Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Mixed ligand complexes in vinyl polymerization-II: [NN-ethylenebis(salicylideneiminato)] (benzoylacetonato)cobalt(III) as an initiator

The polymerization of methyl methacrylate initiated by a mixed ligand complex. [NN-ethylenebis(salicylideneiminato)](benzoylacetonato)cobalt(III) has been studied in bulk and in benzene at 70° and 80°. The rate of polymerization is proportional to (concentration of the chelate)Image and the monomer exponent is close to 1.5. The activation energy and the kinetic and transfer constants are evaluated. A free radical mechanism has been proposed.

Structure-thermal behaviour studies on the salicylato complex of cobalt

The salicylato complex of cobalt was synthesized and its structure established to be [Co(sal)2] · 4 H2O, where, sal =, from elemental analysis, IR spectroscopy, magnetic susceptibility, cryoscopy and conductivity. The X-ray diffractogram of the complex has been given. Thermal decomposition has been studied in air by thermogravimetry (TG), differential thermal analysis and differential scanning calorimetry. TG shows three main steps of decomposition. The intermediates formed at various stages were collected and analysed. From the TG results and chemical analysis of the intermediates, a mechanism has been proposed for the thermal decomposition of the complex, leading to the oxide formation in the final stage.

Interaction of Metal Ions with 2'-Deoxyribonucleotides. Crystal and Molecular Structure of a Cobalt(l1) Complex with 2'-Deoxyinosine 5'-Monophosphate

The crystal structure of the cobalt( 11) complex with 2'-deoxyinosine 5'-monophosphate (5'- dlMP), [Co(5'-dlMP) (H,0),]-2H20, has been analysed by X-ray diffraction. The complex crystallizes in the space group P2,2,2, with a = 6.877(3), b = 10.904(2), c = 25.421 (6) A, and Z = 4. The structure was solved by the heavy-atom method and refined to an R value of 0.043 using 1 776 unique reflections. The cobalt ion binds only to the 6-oxopurine base of the nucleotide at the N(7) position, the octahedral co-ordination of the metal being completed by five water oxygens. The phosphate oxygens are involved in hydrogen bonding with the co-ordinated water molecules. The structure is closely similar to that of the corresponding ribonucleotide complex. The nucleotide has the energetically preferred conformation: an anti base, a C(3') -endo sugar pucker, and a gauche-gauche conformation about the C(4')-C( 5') bond. The significance of sugar puckering in the monomeric complexes of general formula [ M (5'-nucleotide) (H20),] is explained in terms of the structural requirements for metal-water-phosphate bridging interactions.

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.

Kinetics of vapour phase oxidation of furfural on vanadium catalyst

Vapour phase oxidation of furfural over vanadium pentoxide catalyst was studied using an isothermal flow reactor in the temperature range of 220–280°C. Maleic anhydride and carbon dioxide are found to be formed from furfural by a parallel reaction scheme. The following rate equation based on the two-stage redox mechanism—the substance to be oxidized reduces the catalyst which in turn is reoxidized by oxygen from the feed—is found to explain the data satisfactorily.The reoxidation of the reduced catalyst was found to be the rate controlling step.

Mixed ligand complexes in vinyl polymerization-II: [NN′-ethylenebis(salicylideneiminato)] (benzoylacetonato)cobalt(III) as an initiator

The polymerization of methyl methacrylate initiated by a mixed ligand complex. [NN′-ethylenebis(salicylideneiminato)](benzoylacetonato)cobalt(III) has been studied in bulk and in benzene at 70° and 80°. The rate of polymerization is proportional to (concentration of the chelate)1/2 and the monomer exponent is close to 1.5. The activation energy and the kinetic and transfer constants are evaluated. A free radical mechanism has been proposed.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Polymer supported metal complexes as catalysts for oxidation of thiosalts by molecular oxygen IV. Quaternised poly(4-vinyl pyridine) complexes with Cu2+ as template

