Lattice parameters and thermal expansion of δ-VN1−x from 298–1000 K

The thermal expansion of VN_1?x was determined from measurements of the lattice parameters in the temperature range of 298–1000 K and in the composition range of VN_0.707–VN_0.996. Within the accuracy of the results the expansion of the lattice parameter with temperature is not dependent on the composition. The lattice parameter as a function of composition ([N]/[V]=0.707?0.996) and temperature (298–1000 K) is given by $$\begin{gathered} a([N]/[V],T) = 0.38872 + 0.02488([N]/[V]) - \hfill \\ - (1.083 \pm 0.021) \cdot 10^{ - 4} T^{1/2} + (6.2 \pm 0.1) \cdot 10^{ - 6} T. \hfill \\ \end{gathered} $$ . The coefficient of linear thermal expansion as a function of temperature (in the same range) is given by $$\alpha (T) = a([N]/[V],T)^{ - 1} [( - 5.04 \pm 0.01) \cdot 10^5 T^{ - 1/2} + (6.2 \pm 0.1) \cdot 10^{ - 6} ].$$ . The average linear thermal expansion coefficient is $$\alpha _{av} = 9.70 \pm 0.15 \cdot 10^{ - 6} K^{ - 1} (298 - 1 000K).$$ . The data are compared with those of several fcc transition metal nitrides collected and evaluated from the literature.     

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: $$\begin{gathered} H^ + + L \rightleftarrows HL logk_1 = 3,84 \pm 0,03 \hfill \\ 2H^ + + L \rightleftarrows H_2 L logk_2 = 6,43 \pm 0,02 \hfill \\\end{gathered}$$ .     

Dichlorosilylene: Rate constant for reaction with carbon monoxide and nitrous oxide

The absolute rate constanss for the gas-phase reactions of 1,1-dichlorosilylene with carbon monoxide and nitrous oxide have been determined using the flash photolysts-kinetic absorpiton spectroscopy technique. The bimolecular rate constant values at 25° C are: $$\begin{gathered} k\left( {Cl_2 Si + CO} \right) = \left( {6.3 \pm 0.7} \right) \times 10^8 M^{ - 1} s^{ - 1} \hfill \\ k\left( {Cl_2 Si + N_2 O} \right) = \left( {5.7 \pm 0.3} \right) \times 10^8 M^{ - 1} s^{ - 1} \hfill \\ \end{gathered} $$      

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.     

Thermodynamic excess properties of ternary alcohol-hydrocarbon systems. Simplified method for predicting enthalpies from binary data

Two general equations for estimation of excess enthalpies of ternary systems consisting of an alcohol and two hydrocarbons from observed excess properties of the various binary combinations have been developed. The first expression is based on the Kretschmer-Wiebe association model and takes the form $$\Delta \overline H _{ABC}^{ex} = h_A x_A K_A (\phi _{A1} - \phi _{A1}^o ) + Q_{ABC}$$ where $$\begin{gathered} Q_{ABC} = (x_A + x_B )(\phi _A + \phi _B )(\Delta \overline H _{AB}^{ex} )_{phys}^ \bullet + (x_A + x_C )(\phi _A + \phi _C )(\Delta \overline H _{AC}^{ex} )_{phys}^ \bullet \hfill \\ + (x_B + x_C )(\phi _B + \phi _C )(\Delta \overline H _{BC}^{ex} )_{phys}^ \bullet \hfill \\ \end{gathered}$$ \((\Delta \overline H _{ij}^{ex} )_{phys}^ \bullet\) represents the physical interactions in each of the individual binary systems, and the term involving φ _A1 ^o represents the chemical contributions (caused by self-association) to the excess enthalpies of mixing. The second predictive expression is based on the Mecke-Kempter association model and is given by $$\Delta \overline H _{ABC}^{ex} = - h_A x_A [In(1 + K_A \phi _A )/K_A \phi _A - In(1 + K_A )/K_A ] + Q_{ABC}$$ where the first term (contained within brackets) represetns the chemical contributions to the enthalpies of mixing. The predictions of both expressions are compared with experimental data for the excess enthalpies of six ternary systems.     

