Second-order reaction simulation


The most widely used methods try to follow the gradient downliill starting from a transition state. At the transition state itself, the gradient vanishes and the first step must be made along the imaginary eigenvector of the Hessian in the proper coordinates, i.e., mass-weighted Cartesians for the IRC path. As pointed out by Schlegel [1, 2], (B3.5.I4) is a stiff differential equation and its integration by simply making small downliill steps along the gradient, a method equivalent to Euler s method, requires very small steps and consequently much effort. Otherwise, the calculated reaction path diverges from the true one, at first slowly and tlien more rapidly. To deal with this problem requires either constrained minimization steps at each point on the path, or alternatively second-order (both gradient and Hessian) infomiation. This increases the cost of the individual steps but allows much larger steps to be taken.  [c.2353]

The kinetics of hydrolysis reactions maybe first-order or second-order, depending on the reaction mechanism. However, second-order reactions may appear to be first-order, ie, pseudo-first-order, if one of the reactants is not consumed in the reaction, eg, OH , or if the concentration of active catalyst, eg, reduced transition metal, is a small fraction of the total catalyst concentration.  [c.218]

Place 8 g. of the pure powdered azoxybenzene and 25 g. of iron filings (both reagents being quite dry) in a 75 ml. distilling-flask F and mix thoroughly by shaking. Cork the flask and fit to the side-arm a boiling-tube B to act as receiver (Fig. 66) cut or file a groove G in the boiling-tube cork to allow escape of air. Now heat the mixture directly with the Bunsen flame, waving the latter around the base of the flask to ensure uniform heating heat gently at first and later more strongly. The red liquid azobenzene distils over smoothly and eventually solidifies in the receiver. When no more distillate passes over, detach the boiling-tube, and then, in order to eliminate basic impurities which are formed as byproducts in the reaction, add 20-30 ml. of dilute hydrochloric acid (i vol. of concentrated acid 2 vols. of water) which have been heated to about 70° cork the tube securely and shake the mixture, so that impurities in the molten drops of azobenzene are thoroughly extracted by the acid, which usually becomes dark in colour. Now cool in water until the globules of azobenzene solidify, and then filter at the pump. Break up the azobenzene with a spatula on the filter, wash thoroughly with water, and drain. Recrystallise from a minimum of boiling methylated spirit, filtering the hot solution through a small fluted filter-paper. The azobenzene separates as reddish-orange crystals, m.p. 67-68°. Yield, 4 g. A second recrystallisation from methylated spirit may be necessary to obtain a satisfactory melting-point.  [c.213]

Place 8 g. of the pure powdered azoxybenzene and 25 g. of iron filings (both reagents being quite dry) in a 75 ml. dis-tilling-flask F and mix thoroughly by shaking. Cork the flask and fit to the side-arm a boiling-tube B to act as receiver (Fig. 66) cut or file a groove G in the boiling-tube cork to allow escape of air. Now heat the mixture directly with the Bunsen flame, waving the latter around the base of the flask to ensure uniform heating heat gently at first and later more strongly. The red liquid azobenzene distils over smoothly and eventually solidifies in the receiver. When no more distillate passes over, detach the boiling-tube, and then, in order to eliminate basic impurities which are formed as byproducts in the reaction, add 20-30 ml. of dilute hydrochloric acid (i vol. of concentrated acid 2 vols. of water) which have been heated to about 70° cork the tube securely and shake the mixture, so that impurities in the molten drops of azobenzene are thoroughly extracted by the acid, which usually becomes dark in colour. Now cool in water until the globules of azobenzene solidify, and then filter at the pump. Break up the azobenzene with a spatula on the filter, wash thoroughly with water, and drain. Recrystallise from a minimum of boiling methylated spirit, filtering the hot solution through a small fluted filter-paper. The azobenzene separates as reddish-orange crystals, m.p. 67-68°. Yield, 4 g. A second recrystallisation from methylated spirit may be necessary to obtain a satisfactory melting-point.  [c.213]

A concentrated solution of 3 mol of lithium acetylide in 1.4 1 of liquid ammonia was prepared (see Ref. 1) from lithium amide and acetylene, in the presence of a small amount of triphenylmethane. The solution was cooled to -75°C (internal temperature) by means of a liquid nitrogen bath. During this cooling the mixture was vigorously agitated in order to prevent solidification of the ammonia on the walls. At the same time nitrogen was introduced at a rate of 400 ml/min. When the mixture had attained the prescribed temperature, addition of acrolein or croton-aldehyde (2.6 mol freshly distilled) was started, while a vigorous stream of nitrogen was passed through the flask (1.5-2 1/min). The aldehydes were added over 15-20 min with vigorous stirring. Continuous cooling was not necessary as the reactions were not very exothermic. After the addition the cooling bath was removed and the introduction of N2 stopped. The mixture was allowed to stand for 30 min, then it was cautiously poured into a 5-1 wide-necked round-bottomed flask. Ammonium chloride (3 mol) was introduced as quickly as possible in 1-g portions with manual swirling. The ammonia was evaporated by placing the flask in a water bath of 50-60°C. During this evaporation the flask was continuously swirled by hand in Order to suppress bumping. To the slurry (still containing ammonia) which remained, crushed ice, just enough to dissolve the solids, was cautiously added (with swirling). The reaction flask was washed with a small amount (50 ml) of ice-water and this washing was added to the main portion. The mixture was extracted with diethyl ether 10 times in the case of R = CH3, at least 15 times in the case R = H (if desired, continuous extraction can be carried out). The unwashed extracts (note 1) v/ere dried over 100 g of magnesium sulfate. This was filtered off on a sintered-glass funnel and thoroughly rinsed with ether. The greater part of the diethyl ether was distilled off at normal pressure through a 40-cm Vigreux column, avoiding bath temperatures higher than OO C. The remaining liquid (note 2) was distilled very quickly through the same column, the (single) receiver being cooled in ice + ice-water (see Chapter I, Fig. 5). An aqueous forerun mainly consisting of carbinol was trapped in this manner. During the distillation of the acrolein--carbinol the bath temperature should not exceed 90-100°C the viscous residue in this case was subjected to a distillation at very low pressure (< 0.5 mmHg), whereby the (single) receiver was cooled below -40°C, in this way a second crop of carbinol was obtained. Practically no residue remained after the distillation of the crotonaldehyde-carbinol.  [c.79]

Reaction time. Two series of experiments were performed in order to study the influence of the reaction time on the characteristics of surface carbon structures. In the first series, the hydrocarbon deposition was periodically stopped, the catalyst was cooled down under flowing nitrogen and it was removed from the furnace. After taking a small part of the reaction mixture for TEM analysis, the remaining amount of the catalyst was put back into the furnace and the hydrocarbon deposition was further carried out under the same conditions. In the second series, different portions of catalyst were treated by hydrocarbon for different times. The results were similar for both series of catalysts. Typical images of carbon surface structures grown during different times are shown in Fig. 8. In accordance with Ref [4] we observed the dependence of the rate of filament formation on the size of the catalytic particles. In the first (1 minute) reaction period, mostly very thin carbon filaments were observed as grown on the smallest metal particles. These filaments were very irregular and the metal particles were generally found at the tips of the fibres. With increasing reaction time the amount of well-graphitized tubules progressively increased. At the same time the average length of the nanotubules increased. We need, however, to note that a relation exists between the lengths of the tubules and their diameters. The longest tubules are also the thickest. For instance, the tubules of 30-60 pm length have diameters of 35-40 nm corre-  [c.20]

The intervention of acid catalysis leads to irregular or third-order kinetics in several instances involving alcoholysis, aminolysis, or mercaptolysis (Table X, line 8). Small changes in the basicity of the substrate or of the amine produce large effects 4-chloroquinoline, but not the less basic 2-chloro isomer, is susceptible to acid catalysis in amination with alcoholic piperidine both 2- and 4-chloroquinoline show acid catalysis with the slightly less basic reagent, morpholine. Some technical problems, such as separation into two phases, actually gave uniform second-order rate constants due to the acid catalyst (amine salt) and substrate being in different phases, while the same reaction under homogeneous conditions showed irregular kinetics. Regular kinetics may occur during a later part of a reaction after saturation with the acid catalyst is complete (e.g., the hydrochloride of the product of the reaction on line 8, Table X).  [c.333]

To a solution of 0.5 mol of potassium amide in 2 1 of liquid ammonia (prepared as described in Chapter II, Exp. 12, and subsequently freed from small pieces of potassium by filtration through glass-wool) was added in about 5 min a solution of 0.20 mol of 2-butynoic acid (see Exp. 35) in 150 ml of liquid ammonia. During this addition, which was carried out by pouring the solution into the solution of potassium amide, both outer necks of the reaction flask were open. The ammo-niacal solution of the acid was prepared by addition of the required amount of anhydrous liquid ammonia to the acid in a 500-ml round-bottomed flask. After the addition of the dissolved acid to the potassium amide the reaction flask was provided with the dropping funnel and gas outlet, as indicated in Fig. 2. The thick, greyish suspension was stirred for 90 min, then a mixture of 0.25 mol of methyl iodide and 100 ml of diethyl ether was added in 10 min. A considerable part of the suspended material passed into solution. Ten minutes after the addition of the methyl iodide the dropping funnel and gas outlet were removed and 100 g of powdered ammonium chloride were introduced in small portions with vigorous stirring. The ammonia was evaporated by warming the flask in a water--bath at 45 C. In order to effect complete removal of the ammonia, the flask was evacuated by means of the water pump as soon as the stream of escaping ammonia vapour had become faint. During the evacuation, which took about 1 h. the flask was immersed in a water-bath at 40°C. The remaining solid material was dissolved in 300 ml of ice-water, then the solution was acidified to pH 1 with 3 N hydrochloric acid. The mixture was then extracted ten times with diethyl ether and the ethereal extracts were dried (without previous washing) over magnesium sulfate and subsequently concentrated in a water-pump vacuum. Distillation of the remaining liquid in a high vacuum (0.1-0.5 mrnHg) gave 18 g of crude product, which was dissolved in 50 ml of pentane. After standing for 12 h at -25 to -35°C the crystal 1ine material was sucked off on a sintered-glass funnel. After drying in a water-pump vacuum the m.p. was 47-48 C. From the mother liquor a second batch of reasonably pure product was obtained, making the yield 45. .  [c.35]

In general, tin dissolution inside an unlacquered can has a high but diminishing initial rate followed by a steady slow rateThe initial phase is associated with the reduction of cathodic depolarisers, including residual oxygen, and its duration and the corrosion rate reached depend on the nature of the product and on canning technology. In the second phase the cathode reaction is hydrogen ion reduction and the slow rate of tin dissolution, often equivalent to corrosion currents of the order of 10" A/cm, is due to the scarcity of effective cathodes. The area of steel exposed at pores and scratches may be expected to have some influence on the corrosion rate, and small grain size of the tin coating has been considered to be associated with high rates.  [c.505]


See pages that mention the term Second-order reaction simulation : [c.2222]    [c.623]    [c.157]   
Chemical kinetics the study of reaction rates in solution (1990) -- [ c.113 ]