ The protonation constants ofAF and the distribution constants between CHCl₃?H₂O and (C₂H₅)₂O?H₂O were also determined.     

Bemerkung zur Rayleigh-Schrödinger-Störungstheorie

The time-independent Hamiltonians ? ₀ and ?=? ₀ + V have a discrete spectrum, eigenvalues, and eigenvectors E _s ^(o) , ¦s〉^(o) resp. E _s, ¦s〉. If the RS perturbation theory can be applied here then an operator \(\mathfrak{p}\) with the property $$\left| s \right\rangle ^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}\left| s \right\rangle ^{(n)} , E_s^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}E_s^{(n)} $$ exists where ¦s〉⁽ⁿ⁾ and E _s ⁽ⁿ⁾ denote the n-th order corrections of perturbation theory if E _s ^(o) is nondegenerate. In the case of degeneracy the operation \(\mathfrak{p}\) remains defined and can always be used todetermine perturbation corrections of quantum mechanical expressions which are invariant in zerothorder under transformations of the basis in degenerate subspaces of ? ₀. The equations $$\left| s \right\rangle = \sum\limits_n^{0,\infty } {\left| s \right\rangle ^{(n)} = e^\mathfrak{p} \left| s \right\rangle ^{(0)} } , E_s = \sum\limits_n^{0,\infty } {E_s^{(n)} } = e^\mathfrak{p} E_s^{(0)} $$ correspond to a basis transformation where nondegenerate eigenvectors ¦s∝> ^(o) and eigenvalues E _s ^(o) of ? ₀ transform into eigenvectors ¦s∝> and eigenvalues E _s of ?. Examples show the usefulness of this formulation.     

Ion association of dilute aqueous sodium hydroxide solutions to 600°C and 300 MPa by conductance measurements

The limiting molar conductances Λ₀ and ion association constants of dilute aqueous NaOH solutions (<0.01 mol-kg^?1) were determined by electrical conductance measurements at temperatures from 100 to 600°C and pressures up to 300 MPa. The limiting molar conductances of NaOH_(aq) were found to increase with increasing temperature up to 300°C and with decreasing water density ρ_w. At temperatures ≥400°C, and densities between 0.6 to 0.8 g-cm^?3, Λ₀ is nearly temperature-independent but increases linearly with decreasing density, and then decreases at densities <0.6 g-cm^?3. This phenomenon is largely due to the breakdown of the hydrogen-bonded, structure of water. The molal association constants K _Am for NaOH( _aq ) increase with increasing temperature and decreasing density. The logarithm of the molal association constant can be represented as a function of temperature (Kelvin) and the logarithm of the density of water by $$\begin{gathered} log K_{Am} = 2.477 - 951.53/T - (9.307 \hfill \\ - 3482.8/T)log \rho _{w } (25 - 600^\circ C) \hfill \\ \end{gathered} $$ which includes selected data taken from the literature, or by $$\begin{gathered} log K_{Am} = 1.648 - 370.31/T - (13.215 \hfill \\ - 6300.5/T)log \rho _{w } (400 - 600^\circ C) \hfill \\ \end{gathered} $$ which is based solely on results from the present study over this temperature range (and to 300 MPa) where the measurements are most precise.     

Polyhydroxysäuren als Komplexbildner

The reaction of mucic acid (H₆ Mu) with Cobalt(II) and Nickel(II) ions has been studied in 1.0M-Na⁺(NO ₃ ^? ) ionic medium at 25° C using a glass electrode. The e.m.f. data in the range 8≦?log [H⁺]≦10 are explained by assuming $$\begin{gathered} Me^{2 + } + H_4 Mu^{2 - } \rightleftharpoons MeH_3 Mu^ - + H^ + \beta ''_1 \hfill \\ Me^{2 + } + H_4 Mu^{2 - } \rightleftharpoons MeH_2 Mu^{2 - } + 2 H^ + \beta ''_2 \hfill \\ \end{gathered}$$ with equilibrium constants log β′₁ = — 9.36; — 9.34; log β′₂ = — 18.11; — 18.08 for Co(II) and Ni(II) resp.     

Phase transitions and thermodynamic properties of anhydrous caffeine

Caffeine has been found to display a low-temperatureβ- and a high-temperatureα-modification. By quantitative DTA the following data were determined: transformation temperature 141±2°; enthalpy of transition 4.03±0.1 kJ·mole^?1; enthalpy of fusion 21.6±0.5 kJ·mole^?1; molar heat capacity $$\begin{array}{*{20}c} {{\vartheta \mathord{\left/ {\vphantom {\vartheta {^\circ C}}} \right. \kern-\nulldelimiterspace} {^\circ C}}} & {100(\beta )} & {100(\alpha )} & {150(\alpha )} & {100(\alpha )} \\ {{{C^\circ _\mathfrak{p} } \mathord{\left/ {\vphantom {{C^\circ _\mathfrak{p} } {J \cdot K^{ - 1} \cdot mole^{ - 1} }}} \right. \kern-\nulldelimiterspace} {J \cdot K^{ - 1} \cdot mole^{ - 1} }}} & {271 \pm 9} & {287 \pm 10} & {309 \pm 11} & {338 \pm 10} \\ \end{array} $$ in good accord with drop-calorimetric data. For the constants of the equation log (p/Pa)=?A/T+B, static vapour pressure measurements on liquid and solidα-caffeine, and effusion measurements on solidβ-caffeine yielded: $$\begin{array}{*{20}c} {A = 3918 \pm 37; 5223 \pm 28; 5781 \pm 35K^{ - 1} } \\ {B = 11.143 \pm 0.072; 13.697 \pm 0.057; 15.031 \pm 0.113} \\ \end{array} $$ . The evaporation coefficient ofβ-caffeine is 0.17±0.03.     