Solubility constants and free enthalpies of metal sulphides,part 6: A new solubility cell

A solubility cell which can be operated continuously over the temperature range 5–95 °C has been developed. The solubility of Fe_0.88S (monoclinic pyrrhotite) in solutions $$S_0 = ([H^ + ]) = H{\text{ }}m,{\text{ }}[Na^ + ] = (1.00---H) m,{\text{ }}[ClO_{4^ - } ] = 1.00 m)$$ at fixed partial pressures of H₂S has been investigated at 50.7 °C. The hydrogen ion concentration and the total concentration of iron(II) ion in equilibrium with the solid phase was determined by e.m.f. and analytical methods respectively. The data were consistent with $$\log ^* K_{pso} = \log \frac{{[Fe^{2 + } ]pH_2 S}}{{[H^ + ]^2 }} = 3.80 \pm {\text{ }}0.10{\text{ }}[50.7^\circ C,{\text{ }}1 m(Na)ClO_4 ]$$ according to the overall reaction $$1.14{\text{ }}Fe_{0.88} S_{(s)} {\text{ }} + {\text{ }}2H_{(I = 1m)}^ + {\text{ }} \rightleftharpoons {\text{ }}Fe_{(I = 1m)}^{2 + } {\text{ }} + {\text{ H}}_{\text{2}} S_{(g)} {\text{ }} + {\text{ }}0.14{\text{ }}S_{(s)} $$      

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.     

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: $$\begin{array}{*{20}c} {H^ + + Ox^ - \rightleftharpoons HOx} \\ {H^ + + Ox \rightleftharpoons H_2 Ox^ + } \\ {HOx_w \rightleftharpoons HOx_{org} } \\ \end{array} \begin{array}{*{20}c} {\log k_1 = 9.42 \pm 0.08} \\ {\log k_2 = 5.46 \pm 0.10} \\ {\log \lambda = 2.40 \pm 0.10} \\ \end{array} $$      

Auswertung von EMK-Messungen zur Bestimmung thermodynamischer Exzeßgrößen im System Silberchlorid—Lithiumchlorid

The partial molar excessGibbs energies \(\Delta \overline G _{AgCl}^E \) of AgCl in the binary system AgCl?LiCl have been measured over the entire composition range at temperatures between 923.15K and 1175.15K in steps of 50K, using the reversible formation cell $${{Ag\left( s \right)} \mathord{\left/ {\vphantom {{Ag\left( s \right)} {AgCl\left( l \right)}}} \right. \kern-\nulldelimiterspace} {AgCl\left( l \right)}}---LiCl\left( l \right)/C,Cl_2 $$ The measured \(\Delta \overline G _{AgCl}^E \) values were fitted by the use of theRedlich-Kister-Ansatz for thermodynamic excess functions. The evaluatedRedlich-Kister parameters have been used to calculate the molar excessGibbs energies ΔG ^E and the partial molar excessGibbs energies \(\Delta \overline G _{LiCl}^E \) of LiCl. From the temperature dependence of theRedlich-Kister parameters for ΔG ^E the partial and integral molar heats of mixing and excess entropies were calculated. For 1073 K and the mole fractionx=0.5 the following values were obtained: $$\Delta G^E = 2130\left[ {J mol^{ - 1} } \right], \Delta H^E = 1994\left[ {J mol^{ - 1} } \right], \Delta S^E = 0.127 \left[ {J mol^{ - 1} K^{ - 1} } \right]$$      

A solution of the exponential integral in the non-isothermal kinetics for linear heating

A simple and satisfactorily accurate solution of the exponential integral in the nonisothermal kinetic equation for linear heating is proposed: $$\mathop \smallint \limits_0^T e^{ - E/RT} dT = \frac{{RT^2 }}{{E + 2RT}}e^{ - E/RT} $$      

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: $$\begin{gathered} Pb^{2 + } + L^{2 - } \rightleftharpoons PbL log\beta _{101} = 3.62 \pm 0.03 \hfill \\ Pb^{2 + } + H^ + + L^{2 - } \rightleftharpoons PbHL^ - log\beta _{111} = 6.30 \pm 0.07 \hfill \\ \end{gathered} $$      

LiSO 4 − , RbSO 4 − , CsSO 4 − , and (NH4)SO 4 − ion pairs in aqueous solutions at pressures up to 2000 atm

