Kinetics pseudo

Dissolution Kinetics. Pseudo first-order reactions are widely employed in the field of soil-water environmental science for evaluating physical, chemical, or biochemical events. A pseudo first-order dissolution example is given below to demonstrate the use of kinetics in identifying or quantifying minerals in simple or complex systems. Consider a metal carbonate solid (MC03s) reacting with a strong acid (HC1) ... 

Kinetics pseudo-first order reaction with respect to glucose (A)... 

Fe Oj, FejO, nanocomposites, oxidation polymerization, Langmuir adsorption isotherm, Freundlich adsorption isotherm, Dubinin-Radushkevich adsorption isotherm, Tempkin adsorption isotherm, pseudo-first-order kinetic. Pseudo-second-order kinetic, removal efficiency, adsorption capacity... 

Maki-Arvela (1999) has developed a new polyolefin supported sulphonic acid catalyst for esterification of acetic acid with methanol. The esterification kinetics (pseudo-homogeneous) was modeled with a mechanistic rate equation, the parameters of which were determined by non-linear regression. The esterification rate constant of the most active modification of the new catalyst was 9.6 x 10 ° dm /(mol g min) at 328 K, which clearly exceeds the corresponding value obtained with a traditional (Amberlyst 15) polyvinyl benzene supported catalyst, 1.5 x 10 ° dm /(moP g min). 

If the dominant contributions /r,[M.] are approximately constant, this leads to pseudo second-order kinetics with an effective rate constant... 

In classical kinetics, intemiolecular exchange processes are quite different from the uniniolecular, first-order kinetics associated with intramolecular exchange. However, the NMR of chemical exchange can still be treated as pseudo-first-order kinetics, and all the previous results apply. One way of rationalizing this is as... 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

The integrated form of the rate law for equation 13.4, however, is still too complicated to be analytically useful. We can simplify the kinetics, however, by carefully adjusting the reaction conditions. For example, pseudo-first-order kinetics can be achieved by using a large excess of R (i.e. [R]o >> [A]o), such that its concentration remains essentially constant. Under these conditions... 

The concentration of nitromethane, CH3NO2, can be determined from the kinetics of its decomposition in basic solution. In the presence of excess base the reaction is pseudo-first-order in nitromethane. For a standard solution of 0.0100 M nitromethane, the concentration of nitromethane after 2.00 s was found to be 4.24 X 10 M. When a sample containing an unknown amount of nitromethane was analyzed, the concentration remaining after 2.00 s was found to be 5.35 X 10 M. What is the initial concentration of nitromethane in the sample ... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

The data shown in the following table were collected for a reaction known to follow pseudo-zero-order kinetics during the time in which the reaction was monitored. 

Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

The analysis is carried out under conditions in which the reaction s kinetics are pseudo-first-order in picrate. Show that under these conditions, a plot of potential as a function of time will be linear. 

The concentration of phenylacetate can be determined from the kinetics of its pseudo-first-order hydrolysis reaction in an ethylamine buffer. When a standard solution of 0.55 mM phenylacetate is analyzed, the concentration of phenylacetate after 60 s is found to be 0.17 mM. When an unknown is analyzed, the concentration of phenylacetate remaining after 60 s is found to be 0.23 mM. What is the initial concentration of phenylacetate in the unknown ... 

When D and H3O+ are present in excess, the kinetics of the reaction are pseudo-first-order in H2O2, and can be used to determine the concentration of H2O2 by following the production of I2 with time. In one analysis the absorbance of the solution was measured after 240 s at 348 nm (where Beer s law holds for I2). When a set of standard solutions of H2O2 was analyzed, the following results were obtained... 

The concentration of chromic acid can be determined from its reduction by alcohols under conditions when the kinetics are pseudo-first-order in analyte. One approach is to monitor the absorbance of the solution at a wavelength of 355 nm. A standard solution of 5.1 X lO " M chromic acid yields absorbances of 0.855 and 0.709 at, 100 s and 300 s, respectively, after the reaction s initiation. When a sample with an unknown amount of chromic acid is analyzed under... 

