First-order Rate Law Research Articles

The gas-phase elimination kinetics of ethyl 2-furoate and ethyl 2-thiophenecarboxylate

The gas-phase elimination kinetics of ethyl 2-furoate and 2-ethyl 2-thiophenecarboxylate was carried out in a static reaction system over the temperature range of 623.15–683.15 K (350–410°C) and pressure range of 30–113 Torr. The reactions proved to be homogeneous, unimolecular, and obey a first-order rate law. The rate coefficients are expressed by the following Arrhenius equations: ethyl 2-furoate, log k1 (s−1) = (11.51 ± 0.17)–(185.6 ± 2.2) kJ mol−1 (2.303 RT)−1; ethyl 2-thiophenecarboxylate, log k1 (s−1) = (11.59 ± 0.19)–(183.8 ± 2.4) kJ mol−1 (2.303 RT)−1. The elimination products are ethylene and the corresponding heteroaromatic 2-carboxylic acid. However, as the reaction temperature increases, the intermediate heteroaromatic carboxylic acid products slowly decarboxylate to give the corresponding heteroaromatic furan and thiophene, respectively. The mechanisms of these reactions are suggested and described. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 145–152, 2009

KINETIC STUDY OF SYNTHESIZING 1-PHENYl-3-PROPYL ETHER UNDER LIQUID-LIQUID PHASE-TRANSFER CATALYTIC CONDITIONS

The etherification of 1-bromo-3-phenylpropane with phenol to synthesize 1-phenyl-3-propyl ether by phase-transfer catalytic conditions was successfully carried out in an alkaline solution of KOH/organic solvent two-phase medium. In this work, quaternary ammonium salts acted as the phase-transfer catalysts. The main purpose of this study was to investigate the kinetic behavior, mechanism, and activation energy of the reaction system. A rational mechanism for the etherification is proposed according to the experimental evidence. The reaction follows a pseudo first-order rate law. A pseudo steady-state hypothesis (PSSH) was proposed to describe the kinetic behaviors from which the apparent rate constant of the two-phase reaction (kapp) was obtained via experimental data. Kinetics of the reaction including the effects of agitation speed, amount of potassium hydroxide, volume of water, temperature, amount of tetrabutylammonium bromide, quaternary ammonium salts, volume of chlorobenzene, and organic solvents on the reaction rate were investigated in detail. Rational explanations to account for the unique results, especially for the water volume effect on the reaction rate, are also provided.

KINETIC STUDY OF S-ALKYLATION OF 2-MERCAPTOBENZIMIDAZOLE CATALYZED BY TETRABUTYLAMMONIUM BROMIDE

The S-alkylation of 2-mercaptobenzimidazole (MBI) by α-bromo-m-xylene (RBr) under phase transfer catalytic reaction condition was successfully carried out in an aqueous solution of KOH/organic solvent two-phase medium. No product was obtained from N-alkylation during or after the reaction period by using a limited quantity of α-bromo-m-xylene. The reaction is greatly enhanced by adding a small amount of tetrabutylammonium bromide (TBAB) and/or potassium hydroxide. Based on the experimental evidence, a rational reaction mechanism is proposed. A kinetic model is derived, from which a pseudo steady-state hypothesis (PSSH) is applied to the reaction system. The kinetic behaviors and the characteristics of the reaction are sufficiently described by the pseudo first-order rate law. The effects of the reaction conditions, including agitation speed, amount of TBAB catalyst, amount of KOH, quaternary ammonium salts, volume of water, volume of dichloromethane, amount of 2-mercaptobenzimidazole, amount of α-bromo-m-xylene, inorganic salts, organic solvents, and temperature on the conversion of the reactant and the apparent rate constants (kapp) were investigated in detailed. Rational explanations are provided for the observed phenomena from experimental results.