Electrical conductance data at 25°C for Li₂SO₄, Rb₂SO₄, Cs₂SO₄, and (NH₄)₂SO₄ aqueous solutions are reported at concentrations up to 0.01 eq.-liter^?1 and as a function of pressure up to 2000 atm. The molal dissociation constants are as follows: $$\begin{gathered} LiSO_4^ - : - log K_m = - 1.02 + 1.03 \times 10^4 P \pm 0.019 \Delta \bar V^o = - 5.8 \hfill \\ RbSO_4^ - : - log K_m = - 1.12 + 0.58 \times 10^4 P \pm 0.020 \Delta \bar V^o = - 3.3 \hfill \\ CsSO_4^ - : - log K_m = - 1.08 + 1.10 \times 10^4 P \pm 0.014 \Delta \bar V^o = - 6.2 \hfill \\ \left( {NH4} \right)SO_4^ - : - log K_m = - 1.12 + 0.58 \times 10^4 P \pm 0.020 \Delta \bar V^o = - 3.3 \hfill \\ \end{gathered} $$ whereP is in atmospheres and \(\Delta \bar V^o \) is in cm³-mole^?1. These values were obtained by using the Davies-Otter-Prue conductance equation and Bjerrum distance parameters. A simultaneous Λ°,K _m search was used to determine the equilibrium constantK _m, a different procedure than used earlier for KSO ₄ ^? , NaSO ₄ ^? , and MgCl⁺. Recalculated values for these salts are as follows: $$\begin{gathered} KSO_4^ - : - log K_m = - 1.03 + 1.04 \times 10^4 P \pm 0.020 \Delta \bar V^o = - 5.9 \hfill \\ NaSO_4^ - : - log K_m = - 1.00 + 1.30 \times 10^4 P \pm 0.019 \Delta \bar V^o = - 7.3 \hfill \\ MgCl^ + : - log K_m = - 0.75 + 0.71 \times 10^4 P \pm 0.028 \Delta \bar V^o = - 4.0 \hfill \\ \end{gathered} $$      

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.     

An eigenfunction expansion of the non-selfadjoint Sturm–Liouville operator with a singular potential

In this paper, we consider the operator $L$ L generated in $L^{2}\left( \mathbb{R }_{+}\right) $ L 2 R + by the differential expression $$\begin{aligned} l\left( y\right) =-y^{\prime \prime }+\left[ \frac{\nu ^{2}-\frac{1}{4}}{x^{2}}+q\left( x\right) \right] y,\,\,x\in \mathbb{R }_{+}:=\left( 0,\infty \right) \end{aligned}$$ l y = - y ' ' + ν 2 - 1 4 x 2 + q x y , x ∈ R + : = 0 , ∞ and the boundary condition $$\begin{aligned} \underset{x\rightarrow 0}{\lim }x^{-\nu -\frac{1}{2}}y\left( x\right) =1, \end{aligned}$$ lim x → 0 x - ν - 1 2 y x = 1 , where $q$ q is a complex valued function and $\nu $ ν is a complex number with $Re\nu >0$ R e ν > 0 . We have proved a spectral expansion of L in terms of the principal functions under the condition $$\begin{aligned} \underset{x\in \mathbb{R }_{+}}{Sup}\left\{ e^{\epsilon \sqrt{x}}\left| q(x)\right| \right\} <\infty , \epsilon >0 \end{aligned}$$ S u p x ∈ R + e ? x q ( x ) < ∞ , ? > 0 taking into account the spectral singularities. We have also investigated the convergence of the spectral expansion.     

Bemerkungen über Thermochromie von Kobalt(II) chloridlösungen in organischen Medien, 1. Mitt.: Lösungen in verschiedenen Alkoholen

