Etude par Spectrophotometrie d'absorption de l'Equilibre Pu4++Cl−⇋Pu3++1/2 Cl2 dans le melange LiCl−KCl (70–30% mol) fondu

The quantitative study of the equilibrium Pu⁴⁺+Cl⁻⇋Pu³⁺+1/2 Cl₂ in LiCl−KCl (70–30% mol) at 455, 500, 550 and 600°C by visible and near I.R. absorption spectrophotometry allows the calculation of the reaction's equilibrium constant, the mean thermodynamic data ΔH=27±14 kJ·mol⁻¹ and ΔS=37±17 J·mol⁻¹·K⁻¹ and the standard potential of the couple .      

Stable-isotope dilution activation analysis,and determination of Ca,Zn and Ce by means of photon activation

As a new method, stable-isotope dilution activation analysis has been developed. When an element consists of at least two stable isotopes which are converted easily to the radioactive nuclides through nuclear reactions, the total amount of the element (xg) can be determined by irradiating simultaneously the duplicated sample containing small amounts of either enriched isotope (y g), and by using the following equation. $${{x = y\left( {{M \mathord{\left/ {\vphantom {M {M*}}} \right. \kern-\nulldelimiterspace} {M*}}} \right)\left[ {\left( {{{R*} \mathord{\left/ {\vphantom {{R*} R}} \right. \kern-\nulldelimiterspace} R}} \right)\left( {{{\theta _2^* } \mathord{\left/ {\vphantom {{\theta _2^* } {\theta _2 }}} \right. \kern-\nulldelimiterspace} {\theta _2 }}} \right) - \left( {{{\theta _1^* } \mathord{\left/ {\vphantom {{\theta _1^* } {\theta _1 }}} \right. \kern-\nulldelimiterspace} {\theta _1 }}} \right)} \right]} \mathord{\left/ {\vphantom {{x = y\left( {{M \mathord{\left/ {\vphantom {M {M*}}} \right. \kern-\nulldelimiterspace} {M*}}} \right)\left[ {\left( {{{R*} \mathord{\left/ {\vphantom {{R*} R}} \right. \kern-\nulldelimiterspace} R}} \right)\left( {{{\theta _2^* } \mathord{\left/ {\vphantom {{\theta _2^* } {\theta _2 }}} \right. \kern-\nulldelimiterspace} {\theta _2 }}} \right) - \left( {{{\theta _1^* } \mathord{\left/ {\vphantom {{\theta _1^* } {\theta _1 }}} \right. \kern-\nulldelimiterspace} {\theta _1 }}} \right)} \right]} {\left[ {1 - \left( {{{R*} \mathord{\left/ {\vphantom {{R*} R}} \right. \kern-\nulldelimiterspace} R}} \right)} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {1 - \left( {{{R*} \mathord{\left/ {\vphantom {{R*} R}} \right. \kern-\nulldelimiterspace} R}} \right)} \right]}}$$ Where M and M^* are atomic weights of the element to be determined and the enriched isotope used as a spike,θ ₁ andθ ₂ are natural abundances of two stable isotopes in the element,θ ₁ ^* andθ ₂ ^* are isotopic compositions of the above isotopes in the enriched isotope, and R and R^* are counting ratios of gamma-rays emitted by two radionuclides produced in the sample and the isotopic mixture. Neither calibration standard nor correction of irradiation conditions are necessary for this method. Usefulness of the present method was verified by photon activations of Ca, Zn and Ce using isotopically enriched⁴⁸ca,⁶⁸Zn and¹⁴²Ce.     

Kinetics and mechanism of oxidation of the chromium(III)-DL-aspartic acid complex/periodate reaction. Evidence for iron(II) catalysis

The kinetics of oxidation of the chromium(III)-DL- aspartic acid complex, [CrIIIHL]+ by periodate have been investigated in aqueous medium. In the presence of Fe^II as a catalyst, the following rate law is obeyed:

Thermodynamic properties of the ternary oxides in the Eu–Ru–O system by using solid-state electrochemical cells

The Gibbs free energies of formation of Eu₃RuO₇(s) and Eu₂Ru₂O₇(s) have been determined using solid-state electrochemical technique employing oxide ion conducting electrolyte. The reversible electromotive force (e.m.f.) of the following solid-state electrochemical cells have been measured:

Elektrometrische Untersuchungen über die Geschwindigkeit der Bildung von Cu2S in ammoniakalischen Lösungen von Cu+-Ionen mittels Thioacetamid, 4. Mitt.

