Half-order Kinetics Research Articles

A Simplified Analysis of Reaction and Mass Transfer in UASB and EGSB Reactors

The paper is focused on the study of the hydrodynamics, reaction kinetics and mass transfer in lab-scale Upflow Anaerobic Sludge Blanket (UASB) and Expanded Granular Sludge Bed (EGSB) reactors treating wastewaters with low volatile fatty acids concentrations. The fluid pattern in the UASB approached a plug-flow reactor because of the low turbulence provided by the upflow velocity and gas production. The EGSB behaved as a continuous-stirred tank reactor due to the effects of the high recirculation rate. Liquid film mass transfer resistance seemed negligible in the EGSB but important in the UASB reactor. This should be the consequence of the different hydrodynamic conditions in the two reactors. The rate of acetate degradation was best fitted by an apparent half-order kinetics in both reactors. Internal mass transfer limitations, associated to an intrinsic zero-order kinetics, was detected in the degradation of low acetate concentrations by the granular biomass.

Applicability of the UV-Stimulated Oxidation to Tritium Cleanup

The rate of the UV-stimulated HT oxidation was studied in H{sub 2}(HT)-O{sub 2}-O{sub 3} atmospheres with excess O{sub 3}. The concentration of HTO increased linearly with UV irradiation time. The formation rate of HTO was estimated to be 3.4 x 10{sup -2} Bq cm{sup -3} s{sup -1}, which was about 14000 times greater than that of the UV-stimulated HT oxidation in the H{sub 2}(HT)-O{sub 2} atmosphere. Namely the excess O{sub 3} greatly assisted the UV-stimulated HT oxidation. The HTO formation obeyed the half order kinetics to hydrogen pressure and 0.7 order with respect to photon flux. Computer simulation consisting of 33 elementary reactions was employed to make clear the mechanism of the HT oxidation. The computer simulation reproduced the same hydrogen pressure and photon flux dependences as the experimental results. It was revealed that the main path for HTO formation is as follows: (1) HT oxidation is initiated by photolysis of O{sub 3} to O({sup 1}D) radicals; (2) O({sup 1}D) radicals react with H{sub 2}(HT) to form OH(OT) radicals; and (3) OH(OT) radicals produce H{sub 2}O(HTO) by the reaction with H{sub 2}(HT). On the basis of computer analysis, it is concluded that the considerable increase in the rate of HTOmore » formation is due to the increase in O({sup 1}D) production in the presence of O{sub 3}. The present results suggest that the O{sub 3}-assisted UV-stimulated HT oxidation is expected to be applicable to non-catalytic oxidation of tritium in thermonuclear fusion reactors. 8 refs., 6 figs., 1 tab.« less

The treatment trilogy of floating filters: from pilot to prototype to plant

The basic kinetic expressions developed in non-aerated biofilms (denitrification and RBCs) were verified on granular floating media in aerated filters. The limiting parameters of biofilms were verified on a small scale lab unit, using wastewater and media from full scale. It could be shown that the observed relationships corresponded to theoretical expectations and half-order kinetics as well as the significant constants were established. Maximum surface removal rates were measured as 1.7 g N-NH4/m2 d for nitrification, and the most limiting parameter was a half-order oxygen concentration close to saturation. Similar kinetics as on small scale were observed on a full-scale prototype of a new floating aerated biofilter, which can be used for both nitrification and denitrification, as well as complete nitrogen removal from settled wastewater in one reactor. The mixed biofilm nitrified 15 % less than pure tertiary treatment, and 20 % performance was lost between lab and full scale, due mainly to aeration limitations. Also, 35 % lower denitrification rates were observed between ethanol and sewage as carbon source, but addition of ethanol raised the full-scale performance to nitrate removal rates of 1,4 g N-NO3/m2 d. After pilot testing and full-scale demonstration, the process was implemented on several treatment plants, one of which was located in Denmark, to achieve nitrogen residuals below 8 mg TN/1. This plant uses 8 filters of 63 m2 to treat 12 000 m3/d, and the biological reactor occupies a surface similar to the existing conventional primary settler. The results of the first few months of operation are given: as long as the ratio between biodegradable COD and total nitrogen at the filter inlet is above 5, nitrogen removal of 80 % is achieved.

