Zur Bestimmung von Aluminiumhydroxyd und freier S?ure in Aluminiumsulfat und Alaunen

Ohne Zusammenfassung     

Thermodynamic Properties of NaCl Solutions at Subzero Temperatures

Heat capacities at infinite dilution of NaCl (aq) for the temperature range 0 to –25°C and apparent molar volumes at infinite dilution for 0 to –15°C have been estimated from a synthesis of experimental data collected at subzero temperatures. The parameters of the Helgeson–Kirkham–Flowers (HKF) equation for Na⁺ (aq) have been obtained, from which the Gibbs energies of Na⁺ and Cl^– have been calculated. The estimated values of Pitzer-equation parameters for thermal and activity-coefficient properties have been adjusted for subzero temperatures. The experimental phase diagram for the NaCl–H₂O system could be reproduced with these data, demonstrating the low-temperature applicability of the HKF model to extrapolate thermodynamic properties of aqueous-solution species at infinite dilution.     

Isolation of a diketone species that is allylically bound to tungsten, and its relationship to a tungsten η-ketone complex

The diketone complex [W(CO)₂(η-C₅H₄Me){η³-

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(H)---C(O)---C₅Me₅}] (3) was isolated from the reaction of PhC₂H with a mixture of [Ni(CO)I(η-C₅Me₅)] and [W(CO)₃(η-C₅H₄Me)]⁻. Complex 3 contains an organic diketone fragment that is bound in a π-allyl fashion to a tungsten atom. It was fully characterized by standard spectroscopic techniques and by a single-crystal X-ray diffraction study. The relationship of complex 3 to a structurally characterized cyclopentadienyl tungsten η²-ketone species 1, and the likelihood that 3 and the methylcyclopentadienyl analog of 1 share common intermediates, are discussed.     

The Structure of Gaseous Carbon Tetraiodide from Electron Diffraction and All Carbon Iodides,CIn (n = 1–4), and Their Dimers,C2I2n (n = 1–3) from High-Level Computation. Any Other Carbon-Iodide Species in the Vapor?

The geometry of a series of carbon iodides have been determined, CI₄ by gas-phase electron diffraction and CI _n (n = 1–4) and C₂I_2n (n = 1–3) by high-level quantum chemical calulations. The bond length of the tetrahedral CI₄ molecule from electron diffraction is (r _g):2.157(10) Å. The indication of about 20% I₂ in the vapor suggests partial decomposition and it has been thoroughly investigated what other carbon iodide species might be present beside CI₄. There is no appreciable amount of either of the dimeric species in the vapor phase, in spite of the suggestion from thermodynamics. On the other hand, the electron diffraction data are compatible with the presence of about 18% of either of the monomeric free radicals, CI₃ or CI₂, beside CI₄ and I₂. Possible reasons for these observations are discussed. Our correlated level computations, in agreement with other high level computations, found the singlet ¹A₁ state to be the ground state for CI₂. This is in contrast with a recent photoelectron spectroscopic study according to which the triplet state is the ground state though with a large margin of error (1 ± 3 kcal/mol energy difference). The computed singlet-triplet separation strongly depends on the level of the computation, but it is at least 9 kcal/mol. Geometrical parameters, singlet-triplet separations, and dipole moments have been calculated for the CX₂ series (X = F, Cl, Br, I, H) and their variations are discussed. The thermodynamic stability of different carbon iodide species has also been investigated.     

Nonattacking Queens in a Rectangular Strip

The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a polynomial and whose behavior can be described in some detail. We deduce this by converting the problem to one of counting lattice points outside an affinographic hyperplane arrangement, which Forge and Zaslavsky solved by means of weighted integral gain graphs. We extend their work by developing both generating functions and a detailed analysis of deletion and contraction for weighted integral gain graphs. For chess pieces we find the asymptotic probability that a random configuration is nonattacking, and we obtain exact counts of nonattacking configurations of small numbers of queens, bishops, knights, and nightriders.     

Outerplanar Thrackles

We show that a graph drawing is an outerplanar thrackle if and only if, up to an inversion in the plane, it is Reidemeister equivalent to an odd musquash. This establishes Conway’s thrackle conjecture for outerplanar thrackles. We also extend this result in two directions. First, we show that no pair of vertices of an outerplanar thrackle can be joined by an edge in such a way that the resulting graph drawing is a thrackle. Secondly, we introduce the notion of crossing rank; drawings with crossing rank 0 are generalizations of outerplanar drawings. We show that all thrackles of crossing rank 0 are outerplanar. We also introduce the notion of an alternating cycle drawing, and we show that a thrackled cycle is alternating if and only if it is outerplanar.