Quantitative studies of the rate of Cu₂S-formation by thioacetamide (TAA) were made with the help of the polarographic method of continuous registration at constant potential, and the following equation for the reaction rate between Cu⁺-ions andTAA in ammoniacal solutions was derived: 1 $$ - \frac{{d[Cu^I ]}}{{dt}} = k \cdot \frac{{[Cu^I ] \cdot [CH_3 CSNH_2 ]}}{{[NH_3 H_2 O]^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \cdot [H^ + ]}}\frac{{^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$4$}}} }}{{^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}} }} \cdot \frac{{f_{Cu} }}{{f_{H^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {10}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${10}$}}} } }}$$ The value at 25.0° of the rate constantk is (1.6±0.2)·10^?2 mole^7/20·litre^?7/20·sec^?1. The validity of equation (1) has been proved over the pH range 8.5–9.5 and the ammonia concentration of 4.0·10^?2–4.0·10^?1 mole per litre, by only a small excess ofTAA and moderate reaction rates.     

Photoelectrode characteristics of an organic bilayer in water phase containing a redox molecule

We have recently reported that the organic bilayer of 3,4,9,10-perylenetetracarboxyl-bisbenzimidazole (PTCBI, n-type semiconductor) and 29H,31H-phthalocyanine (H₂Pc, p-type semiconductor), which is a part of a photovoltaic cell, acts as a photoanode in the water phase (Abe et al., ChemPhysChem 5:716, [2004]); in that case, the generation of the photocurrent involving an irreversible thiol oxidation at the H₂Pc/water interface took place to be coupled with hole conduction through the H₂Pc layer, based on the photophysical character of the bilayer. In the present work, the photoelectrode characteristics of the bilayer were investigated in the water phase containing a redox molecule , where the photo-induced oxidation and reduction for the couple were found to take place at the bilayer. The photoanodic current involving the oxidation efficiently occurred at the interface of H₂Pc/water, similar to the previous example. In the view of the voltammograms obtained, it was noted that there are pin-holes in the H₂Pc layer of the bilayer, leading to a cathodic reaction with at the PTCBI surface especially in the dark; that is, the band bending at the PTCBI/water interface can essentially be reduced by applying a negative potential [e.g., < ∼ 0 V (vs Ag/AgCl)] to the PTCBI, when the cathodic reaction may take place through the conduction band of the PTCBI. Moreover, under that applied potential condition of irradiation, the photogenerated electron carrier part can move to the PTCBI surface, thus enhancing the reduction of .     

Dampfdruckmessungen an festem β-Mn und ZrMn2

Using theTorker-technique, the vapour pressures of β-Mn in the temperature range 1230–1370° K have been determined. From these measurements the heat of sublimation of α-Mn at 0° K has been obtained ΔH ₀ ^o=67800±800 cal/g-atom. From measurements of the dissociation pressures of ZrMn₂ the enthalpy ΔH ₀ ^o of the reaction. $${1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3} Zr (s) + {2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}Mn (g) = Zr_{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} Mn_{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} (s)$$ has been evaluated. ΔH ₀ ^o=?49150±700 cal/GFW. Combining this value with the heat of sublimation of α-Mn leads to the heat of formation of Zr_1/3Mn_2/3 ΔH ₀ ^o=?3900±1200 cal/GFW.     

Improvement of the electrochemical properties of “as-grown” boron-doped polycrystalline diamond electrodes deposited on tungsten wires using ethanol

The electrochemical properties of boron-doped diamond (BDD) polycrystalline films grown on tungsten wire substrates using ethanol as a precursor are described. The results obtained show that the use of ethanol improves the electrochemistry properties of “as-grown” BDD, as it minimizes the graphitic phase upon the surface of BDD, during the growth process. The BDD electrodes were characterized by Raman spectroscopy, scanning electronic microscopy, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS). The boron-doping levels of the films were estimated to be ∼10²⁰ B/cm³. The electrochemical behavior was evaluated using the and redox couples and dopamine. Apparent heterogeneous electro-transfer rate constants were determined for these redox systems using the CV and EIS techniques. values in the range of 0.01–0.1 cm s⁻¹ were observed for the and redox couples, while in the special case of dopamine, a lower value of 10⁻⁵ cm s⁻¹ was found. The obtained results showed that the use of CH₃CH₂OH (ethanol) as a carbon source constitutes a promising alternative for manufacturing BDD electrodes for electroanalytical applications.     

Half-width and asymmetry of glow peaks and their consistent analytical representation

The kinetic equation which describes many electronic as well as atomic or chemical reactions under the condition of a steadily linear raise of the temperature, is considered in a mathematically exact and straightforward way. Therefore, the equation has been transformed into a dimensionsless form, using with profit the maximum condition for the intensity peak. The two temperatures T₁ and T₂, corresponding to the half-height of the intensity peak, are found as unique polynomials of the small argument \(\bar y \equiv {{k\bar T} \mathord{\left/ {\vphantom {{k\bar T} E}} \right. \kern-0em} E}\) only ( \(\bar T\) =temperature of peak maximum). Thereupon, further combinations give half-widthδ, peak asymmetryA=δ₂/δ₁ or \(\tilde A = {{\bar C} \mathord{\left/ {\vphantom {{\bar C} {(1 - \bar C)}}} \right. \kern-0em} {(1 - \bar C)}}\) and the maximum of the intensity peakJ; they again all depend only on¯y. In some cases this dependence is weak, so that e.g. it is deduced that the half-width energy product divided by \(\bar T^2 \) is an invariant, different for every kinetic orderπ: $$\frac{{\delta \cdot E[eV]}}{{\bar T^2 }} = \left\{ {\begin{array}{*{20}c} {{1 \mathord{\left/ {\vphantom {1 {4998 K for monomolecular process}}} \right. \kern-\nulldelimiterspace} {4998 K for monomolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {3542 K for bimolecular process}}} \right. \kern-\nulldelimiterspace} {3542 K for bimolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {2872 K for trimolecular process}}} \right. \kern-\nulldelimiterspace} {2872 K for trimolecular process}}} \\ \end{array} } \right.$$ By means of these correlations, activation energy valuesE [eV] can be determined accurately to within 0.5 %, so that for most experiments the inaccuracy of theδ values becomes dominant and limiting. A special nomogram for the express estimation ofE from experimentally observedδ and \(\bar T\) is demonstrated.     

Determination of standard pH values for sodium hydrogen diglycolate buffer (0.05m) from 5–65°C

Values of pa _H ^o for 0.05 mole-kg^?1 aqueous solutions of sodium hydrogen diglycolate in the temperature range 5–65°C have been obtained from cells without transport, and can be fitted to the equation $$\begin{gathered} pa^\circ _H = 3.5098 + 2.222 \times 10^{ - 3} ({T \mathord{\left/ {\vphantom {T {K - 298.15}}} \right. \kern-\nulldelimiterspace} {K - 298.15}}) \hfill \\ + 2.628 \times 10^{ - 5} ({T \mathord{\left/ {\vphantom {T {K - 298.15}}} \right. \kern-\nulldelimiterspace} {K - 298.15}})^2 \hfill \\ \end{gathered} $$ The analysis has been carried out by a multilinear regression procedure using a form of the Clarke and Glew equation. This buffer standard may be a useful alternative to the saturated potassium hydrogen tartrate buffer.     

Hydrogenating properties of complex rhenidm(VLI) oxides with perovskite structure

Conclusions Rhenium oxides with perovskite structure of the general formula where B^III=Y and Sm, and Ba₃LaZnReWO₁₂ containing Re(VII), exhibit catalytic activity in hydrogenation of ethyl acetate.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1236–1238, June, 1986.     

Effect of long-chain branching on the relation between steady-flow and dynamic viscosity of polyethylene melts

The steady-state viscosity η, the dynamic viscosity η′, and the storage modulus G′ of several high-density and low-density polyethylene melts were investigated by using the Instron rheometer and the Weissenberg rheogoniometer. The theoretical relation between the two viscosities as proposed earlier is:\documentclass{article}\pagestyle{empty}\begin{document}$ \eta \left( {\dot \gamma } \right){\rm } = {\rm }\int {H\left( {\ln {\rm }\tau } \right)} {\rm }h\left( \theta \right)g\left( \theta \right)^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \tau {\rm }d{\rm }\ln {\rm }\tau $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \theta {\rm } = {\rm }{{\dot \gamma \tau } \mathord{\left/ {\vphantom {{\dot \gamma \tau } 2}} \right. \kern-\nulldelimiterspace} 2} $\end{document}; \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} is the shear rate, H is the relaxation spectrum, τ is the relaxation time, \documentclass{article}\pagestyle{empty}\begin{document}$ g\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{\theta \mathord{\left/ {\vphantom {\theta {\left( {1 + \theta ^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 + \theta ^2 } \right)}}} \right] $\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$ h\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} \mathord{\left/ {\vphantom {{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right. \kern-\nulldelimiterspace} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right] $\end{document}. Good agreement between the experimental and calculated values was obtained, without any coordinate shift, for high-density polyethylenes as well as for a low density sample with low n_w, the weight-average number of branch points per molecule. The correlation, however, was poor with low-density samples with large values of the long-chain branching index n_w. This lack of coordination can be related to n_w. The empirical relation of Cox and Merz failed in a similar way.     