Measurement of Gap and Grain-Boundary Inventories of 129I Used in Candu Fuels

AbstractCombined gap and grain-boundary inventories of 129I in 14 used CANDU fuel elements were measured by crushing and simultaneously leaching fuel segments for 4 h in a solution containing KI carrier. From analogy with previous work a near one-to-one correlation vas anticipated between the amount of stable Xe and the amount of 129I in the combined gap and grain-boundary regions of the fuel. However, the results showed that such a correlation was only apparent for low linear power rating (LLPR) fuels with an average linear power rating of 642 kV/m. For high linear power rating (HLPR) fuels (>44 kw/m), the 129I values were considerably smaller than expected. The combined gap and grain-boundary inventories of 129I in the 14 fuels tested varied from 1.8 to 11.01, with an average value of 3.6 ± 2.4% which suggests that the average value of 8.1 ± 1% used in safety assessment calculations overestimates the instant release fraction for 129I. Segments of used CANDU fuels were leached for 92 d (samples taken at 5, 28 and 92 d) to determine the kinetics of 129I release. Results could be fitted tentatively to half-order reaction kinetics, implying that 129I release is a diffusion-controlled process for LLPR fuels, and also for HLPR fuels, once the gap inventory has been leached. However, more data are needed over longer leaching periods to gain more understanding of the processes that control grain-boundary release of 129I from used CANDU fuel.

Hydrocracking of n-butane and n-heptane over a sulfided nickel erionite catalyst

A sulfided Ni/H-erionite catalyst was prepared from the natural mineral, and its catalytic characteristics for hydrocracking n-alkanes were studied. Because of its shape selectivity toward straight chain hydrocarbons, branched products were largely absent and the major cracked product was propane. The observed product distribution could not be explained by simple primary cracking of the feed molecule or by secondary cracking or recombination of the primary products. It is proposed that the feed molecule participated in a set of reactions, including hydrogenation, dehydrogenation, hydrogen transfer, oligomerization and cracking. These reactions are also needed to explain the yield of less than two moles of product from each mole of feed converted. A set of six first order differential equations representing the proposed molecular transformations is shown to fit the product distribution data for n-butane very well. A fit of the n-heptane data was not attempted; however, it is proposed that the mechanism is analogous to that proposed for n-butane. The rate of cracking of n-butane is first order in n-butane concentration, while the rate of n-heptane cracking appeared to follow half order kinetics. For n-butane cracking, the apparent activation energy of all the important reactions are roughly equal, resulting in a product distribution which is nearly independent of temperature. For n-heptane, a larger difference between the apparent activation energy of n-heptane cracking and secondary cracking of its primary products, lead to a temperature dependence in product selectivity.

On the role of the solid–gas interface in the thermolysis of trimethylgermane and trimethylstannane

Metal film surfaces have a profound effect on the thermal decomposition of Me3MH (M = Ge and Sn), both of which unusually decompose by half-order kinetics at elevated temperature.

Degradation of silane- and peroxide-cross-linked polyethylene and ethylene propylene rubber

The degradation behavior and kinetics of degradation of polyethylene (PE), ethylene propylene rubber (EPR), silane-grafted PE (PE gS) and EPR (EPR gS), and silane and dicumyl peroxide (DCP) cross-linked PE, EPR and their blends, have been studied by thermogravimetry in both nitrogen and air. The effect of silane grafting and subsequent cross-linking on the degradation characteristics is more pronounced in air than in N 2. The temperatures at which maximum rates of degradation occur ( T max), are significantly higher for silane-grafted PE and EPR than the control PE in air. In N 2, both cross-linked and control PE follow first-order decomposition kinetics while control and grafted EPR follow half-order kinetics. In air, all the systems except DCP-cured EPR follow first-order kinetics. The activation energies for degradation of silane-grafted and silane-cross-linked materials are significantly higher than those of peroxide-cross-linked materials. The onset temperature of oxidative degradation, as measured by differential scanning calorimetry, is markedly higher and the air ageing properties are also better for silane-cross-linked material than for peroxide-cross-linked material. The increased stability of the silane-cross-linked material has been explained in terms of its polyfunctional network structure.