The thermochromism of solutions of cobalt(II) chloride in methanol, ethanol, n- and iso-propyl, n-, iso- and sec. butyl alcohol was studied spectrophotometrically. The blue color of these solutions fades with decreasing temperature, solutions in primary alcohols being especially variable, becoming pink at sufficiently low temperature. Solutions in secondary alcohols are, on the other hand, much less variable. The thermochromism can be ascribed, in general, to the shift of the equilibrium $$[CoL_2 Cl_2 ] + (3 - 4) L\begin{array}{*{20}c} \to \\ \leftarrow \\ \end{array} ([CoL_5 Cl]^ + or [CoL_6 ]^{2 + } ) + (1 - 2) Cl^ - $$ (L: solvent molecule). In the case of methanol, however, the two equilibria $$[CoLCl_3 ]^ - + 4 L \begin{array}{*{20}c} \to \\ \leftarrow \\ \end{array} [CoL_5 Cl]^ + + 2 Cl^ - $$ and $$[CoL_5 Cl]^ + + L\begin{array}{*{20}c} \to \\ \leftarrow \\ \end{array} [CoL_6 ]^{2 + } ) + Cl^ - $$ seem to be shifted one after another. The significance of the difference between primary and secondary alcohols is briefly discussed in connection with some related effects, i.e. the pressure effect studied byKitamura andOsugi ⁷ and the water effect found byKato et al.¹⁰.     

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.     

Komplexe aus Cadmium(II)- und Oxalat-ion

Complex formation between Cd(II) and oxalate has been studied before the precipitation at 25°C and 1M-NaClO₄, by means of glass- and cadmium amalgam electrodes. The e.m.f. data are explained with the following equilibrium: $$Cd^{2 + } + C_2 O_4^{2 - } \rightleftharpoons CdC_2 O_4 \log {\text{ }}\beta _1 = 2.75 \pm 0.05$$      

Die integrale Lösungswärme von Jod in Schwefelkohlenstoff

Values of the integral heat of solution of iodine in carbon disulfide were determined at different mole ratiosr=n(CS₂)/n(I₂) in the range 34<r<2650 and 298,15 K by isoperibol calorimetry. The experimental data may be expressed by the empirical equation $$\Delta H_m \prime /cal Mol^{ - 1} = 2973 + 1759\frac{r}{{r + 1}} - 0,0821{\text{ }}r,$$ where ΔH _m' is the molar enthalpy change for the process $$I_2 (c) + r{\text{ }}CS_2 (l) = [I_2 ,r{\text{ }}CS_2 ](sol).$$ Since the last term in the above equation can be explained by assuming the presence of a trace impurity in the solvent, the “true” heat of solution is given by $$\Delta H_m /cal Mol^{ - 1} = 2973 + 1759\frac{r}{{r + 1}}.$$ Smoothed values of this quantity are given in table 3 for selected values of the mole ratio,r. The results are discussed in terms of the regular solution theory.     

Relation générale entre l'indice de liaison et la distance interatomique dans les molécules conjuguées,planes et linéaires

Two general relation between bond orderl and bond distance d (Å) are proposed:

1. between atomssp ₂-hybridised of second and third row: $$d_{PQ} = \left[ {0,731 + 0,3181\left( {n_P + n_Q } \right) - 0,1477\left( {\zeta _P + \zeta _Q } \right)} \right] - 0,020 + 0,0523\left( {\zeta _P + \zeta _Q } \right)l_{PQ} $$ ,ζ=Z/n,Z=Slater's effective nuclear charge of theπ-orbital).
2. between atomssp-hybridised of the second row: $$d_{PQ} = \left[ {1,904 - 0,123\left( {\zeta _P + \zeta _Q } \right)} \right] - \left[ {0,075 + 0,023\left( {\zeta _P + \zeta _Q } \right)} \right]l_{PQ} $$ (l=total bond orderπ+π′).

     

A topological index for the totalπ-electron energy

A modified topological index \(\tilde Z_G \) is proposed to be defined as $$\tilde Z_G = \sum\limits_{k = 0}^{[N/2]} {( - 1)^k } a_{2k} $$ for characterising theπ-electronic system of a conjugated hydrocarbonG withN carbon atoms, wherea _2k is the coefficient of the characteristic polynomial ofG defined as $$P_G (X) = ( - 1)^N \det |A - XE| = \sum\limits_{k = 0}^N { a_k X^{N - k} } $$ with an adjacency matrixA and the unit matrixE. \(\tilde Z_G \) is identical toZ _G for a tree graph, or a chain hydrocarbon.Z _G increases with a (4n+2)-membered ring formation and decreases with a 4n-membered ring formation. The totalπ-electron energyE _π of the Hückel molecular orbital is shown to be related with \(\tilde Z_G \) asE _π =Cln \(\tilde Z_G \) . With this relation generalised and extended Hückel rules for predicting the stability of an arbitrary network are proved.