The mechanism of pyridine hydrogenolysis on molybdenum-containing catalysts : III. Cracking, hydrocracking, dehydrogenation and disproportionation of pentylamine

The conversion of pentylamine on a MoO3-Al2O3 catalyst was studied between 250 and 350 °C, at various hydrogen pressures. The reactions observed were cracking to pentene and ammonia, hydrocracking to pentane and ammonia, dehydrogenation to pentanimine and butylcarbonitrile, and disproportionation to ammonia and dipentylamine.\ud \ud The equilibrium between pentylamine, dipentylamine and ammonia appeared to be established under most of the experimental conditions. The equilibrium constant is about 9 at 250 °C and about 5 at 320 °C. The disproportionation reaction is zero order in hydrogen and of −1 order in the initial pentylamine pressure.\ud \ud Dehydrogenation was observed at low hydrogen pressures, and especially at higher temperatures; the reaction is first order in pentylamine.\ud \ud Both cracking and hydrocracking take place, mainly above 300 °C. Hydrocracking appears to be half order in hydrogen; the rate of cracking is almost independent of the hydrogen pressure. The hydrocarbon formation is of zero order in pentylamine or dipentylamine.\ud \ud The same type of reactions (except hydrocracking) take place on alumina, but with a far lower reaction rate

On the construction of global models describing rotating bodies; uniqueness of the exterior gravitational field

The problem of constructing global models describing isolated axially symmetric rotating bodies in equilibrium is analyzed. It is claimed that, whenever the global spacetime is constructed by giving boundary data on the limiting surface of the body and integrating Einstein's equations both inside and ouside the body, the problem becomes overdetermined. Similarly, when the spacetime describing the interior of the body is explicitly given,the problem of finding the exterior vacuum solution becomes overdetermined. We discuss in detail the procedure to be followed in order to construct the exterior vacuum field created by a given but arbitrary distribution of matter. Finally, the uniqueness of the exterior vacuum gravitational field is proven by exploiting the harmonic map formulation of the vacuum equations and the boundary conditions prescribed from the matching.Comment: Latex, 10 pages, no figure

The mechanism of pyridine hydrogenolysis on molybdenum-containing catalysts : IV. The conversion of piperidine

The conversion of piperidine was investigated on a CoO-MoO3-Al2O3 catalysts as a function of the temperature, reaction time, initial piperidine partial pressure and the hydrogen pressure.\ud \ud At 60 atm of hydrogen and conversions below 50% piperidine is selectively converted to ammonia and N-pentylpiperidine. This reaction appears to be a two-step process, ring-opening to pentylamine followed by a fast alkyl transfer from pentylamine to piperidine. The piperidine conversion is first order in piperidine as well as in hydrogen, and of -1 order in the total pressure of the nitrogen bases.\ud At higher conversions the rate of formation of pentane and ammonia are influenced by the rate of the (hydro)cracking steps, and also by the equilibrium constants of the alkyl transfer equilibria. The rate of a (hydro)cracking reaction is lower when a ring is present in the nitrogen base. The activation energies of these reactions were 160 kJ mol−1, about 60 kJ mol−1 greater than those of alkyl transfer reactions.\ud At 1 atm of hydrogen the product composition was completely different from that observed at higher pressures of hydrogen.\ud The mechanism of the reactions is briefly discussed

Singularity-Free Cylindrical Cosmological Model

A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic.Comment: LaTeX 2e, 8 page

Monolayer- and crystal-type MoO3 catalysts: Their catalytic properties in relation to their surface structures

Various MoO3 catalysts have been prepared by means of adsorption of molybdenum on supports from molybdate solutions or from the gas phase. Complete monomolecular layers of Mo6+ oxide can be prepared on the carriers Al2O3, Cr2O3, TiO2, CeO2, and ZrO2, whereas on SiO2 crystallites of MoO3 are formed. Reduction experiments show that the higher valencies of Mo are stabilized in the case of a monomolecular layer. Alcohol dehydration, pentene hydrogenation, and poisoning of these reactions with pyridine reveal that MoO2 present as a monolayer is less acidic than crystalline MoO2. On the complete monolayer catalysts investigated, mostly more than 70% of the dehydration and hydrogenation activities can be correlated with sites showing a relatively high acidity which are equivalent to 10–20% of the Mo content. The CO oxidation rates on the oxidized catalysts are antiparallel to those of the reactions on the reduced ones mentioned above; relatively basic sites preferentially chemisorb CO. The conclusion is that the activity pattern of the catalysts is a function of the acidity of the supports. It is suggested that Mo5+ ions contribute to the formation of the active acid sites after reduction with hydrogen