Pressure and isotope effects on the proton jump of the hydroxide ion at 25°C

The limiting molar conductances Λ⁰ of potassium deuteroxide KOD in D₂O and potassium hydroxide KOH in H₂O were determined at 25°C as a function of pressure to disclose the difference in the proton-jump mechanism between an OH^? (OD^?) and a H₃O⁺ (D₃O⁺) ion. The excess conductance of the OD^? ion in D₂O λ _E ^O (OD ^-), as estimated by the equation $$\lambda _E^O (OD^ - ) = \Lambda ^O (KOD/D_2 O) - \Lambda ^O (KCl/D_2 O)$$ increases a little with pressure as well as the excess conductance of the OH^? ion in H₂O $$\lambda _E^O (OH^ - ) = \Lambda ^O (KOH/H_2 O) - \Lambda ^O (KCl/H_2 O)$$ However, their rates of increase with pressure are much smaller than those of the excess deuteron and proton conductances, λ _E ^O (D ⁺) and λ _E ^O (H ⁺). With respect to the isotope effect on the excess conductance, λ _E ^O (OH ^-)/λ _E ^O (D ⁺) decreases with presure as in the case of λ _E ^O (H ⁺)/λ _E ^O (D ⁺), but the value of λ _E ^O (OH ^-)/λ _E ^O (OD ^-) itself is much larger than that of λ _E ^O (H ⁺)/λ _E ^O (D ⁺) at each pressure. These results are ascribed to the difference in the pre-rotation of water molecules, which is brought about by the difference in the intial orientation of the rotating water molecule adjacent to the OH^? (OD^?) or the H₃O⁺ (D₃O⁺) ion.     

Protonierungskonstanten der 8-Hydroxychinolinat-Ionen bei 25°C und in 1m-NaClO4

The protonation of the 8-hydroxyquinolinate ion (Ox ^?) has been studied at 25°C in 1m-NaClO₄ by the potentiometric method and the distribution between CHCl₃ and H₂O. The experimental data are explained by the following equilibria: $$\begin{array}{*{20}c} {H^ + + Ox^ - \rightleftharpoons HOx} \\ {H^ + + Ox \rightleftharpoons H_2 Ox^ + } \\ {HOx_w \rightleftharpoons HOx_{org} } \\ \end{array} \begin{array}{*{20}c} {\log k_1 = 9.42 \pm 0.08} \\ {\log k_2 = 5.46 \pm 0.10} \\ {\log \lambda = 2.40 \pm 0.10} \\ \end{array} $$      

Kinetics and mechanism of the collision-activated dissociation of the acetone cation

For center-of-mass collision energies E_cm = 1–60 eV, the major fragment ions for the collision-activated dissociation (CAD) of the acetone cation are the acetyl cation (m / z 43; absolute branching ratios of 0.96–0.60) and the methyl cation (m/ z 15; absolute branching ratios of 0.02–0.26); the absolute total cross-sections were 24–35) Ų. The breakdown curves (viz, plots of the absolute branching ratios versus E_cm) show complex, complementary energy dependences for production of MeCO⁺ and Me⁺, indicating apparent closure of the Me⁺ channel for E_cm > 30 eV. Our observations are consistent with a competition between three fast, primary (direct) reactions, each of which opens sequentially at its respective threshold energy (viz, reactions 8, 10, and 8′). 1 $$Me_2 CO^ + \cdot \to MeCO^ + + Me \cdot (X^2 A''_2 ) \Delta H = 0.82 eV$$ 1 $$ \to MeCO^ + + Me \cdot (B, 1^2 A'_1 ) \Delta H = 6.55 eV$$ 1 $$ \to Me^ + + Me \cdot + CO \Delta H = 4.24 eV$$ That is, the breakdown curves for MeCO⁺ and Me⁺ (and other CAD fragments) are consistent with the interpretation by other authors that the collisional activation of the acetone cation involves electronic transitions, so that CAD occurs primarily from isolated electronic states (i.e., non-quasi-equilibrium theory (QET) behavior). For acetone we found a correspondence between the photoelectron-photoion-coincidence and CAD breakdown curves. This may indicate that collisional activation in non-QET systems corresponds to scattering angles that emphasize optically allowed transitions accessed by photoionization.     

Potentiometric investigation of complexes between lead(II) and ethylenedithiodiacetic acid

Complex formation between lead(II) and ethylenedithio diacetic acid (H₂ L) has been studied at 25°C in aqueous 0.5M sodium perchlorate medium. Measurements have been carried out with a glass electrode and with a lead amalgam electrode. In acidic medium and in the investigated concentration range experimental data can be explained by assuming the following equilibria: $$\begin{gathered} Pb^{2 + } + L^{2 - } \rightleftharpoons PbL log\beta _{101} = 3.62 \pm 0.03 \hfill \\ Pb^{2 + } + H^ + + L^{2 - } \rightleftharpoons PbHL^ - log\beta _{111} = 6.30 \pm 0.07 \hfill \\ \end{gathered} $$      

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.