Half-order Kinetics Research Articles

Aggregation and reactivity of the dilithium and dicesium enediolates of 1-naphthylacetic acid.

UV-vis spectra of the dilithium, 1-Li, and dicesium, 1-Cs, enediolates of alpha-naphthylacetic acid show no systematic change with concentration in dilute THF solution, but addition of small amounts of HMPA causes a bathochromic shift in the spectrum of 1-Li. These results indicate that these salts are aggregated and that HMPA breaks up the aggregates of 1-Li. The quantitative effect of small increments of HMPA indicates that 1-Li is a dimer. Alkylation reactions of 1-Cs show half-order kinetics in enediolate indicating that this salt is also dimeric but that the small amount of monomer in equilibrium is the actual reactant. Alkylation of 1-Li, however, is much slower and shows first-order kinetics interpreted as a direct reaction of the dimer; the amount of monomer in this case is too small to compete. A solution of 1-Li in THF containing 10% HMPA is much more reactive in alkylation than 1-Li alone and the first-order dependence in 1-Li is now interpreted as reaction of the monomer. Compound 1-Li is found to form a mixed aggregate with LDA, a finding that has possible synthetic significance since enediolates used in syntheses are frequently prepared using LDA. Structures of these compounds are suggested based on model ab initio computations.

A Kinetic Model for Autotrophic Denitrification using Sulphur:Limestone Reactors

Abstract The kinetics of autotrophic denitrification of groundwater by Thiobacillus denitrificans in a sulfur:limestone upflow reactor was examined in order to predict effluent concentrations. Experiments were performed using water containing 60 and 90 mg NO3—N/L and sulfur and limestone with average particle size of 3.5 mm. Results clearly showed that nitrate was completely removed from 60 and 90 mg NO3—N/L influent concentrations. The results showed that the autotrophic denitrification rates in sulfur:limestone reactors can be described by half-order kinetics. The half-order reaction rate constants for the entire media were estimated at 1.34 and 1.54 mg1/2/L1/2 h for influent concentrations of 60 and 90 mg NO3—N/L, respectively.

Kinetics and mechanism of the reduction of some azo-dyes by inorganic oxysulfur compounds

The kinetics of the reduction of Sunset Yellow (E-110, C.I. 15985), SY, and Ponceau-4R (E-124, C.I. 16255), PR, dyes by dithinoite and bisulfite was studied using stopped-flow and conventional UV/vis spectrophotometer under pseudo- first order conditions. The reaction followed a total one and half-order kinetics, first order with respect to dye and half-order with respect to dithionite, while with bisulfite overall second-order kinetics has been revealed. The reduction using dithionite has higher rate constant than bisulfite. With dithionite, PR has higher rate constant compared with SY, while the reverse has been observed with bisulfite. The direct involvement of SO 2 ·− radical in the reduction mechanism has been established. The formation of carbon-4 sulfonate adducts was concluded in the case of using bisulfite. Addition of β-cyclodextrin showed an enhancement in the reduction rate of SY, while no detectable effect was noticed with PR. This increase in the rate constant is attributed to the inclusion of p-sulfophenylazo side of SY into β-cyclodextrine cavity. Addition of cationic surfactant, CTAB, retarded the rate for both dyes due to the squeezed of dye molecules in the micellar core. The reaction was found to be an enthalpy controlled. Finally the reduction mechanism was proposed.

Kinetic Investigation of the Heterogeneous Synthesis of Flavanone over MgO

The synthesis of flavanone was studied over a magnesium oxide solid catalyst in a batch reactor. The reaction scheme consists of the Claisen–Schmidt condensation of 2'-hydroxyacetophenone with benzaldehyde towards the formation of a 2'-hydroxychalcone intermediate and the subsequent isomerization of this intermediate to flavanone. An initial parametric study yielded a range of values for key experimental parameters (i.e., catalyst particle size and weight percentage and stirring rate) for which the batch reactor system operates in the kinetic regime. The kinetic investigation that followed indicates that over the MgO catalyst studied the Claisen–Schmidt condensation reaction follows first-order kinetics in 2-hydroxyacetophenone and half-order kinetics in benzaldehyde, while the 2'-hydroxychalcone isomerization follows first-order kinetics; activation energies of 40 and 48 kJ/mol were obtained for the two reactions, respectively.