Ca-Mg inter-diffusion in synthetic polycrystalline dolomite-calcite aggregate at elevated temperatures and pressure

This study measures the reaction rate of dolomite and aragonite (calcite) into Mg-calcite at 800, 850, and 900°C and 1.6 GPa. The dry synthetic dolomite-aragonite aggregate transformed very rapidly into dolomite-calcite polycrystalline aggregate while Mg-calcites formed at a relatively slow rate, becoming progressively richer in Mg with run time. We modeled the reaction progress semi- empirically by the first-order rate law. The temperature dependence of the overall transport rate of MgCO3 into calcite can be described by the kinetic parameters (E= 231.7 kJ/mol and Ao=22.69 h �1 ). Extrapolation using the Arrhenius equation to the conditions during exhumation of UHPM rocks indicates that the reaction of dolomite with aragonite into Mg-saturated calcite can be completed as the P-T path enters the Mg-calcite stability field in a geologically short time period ( 340°C and >10 My). SEM-EDS analysis of individual calcite grains shows compositional gradients of Mg in the calcite grains. The Mg-Ca inter- diffusion coefficient at 850°C is around 1.68×10 �14 m 2 /sec if diffusion is the major control of the reaction. The calculated closure temperatures for Ca-Mg inter-diffusion as a function of cooling rate and grain size reveal that Ca/Mg resetting in calcite in a dry polycrystalline carbonate aggregate (with grain size around 1 mm) may not occur at temperatures below 480°C at a geological cooling rate around 10°C/My, unless other processes, such as short-circuit interdiffusion along grain boundaries and dislocations, are involved.

Investigation on lipase-catalyzed solution polymerization of cyclic carbonate

In this study, 26-membered macrocyclic carbonate, cyclobis(decamethylene carbonate) [(DMC) 2] was attempted to undergo ring-opening polymerization by lipase catalysis in toluene. Novozym-435 exhibited even higher catalytic activity towards (DMC) 2 polymerization compared with SnOCt 2 while high molecular weight ( M n) of 5.4 × 10 4 and yield of 99% was still achieved at ultra-low enzyme/substrate (E/S) weight ratio of 1/200. 1H NMR spectra demonstrated the existence of terminal hydroxyl group. Solid phase polymerization in the absence of toluene unexpectedly took place at the temperature lower than (DMC) 2’s melting point of 110 °C. Compared with solvent-free case, the addition of toluene solvent resulted in marked increase in reaction rate. As to the polymerization during 48 h with the E/S weight ratio of 1/100, a region existed at around toluene/carbonate (vol/wt, ml/g) ratio of 1∼2 where the polymerizations gave optimal results in terms of both higher molecular weight and monomer conversion. It was found that much higher molecular weight polymers may be obtained by decreasing enzyme concentrations. Plots of ln{[M] 0:[M] t } versus reaction time were in linear agreement, indicating no chain termination, and monomer consumption follows a first-order rate law. The Novozym-435 catalyzed polymerization of (DMC) 2 in toluene presented pseudo-living characteristic. Compared with 6-membered trimethylene carbonate, much lower reaction activity of large-sized (DMC) 2 is observed, which is opposite to the result concerning the enzymatic polymerization of lactones with different ring-size.

Kinetics and Mechanisms of the Homogeneous, Unimolecular Gas-Phase Elimination of Trimethyl Orthoacetate and Trimethyl Orthobutyrate

The gas-phase elimination kinetics of the title compounds have been examined over the temperature range of 310-369 degrees C and pressure range of 50-130 Torr. The reactions, in seasoned vessels, are homogeneous, unimolecular, and follow a first-order rate law. The products are methanol and the corresponding methyl ketene acetal. The rate coefficients are expressed by the Arrhenius equation: for trimethyl orthoacetate, log k1 (s(-1)) = [(13.58 +/- 0.10) - (194.7 +/- 1.2) (kJ mol(-1))](2.303RT)(-1)r = 0.9998; and for trimethyl orthobutyrate, log k1(s(-1)) = [(13.97 +/- 0.37) - (195.3 +/- 1.6) (kJ mol(-1))](2.303RT)(-1)r = 0.9997. These reactions are believed to proceed through a polar concerted four-membered cyclic transition state type of mechanism.

