Intrinsic adsorption properties of CO2 on 5A and 13X zeolite

Data for the adsorption of CO₂ on 5A (CaA) and 13X (NaX) zeolite are critically evaluated. In addition, fresh data for the adsorption of CO₂ on 13X zeolite is reported. Three intrinsic properties are examined: q _max , the saturation loading, K _H , the Henry constant, and (?ΔH) _q , the isosteric heat of sorption. Below a reduced temperature T _r , of 0.9, the q _max values for both 5A and 13X zeolites are similar to theoretical values that may be derived using zeolitic crystallographic properties and the sorbate density calculated using the Rackett equation. For the region 0.9 ≤ Tr ≤ 1.0, the calculated q _max values exceed the theoretical values similarly calculated, indicating that the molecules have a smaller molar volume than in a similar liquid phase. This is a similar result to that observed in ionic liquids. Linear regressed equations are derived for q _max for the region 0.9 ≤ Tr ≤ 1.25. The Henry constant values for 5A are remarkably consistent for the five studies examined, with a correlation coefficient, R, of 0.999 for the van’t Hoff equation, but for the seven studies examined in 13X the data is more disperse as indicated by a correlation coefficient R of 0.899 for the van’t Hoff equation. The values of (?ΔH) _q , the isosteric heat of sorption are in agreement with the literature. An explanation is advanced for the discrepancy between the higher heats of sorption values obtained calorimetrically from those obtained from isosteric adsorption studies. Finally, the fresh data is observed to fit the Toth model with regression coefficients of 0.999. However, the parameters obtained for the Toth equation by regression are significantly different from the intrinsic properties derived earlier, indicating the difficulty of deriving intrinsic parameters from isotherm fits.     

Stereoisograms for reorganizing the theoretical foundations of stereochemistry and stereoisomerism. Part 3: rational avoidance of misleading standpoints for pro-R/pro-S-descriptors

The stereoisogram approach is introduced to settle the misleading terminology due to ‘prochirality’ in modern stereochemistry. After the term prochirality is redefined as having a purely geometric meaning, a method based on probe stereoisograms and another method based on equivalence classes (orbits) are introduced to determine prochirality and/or pro-RS-stereogenicity. Enantiotopic and RS-diastereotopic relationships appearing in probe stereoisograms are respectively used to determine prochirality and pro-RS-stereogenicity, where ‘stereoheterotopic’ relationships used in modern stereochemistry are abandoned. Alternatively, an enantiospheric orbit for specifying prochirality and an RS-enantiotropic orbit for specifying pro-RS-stereogenicity are emphasized by using coset representations and Young tableaux. The pro-R/pro-S-system is clarified to be based on pro-RS-stereogenicity and not on prochirality.     

Theory of electrode reactions of redox couples confined to electrode surfaces at monolayer levels: Part II. Cyclic voltammetry and ac impedance measurements

The expression of the current-potential relationship derived in Part I for simple one-step surface redox-electrode reactions of the species confined to electrode surfaces is applied to cyclic voltammetry and the method of faradaic impedance measurements. A method to obtain cyclic voltammograms is presented for a quasi-reversible or general case and equations for reversible and irreversible cyclic voltammograms are derived. The effect of the interaction parameters, W/RT and ΔW^≠/RT, kinetic parameters, Λ and α, and coordination number z on the waveform of the cyclic voltammograms is discussed. An interesting feature in the voltammograms, i.e. the appearance of two peaks, is predicted when W/RT < −2.19 for z = 6 in spite of the simple one-step redox process. Furthermore, equations for the faradaic resistance and capacitance are derived and it is shown that the faradaic impedance is independent of the frequency of ac perturbation.     

Rectangular source integral and recurrence relations

In this paper Hubbell's rectangular source integral H′(a,b), which is a double integral, is expressed as a series of many converging single integrals I_n (a,b). Recurrence relations relate these integrals. Once one integral I₁ is computed, recurrence relations are used to compute other integrals. I₁(a,b) can be computed analytically. H′(a,b) is approximated by considering the first seven terms in the series and the results are found to give good results for various values of a and b. Results are presented for the values of a and b (0.1 to 20 and to 2), respectively. The rate of convergence depends on the values of a and b.     