Kinetic study on the selective catalytic oxidation of 2-propanol to acetone over nickel foils

The kinetics of the catalytic oxidation of 2-propanol with molecular oxygen on clean and oxygen-pretreated Ni foil samples was studied by using a microbatch reactor with mass spectrometry detection. It was found that, under the right conditions, high selectivity for acetone formation can be achieved in this system. Specifically, it was determined that high partial oxidation selectivity requires the use of temperatures below 700 K and oxygen partial pressures higher than stoichiometric, i.e. oxygen-to-alcohol ratios above 1:2. Zero- and half-order kinetics with respect to 2-propanol and oxygen pressures, respectively, were observed for the conversion of 2-propanol to acetone on the clean Ni catalyst. A thin oxide-like layer was determined to be the active catalyst for this reaction, and the rate of oxidation was found to be significantly higher on oxygen-pretreated Ni surfaces. Our kinetic evidence also indicates that the undesirable complete oxidation of the alcohol to CO 2 and water is mainly a sequential reaction that takes place on the acetone produced from the alcohol, not a primary alcohol oxidation step. Finally, it was found that dehydrogenation of 2-propanol to acetone in the absence of oxygen is also possible, but occurs at a significantly slower rate than when oxygen is present in the gas mixture, and leads to poisoning of the surface of the catalyst via the deposition of carbonaceous deposits.

Photocatalytic degradation of pesticide–acaricide formetanate in aqueous suspension of TiO2

The photocatalytic degradation of formetanate (FMT) was studied using titania Degussa P-25 as a catalyst. The disappearance of formetanate was proved to follow a half-order kinetics. This implies that two active sites are involved in the adsorption of one molecule of formetanate (dissociative adsorption). In our conditions, complete mineralization of 20ppm of pure formetanate occurred within 125min of UV-radiation. The presence of (i) formulation agents and (ii) of humic acids seemed to have an inhibiting effect on the initial rate. In all cases, mineralization of FMT led to a greater percentage of ammonium than of nitrate. Photocatalysis proved to be an excellent new advanced oxidation technology (AOT) to eliminate formetanate residues present in real surface and ground waters.

Reaction Kinetics of Immobilized-Cell Denitrification. I: Background and Model Development

A simplified, quasi-steady-state model has been formulated for groundwater denitrification using immobilized cells. The model takes into account the diffusion-limited penetration of nitrate and nitrite into the immobilized-cell biocatalyst particle, uniform intraparticle cell density, equivalent slab geometry for the spherical particle, zero-order intrinsic reaction kinetics of the immobilized cells, sequential reduction of nitrate to nitrite and nitrite to dinitrogen within the particle, no inhibition of the sequential reactions by either nitrate or nitrite, and ideal plug flow conditions in the bioreactor. As a result, the reaction in the bulk fluid of the plug-flow bioreactor can be described by a half-order kinetics, and the process is characterized by the half-order reaction rate constants for nitrate and nitrite reduction. These constants incorporate the intrinsic reaction kinetics of the immobilized cells, the size and packing density of biocatalyst particles in the reactor, and the effective diffusion coefficients of nitrate and nitrite in the particle matrix.

Reaction Kinetics of Immobilized-Cell Denitrification. II: Experimental Study

Laboratory experiments were conducted to characterize the performance of an immobilized-cell denitrification process treating nitrate-contaminated groundwater and to provide supporting data for the validation of a quasi-steady state model based on half-order reaction kinetics. The treatment process consists of laboratory-scale, plug-flow reactors packed with biocatalyst particles. Pseudomonas denitrificans (American Type Culture Collection 13867), a heterotrophic denitrifier, was cultured and immobilized in calcium alginate particles. Ethanol was used as the source of organic carbon. Thirty concentration profiles were obtained at four levels of nitrate concentration and at three ranges of flow rate. An analysis of the nitrate and nitrite concentration profiles suggested that a half-order reaction rate model could be used to describe the reduction of both nitrate and nitrite. The half-order reaction rate constants for nitrate and nitrite reduction were dependent on the age of the biocatalyst particles and ...

Degradation of soil fumigants as affected by initial concentration and temperature.

Soil fumigation using shank injection creates high fumigant concentration gradients in soil from the injection point to the soil surface. A temperature gradient also exists along the soil profile. We studied the degradation of methyl isothiocyanate (MITC) and 1,3-dichloropropene (1,3-D) in an Arlington sandy loam (coarse-loamy, mixed, thermic Haplic Durixeralf) at four temperatures and four initial concentrations. We then tested the applicability of first-order, half-order, and second-order kinetics, and the Michaelis-Menten model for describing fumigant degradation as affected by temperature and initial concentration. Overall, none of the models adequately described the degradation of MITC and 1,3-D isomers over the range of the initial concentrations. First-order and half-order kinetics adequately described the degradation of MITC and 1,3-D isomers at each initial concentration, with the correlation coefficients greater than 0.78 (r2> 0.78). However, the derived rate constant was dependent on the initial concentration. The first-order rate constants varied between 6 and 10x for MITC for the concentration range of 3 to 140 mg kg(-1), and between 1.5 and 4x for 1,3-D isomers for the concentration range of 0.6 to 60 mg kg(-1), depending on temperature. For the same initial concentration range, the variation in the half-order rate constants was between 1.4 and 1.7x for MITC and between 3.1 and 6.1x for 1,3-D isomers, depending on temperature. Second-order kinetics and the Michaelis-Menten model did not satisfactorily describe the degradation at all initial concentrations. The degradation of MITC and 1,3-D was primarily biodegradation, which was affected by temperature between 20 and 40 degrees C, following the Arrhenius equation (r2 > 0.74).