Mechanism of Pyridine−Ligand Exchanges at the Different Labile Sites of 3d Heterometallic and Mixed Valence μ3-oxo Trinuclear Clusters

The syntheses and single crystal X-ray structural analysis of five novel hetero- and homometallic mu 3-oxo trinuclear cluster with the formula [Fe (III) 2M (II)(mu 3-O)(mu-O 2CCH 3) 6(4-Rpy) 3]. x(4-Rpy). y(CH 3CN) where R = Ph for 1(Fe 2Mn), 2(Fe 2Fe), 3(Fe 2Co), 4(Fe 2Ni) and R = CF 3 for 5(Fe 2Co), are reported. The persistence of the structure for compounds 2- 5 in dichloromethane solution in the temperature range 190-320 K is demonstrated by (1)H and (19)F NMR spectroscopy. Even at the lowest temperature, the electron exchange in the homometallic mixed-valence compound 2(Fe 2Fe) is in the fast regime at the NMR time scale. Variable temperature and pressure NMR line broadening allowed quantifying the fast coordinated/free 4-Rpy exchanges at the two labile metal centers in these clusters: 2: Fe (III)( k (298)/10 (3) s (-1) = 16.6; Delta H (++) = 60.32 kJ mol (-1); Delta S (++) = + 34.8 J K (-1) mol (-1); Delta V (++) = + 12.5 cm (3) mol (-1)); 3: Fe (11.9; 58.92; +30.7; +10.6) and Co (2.8; 68.24; +49.8; +13.9); 4: Fe(12.2; 67.91; +61.0; -) and Ni (0.37; 78.62; +67.8; +12.3); 5: Fe (46; 58.21; +39.3; +14.2) and Co (4.7; 55.37; +11.2; +10.9). A limiting D mechanism is assigned to these exchange reactions. This assignment is based on a first-order rate law, the detection of intermediates, the positive and large entropies and volumes of activation. The order of reactivity k (Co) > k (Ni) is expected for a D mechanism at these metal centers: their low exchange rates are due to their strong binding with the 4-Rpy donor. Surrounded by oxygen donors the d (5) iron(III) usually reacts associatively; however, here due to low affinity of this ion for nitrogen the mechanism is D and the rate of exchange is very fast, even faster than on the divalent ions. There is no significant effect of the divalent ion in cluster 2, 3, and 5 on the exchange rates of 4-Phpy at the iron center, which seems to indicate that the specific electronic interactions between the three ions making the clusters do not influence the Fe (III)-N bond strength.

Oxidation of uranium(IV) with oxygen in NaHCO3 solution

The kinetics of U(IV) oxidation with atmospheric oxygen in NaHCO3 solutions was studied by spectrophotometry. In 1 M NaHCO3 at [U(IV)]0 = 20 mM, an induction period is observed, which virtually disappears with decreasing [U(IV)]0 to 1.0 mM. The induction period is caused by the fact that initially U(IV) exists in a weakly active polymeric form. Addition of U(VI) to the initial solution accelerates the oxidation. In a 1 M NaHCO3 solution containing 0.1–1.0 mM U(IV), the U(IV) loss follows the first-order rate law with respect to U(IV) and O2. The pseudo-first-order rate constants, bimolecular rate constants, and activation energy of the U(IV) oxidation were calculated. In dilute NaHCO3 solutions (0.5–0.01 M), the hydrolysis and polymerization of U(IV) become more pronounced. The autocatalysis mechanism presumably involves formation of a complex [U(IV) · U(VI)] with which O2 reacts faster than with U(IV). Oxidation of U(IV) occurs by the two-electron charge-transfer mechanism.

Characterization of Mononuclear and Dinuclear Germylplatinum Complexes and Ge−Ge Bond Formation at the Platinum Center