The influence of the precipitation rate on the properties of porous chromia

The properties were studied of heated (320°C) chromia samples, prepared by two precipitation methods: \ud \ud 1. (1) addition of ammonia to chromium salt solutions,\ud 2. (2) OH− formation in chromium salt solutions through hydrolysis of urea.\ud \ud Samples formed by means of the first method are macro or mesoporous and have a lower specific surface area (~200 m2·g−1) than those formed by urea hydrolysis (~300 m2·g−1). Only in the case of a very slow addition of the ammonia solution these properties of the chromia's become equal. Experiments show that the micro porous type samples with high surface area are only formed if the pH range 5.1 to 5.7 is passed slowly. The formation of polychromium complexes of uniform size is suggested.\ud \u

Generalisation of the Einstein-Straus model to anisotropic settings

We study the possibility of generalising the Einstein--Straus model to anisotropic settings, by considering the matching of locally cylindrically symmetric static regions to the set of $G_4$ on $S_3$ locally rotationally symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry are only possible for a restricted subset of the LRS models in which there is no evolution in one spacelike direction. These results are applied to spatially homogeneous (Bianchi) exteriors where the static part represents a finite bounded interior region without holes. We find that it is impossible to embed finite static strings or other locally cylindrically symmetric static objects (such as bottle or coin-shaped objects) in reasonable Bianchi cosmological models, irrespective of the matter content. Furthermore, we find that if the exterior spacetime is assumed to have a perfect fluid source satisfying the dominant energy condition, then only a very particular family of LRS stiff fluid solutions are compatible with this model. Finally, given the interior/exterior duality in the matching procedure, our results have the interesting consequence that the Oppenheimer-Snyder model of collapse cannot be generalised to such anisotropic cases.Comment: LaTeX, 24 pages. Text unchanged. Labels removed from the equations. Submitted for publicatio

The mechanism of pyridine hydrogenolysis on molybdenum-containing catalysts : II. Hydrogenation of pyridine to piperidine

The kinetics of pyridine hydrogenation was studied at high hydrogen pressures on a Mo-Al oxide and a Co-Mo-Al oxide catalyst. The rate equation was found to be r = kPpyrPH2n/Ppyro, in which n is 1.5 at 300 and 375 °C and 1.0 at 250 °C. This rate equation can be derived assuming strong adsorption of pyridine and its products with identical adsorption constants.\ud The (hydro)cracking of piperidine appears to have a low order in hydrogen, probably lower than 0.5.\ud The adsorption behavior of nitrogen bases and hydrogen on alumina and the molybdenum-containing catalysts was investigated by the gas chromatographic method. The adsorption of the nitrogen bases appeared to be very strong on both catalysts, and varied in the order piperidine > pyridine > ammonia.\ud Hydrogen also showed a strong adsorption. Hydrogen and nitrogen bases appeared to adsorb on different sites

The nature of the potassium compound acting as a promoter in iron-alumina catalysts for ammonia synthesis

The chemical form of the potassium promoter on an iron-alumina catalyst during ammonia synthesis has been studied by two methods, viz, (i) the measurement of the equilibrium constant of the process KNH2 + H2 KH + NH3, and (ii) chemical analysis of the used catalyst. The equilibrium constant measurements gave K723 = (12.9 ± 0.5) × 10−3, ΔHf2980(KNH2) = −119 ± 3 kJ mol−1 and S2980(KNH2) = 109 ± 4 J mol−1 K−1. The chemical analysis showed that no KNH2 is present on the catalyst during synthesis. From these results and with the aid of thermodynamic considerations it is concluded that KNH2, K and K2O are not stable compounds under conditions of ammonia synthesis. X-Ray diffraction showed that part of the potassium reacts with Al2O3, probably leaving part of the potassium in the form of KOH which is quite stable under ammonia synthesis conditions

On marginally outer trapped surfaces in stationary and static spacetimes

In this paper we prove that for any spacelike hypersurface containing an untrapped barrier in a stationary spacetime satisfying the null energy condition, any marginally outer trapped surface cannot lie in the exterior region where the stationary Killing vector is timelike. In the static case we prove that any marginally outer trapped surface cannot penetrate into the exterior region where the static Killing vector is timelike. In fact, we prove these result at an initial data level, without even assuming existence of a spacetime. The proof relies on a powerful theorem by Andersson and Metzger on existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor change