The numbers of chiral and achiral alkanes and monosubstituted alkanes

Whereas the theory for the enumeration of the optical isomers of the lakyl radicals and the alkanes has long been understood, this is not the case for the corresponding archiral isomers. We present for the first time recurrence formulae for counting the number of archiral isomers of the alkyl radicals and the alkanes. For chiral and archiral alkanes and monosubstituted alkanes, numerical results up to C₁₄ are tabulated.After presenting the history of the problem and the necessary definitions, we proceed to derive functional equations on the various generating functions, which readily yield the more explicit recurrence formulae usefule for numerical calculations. In the process, we first re-derive Pólya's expression for planted steric trees using his classical enumeration theorem. This result is then extended to the enumeration of free steric trees using the now standard tree-counting method due to Otter and known as a dissimilarity characteristic equation.By definition, a steric tree is a quartic tree (all points having degree 1 or 4) in which the four neighbors of every carbon point are given a tetrahedral configuration. Building on the methods of the first two authors for counting chiral and archiral trees in the plane, we obtain the formula for counting achiral steric trees, thus setting a problem first enunciated by van't Hoff and Le Bel in 1874.     

Reactions of Silver (I) salts in potassium halide matrices: A differential scanning calorimetry study

Reactions of AgCl, AgSO₄, and Ag₂CO₃ in and with pressed KCl, KBr, and KI disks as well as those of unpressed mixtures were followed by TG and DSC. Except for Ag₂CO₃ and Ag₂SO₄ in KI, the curves obtained were readily interpreted in terms of eutectic melting, decomposition, and complex formation.     

The interference of heteronuclear chromium(III) tartrate complexes in the EDTA titration of cobalt(II), copper(II), zinc(II) and cadmium(II)

When present together in solution, chromium(III) and tartrate can interfere seriously in the titration of Co(II), Cu(II), Zn(II) and Cd(II) with EDTA. Ternary (heteronuclear) tartrate complexes containing Cr(III) and bivalent metal ion in the ratio 1:1 are formed. The conditions for the formation of these complexes have been investigated. Cadmium(II) can be determined without interference by employing potentiometric end-point detection.     

Double-layer effects on simple electrode reactions II. The effects of specifically adsorbed anions and ion-pairing on the reduction of Eu3+ and Cr3+

The kinetics of the reduction of Eu³⁺ and Cr³⁺ at mercury electrodes have been studied in various mixed perchlorate electrolytes containing iodide, bromide, and p-toluene-sulfonate as adsorbing anions. Specific adsorption data were obtained by means of the constant ionic strength approach due to Hurwitz and Parsons. The rate enhancements observed in the presence of the first two (monatomic) anions were in good agreement with the predictions of the simple Frumkin model only when the experimental, rather than calculated diffuse-layer capacitances were employed in the data analysis. It was demonstrated that the effects of ion-pairing and ligand-bridging of the reactants with the adsorbing anions were negligible under the experimental conditions chosen. From experiments with these systems and also with weakly adsorbing chloride electrolytes it was concluded that ion-pairing did not enhance the electrochemical reactivity of either Eu³⁺ or Cr³⁺. The value of the analyses described in separating various contributions to the catalytic effects of adsorbing anions is emphasized.     

On the thin cell method in time domain spectroscopy

A simple physical picture is given of Fellner-Feldegg's thin cell method in time domain spectroscopy. From this picture an accurate analytical relation is derived for the total reflection coefficient.     

Possibilites et limites de l'analyse par activation neutronique multielementaire d'echantillons biologiques avec ou sans separation de la matrice activable

The possibilities and limits of the multi-elemental determinations in biological samples by neutron activation analysis with and without chemical separation are discussed.      

Intramolecular Diels-Alder reactions: Construction of aza- and diaza-steroid type skeletons

The preparation of 2-(4-phenyl)butadienyl-piperidine 5 is described. An intramolecular Diels-Alder reaction of the intermediately formed fumaramide thereof produces stereoselectively the tricyclic lactam 6 . Its structure, as well as the configurational relationship of its 5 asymmetric centers, is corroborated on the basis of the NMR.-data. Cycloacylation of the thermodynamically stable precursors 13 and 20 leads to pentacyclic aza- or diaza-steroid type skeletons. Their structures ( 14, 16 , and 21 ) and in particular their relative configurations are elaborated. A few qualitative kinetic aspects of this intramolecular (4+2)-cycloaddition are presented.     