The reaction of the zerovalent platinum complex [Pt(PPh3)2(η2-C2H4)] (1) with the germanium trihydride GeH3Mes (Mes = 2,4,6-trimethylphenyl) produced various germylplatinum complexes by control of the molar ratio. When complex 1 reacted with GeH3Mes in a molar ratio of 1:1, dimerization of the platinum unit occurred at −30 °C to afford the unsymmetrical diplatinum complex [Pt2(PPh3)3(μ-GeH2Mes)2] (2) and the symmetrical diplatinum complex [Pt(PPh3)(μ-GeH2Mes)]2 (3), for which the 1H NMR spectrum indicated a mixture of cis/trans-isomers in a ratio of 2:3. When a toluene solution of 2 increased in temperature from −20 °C to room temperature, liberation of a PPh3 group occurred at the Pt(PPh3)2 site, followed by rotation of the bridging germyl group to form a mixture of cis/trans-3. Otherwise, treatment of 1 with GeH3Mes at a molar ratio of 1:2 afforded the bis(germyl)platinum complex [Pt(PPh3)2(GeH2Mes)2] (4) at −30 °C, and then 4 converted to the digermanylplatinum hydride [Pt(PPh3)2(H)(GeHMesGeH2Mes)] (5) at room temperature in toluene. The conversion rate obeyed a first-order rate law, and the activation parameters ΔH⧧ and ΔS⧧ were calculated at 20(2) kcal mol−1 and −7(8) cal K−1 mol−1, respectively. These results suggest that in later transition metal platinum complexes, Ge−Ge bond formation is carried out by intramolecular germyl migration.

A gas-phase kinetic study on the thermal decomposition of 2-chloropropene

The gas-phase thermal decomposition of 2-chloropropene in the presence of a radical inhibitor was studied in the temperature range of 668.2–747.2 K and pressure between 11–76 Torr using the conventional static system. The dehydrochlorination to propyne and HCl was the only reaction channel and accounted for >98% of the reaction. The formation of propyne was found to be homogeneous and unimolecular and follows a first-order rate law. The observed rate coefficient is expressed by the following Arrhenius equation: $$ k_{total} = 10^{13.05 \pm 0.46} (s^{ - 1} )\exp ^{ - 242.6 \pm 6.2({{kJ} \mathord{\left/ {\vphantom {{kJ} {mol}}} \right. \kern-\nulldelimiterspace} {mol}})/RT} . $$ The hydrogen halide elimination is believed to proceed through a semipolar four-membered cyclic transition state. The presence of a methyl group on the α-carbon atom lowered the activation energy by 47 kJ mol−1. The experimentally observed pressure dependence of the rate constant is compared with the theoretically predicted values that are obtained by RRKM calculations.

Bamberger rearrangement on solid acids

Bamberger rearrangement of phenylhydroxylamine (PHA) to para-aminophenol (PAP) is investigated at 353 K, with water as solvent, on a series of solid acid catalysts. The catalysts are characterized by a micro-calorimetric technique using the adsorption of ammonia for acid strength. The solid acid catalysts under study include beta zeolite, K10 clay, sulphonated silica, and sulphated zirconias, obtained by different procedures. Both activity and selectivity are affected by the choice of the catalyst. The selectivity towards PAP is found to be 17% for K10 clay, 70% for sulphonated silica, 84% for beta zeolite and >90% for sulphated zirconia, respectively. The reaction obeys a first-order rate law and the rate constant shows a linear dependence on the number of acid sites. On sulphated zirconia calcined at 973 K, a quantitative reaction is obtained, and the catalyst can be recycled, giving the first example of selective Bamberger rearrangement catalysed by solids.

Redox equilibrium U(IV) + 2Fe(CN) 6 3− ⇄ U(VI) + 2Fe(CN) 6 4− in solutions of unsaturated heteropoly anions: Potentials of redox couples, stability of U(IV) complexes, reaction mechanism

The kinetics and equilibria of the reactions UO22+ + 2L + 2Fe(CN)64− ⇄ UL0 + 2Fe(CN)63− in 0.1–1.0 M HCl solutions (ionic strength 1.0), where L is heteropoly anion of the composition P2W17O6110− or SiW11O398−, were studied speelrophotometrically. Measurement of the redox potential of the ferri/rerrocyanide couple in acid solutions allowed estimation of the stability constants of the complxes UIV(P2W17O61)216− and UIV(SiW11O39)212−, equal in 1 M H+ solutions to 1018.6 and 1021.O, respectively. Accumulation of UIVL2 formed by reduction of UO22+ follows a first-order rate law, i.e., it involves the formation of UO2+ which slowly reacts with L. The arising complex rapidly reacts with UO2+. The loss of UL2 occurs via formation of the complex of nonoxygenated U(V) with the heleropoly anion.