Hydroprocessing of a Maya Residue. II. Intrinsic Kinetics of the Asphaltenic Heteroatom and Metal Removal Reactions

The intrinsic kinetics of asphaltenic metal and heteroatom removal reactions are reported. The asphaltenic sulfur, nitrogen, nickel, and vanadium were determined in isolated asphaltenes from raw material and products. The kinetic study was carried out at high temperatures (375−415 °C) and hydrogen pressure, 12.5 MPa, in a perfectly mixed reactor in continuous operation. Concentration data fit half-order kinetics with respect to asphaltenic sulfur, nitrogen, and metal (Ni and V) concentration, the activation energies being 35.6, 39.3, 47.7, and 45.3 kcal/mol, respectively.

The kinetics of the oxidation of pyrite by ferric ions and dissolved oxygen: an electrochemical study

The dissolution of pyrite is important in the geochemical cycling of iron and sulphur, in the formation of acid mine drainage, and in the extraction of metals by bacterial leaching. Many researchers have studied the kinetics of dissolution, and the rate of dissolution has often been found to be half-order in ferric ions or oxygen. Previous work has not adequately explained the kinetics of dissolution of pyrite. The dissolution of pyrite is an oxidation-reduction reaction. The kinetics of the oxidation and reduction half-reactions was studied independently using electrochemical techniques of voltammetry. The kinetics of the overall reaction was studied by the electrochemical technique of potentiometry, which consisted of measuring the mixed potential of a sample of corroding pyrite in solutions of different compositions. The kinetics of the half reactions are related to the kinetics of the overall dissolution reaction by the condition that there is no accumulation of charge. This principle is used to derive expressions for the mixed potential and the rate of dissolution, which successfully describe the mixed potential measurements and the kinetics of dissolution reported in the literature. It is shown that the observations of half-order kinetics and that the oxygen in the sulphate product arises from water are both a direct consequence of the electrochemical mechanism. Thus it is concluded that the electrochemical reaction steps occurring at the mineral-solution interface control the rate of dissolution. Raman spectroscopy was used to analyze reaction products formed on the pyrite surface. The results indicated that small amounts of polysulphides form on the surface of the pyrite. However, it was also found that the mixed (corrosion) potential does not change over a 14-day leaching period. This indicates that even though polysulphide material is present on the surface, it does not influence the rate of the reactions occurring at the surface. Measurements of the sulphur yields as a function of electrode potential indicate that thiosulphate is not the only source of the sulphur product.

UV-induced self-assembly of the inclusion complexes formed between a long-chain photochromic spiropyran and cyclodextrins

Photochromic spiropyran with a long chain alkyl substitute can form axial complexes with α-, β-, and γ-cyclodextrin, respeetively. The complexes show normal photochromism. The novel property of the colored forms of the inclusion complexes is that they can assemble into dimers at relatively low concentration or J-aggregates at relatively high concentration. For α-, β-, and γ-cyclodextrin, λmax of the J-aggregates appear at 700 650, and 630 nm, respectively. The sizes of the cavities of cyclodextrins have very little effect on the spectra and decoloration kinetics of the dimers, but have great effects on the spectra of the J-aggregates. Unlike the charge transfer complex of Krongauz, the decoloration process of the dimers or J-aggregates cannot be described by an exponential or a two-exponential kinetics, but obey half-order kinetics very well. Another result that can be deduced from the kinetic analysis is that unlike the dimers formed in apolar solvents or in polymers, which consist of a colored molecule (B’) and a colorless molecule (A) with a composition of A’B’, in the present system, the dimer of the inclusion complex consists of two colored molecules (B). All these results can be interpreted by the proposed structure model and decoloration mechanism.

The influence of TiO2 characteristics on the catalytic Cr(VI) photoreduction

The Cr(VI) catalytic reduction with UV light irradiation has been studied using four different TiO2 samples which are prepared by hydrolysis of titanium tetraisopropoxide and then fired at four different temperatures. Except the difference of photoreduction rate constants, the kinetics of Cr(VI) photoreduction and pH influence on the reaction are similar in catalytic and catalyst free systems. At low pH the rate constant of catalytic Cr(VI) photoreduction is higher than that at high pH in both systems. While pH is lower than 2.5, the reaction of Cr(VI) photoreduction fits half order kinetics. At pH 4.0, the reaction of Cr(VI) photoreduction is changed into first order kinetics. The catalytic activities of TiO2 samples, fired at four different temperatures, are different. For catalysts, crystalline form and Cr(VI) adsorption ability of TiO2 are the major characteristics which influence the catalytic ability. The high adsorption amount can enhance the Cr(VI) photoreduction efficiency. However, the dependence of photoreduction ability on crystalline form of catalyst is more important than that on adsorption ability of catalyst. For TiO2 with different crystalline forms, their catalytic photoreduction abilities show different responses to the solution pH values.

Hydroprocessing of a Maya Residue. Intrinsic Kinetics of Sulfur-, Nitrogen-, Nickel-, and Vanadium-Removal Reactions

A residue from a Maya crude was processed in a hydrotreating unit with a continuous stirred tank reactor at high temperatures (375−415 °C) and hydrogen pressures (10−15 MPa). A commercial guard-bed demetalation catalyst Ni−Mo supported on γ-Al2O3 was used. In this paper, the intrinsic kinetics of the sulfur-, nitrogen-, nickel-, and vanadium-removal reactions are reported. The sulfur-removal reactions fit second-order kinetics, the nitrogen-removal reactions half-order kinetics, the nickel-removal reactions first-order kinetics, and the vanadium-removal reactions half-order kinetics. The nickel-removal reactions showed the highest value for the activation energy. The sulfur-removal reactions were the only ones that had a dependence on the hydrogen pressure in every range of hydrogen pressures studied, 10−15 MPa, and a kinetic order of 0.4 has been observed. For nitrogen-, nickel-, and vanadium-removal reactions, an increase of the pseudokinetic constants was only observed between 10 and 12.5 MPa. The perc...

Photoinduced self-assembly of the supramolecular photochromic systems – photoinduced dimer formation of the inclusion complexes of an indolinospiropyran with CDs

The photochromic spiropyran with a long alkyl chain can form inclusion complexes with cyclodextrins (CDs) in aqueous solution. The complexes are axial inclusion complexes formed between the long alkyl chain and CDs, with the spiropyran head group located outside the cavities of CDs. Under UV irradiation, the inclusion complexes show normal photochromism. The coloured form(B) of the complexes can assemble into a dimer. Unlike the dimer formed in apolar solvents or in polymers, which consists of a coloured molecule (B) and a colourless molecule (A) with a composition of AB, the dimer consists of two coloured molecules (B) in the present system. Corresponding to its structure, the decolouration process can not be described by an exponential or a two-exponential kinetics, but obeys half-order kinetics very well.

Biological denitrification of a textile effluent in a dynamic sand filter

Post-denitrification of a pre-treated textile effluent was tested in a pilot-scale dynamic up-flow sand filter, which has been used as a biofilm reactor, together with filtration of suspended solids (SS) and decolorization. The potential application of the reactor as a three-in-one unit (decolorization, filtration and denitrification) has been successfully tested. Biomass growth and the sloughing of biological film did not prevent the removal of high concentrations of influent SS. Both pilot- and bench-scale tests confirmed that the intrinsic denitrification kinetics was zero-order, corresponding to a half-order removal rate if nitrate concentration is lower than 10 mgN l−1. Zero-order and half-order kinetic constants have also been calculated. At low nitrate loading rates (up to 2 kgN m−3 d−1) the filter followed the ideal plug-flow hydrodynamic model. In the lower part of the filter, zero-order kinetics fitted denitrification removal rates, while in the upper part of the filter denitrification followed half-order kinetics. At nitrate loading rates higher than 2.5 kgN m−3 d−1, nitrogen bubbles developed and partially mixed the reactor. Consequently, flatter concentration profiles were detected in the reactor and denitrification followed half-order kinetics along the entire filter.