KINETICS AND MECHANISM OF THE OXIDATION OF THIOUREA BY METHYLENE BLUE IN ACIDIC MEDIUM

Abstract The title reaction has been investigated kinetically in methanol-water medium (3% v/v) and in presence of hydrochloric acid. The reaction follows a half order kinetics in methylene blue (MB) and a first order kinetics in thiourea (TU). At higher [TU] or at lower [MB] (ca. 1.5 × 10−5 M), the order in the oxidant changes from 1/2 to zero. The rate increases linerarly on increasing [H+]. Addition of EDTA and the variation in ionic strength has no influence on the rate except the addition of potassium chloride which may be attributed to the environmental effect. The increase in dielectric constant increases the rate. The external addition of the reaction products does not influence the rate but higher concentrations of leucomethylene blue tend to exert a slightly retarding influence. Activation parameters have been evaluated and a reaction scheme has been proposed postulating a sterically controlled nucleophilic attack of thiourea molecule on half-reduced methylene blue radical as the rate limiting step.

Concepts and Models for Biofilm Reactor Performance

This paper reviews the state of knowledge of the basic mechanisms governing transformation of pollutants and the present approaches with which to predict the performance of biofilm reactors. The design of biofilm reactors is based mainly on empirical loading criteria or empirical design formulae. Introduction of more stringent effluent requirements, new types of biofilm reactors, as well as application of biofilm reactors to more untraditional types of waste materials, calls for new design procedures with higher degrees of confidence. Most new attempts to model biofilm reactors are based on fundamental principles for mass transport to and through biofilms coupled with kinetic expressions for pollutant transformations in the biofilms. A simple simulation model based on half order kinetics is able to describe the removal of soluble substrates, mineralisation of organic matter, nitrification and denitrification. A simple first order kinetics is able to predict degradation of some xenobiotics. Advanced simulation models appearing in the past few years show a strong promise for detailed analysis of the effect of variation in influent waste characteristics, population dynamics, reactor configuration, etc. However, none of the models are able to predict properly the removal of particulate matter and mixtures of several groups of industrial organic chemicals. Again, insight in the basic removal mechanisms is required.

Examination of the Zinc Cementation of Cadmium in Aqueous Solutions

The kinetics of the cementation of cadmium by zinc have been studied over a range of solution pH values and initial cadmium concentrations. The kinetics were interpreted in terms of a model postulating a transition from a migration controlled mechanism with consequent half order kinetics to a diffusion controlled regime following first order kinetics. The conditions under which each mechanism was found to apply were consistent with the model in which the immediate reductant was hydride ion generated by the interaction of hydrogen ions with the zinc. The reaction stoichiometry was remarkable in that conditions were observed under which more than the theoretical one mole of cadmium per mole of zinc could be reduced. This was ascribed to the electrolysis of water by the induced electrochemical system. A lag in both cadmium cementation and zinc dissolution was observed in many runs. The zinc dissolution was found to commence about 25% sooner than cadmium cementation, a fact ascribed to the establishment of the reducing electrochemical system.

Temperature programmed desorption studies of hydrogen on Zn(0001) surfaces

We report for the first time temperature programmed desorption (TPD) spectra of H 2 from Zn(0001) surfaces. Hydrogen is adsorbed in its atomic state, as evidenced by the fact that adsorption must be performed using pre-dissociated hydrogen. However, the observed TPD spectra do not show second-order kinetics, as would be expected for recombinative desorption. Instead, the peak shapes and the coverage dependence of peak temperatures both appear to obey half-order kinetics, with a desorption energy of 11.1 ± 0.3 kcal/mol. The kinetic order strongly suggests that island formation occurs, due to attractive interactions between neighboring adsorbed H atoms. An explanation for the attractive interactions is proposed, based on the bonding mechanism in diatomic ZnH and an elementary description of the band structure of Zn metal.

Modeling of experiments on biofilm penetration effects in a fluidized bed nitrification reactor

A four-component, diffusion-reaction model with double Michaelis-Menten kinetics was used to describe the experimental data obtained from a laboratory biofilm, fluidized-bed nitrification reactor. Theory and experiment demonstrated that the stoichiometric ratio (3.5 mg O(2)/mg NH(4)(+)-N) can be employed as a criterion to determine whether the limiting substrate is oxygen or ammonia. For the present work, in the range of concentrations where limitation occurred, 4 mg/L NH(4)(+)-N and 14 mg/L O(2), the ratio of oxygen to ammonia in the bulk liquid determined which substrate was penetration-limiting-O(2) if <3.5 and NH(4)(+) if > 3.5. Half-order kinetics with respect to the limiting substrate described the apparent overall rates. Simulations provided biofilm concentration profiles which demonstrated the role of the oxygen-ammonia ratio. Experiments indicated that, generally, high NO(2)(-) concentrations can be expected. These depend on the residence time, biofilm area, and oxygen concentration. This dependency was investigated with the model, as was the parametric sensitivity with respect to the saturation constants. Particularly important for the NO(2)(-) levels were the ratios of the saturation constants for oxygen.

