Second-order reaction worked example

Worked Example 8.17 The following kinetic data were obtained for the second-order reaction between osmium tetroxide and an alkene, to yield a 1,2-diol. Values of k are pseudo-order rate constants because the 0s04 was always in a tiny minority. Determine the second-order rate constant k2 from the data in the following table ... 

The work discussed in this section clearly delineates the role of droplet size distribution and coalescence and breakage phenomena in mass transfer with reaction. The population balance equations are shown to be applicable to these problems. However, as the models attempt to be more inclusive, meaningful solutions through these formulations become more elusive. For example, no work exists employing the population balance equations which accounts for the simultaneous affects of coalescence and breakage and size distribution on solute depletion in the dispersed phase when mass transfer accompanied by second-order reaction occurs in a continuous-flow vessel. Nevertheless, the population balance equation approach provides a rational framework to permit analysis of the importance of these individual phenomena. 

For many years the hydrogen-iodine reaction had been the traditional example of opposing second-order reactions. Recent work by J. H. Sullivan indicates that the mechanism is not as simple as we have assumed here in fact, the mechanism now seems to be unresolved. For a discussion and references see R. M. Noyes, J.Chem. Phys. 48, 323 (1968). 

The problem of reactions that do not go to completion is a frequently occurring one. We have shown here only the mechanics of deahng with a reversible system in which the reaction in each direction is first-order. Other cases that might arise are reversible second-order reactions, series reactions in which only one step is reversible, etc. These cases are quite complicated mathematically, and their treatment is beyond the scope of this book. However, many such systems have been elegantly described (see, for example, Schmid and Sapunov, 1982). The interested reader is directed to these worked-out exercises in applied mathematics for more details. 

Work Example 4.13 for the case where the reaction is second order of the single reactant type. It is irreversible and density is constant. The reactor element inside the loop is a PER. 

Bromination data became accessible over a large reactivity range when it became possible to follow low bromine concentrations. All the modern kinetic techniques are based on the fact that, since bromination is a second- or third-order reaction, bromination half-lives of a few milliseconds to several seconds can be obtained by working at very low reagent concentrations. For example, second-order rate constants as high as 109 m 1 s 1 can be readily measured if the reagent concentrations are 10-9m, the half-life of the bromine-olefin mixture then being 1 s. 

Worked Example 8.16 The reaction of the ester ethyl methanoate and sodium hydroxide in water is performed with NaOH in great excess ([NaOH]o = 0.23 mol dm-3). The reaction has a half-life that is independent of the initial concentration of ester present. 13.2 per cent of the ester remains after 14 min and 12 s. What is the second-order rate constant of reaction k2l... 

Early attempts at observing electron transfer in metalloproteins utilized redox-active metal complexes as external partners. The reactions were usually second-order and approaches based on the Marcus expression allowed, for example, conjectures as to the character and accessibility of the metal site. xhe agreement of the observed and calculated rate constants for cytochrome c reactions for example is particularly good, even ignoring work terms. The observations of deviation from second-order kinetics ( saturation kinetics) allowed the dissection of the observed rate constant into the components, namely adduct stability and first-order electron transfer rate constant (see however Sec. 1.6.4). Now it was a little easier to comment on the possible site of attack on the proteins, particularly when a number of modifications of the proteins became available. 

If the rate equation is to be employed in its integrated form, the problem of determining kinetic constants from experimental data from batch or tubular reactors is in many ways equivalent to taking the design equations and working backwards. Thus, for a batch reactor with constant volume of reaction mixture at constant temperature, the equations listed in Table 1.1 apply. For example, if a reaction is suspected of being second order overall, the experimental results are plotted in the form ... 

The slope of the straight line is the rate constant k, and the intercept is 1/[A]0. Thus, by plotting 1/[A] versus time, we can test whether the reaction is second order and can determine the value of the rate constant (see Worked Example 12.8). 

A reaction A—-—>P is to be performed in a CSTR. The reaction follows first-order kinetics and at 50 °C, the conversion reaches 99% in 60 seconds. The reaction is to be performed in a CSTR with the same productivity as the semi-batch reactor (Worked Example 7.1). The overall heat transfer coefficient of the reactor is 500 Wm"2 K"1. The maximum temperature difference with the cooling system is 50 K. 

A) The first question can be done in your head, but you may be asked to show your work, so it is useful to be able to solve the problem both ways. The quick inspection method is to look at what happens to the rate when only one substance changes. For example, in experiment 2 the concentration of A doubles while the concentration of B stays the same. The reaction rate increases by 4, which indicates the reaction is second order for A. In experiment 3, the concentration of B doubles while A remains constant. This change produces no change in reaction rate, meaning that the reaction is zero order for B. By inspection, the rate equation becomes Rate = k[A]2. Using rates equations, you can also determine the rate law. This requires solving for the variables m and n in the equation ... 

Among examples studied are the nitrosation of hydroxylamine and its methyl derivatives (M. N. Hughes et al., 1968), hydrazine (Perrott et al., 1976) and the methylhydrazines (Perrott et al., 1977). In all cases reaction occurred via the conjugate acid of the substrate, and although thiocyanate ion catalysis is more pronounced than that of bromide ion, the second order rate constants for reaction (25) were found to be approximately 100 times less than for nitrosyl bromide. More recent work with both morpholine and aniline showed the... 

Second-order rate coefficients, kH (= rate/[S] [H30+]), for the hydrolyses of some typical acetals, ketals, and orthoesters in purely aqueous solutions are collected in Table 12. In a compilation of data from one single source [162], ftH values can be found for the reactions of a large number of diethyl acetals and ketals in 50 % dioxane—water at 25 °C. In more recent studies, kH values have been determined for the hydrolyses of substituted benzaldehyde diethylacetals [163] and benzophenone diethyl-ketal [164] in the same solvent (Table 13). The hydrolyses of para-substituted methyl orthobenzoates have been studied in 70 % methanol-water [169]. A large amount of other work is concerned with various special examples. 

Rather little work has been carried out on the mechanisms of these protiodealkylation reactions. The reaction with HCI in methanol or methanol/benzene is second order. Stereochemical studies are restricted by the fact that, though tetraalkyltin compounds with chirality centred on tin are optically stable, the reaction products R3SnX are not, and compounds with chirality centred on the a-carbon atom in R would have to have the structure RR R"CSn or RR CDSn for the product to be configurationally stable. The only examples appear to be that the reaction of trimethyl(l-methyl-2,2-diphenylcyclo-propyl)tin with HCI or HBr,30 and of cis- and /ra .v-5-methyl- or -5-t-butylcyclohexyl-triisopropyltin with deuteriotrifluoroacetic acid31 proceed with complete retention (equations 5-27 and 5-28), which would be compatible with either an SE2(open) or SE2(cyclic) mechanism. 

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