Reactions of the second order

There can arise two possibilities in the case of reactions of the second order the rate may be proportional to the product of two equal initial concentrations or to the product of two different initial concentrations. The first case corresponds to a situation where a single reactant is involved, the process being represented as ... 

All chemical reactions proceed in stages and usually by the interaction of two molecules (reactions of the second order or bimolecular reactions). Hence our reaction will take place in stages and should be formulated as follows ... 

Riesenfeld and Bohnholtzer and Riesenfeld and Schumacher used ozone concentrated by liquefaction and distillation. From their kinetic measurements they conclude that a reaction of the second order and one of the first order take place simultaneously at quite low pressures, 6-60 mm. Hg the first order reaction predominates. The velocity constants of the second order reaction are not influenced by the total pressure, while those of the first order reaction appear to be inversely proportional to the total pressure. The figures given show that the first order reaction at the lower pressures is considerably influenced by the surface, and is quite probably a heterogeneous reaction, though the authors themselves do not consider this to be definitely shown. The decomposition appears to be rather sensitive to catalysts such as dust particles. 

Phosphine yields a copper-coloured precipitate, possibly an arsenide of phosphorus.6 Phosphorus trichloride causes reduction to arsenic,7 as also do the tribromide and triiodide, though less readily. Hypophos-phorous acid causes a similar reduction to arsenic 8 in hydrochloric acid solution the velocity of the reaction at various concentrations corresponds with that of a reaction of the second order and may be expressed by 9... 

MM A. Figure 6 shows the over-all reaction rate plotted logarithmically vs. time in case of the y-emulsion polymerization of MM A. After the sharp rise of Ufir, a period of zero order of Ubf seems to follow. But then Ubf increases further and reaches a maximum at about 50% conversion. Soon afterwards, the curve drops sharply, and Ubf decreases almost as fast as if the radiation source were removed at this point. This decrease does not follow, or follows for only a short time, a first-order law with respect to monomer concentration. There also is no reaction of the second order with respect to [M]. 

Suppose now we are at equilibrium, when association and dissociation compensate each other. We may then apply the detailed balancing principle and say that the dissociation process must be a bimolecular reaction of the second order.4 From a knowledge of the equilibrium constant and of the experimental association rate, we may then infer the pseudoexperimental dissociation rate at equilibrium. It is rather fortunate that the association process does not require an activation energy, since in this case, its rate is the same out of equilibrium, where the experiments have been carried out, as it is at equilibrium, where the values are interesting. We then understand that the dissociation reactions of a diatomic molecule by a bimolecular process offer the two interesting possibilities ... 

II. —Reactions of the second order. Let a and b respectively denote the concentration of two different substances, say, in such a reacting system as occurs when acetic acid acts on alcohol, or bromine on fumaric acid, then, according to the law of mass action, the velocity of the reaction at any moment is proportional to the product of concentration of the reacting substances. For every gram molecule of acetic acid transformed, the same amount of alcohol must also disappear. When the system contains a — x gram molecules of acetic acid it must also contain b - x gram molecules of alcohol. Hence... 

Reactions which progress according to this equation are called reactions of the second order. If the two reacting molecules are the same, then a = b. From (2), therefore, we get log 1 x J = 0 x go. Such indeterminate fractions will be discussed later on. But if we... 

In discussing the velocity of reactions of the second order, we found that if the concentration of the two species of reacting molecules is the same, the expression... 

C3H5 A. (OH)2 + H. OH = A. H + C3H6(OH)3 (Glycerol). These reactions are interdependent. The rate of formation of glycerol is conditioned by the rate of formation of monoacetin the rate of monoacetin depends, in turn, upon the rate of formation of diacetin. There are, thei efore, three simultaneous reactions of the second order taking place in the system. 

Comparing Eq. (10.42) with Eq. (10.52), one can draw the conclusion that Brownian coagulation (10.42) corresponds to a chemical reaction of the second order, and gradient coagulation (10.52) - to a reaction of the first order. 

Thus, in the case of coagulation in a turbulent flow, coagulation frequency corresponds to a reaction of the second order and is proportional to a , as in the laminar flow. 

According with (3.32) it is not difficult to determine critical values of chemical reaction rates constants which are necessary for fast processes realization in the absence of diffusion limitations. In Figure 3.28 the dependence of critical values of rate constant of low-molecular reaction of the second order on reaction mixture movement linear rate V in tubular turbulent apparatus and also on its construction is presented as an example. Increase of V and reaction zone diameter d allows carrying out of chemical reactions in optimal conditions with values of rates constants high enough. In particular, at technically acceptable values of d and V chemical reaction proceeding in the absence of diffusion resistances is limited by the value of constant of low-molecular compounds reaction rate - k 5 10 Fmole-sec. 

The possibility of formation of corresponding liquid flows mixing fronts under fast chemical reaction proceeding and without it (see 1.3.1) determines the interest in investigation of reaction rate constant effect on conditions of quasi-plug-flow mode formation in turbulent flows (plan reaction front). Low-molecular chemical reactions of the second order proceeding with rate constants in the range of k = 10 +10 1/mole-sec were experimentally studied. 

As it follows from the data, cited above, at til min =2.82 and at i > 27 min transesterification reaction becomes classical reaction of the second order. 

The reaction between SO3 and the aromatic substrate is an electrophilic substitution reaction of the second order, and in the specific case of LAB, this reaction proceeds in accordance with the mechanism shown in Figure 5.5 [3]. 

In the following, dilution effects on kinetics are illustrated with an elementary reaction of the second order ... 

Fio. 2. Reaction of the second order between two substrates of equal concentration. The velocity coefficient (k) can be derived from the slope of the strai t line of... 

The oxidation of carbonyl compounds resembles in their regularities the oxida tion of alcohols. For example, diethyl ketone is oxidized W Co in a reaction of the second order with the pH-dependent constant k xp = 310 (1 + 13.8[H30 ]) l/(mol s) at 293 K. The dependence of on [H30 ] is explained by the equilibrium... 

When two molecular species undergo change in concentration during the reaction (bimolecular reaction or reaction of the second order) the velocity of the reaction will be... 

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