The catalytic reaction between adsorbed oxygen and hydrogen on Rh(111)

The adsorption rate for O 2 on Rh(111) at 335 K exhibits Langmuir (1 − θ) kinetics rather than the expected (1 − θ) 2 dependence. Adsorption occurs with a sticking coefficient near unity on empty sites, producing a mixture of ordered and disordered domains. At θ ⩽ 0.5, the intensity of the (1, 1 2 ) overlayer beam increases in proportion to θ 2 as expected for ordered oxygen island formation. Extensive ordering occurs only in the very last stages of monolayer formation. The reaction of the ordered-O layer with H 2(g) to produce H 2O takes place rapidly above 275 K in the 10 −8−10 −6 Torr range and can be followed quantitatively by observation of the (1, 1 2 ) LEED beam intensity. The reaction accurately exhibits kinetics which are first order in H 2 pressure, implying an efficient trapping mechanism for adsorbed hydrogen on the ordered-O layer. The activation energy for reaction is 5.3 ± 0.3 kcal mole ; each reaction event leads to a loss of order from a ∼-300 Å 2 domain. This suggests that near saturation coverage, extensive disordering occurs for small decreases in ordered oxygen coverage during reaction with H z(g) and is consistent with the massive ordering behavior seen in the final stages of oxygen adsorption. The reaction of H 2(g) with disordered oxygen species follows approximate half-order kinetics in P H 2 as expected for a mechanism which does not involve hydrogen atom trapping.

Further studies on metal-promoted vinylcyclopropane to cyclopentene rearrangements. Structure and thermolysis of rhodium complexes of exo-6-vinylbicyclo[3.1.0]hex-2-ene and the crystal structure of the 1,6–8-η4-5-allylcyclopent-2-enyl(hexafluoroacetylacetonato)rhodium(III) tetramer

The reactions of exo-6-vinylbicyclo[3.1.0]hex-2-ene with bis(ethylene)rhodium(I) complexes lead to displacement of ethylene and formation of ring-opened σπ-bis-allylrhodium derivatives. The hexafluoroacetylacetonate (11) is tetrameric in the solid state and its structure has been determined by X-ray methods. Crystals of [C13H11F6RhO2]4 are monoclinic, space group P21/c, a= 19.641(7), b= 14.353(7), c= 44.87(1)A, β= 98.03(3), Z= 8; 3 266 observed reflections [I/σ(I) > 3.0] were collected by diffractometer and refined to R 0.077.The four rhodium atoms form the corners of a puckered square and are each π-bonded to one hydrocarbon at C(2),C(3) and to another σ at C(1) and π at C(6)–(8). This complex rearranges in acetone solution at 338 K, mainly to the corresponding derivative of bicyclo[3.3.0]octa-2,6-diene; thermolysis of the corresponding dimeric acetylacetonate (12) has been studied in detail by 1H n.m.r. The reaction exhibits half-order kinetics over the conentration range 0.02–0.2M in deuteriobenzene, rearranging rapidly (t1/2[0.205M] 30.30 min) to a mixture of acetylacetonato(bicyclo[3.3.0]octa-2,6-diene)rhodium(I)(2) and acetylacetonato-(endo-6-vinylbicyclo[3.1.0]hex-2-ene)rhodium(I)(1) in 88 : 12 ratio. In deuteriodichloromethane, the ratio is 33 : 67. The cyclopentadienyl complex (14) is monomeric, and thermally stable below 373 K. Reaction of the rhodium chloride complex (13) with bicyclo[2.2.1]hepta-2,5-dienesilver hexafluorophosphate leads directly to a rearranged cation (17) at 273 K.The mechanisms of these transformations are discussed.