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

For those pesticides that are cometabolized, ie, not utilized as a growth substrate, the assumption of first-order kinetics is appropriate. The more accurate kinetic expression is actually pseudo-first-order kinetics, where the rate is dependent on both the pesticide concentration and the numbers of pesticide-degrading microorganisms. However, because of the difficulties in enumerating pesticide-transforming microorganisms, first-order rate constants, or half-hves, are typically reported. Based on kinetic constants, it is possible to rank the relative persistence of pesticides. Pesticides with half-hves of <10 days are considered to be relatively nonpersistent pesticides with half-hves of >100 days are considered to be relatively persistent. 

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. 

Mechanism. The thermal cracking of hydrocarbons proceeds via a free-radical mechanism (20). Siace that discovery, many reaction schemes have been proposed for various hydrocarbon feeds (21—24). Siace radicals are neutral species with a short life, their concentrations under reaction conditions are extremely small. Therefore, the iategration of continuity equations involving radical and molecular species requires special iategration algorithms (25). An approximate method known as pseudo steady-state approximation has been used ia chemical kinetics for many years (26,27). The errors associated with various approximations ia predicting the product distribution have been given (28). 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

An anaerobic digester is a no-recycle complete mix reactor. Thus, its performance is independent of organic loading but is controlled by hydraulic retention time (HRT). Based on kinetic theoiy and values of the pseudo constants for methane bac teria, a minimum HRT of 3 to 4 days is required. To provide a safety factor and compensate for load variation as indicated earlier, HRT is kept in the range 10 to 30 days. Thickening of feed sludge is used to reduce the tank volume required... 

The points that we have emphasized in this brief overview of the S l and 8 2 mechanisms are kinetics and stereochemistry. These features of a reaction provide important evidence for ascertaining whether a particular nucleophilic substitution follows an ionization or a direct displacement pathway. There are limitations to the generalization that reactions exhibiting first-order kinetics react by the Sj l mechanism and those exhibiting second-order kinetics react by the 8 2 mechanism. Many nucleophilic substitutions are carried out under conditions in which the nucleophile is present in large excess. When this is the case, the concentration of the nucleophile is essentially constant during die reaction and the observed kinetics become pseudo-first-order. This is true, for example, when the solvent is the nucleophile (solvolysis). In this case, the kinetics of the reaction provide no evidence as to whether the 8 1 or 8 2 mechanism operates. 

The intermediate diphenylhydroxymethyl radical has been detected after generation by flash photolysis. Photolysis of benzophenone in benzene solution containing potential hydrogen donors results in the formation of two intermediates that are detectable, and their rates of decay have been measured. One intermediate is the PhjCOH radical. It disappears by combination with another radical in a second-order process. A much shorter-lived species disappears with first-order kinetics in the presence of excess amounts of various hydrogen donors. The pseudo-first-order rate constants vary with the structure of the donor with 2,2-diphenylethanol, for example, k = 2 x 10 s . The rate is much less with poorer hydrogen-atom donors. The rapidly reacting intermediate is the triplet excited state of benzophenone. 

The silica dispersion showed the smallest retention volume. It should be noted, however, that the authors reported that the silica dispersion required sonicating for 5 hours before the silica was sufficiently dispersed to be used as "pseudo-solute". The retention volume of the silica dispersion gave the value of the kinetic dead volume, /.e., the volume of the moving portion of the mobile phase. It is clear that the difference between the retention volume of sodium nitroprusside and that of the silica dispersion is very small, and so the sodium nitroprusside can be used to measure the kinetic dead volume of a packed column. From such data, the mean kinetic linear velocity and the kinetic capacity ratio can be calculated for use with the Van Deemter equation [12] or the Golay equation [13]. 

The isolation experimental design can be illustrated with the rate equation v = kc%CB, for which we wish to determine the reaction orders a and b. We can set Cb >>> Ca, thus establishing pseudo-oth-order kinetics, and determine a, for example, by use of the integrated rate equations, experimentally following Ca as a function of time. By this technique we isolate reactant A for study. Having determined a, we may reverse the system and isolate B by setting Ca >>> Cb and thus determine b. 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

Considering the attention that we have given in this chapter to concentrationtime curves of complex reactions, it may seem remarkable that many kinetic studies never generate a comprehensive set of complicated concentration-time data. The reason for this is that complex reactions often can be studied under simplified conditions constituting important special cases for example, whenever feasible one chooses pseudo-first-order conditions, and then one studies the dependence of the pseudo-first-order rate constant on variables other than time. This approach is amplified below. 

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