Recurrent relations for the approximation of the physicochemical constants of homologues

In addition to the earlier revealed physicochemical constants of homologues whose changes in arbitrary series obey the simplest linear recurrent relations A (n + k) = aA(n) + b, such equations are shown to be applicable to the approximation of the solubility of organic compounds in water (k = 1), temperature dependences of the solubility of organic and inorganic compounds in water (k = ΔT), and nematic-isotropic phase transition temperatures for liquid crystals (k = 2). The a and b coefficients of linear recurrent relations are only determined by the nature of the homologous difference, and, if the homologous difference is the same, they are close for different series. This enables various properties of virtually arbitrary organic compounds to be described by unified recurrent equations, which is equivalent to the existence of a general method for their calculation. For continuous properties (for the example of the temperature dependence of solubility), a method for solving recurrent equations with nonintegral or nonequidistant argument values is suggested.     

End-point construction and systematic titration error in linear titration curves-precipitation reactions

The systematic titration error which is introduced by the intersection of tangents to hyperbolic titration curves is discussed for precipitation reactions. A simple expression for the systematic titration error is derived, and S/C_x² is proposed as a measure of the sharpness of the titration curve. The effects of the conditional solubility product (S), the concentration of the unknown component (C_x), and the ranges used for the construction of the end-point, are considered. A graphical method is presented for the selection of pairs of ranges which result in small systematic titration errors. For equal values of S/C_x² and 1/KC_x, the optimum combinations of ranges are different for precipitation and complexation titrations. The differences are not large for values smaller than about 0.002. For titration curves with a reversed L-shape, the error is calculated when the end-point is constructed by the intersection of the tangent to the second branch of the curve with volume axis; in this case equal ranges result in the same titration error for equal values of S/C_x² and 1/KC_x. The systematic titration error is equal to -S/C_x² when the tangent to the curve is taken at f_a = 3.0.     

Structural chemistry of Ba2CdS3, Ba2CdSe3, BaCdS2, BaCu2S2 and BaCu2Se2

The structures of all compounds were determined from three dimensional single crystal X-ray diffraction data and refined by least squares. Ba₂CdS₃ and Ba₂CdSe₃ are isostructural, Pnma, a = 8.9145(6)Å, b = 4.3356(2)Å, c = 17.2439(9)Å for the former compound and a = 9.2247Å, b = 4,4823(6)Å, c = 17.8706(11)Å for the latter, z = 4, R = 0.0751 and R = 0.0462, respectively. The compounds are isostructural with the previously reported Mn analogues and with K₂AgI₃. Cd ions are in tetrahedral environment and the tetrahedra form infinite linear chains by corner sharing. Ba ions are in 7-fold coordination in which 6 anions form a trigonal prism and 1 anion caps one of the rectangular faces. BaCdS₂, Pnma, a = 7.2781(3)Å, b = 4.1670(1)Å, c = 13.9189(6)Å, z = 4, R = 0.0685. Cd ions can be considered to have a triangular planar coordination with CdS distances of 2.47 and 2.53 Å (twice). Two additional S ions are at 2.89 and 3.22 Å to complete a triangular bipyramidal configuration. Ba is in 7-fold coordination with the anions forming a trigonal prism which is capped on one rectangular face. The compound is isostructural with BaCdO₂ and is related to the structure of BaMnS₂. BaCdSe₂ could not be prepared. BaCu₂S₂ and BaCu₂Se₂ are isostructural, Pnma, a = 9.3081(4)Å, b = 4.0612(3)Å, c = 10.4084(5)Å for the sulfide and a = 9.5944(6)Å, b = 4.2142(4)Å, c = 10.7748(8)Å for the selenide, z = 4, R = 0.0634 and 0.0373, respectively. Ba ions are in the usual 7-fold, capped hexagonal prism, coordination. However, 9 Cu ions also can be considered to form a trigonal prism with all rectangular faces capped, around Ba since the BaCu distances range from 3.24 to 3.54 Å for the sulfide and from 3.37 to 3.67 Å for the selenide. One of the Cu ions is in a very distorted tetrahedral environment and the second one is located in a more regular tetrahedral configuration of the anions. Two independent infinite chains of tetrahedra are present. They are formed by sharing of two adjacent edges of each tetrahedron and then these chains in turn are linked by corner sharing into a three-dimensional network of tetrahedra.     