DSC study of the decomposition of azodicarbonamide in different media

The decomposition of azodicarbonamide (Genitron AC-2) in the solid state was investigated by DSC. It was found that the decomposition under non-isothermal conditions can be described by the autocatalytic reaction scheme $$X\xrightarrow{{k_1 }}Y,X + Y\xrightarrow{{k'_2 }}2Y$$ where the following dependences hold for the rate constants: $$k_1 = 4.8 \times 10^{19} e - {{243 600} \mathord{\left/ {\vphantom {{243 600} {RT_s - 1}}} \right. \kern-\nulldelimiterspace} {RT_s - 1}}$$ and $$k'_2 = 1.0 \times 10^{13} e - {{133 500} \mathord{\left/ {\vphantom {{133 500} {RT_s - 1}}} \right. \kern-\nulldelimiterspace} {RT_s - 1}}$$ The first pre-exponential factor includes the thermal history of the sample, especially the quick heating to a certain temperature, from which normal slow heating starts. Due to this fast heating, the decomposition reaction of AZDA may be understood as the collapse of its crystal lattice into nucleation centres with critical dimensions.     

Effect of the excluded volume on specific rate of combination reactions between polymer radicals

The specific rate k_D for reaction between polymer radicals is formulated when the potential of average force on the basis of the excluded volume affects the motion of the polymer radicals. This rate is given by \documentclass{article}\pagestyle{empty}\begin{document}$ k_D = Fk_S \left( {{\rm with}\ {F} = \sum\limits_{s = 0}^\infty {{{[ ‐ 2(\alpha ^2 ‐ 1)]} \mathord{\left/ {\vphantom {{[ ‐ 2(\alpha ^2 ‐ 1)]} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} \right. \kern‐\nulldelimiterspace} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} } \right) $\end{document} where k_S is specific rate of reaction between radical chain ends and α is the average expansion of the polymer arising from the long-range effects. The effect of the excluded volume reduces k_D. F depends on the degree of polymerization of the polymer radical when α ≠ 1. These results are discussed in terms of the experimental data for very low polymer concentrations.     

Atomic potentials from SCF data

The possibility is explored of representing atomic potentials, derived from SCF data, with function

$$V(R) = R^{ - 1} \mathop {\sum _i }\limits_1^\lambda n_i \{ exp ( - 2 \alpha _i R) [(2 \alpha _i - {{V_i^0 } \mathord{\left/ {\vphantom {{V_i^0 } {n_i }}} \right. \kern-\nulldelimiterspace} {n_i }}) R + 1] - 1\}$$     

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.     

Flow-dependent rejection of polystyrene from microporous membranes

Dilute solutions of polystyrene (molecular weight 1 × 10⁵?2 × 10⁷) in a mixed solvent of 90% carbon tetrachloride-10% methanol were filtered through track-etched porous mica membranes. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was measured as a function of polymer size r_s, pore radius r_o, and solvent flow rate q through each pore. Polymer size was characterized by the Stokes-Einstein radius, as determined from diffusion coefficients measured by quasielastic light scattering, and chain relaxation times τ were estimated from measured intrinsic viscosities. In the case of chains whose unperturbed radius was smaller than the pore, σ depended on the ratio r_s/r_o in the manner predicted by a hard-sphere theory, as long as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \tau < < 1 $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q, toward zero at high q. The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r_s > r_o by a single similarity variable \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} \mathord{\left/ {\vphantom {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} {(\dot \gamma \tau)^n}}} \right. \kern-\nulldelimiterspace} {(\dot \gamma \tau)^n}} \sim ({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})^{1 - 3n} q^{- n} $\end{document}; a least-squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.     