Very low-pressure pyrolysis (VLPP) of hydrazine, ethanol, and formic acid on fused silica

The heterogeneous decomposition kinetics of N 2H 4 into N 2, NH 3, and H 2 have been investigated in a heat-treated fused-silica Knudsen cell flow reactor operating at pressures ~10 −6−10 −3 Torr and temperatures of 600 to 1300 K. At temperatures above 1050 K, decomposition is best described by a rate half-order in N 2H 4 concentration with an activation energy of 37 kcal mole −1. The H 2 N 2 ratio increases with temperature. NH 2 radicals were carefully looked for but not detected, indicating that they constituted < 0.05 of the products even at 1300 K. At lower temperatures a relatively irreproducible reaction produces only N 2 and NH 3 products with activation energy of ~12 kcal mole −1. The heterogeneous dehydration of C 2H 5OH and of HCOOH were briefly studied under very low-pressure conditions at temperatures above 1000 K and were found to generally obey half-order kinetics. Results for all high temperature reactions are concordant with a mechanism involving a fast heterolytic adsorption followed by a unimolecular rate-limiting surface process.

Soil Persistence of Isopropalin and Oryzalin

The aerobic rate of disappearance of isopropalin (2,6-dinitro-N,N-dipropyl-cumidine) was slower than that of oryzalin (3,5-dinitro-N4,N4-dipropylsulfanilamide) in soil. The aerobic half-lives for isopropalin were 3.5 months and 13.3 months and for oryzalin 1.40 months and 4.35 months at 30 and 15 C respectively. A simple system was devised to create anaerobiosis in soil at 80% of field capacity. Both herbicides dissipated more rapidly under anaerobic conditions. The first order half-lives at 30 C in anaerobic soil were 0.17 months for isopropalin and 0.34 months for oryzalin. Neither first, second, nor half order kinetics were clearly superior in describing the degradation processes. Arrhenius activation energies suggested that the degradation processes were non-biological.

Cold storage degradation of the herbicide metribuzin in field soil samples awaiting analysis

AbstractIn conjunction with a study of herbicide degradation in the field, metribuzin (4‐amino‐6‐tert‐butyl‐4,5‐dihydro‐3‐methylthio‐l,2,4‐triazin‐5‐one) was shown to be degraded at‐37±5°C in soil samples awaiting analysis. Products of this degradation process include the known derivatives DADK (6‐tert‐butyl‐2,3,4,5‐tetrahydro‐l,2,4‐triazine‐3,5‐dione) and DK (4‐amino‐6‐tert‐butyl‐2,3,4,5‐tetrahydro‐l,2,4‐triazine‐3,5‐dione) and these products themselves have been shown to be degraded further under the same storage conditions. Loss of the herbicide can be approximated using half order kinetics with respect to metribuzin; however, loss of both previously identified metabolites is most rapid when metabolite concentrations are highest. Assuming half order kinetics, samples of Almasippi very fine sandy loam containing metribuzin (0.5 mg/kg) can be expected to lose 50% of the herbicide in 282 days at ‐ 37°, a period which is short enough to affect residue analysis results significantly should samples be stored for extended lengths of time prior to analysis. Implied in these results is the desirability of immediate analysis following collection of samples; otherwise rates of loss during storage must be determined to allow adjustment of results to compensate for residue losses in samples awaiting analysis.

ChemInform Abstract: OXIDATION OF N‐ALKANES PHOTOSENSITIZED BY 1‐NAPHTHOL

The addition of 1-naphthol accelerates the photo-decomposition of n-alkanes when floating on water. The products of oxidation are mainly long chain alcohols, with smaller amounts of peroxides and hydroperoxides. The amounts formed during irradiation have been determined by chemical analysis and also from the changes produced in the interfacial tensions of the solutions. Differences are observed in the behaviour of alkanes with odd and even numbers of carbon atoms in their chains, the latter being the more stable. A mechanism of oxidation has been proposed which, overall, follows half order kinetics with respect to the naphthol concentration in solution.

Oxidation of n-alkanes photosensitized by 1-naphthol

The addition of 1-naphthol accelerates the photo-decomposition of n-alkanes when floating on water. The products of oxidation are mainly long chain alcohols, with smaller amounts of peroxides and hydroperoxides. The amounts formed during irradiation have been determined by chemical analysis and also from the changes produced in the interfacial tensions of the solutions. Differences are observed in the behaviour of alkanes with odd and even numbers of carbon atoms in their chains, the latter being the more stable. A mechanism of oxidation has been proposed which, overall, follows half order kinetics with respect to the naphthol concentration in solution.