He− formation by two- and three-electron capture

Spin flip cross-section for the polarized electron and unpolarized hydrogen like ion scattering are reported. In solving the problem the spin-orbit interaction is included in the Hamiltonian for non-zero projectile angular momentum. Contribution ofs-wave is obtained by solving the static exchange equation. Results for the spin flip cross-section have been obtained from nuclear chargeZ=6 toZ=16, and to see the relativistic effect the spin flip cross-section is calculated forZ=80. At low values ofZ thes-wave contributions are most dominant. For largeZ the contribution of spin-orbit is not insignificant.     

Influence of X-ray tube spectral distribution on uncertainty of calculated fluorescent radiation intensity

The relative radiation intensity (R_i) defined as fluorescent radiation intensity of analyte in specimen to fluorescent radiation intensity of pure element or compound, e.g., oxide is used in calculation in both fundamental parameter methods and in theoretical influence coefficient algorithms. Accuracy of calculated R_i is determined by uncertainties of atomic parameters, spectrometer geometry and also by X-ray tube spectral distribution. This paper presents the differences between R_i calculated using experimental and theoretical X-ray tube spectra evaluated by three different algorithms proposed by Pella et al., Ebel, and Finkelshtein–Pavlova. The calculations are performed for the most common targets, i.e., Cr, Mo, Rh and W. In this study, R_i is calculated for V, Cr, Mn, Fe, Co, Ni, Cu and Mo in steels as an example. The differences between R_i calculated using different X-ray tube spectrum algorithms are presented when pure element standard, multielement standard similar to the analyzed material and one pure element standard for all analytes is used in X-ray fluorescence analysis. The differences between R_i for intermediate-thickness samples (and also for thin films) and for X-ray tube, which ran for many hours, are also evaluated.     

Large atomic natural orbital basis sets for the first transition row atoms

Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu atoms. The primitive sets are taken from the large sets optimized by Partridge, namely (21s13p8d) for Sc and Ti and (20s12p9d) for V to Cu. These primitive sets are supplemented with threep, oned, sixf, and fourg functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d ⁿ 4s ² and 3d ⁿ⁺¹4s ¹ occupations. For Ni, the¹ S(3d ¹⁰) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.     

An alternative way to analyze the electron distribution in ab initio calculations

An alternative method is proposed to analyze the electron distribution in molecules. Explicit formulae are given to calculate the number of electrons N(S) in a sphere with radius S and the spherically averaged electron density ?_o(S) around any center for gaussian-type functions. Also the formulae for the number of electrons in a parallelepiped are given. The calculated electron number in a sphere and in a parallelepiped can be compared with experimental values determined by X-ray analysis. The plots of N(S) and ?_o(S) against S are one-dimensional ways to represent the electron distribution in molecules. Several examples of possible applications are shown for some hydrides.     

La methode polarovoltrique : Principes généraux et bases de la méthode

The various steps in the development of the polarovoltric method and its utilisation in an automatic titration apparatus employing 2 polarized platinum electrodes are described. The method is based on the use of 2 types of polarization relationships applied to different chemical systems. These relationships are of the type I = f(V) and V = f(U), where V is the potential measured at the electrodes and U the potential applied to the electrodes across a resistance R, and are obtained directly from 2 indicating electrodes without the need for a reference electrode.The advantage of these relationships over the classic I= f(E) curves, where E is the potential of the indicating electrode with respect to a reference electrode, is to facilitate the prediction of the titration curves as a function of the resistance R and the applied voltage U. The use of these relationships has shown that a fixed applied voltage U of 3 V and a fixed series resistance R of 0.5 megohm are the most suitable for a differential polarovoltmeter for semi-automatic titrations.A symbolic notation is described which indicates the origin of the observed variations in potential. This notation permits a simple interpretation of polarovoltric curves and the rational use of unsymmetrical electrode arrangements.     

Infrared band intensities: a comparative study of the transition moment matrix elements for the fundamental and overtones: Part II. Application to CO,HCl and OH

The various expressions considered in Part I for the transition moment matrix elements of fundamental and first two overtones are applied to carbon monoxide. The coefficients a_ij in the expressions R^io = Σa_ijp_j (where R^io is the transition moment integral for the O → i vibrational transition and p_j is the dipole moment derivative ?^jP/?XXX^j, XXX = (r — r_e)/r_e, r_e is equilibrium bond distance) are reported for i,j = 1, 2, 3. It is found that these coefficients do not vary by more than 5% when compared for the same i,j values in various expressions irrespective of the most exhaustive treatments used in deriving the original expressions. On the basis of the values of the coefficients obtained for CO, generalisations have been suggested on the effects of inclusion of mechanical and electrical anharmonicity to the intensities of fundamental and first two overtones. It is generally observed that the contribution of p'₁, is about 100 fold more than the contribution of p'₂, for R¹⁰. On the other hand the contributions of p'₁, and p, for R²⁰ and R³⁰ are of nearly equal magnitude but opposite in sign. The contribution of p'₁ to R¹⁰ is much higher than its contribution to R²⁰ and R²⁰. The various observations lead us to conclude that, whereas the effect of inclusion of mechanical anharmonicity on the intensity of the fundamental band is negligible, this effect is almost comparable to the effect of inclusion of electrical anharmonicity for the first two overtones. Simple forms of the a_ij expressions are applied to HC1 and OH to demonstrate the effect of variation of molecular constants on the a_ij values. On the basis of the observed trend in the values of these coefficients for CO, HCl and OH general remarks on the effects of hydrogen bonding on IR band intensities are given.     

Bound state energies for the exponential cosine screened Coulomb potential

The energy eigenvalues of bound states of an electron in the general exponential cosine screened Coulomb potential are obtained using the shifted 1/N expansion method. The energies for the states from 1s to 8k are calculated from six to eight significant figures. The energy eigenvalues for the 1s, 2s – 2p, 3s – 3d, and 4s – 4f states are also presented as a function of the screening parameter λ. Results are compared with the ones obtained by other workers. The agreement reduces roughly for large λ. It is also observed that the convergence of the expansion series increases remarkably asl increases.     

Electron tunneling in solid phase redox reactions. Experimental values of parameters characterizing the rate of tunneling and theoretical models for long range electron transfer

The problem of the quantitative analysis of the kinetic data for the tunnel electron transfer reactions in solids is discussed. Various procedures are considered with the help of which one can determine from the experimental data the parameters v and a in the equation w = v exp (?2r/a) describing the dependence of the electron tunneling frequency w on the distance r between the reacting particles. For numerous tunnel reactions studied in the literature these parameters are calculated and their values are analyzed in terms of theoretical models of electron tunneling. The physical background of these models is discussed in detail to make it more understandable for experimentalists. The limits of applications for these models are discussed. A novel model for nuclear motion in the process of electron tunneling is proposed to account for the unusually high values of the frequency factor found for some of the reactions.     

Compared electronic structures of negative ionsM p C n − : II. Transition metals in Hückel theory

