Reactions of Higher Order

Hence the ash was laid down about 1,700,000 years ago this is the presumable age of the skeletons found in association with it. 

If reaction occurs by collision and interaction of two molecules A and B, the rate of reaction will be proportional to the number of collisions. The number of collisions in unit volume is seen from simple kinetic considerations to be proportional to the product of the concentrations of A and B. Hence we may write as the differential rate expression for this second-order reaction 

Here —d[A]lcIt is the rate of decrease in concentration of [A] and —d[B]ldt is that of [B] they are equal, the reaction being A -f B - products. The factor k is the second-order rate constant. Its dimensions are seen to be liter mole , the reciprocal of concentration, times s-.  

It must be emphasized that the stoichiometric equation for a reaction does not determine its rate equation. Thus the oxidation of iodide ion by persulfate ion 

This is followed by a rapid reaction between the products and another iodide ion.  

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The explanation for the variation of R with N, the molecular source concentration, lies in reactions of higher order involving transfer of the hydrogen ion from one methanol molecule to another, of the type... 

Reactions of higher orders than two are less common, though some third-order reactions are encountered. Proceeding in a similar way for reaction of nh order,... 

Reactions of higher order are very rare, and most of the complicated reactions take place in stages. Such reactions which occur in stages are called consecutive or successive reactions and are very common. If a substance A is reacted to yield a product C via the formation of an intermediate substance B, then the overall process consists of the two reactions shown below ... 

High reactant concentrations favor the reaction of higher order, while low reactant concentrations favor the reaction of lower order. 

However, micelles do not always favor reactions of higher order. In dilute OH-, reaction of activated amides, for example (18), is typically second order in OH-, but the order decreases to one with increasing [OH-] because the tetrahedral intermediate is converted rapidly into products (Menger and Donohue, 1973 Cipiciani et al., 1979). These reactions are speeded by cationic micelles, but in the micelles they are always first order in OH-, even when the total concentration of OH- is low. This is simply because the micelles concentrate OH-, so that the tetrahedral intermediate in (18) is... 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

For reactions in parallel, the concentration level of reactants is the key to proper control of product distribution, A high reactant concentration favors the reaction of higher order, a low concentration favors the reaction of lower order, while the concentration level has no effect on the product distribution for reactions of the same order. 

The First-Order Linear Inhomogeneous Differential Equation (FOLIDE) First-Order Reaction Including Back Reaction Reaction of Higher Order Catalyzed Reactions... 

The possibility of working in dilute solutions (10-3 M to 10 5 M, in some instances even more dilute) offers an additional advantage because some reactions are under these conditions not complicated by consecutive and competitive reactions of higher order which appear at higher concentrations. 

For the reaction A + A — P, we can write —dAJdt = k(A)(A) = k A2. In this case, the rate involves a higher power of the concentration (n = 1 + 1 = 2) and the reaction is second-order. For the reaction A -I- B —> P, the rate is proportional to the first power of each reactant and —d(A)(B)/dt = k(A)(B). The reaction is first-order with respect to A or B, but the overall reaction is second-order, because the right-hand side of the equation contains the product of two concentrations. The value of tV2 will depend on the initial reactant concentration(s), and the second-order rate constants have the dimensions of reciprocal concentration times time. Reactions of higher order, such as third order, are relatively rare, and their rates are proportional to the product of three concentration terms. 

The same results can be obtained for any reactions of higher order in which forward and back reactions are at least bimolecular. Conversely, only those higher-order reactions for which the reverse step is unimolecular can show a nonequilibrium dependence of the rate constant, e.g., A + B + C D [8. W. Benson and A. E. Axworthy, Jr., J. Chem, Phys., 21, 428 (1953)]. 

The example of this reaction demonstrates another important facet of kinetics. Figure 5.4 shows side by side the experimental data plotted as a first order-first order reversible reaction and as an irreversible reaction of order 1.5. Over a limited conversion range (here about two thirds of the way to equilibrium) the second plot is linear within the scatter of the data points. Although evaluation of the full conversion range leaves no doubt that the reaction is indeed reversible and first order-first order, its rate up to a rather high conversion is approximated surprisingly well by the equation for an irreversible reaction of higher order, in this instance of order 1.5 ... 

Unless results at conversions close to equilibrium are available, a reversible reaction can be mistaken for an irreversible reaction of higher order. 

The mathematics of reversible reactions of higher order than second are cumbersome. Rather than struggling with them, the chemist or engineer interested in their kinetics will design his experiments to circumvent this obstacle by determining pseudo-orders or evaluating initial rates (see Section 3.3.2 and 3.3.3). 

Combinations of parallel steps of different orders are common in practice. The most frequently encountered situation is the formation of a heavy by-product by higher-order dimerization or oligomerization parallel to a first-order main reaction. In other common cases, the side reaction is a first-order decomposition of a reactant parallel to a main reaction of higher order. 

The first of these rules had already been stated for pathways of first-order steps, the second is a consequence of the stronger concentration dependence of reactions of higher order (see also Section 5.2.3). 

If not carried to high conversion, the rate of a reversible reaction may be indistinguishable from that of an irreversible reaction of higher order. 

First-order reactions are by far the most common. They are also the simplest to study experimentally. For reactions of higher order, experimental conditions can usually be arranged so that they are first-order (see below). This simplifies the situation considerably. 

As seen in Fig. 3, the conversion curves especially at higher conversions have the character of reactions of higher order which seems to indicate that the polymerization becomes diffusion controlled. In actual fact, precipitation of polymer occurred during polymerization. The reaction rate decreases sharply in the initial stages of the polymerization. With... 

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