Computational Study on the Aminolysis of β-Hydroxy-α,β-Unsaturated Ester via the Favorable Path Including the Formation of α-Oxo Ketene Intermediate

The possible mechanisms of the aminolysis of N-methyl-3-(methoxycarbonyl)-4-hydroxy-2-pyridone (beta-hydroxy-alpha,beta-unsaturated ester) with dimethylamine are investigated at the hybrid density functional theory B3LYP/6-31G(d,p) level in the gas phase. Single-point computations at the B3LYP/6-311++G(d,p) and the Becke88-Becke95 1-parameter model BB1K/6-311++G(d,p) levels are performed for more precise energy predictions. Solvent effects are also assessed by single-point calculations at the integral equation formalism polarized continuum model IEFPCM-B3LYP/6-311++G(d,p) and IEFPCM-BB1K/6-311++G(d,p) levels on the gas-phase optimized geometries. Three possible pathways, the concerted pathway (path A), the stepwise pathway involving tetrahedral intermediates (path B), and the stepwise pathway via alpha-oxo ketene intermediate due to the participation of beta-hydroxy (path C), are taken into account for the title reaction. Moreover, path C includes two sequential processes. The first process is to generate alpha-oxo ketene intermediate via the decomposition of N-methyl-3-(methoxycarbonyl)-4-hydroxy-2-pyridone; the second process is the addition of dimethylamine to alpha-oxo ketene intermediate. Our results indicate that path C is more favorable than paths A and B both in the gas phase and in solvent (heptane). In path C, the first process is the rate-determining step, and the second process is revealed to be a [4+2] pseudopericyclic reaction without the energy barrier. Being independent of the concentration of amine, the first process obeys the first-order rate law.

Photochemical reactions of hypericin with alcohols and albumins. Kinetics and mechanism of the primary processes

The photochemical reactions of the hypericin sodium salt with alcohols and albumins yielding the corresponding semiquinone radical were studied by means of microsecond and nanosecond pulse photolysis. The decay of the semiquinone radical follows the second-and first-order rate law for alcohol solutions and the NaHY-albumin system, respectively. The lifetime and the yield of the semiquinone radical decrease in the presence of oxygen. In the oxygen-saturated solutions, the lifetime of the semiquinone radical increases with an increase in the albumin concentration in the solution from 1 to 50 mg/ml. This effect is caused by a decrease in the reactivity of the semiquinone radical toward oxygen due to the steric hindrance created by albumin and is not associated with an increase in the solvent viscosity.

Mobility of nitrogen in ε-Fe 3N below 150 °C: The activation energy for reordering

Previously quenched (from 573 K) ε-iron nitride powder of a composition close to Fe 3N, which shows partial disorder in the interstitial N superstructure, can be reordered by annealing between 373 and 408 K. The kinetics of the reordering can experimentally be traced by the axial ratio ( c hcp/ a hcp), as measured by X-ray powder diffraction, and can be described by a first-order rate law for the time-dependence of ( c hcp/ a hcp) with an Arrhenius-type temperature dependence of the rate constant. The determined activation energy of 144 ± 5 kJ mol −1 can be associated with specific jumps of N atoms from disorder to order sites. The order-of-magnitude of the pre-exponential factor of (7 ± 10) × 10 13 s −1 can be related with the vibration frequency of the N atom in an octahedral site.

Sonochemical and sonophotocatalytic degradation of malachite green: The effect of carbon tetrachloride on reaction rates

A comparative study between the sonolytic, photocatalytic and sonophotocatalytic oxidation processes of aqueous solutions of malachite green was carried out in the presence of carbon tetrachloride, under a low power ultrasonic field (<15W) and using titanium dioxide as a photocatalyst. The effect of a number of parameters such as ultrasonic intensity, TiO2 crystalline structure and the presence of CCl4 were studied using an inexpensive reactor. Enhanced rates of sonolytic degradation of malachite green in the presence of CCl4 were demonstrated. On the other hand, the simultaneous use of sonolysis and photocatalysis in the presence of CCl4 does not improve the degradation rate of malachite green in comparison with the one obtained using only sonolysis, but it makes possible a faster oxidative degradation of some reaction intermediaries. Finally, in air saturated solutions both processes, the sonolytic and the photocatalytic one, follow a first-order rate law.