Copper(II) complexes of quaternised poly(4-vinylpyridine) (PVP) of different degrees of quaternisation and copper content have been prepared by crosslinking the polymer with 1,2-dibromoethane in the presence of Cu2+ ion as template. The stability constant of the PVP---Cu(II) complexes is found to increase with the degree of crosslinking quaternisation of the resin, but the rate at which Cu2+ is adsorbed by the resin decreases. An optimum combination of both stability and rate can be achieved with a moderate degree (31%) of crosslinking. A kinetic study reveals that quaternisation increases significantly the catalytic activity of the complex for the oxidation of S2O2−3 by O2 compared with PVP----Cu(II) without quaternisation, but it deactivates the complex for the oxidation of both S3O2−6 and S4O2−6. The batch reactor oxidation kinetics at pH 2.16, where the rate is observed to be maximum, is well explained by the Langmuir—Hinshelwood model assuming the coordination of both O2 and thioanion to Cu(II) as a precursor to the oxidation reaction.

Natural frequencies of circumferentially truncated sector plates with simply supported straight edges

The classical Rayleigh-Ritz method in conjunction with suitable co-ordinate transformations is found to be effective for accurate estimation of natural frequencies of circumferentially truncated circular sector plates with simply supported straight edges. Numerical results are obtained for all the nine combinations of clamped, simply supported and free boundary conditions at the circular edges and presented in the form of graphs. The analysis confirms an earlier observation that the plate behaves like a long rectangular strip as the width of the plate in the radial direction becomes small.

Mixed ligand complexes in vinyl polymerization. I. [N,N-ethylenebis (salicylideneiminato)](acetylacetonato)cobalt(III) as an initiator

Polymerization of methyl methacrylate in the presence of a mixed ligand complex, [N,N-ethylenebis(salicylideneiminato)](acetylacetonato)cobalt(III) in benzene was studied. The rate of polymerization was proportional to the square root of the concentration of the chelate and the monomer exponent was 1.67 and 1.69 at 60 and 70°C, respectively. The activation energy and the kinetic and transfer constants were evaluated. A free-radical mechanism has been proposed.

An XPS study of the surface oxidation states of metals in some oxide catalysts

Calcined samples of chromia supported on Al2O3, ZnO, or SnO2 show both Cr(VI) and Cr(III) on the surface, Cr(VI) being preponderant in the case of Al2O3-supported catalysts. The proportion of Cr(VI) decreases with increase in Cr content of the calcined catalysts. Reduction of the supported chromia catalysts in H2 at 720 K for 1 hr gives rise to Cr(III) and Cr(V). On carrying out the dehydrogenation of cyclohexane on the chromia catalysts a higher proportion of Cr(V) is found than after treatment with hydrogen. Vanadia supported on Al2O3 or MoO3 shows significant proportion of V(IV) on carrying out the oxidation of toluene on the catalysts. Calcined MoO3 (10%)/Al2O3 shows only Mo(VI) on the surface at 300 K, but on heating to 670 K in vacuum shows the presence of a considerable proportion of Mo(V) which on cooling disproportionates to Mo(IV) and Mo(VI). Mo(V) is noticed on surfaces of this catalyst on reduction with hydrogen as also on carrying out dehydrogenation of cyclohexane. While Bi2MoO6 shows only Mo(VI) on the surface at 300 K, heating it to 670 K in vacuum changes it entirely to Mo(V) which then gives rise to Mo(IV) and Mo(VI) on cooling.

Kinetics of vapour phase oxidation of furfural on vanadium catalyst

Vapour phase oxidation of furfural over vanadium pentoxide catalyst was studied using an isothermal flow reactor in the temperature range of 220–280°C. Maleic anhydride and carbon dioxide are found to be formed from furfural by a parallel reaction scheme. The following rate equation based on the two-stage redox mechanism—the substance to be oxidized reduces the catalyst which in turn is reoxidized by oxygen from the feed—is found to explain the data satisfactorily. The reoxidation of the reduced catalyst was found to be the rate controlling step.

Catalyst effectiveness factor for redox model kinetic equation

A generalized isothermal effectiveness factor correlation has been proposed for catalytic reactions whose intrinsic kinetics are based on the redox model. In this correlation which is exact for asymptotic values of the Thiele parameter the effect of the parameters appearing in the model, the order of the reaction and particle geometry are incorporated in a modified form of Thiele parameter. The relationship takes the usual form: Image and predicts effectiveness factor with an error of less than 2% in a range of Thiele parameter that accommodates both the kinetic and diffusion control regimes.