Low temperature absorption spectra of TcO 4 − and ReO 4 − in KClO4

The low temperature spectra of TcO ₄ ^– and ReO ₄ ^– both show two band systems with pronounced vibrational structures. The bands are identified as¹ A ₁¹ T ₂ transitions. No other bands are observed with certainty. It seems likely that the KClO₄ crystals contain KReO₄ crystallites. They are therefore not pure mixed crystals. It is concluded that the virtual orbital (2e) used in the construction of the low lying states resembles an atomic nd orbital more and more when going from n=3, Mn to n=5, Re.

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Zusammenfassung Die Tieftemperaturspektren von TcO ₄ ^– und ReO ₄ ^– zeigen beide zwei Bandensysteme mit ausgeprägten Schwingungsstrukturen. Die Banden werden als ¹ A ₁¹ T ₂-Übergänge identifiziert. Keine anderen Banden werden mit Sicherheit beobachtet. Es scheint wahrscheinlich, daß die KClO₄-Kristalle KReO₄-Kristallite enthalten und deswegen keine reinen Mischkristalle sind. Es wird geschlossen, daß das virtuelle Orbital (2e), welches zur Konstruktion der tiefliegenden Zustände gebraucht wird, in der Reihe n=3, Mn bis n=5, Re immer weitgehender einem nd-Atomorbital ähnelt.

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Nachwuchsstipendiat, Schweizerischer Nationalfonds.     

Pretreated bright palladium electrode in potentiometric redox titrations Titration of Cr(2)O(7)(2-) and Ce(4+) with Fe(2+)

The behaviour of the bright palladium electrode toward the redox systems Cr(2)O(7)(2-)/Fe(2+) and Ce(4+)/Fe(2+) (in potentiometric titration) has been investigated as a function of pretreatment of the electrode. Anodization of the electrode at potentials higher than 800 mV increases DeltaE at the equivalence point by 300-400 mV for the dichromate titration. The sharp change in potential is due to the reaction between PdO(2) and Fe(2+). The equivalence point corresponds to the beginning of the potential drop, rather than the inflexion point, especially for dilute solutions. If the electrode is ignited before use the surface oxide PdO is oxidized to PdO(2) by Cr(V), the potential increases during the titration and DeltaE is 200 mV bigger than when an untreated electrode is used. In the titration of Ce(4+) with Fe(2+) the DeltaE is largest with untreated electrodes, and if the anodized electrode is used, the titration curves clearly show the reaction between PdO(2) and Fe(2+).     

Purine N-oxides—XLI : The 3-acyloxypurine 8-substitution reaction: On the mechanism of the reaction

The 3-acyloxypurine 8-substitution reaction involves elimination of the 3-acyloxy group and nucleophilic substitution at C-8 to yield 8-substituted xanthines or guanines. In aqueous solutions the reaction of 3-acetoxyxanthine proceeds slowly below pH 2, but is greatly accelerated with an increase of the pH from 3 to 7. It is proposed that the slow reaction involves heterolytic cleavage of the 3-acetoxy moiety from 3-acetoxyxanthine to yield a nitrenium ion at N-3 followed by intermolecular nucleophilic substitution of the incipient carbonium ion at the allylic C-8 position, also the most probable mechanism in polar aprotic solvents. The beginning of the fast reaction coincides with the beginning of ionization of the imidazole hydrogen of 3-acetoxyxanthine. It is proposed that this ionization induces a similar but more rapid departure of the 3-acetoxy group from the anion of 3-acetoxyxanthine to produce dehydroxanthine. The latter, upon protonation, yields the same reactive carbonium ion at C-8 that is formed in the slow reaction. Some reduction of 3-acetoxyxanthine to xanthine accompanies the fast reaction. That reduction has the characteristics of a free-radical mediated reaction. It is proposed that reduction results from a homolytic cleavage of the NO bond in the 3-acetoxyxanthine anion to produce a radical-anion, which abstracts hydrogen from water to yield xanthine. These reaction mechanisms and possible alternatives are evaluated.