Adsorption kinetics, thermodynamics and desorption of natural dissolved organic matter by multiwalled carbon nanotubes

Multiwalled carbon nanotubes (CNTs) were thermally treated and were employed as adsorbents to study their adsorption kinetics and thermodynamics of natural dissolved organic matter (NDOM) from aqueous solutions. The adsorption kinetics follows the first-order rate law while the adsorption thermodynamics indicates the exothermic and spontaneous nature. A comparative study on the adsorption/desorption properties of NDOM between CNTs and granular activated carbon (GAC) was also conducted and revealed that the CNTs possess more NDOM adsorption capacities and show less weight loss through 10 cycles of water treatment and reactivation than the GAC. This suggests that the CNTs are promising NDOM adsorbents for preventing the microbiological degradation of drinking water quality as well as the formation of disinfection by products in water treatment.

Chemical Dynamics and Critical Phenomena: Electrical Conductivity and Reactivity of Benzyl Bromide in Triethylamine+Water Near its Consolute Point

The binary liquid mixture of triethylamine+water has a lower consolute point at a critical composition of 32.27mass% triethylamine. Starting at a temperature within the one-phase region, the electrical conductivity of a sample of this mixture was measured and found to increase smoothly with increasing temperature before falling sharply at 291.24K (18.09°C). Since opalescence was visible at this temperature, it was identified with the critical solution temperature of the binary mixture. A solution of 90μL of benzyl bromide dissolved in 90mL of 32.27mass% triethylamine+water was prepared, and the resulting Menschutkin reaction between benzyl bromide and triethylamine was allowed to come to equilibrium. The electrical conductivity of this equilibrium mixture was measured in the one-phase region and was found to increase smoothly with increasing temperature before rising sharply at 291.55K (18.40°C). This temperature was identified as the critical temperature of the ternary. The rate of approach of the ternary mixture to chemical equilibrium was also measured and shown to be governed by a first-order rate law. The temperature dependence of the rate coefficient followed the Arrhenius equation up to a temperature of about 290.74K (17.59°C). Above this temperature, the rate coefficient fell by as much as 22% below the value predicted by extrapolation of the Arrhenius equation. This suppression in the rate reaction in the vicinity of the critical temperature can be interpreted as evidence for the existence of critical slowing down.

Kinetic Studies of Reaction between Sodium Borohydride and Methanol, Water, and Their Mixtures

This paper reports the kinetics of hydrogen generation from the reaction between sodium borohydride and methanol, water, and their mixtures over a temperature range between −20 and +50 °C. Hydrogen generation was found to obey a first-order rate law with respect to sodium borohydride concentration for each of the four reacting mixtures of methanol, “nearly dry” methanol (2:1 water to sodium borohydride mole ratio), “wet” methanol (10:1 water to sodium borohydride ratio), and water, with activation energies of 53.0 ± 3.4, 52.3 ± 9.5, 36.1 ± 2.8, and 86.6 ± 8.0 kJ/mol, respectively. Methanolysis of sodium borohydride was shown to be a feasible method for low-temperature hydrogen generation. However, this noncatalytic reaction system exhibited large lag time and slow reaction kinetics at low temperatures. Our study indicates that the reaction system based on sodium borohydride and the nearly dry methanol can be a potential high gravimetric density hydrogen storage system.

Selective synthesis of erythrulose and 3-pentulose from formaldehyde and dihydroxyacetone catalyzed by phosphates in a neutral aqueous medium

The aldol condensation of formaldehyde and the lower carbohydrate dihydroxyacetone in a neutral aqueous medium is effectively catalyzed by solid compounds (hydroxylapatite and calcium phosphate and carbonate), natural minerals (apatite and vivianite), and soluble phosphates. In excess formaldehyde, the decrease in the concentration of the lower carbohydrate is described by a first-order rate law with respect to dihydroxyacetone. The major products of the reaction between formaldehyde and dihydroxyacetone in the presence of the above catalysts are erythrulose (45–50% selectivity) and 3-pentulose (35–40% selectivity). Branched pentulose and hexulose are also identified among the reaction products.