Kinetics and mechanism of the oxidation of hydrogen peroxide by the octacyanotungstate(V) ion in alkaline aqueous media

Summary The oxidation of H₂O₂ by [W(CN)₈]^3– has been studied in aqueous media between pH 7.87 and 12.10 using both conventional and stopped-flow spectrophotometry. The reaction proceeds without generation of free radicals. The experimental overall rate law, , strongly suggests two types of mechanisms. The first pathway, characterized by the pH-dependent rate constant k _s, given by , involves the formation of [W(CN)₈· H₂O₂]^3–, [W(CN)₈· H₂O₂·W(CN)₈]^6– and [W(CN)₈· HO]^3– intermediates in rapid pre-equilibria steps, and is followed by a one-electron transfer step involving [W(CN)₈·HO]^3– (k _a) and its conjugate base [W(CN)₈·O]^4– (k _b). At 25 °C, I = 0.20 m (NaCl), the rate constant with H _a =40±6kJmol^–1 and S _a =–151±22JK^–1mol^–1; the rate constant with H _b =36±1kJmol^–1 and S _b =–136±2JK^–1mol^–1 at 25 °C, I = 0.20 m (NaCl); the acid dissociation constant of [W(CN)₈·HO]^3–, K ₅ =(5.9±1.7)×10^–10 m, with and is the first acid dissociation constant of H₂O₂. The second pathway, with rate constant, k _f, involves the formation of [W(CN)₈· HO₂]^4– and is followed by a formal two-electron redox process with [W(CN)₈]^3–. The pH-dependent rate constant, k _f, is given by . The rate constant k ₇ =23±6m ^–1 s ^–1 with and at 25°C, I = 0.20 m (NaCl).     

Systematics of evaporation

Beginning with rather basic principles, general relations are obtained for evaporative rate constants. These are established both as a function of energy and of temperature. In parallel with this, expressions are developed for the kinetic energy distribution of the separating species. Explicit evaluation of the rate constants in the case of “chemical” evaporation from an entity containingn monomeric units yields as a typical result $$k(T)(s^{ - 1} ) = 3 \cdot 10^{13} n^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \exp [6/n^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ]\exp ( - \Delta E_a (n)/k_B T)$$ Experimental evidence in support of this relation is cited. Applications to thermionic emission are also noted.     

Thermodynamic studies on Pr2TeO6

The standard Gibbs energy of formation of Pr₂TeO₆ $ (\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)) $ was derived from its vapour pressure in the temperature range of 1,400–1,480 K. The vapour pressure of TeO₂ (g) was measured by employing a thermogravimetry-based transpiration method. The temperature dependence of the vapour pressure of TeO₂ over the mixture Pr₂TeO₆ (s) + Pr₂O₃ (s) generated by the incongruent vapourization reaction, Pr₂TeO₆ (s) = Pr₂O₃ (s) + TeO₂ (g) + ½ O₂ (g) could be represented as: $ { \log }\left\{ {{{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} \mathord{\left/ {\vphantom {{p\left( {{\text{TeO}}_{ 2} ,\;{\text{g}}} \right)} {{\text{Pa}} \pm 0.0 4}}} \right. \kern-0em} {{\text{Pa}} \pm 0.0 4}}} \right\} = 19. 12- 27132\; \left({\rm{{{\text{K}}}}/T} \right) $ . The $ \Updelta_{\text{f}} G^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ could be represented by the relation $ \left\{ {{{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} \mathord{\left/ {\vphantom {{\Updelta_{\text{f}} G^{^\circ } \left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} ,\;{\text{s}}} \right)} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} \pm 5.0} \right\} = - 2 4 1 5. 1+ 0. 5 7 9 3\;\left(T/{\text{K}}\right) .$ Enthalpy increments of Pr₂TeO₆ were measured by drop calorimetry in the temperature range of 573–1,273 K and heat capacity, entropy and Gibbs energy functions were derived. The $ \Updelta_{\text{f}} H_{{298\;{\text{K}}}}^{^\circ } \;\left( {{ \Pr }_{ 2} {\text{TeO}}_{ 6} } \right) $ was found to be $ {{ - 2, 40 7. 8 \pm 2.0} \mathord{\left/ {\vphantom {{ - 2, 40 7. 8 \pm 2.0} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}}} \right. \kern-0em} {\left( {{\text{kJ}}\,{\text{mol}}^{ - 1} } \right)}} $ .