Surface Chemistry and Extreme-Pressure Lubricant Properties of Dimethyl Disulfide

The growth kinetics of a film formed by the thermal decomposition of dimethyl disulfide on an iron foil are measured using a microbalance where the growth kinetics are parabolic (film thickness X varies with time as X2 ∝ t) at high reaction temperatures and pressures, indicating that it is limited by diffusion through the film. The activation energy for this process is 54.5 ± 0.5 kcal/mol. The growth rate becomes linear as the reaction temperature and/or reactant pressure is lowered, indicating that, under these circumstances, the reaction rate is limited by thermal decomposition of dimethyl disulfide at the growing interface. The activation energy for thermal decomposition at the interface is found to be 37.6 ± 0.7 kcal/mol, and a half-order kinetics pressure dependence for the surface reaction rate is found consistent with a reaction limited by the rate of dimethyl disulfide dissociation. Analysis of the resulting film using Raman and X-ray photoelectron spectroscopies as well as X-ray diffraction reveal the formation of FeS, which may be slightly nonstoichiometric. This film is similar to that formed by methanethiol, suggesting that they may both initially form a surface thiolate species that further reacts to form FeS. The half-order reaction kinetics noted above are consistent with this. Measurement of dimethyl disulfide as an extreme-pressure (antiseizure) additive reveals a plateau at an applied load of ∼4000 N in the seizure load versus additive concentration curve. It has previously been suggested that the plateau corresponds to the load at which the interface reaches the melting point of the solid lubricant layer (in this case proposed to be FeS). Estimation of the interfacial temperature using a method developed previously yields an interfacial temperature of ∼1480 K, in good agreement with the melting point of FeS.

Biological denitrification of a textile effluent in a dynamic sand filter

Post-denitrification of a pre-treated textile effluent was tested in a pilot-scale dynamic up-flow sand filter, which has been used as a biofilm reactor, together with filtration of suspended solids (SS) and decolonization. The potential application of the reactor as a three-in-one unit (decolorization, filtration and denitrification) has been successfully tested. Biomass growth and the sloughing of biological film did not prevent the removal of high concentrations of influent SS. Both pilot- and bench-scale tests confirmed that the intrinsic denitrification kinetics was zero-order, corresponding to a half-order removal rate if nitrate concentration is lower than 10 mgN l−1. Zero-order and half-order kinetic constants have also been calculated. At low nitrate loading rates (up to 2 kgN m−3 d−1) the filter followed the ideal plug-flow hydrodynamic model. In the lower part of the filter, zero-order kinetics fitted denitrification removal rates, while in the upper part of the filter denitrification followed half-order kinetics. At nitrate loading rates higher than 2.5 kgN m−3 d−1, nitrogen bubbles developed and partially mixed the reactor. Consequently, flatter concentration profiles were detected in the reactor and denitrification followed half-order kinetics along the entire filter.

Kinetics of Conradson Carbon Residue Conversion in the Catalytic Hydroprocessing of a Maya Residue

A residue from a Maya crude was hydroprocessed in a continuous hydroprocessing unit provided with a continuous stirred-tank reactor. The kinetic study of Conradson carbon residue (CCR) conversion was carried out, and the data of CCR conversion fit half-order kinetics, with the activation energy being 277.58 kJ/mol. No dependence of the rate constants on hydrogen pressure was observed. The relationship between CCR and different parameters was studied, and it was found that asphaltenes, hydrogen content, H/C atomic ratio, and residue content (350 °C) were linearly related with CCR content. Gas yield was also found to be linearly related with CCR conversion. A structural analysis was carried out by 13C NMR and 1H NMR, and a linear relationship was found between CCR and aromatic carbon contents for the products obtained at 415 °C, when the products obtained at the same temperature are compared. However, a general relationship for all temperatures was not found.

Kinetics of soot—O 2, soot—NO and soot—O 2—NO reactions over spinel-type CuFe 2O 4 catalyst

Kinetics of soot-O 2, soot-NO and soot-O 2-NO reactions over CuFe 2O 4 were investigated by using temperature programmed reaction (TPR) technique in which a soot-catalyst mixture was loaded in a reactor and exposed to a fluent stream containing gaseous reactant(s) under a constant heating rate. Within the temperature range where a substantial amount of the charged soot remained and the reaction can be regarded to be the zero order in the amount of soot, the kinetic analysis of non-steady TPR results was possible. The half-order kinetics in the partial pressure of O 2 ( P O 2 ) was obtained for the soot-O 2 reaction. The soot-NO reaction was complicated in the temperature dependence of CO 2 and N 2 formation as well as in the reaction order with respect to P NO; the reaction order was first at lower temperatures and increased with increasing temperature. In the soot-O 2-NO reaction, i.e. the so-called simultaneous soot-NO x removal, the rate of CO 2 formation and those of both N 2 and N 2O formation depended on partial pressures as P 0.6 NO P 0.6 O 2 and P 1.0 NO P 0.4 O 2 , respectively. Based on the kinetic results, possible reaction mechanisms were discussed.