SIMS experiments on transition metal carbides produce negative cluster ionsM _p C _n ^? (n < 10) where the transition metalM is Ti, Zr, V, Cr, W, Fe and Ni withp=1 and V withp=2. TheM _p C _n ^? ions show very pronounced alternations in their emission intensities I(M _p C _n ^? ) versusn with strong maxima for evenn whateverM. Since such phenomena are due to the stability properties of the clusters themselves (correspondence rule), it means that the negative ions are the most stable ones for evenn. It is thus possible to get the general outlines of their electronic structures from the Pitzer and Clementi model (sp hybridization in Hückel approximation): the clusters are assumed to be linear chains of “cumulene”-type :=C=..C=C=M and the alternations in the relative stabilities of these chains are due to the fact that the HOMO (highest occupied molecular orbital) of the clusters lies in a double degenerate π level band. Now HOMO may be either full (or almost full) or half-filled (or nearly half-filled), and an aggregate with a complete (or almost complete) HOMO is more stable than an aggregate with a half-filled HOMO. Consequently, the number of π electrons is governing the parity effect in the stability alternations. However, this number is depending on the number of σ electrons of the chain and on the existence of onedδ level (due to theM atom) which is either empty for deficientd electron elements (Ti, Zr, V, Cr, W) or filled for richd electron elements (half-filled for Fe or full up for Ni). As theMC _n ^? chain must have a full (or nearly full) HOMO ifn is even, it is then possible to infer a likely electronic configurations of these clusters, and hence to determine their relative stabilities, and to verify that “even” clusters are more stable than “odd” ones. Thus such Hückel model results can be used as a guide for more sophisticated calculations (ab initio, etc...).     

Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase

Costas, M. and Sanctuary, B.C., 1984. Equation of state molecular parameters for a theory of pure r-mer fluids in the liquid phase. Fluid Phase Equilibria, 18: 47–60.Equation of state parameters for a theory of pure r-mers (Costas and Sanctuary, 1981) are presented for sixty common substances. The equation of state is tested for its ability to reproduce and predict thermodynamic data in the liquid phase. The theory has only two adjustable parameters: ν^*, the close-packed volume of the r-mer, and ?^* = z?/2, where ? is the nonbonded mer-mer attractive interaction energy and z is the lattice coordination number, set to be a constant equal to 12. The number of r-mers per molecule, r, is also fixed for a given liquid to be equal to the number of atoms in the molecule other than hydrogen. The fitting proceduce is fast and simple. The adjustment only involves the use of widely available density data. Comparisons between experimental and calculated first- and second-order thermodynamic properties are shown for several substances. A comparison with the equation of state due to Jain and Simha (1981) for PVT data for n-dodecane is presented. The theory qualifies as a useful tool, especially in engineering applications, for estimating thermodynamic properties in the liquid phase.     

Dinucleotides of 4′-C-vinyl- and 5′-C-allylthymidine as substrates for ring-closing metathesis reactions

Thymidine derivatives containing a 4′-C-vinyl group or a 5′-C-allyl group are synthesized and used as building blocks for three different dinucleotides. These are evaluated as substrates for ring-closing metathesis cyclisations, and a protected 5′-C-allylthymidine homo-dimer is found to be the most reactive. A protected precursor for a conformationally restricted cyclic dinucleotide with a four carbon 5′-C to 5′-C connection is hereby efficiently obtained, whereas a corresponding three carbon 4′-C to 5′-C connection is obtained in a lower yield.     

Die Berechnung komplexer Absorptionsgleichgewichte ionogener Substanzen in wäßrigen Lösungsmitteln mit Hilfe eines Reaktionsmodells

The solubility of ionogen substances in water and aqueous ionic solutions is important for calculation of absorption processes. Aqueous solutions with complex reaction systems behave themselves extremely nonideal. In simple cases equilibria can be determined with the concept of nonideal thermodynamics. The model used in this work is based on ideal calculation of reaction equilibria and gas solubility. The model parameters (equilibrium constants andHenry constants) for the systems SO₂-H₂O,MEA-H₂S-H₂O,DEA-H₂S-H₂O andMEA-CO₂-H₂O are computed by regression of experimental data. Equilibrium reactions are selected according toBrinkley's method. The selection of the reacting species has decisive influence on the accuracy of the data fitting. Data regression is done numerically and leads to the formulation of nonlinear systems of equations, which have to be solved for each data point. This solutions are performed in an inner loop. By using the maximum-likelihood-principle the model parameters are optimized in the superior regression loop. Experimental data for the regression are the partial pressure and the total concentration of gas in the liquid phase. The used model is able to fit these data satisfactoryly. The model parameters, which are calculated from simultaneous data regression for different temperatures, ensure a simple correlation ofvan't Hoff. However, for similar reactions equilibria in different reaction systems, it is impossible to compute the same values for the equilibrium constants.