Stoichiometry and rate law

Several studies have been made of oxidations of ketols by Cu(II). Simple cupric salts deposit cuprous oxide, but this has been overcome by using a citrate complex of Cu(II) or a 1 1 (mole) pyridine-water mixture. A recent detailed account is that of Wiberg and Nigh ° , who found the stoichiometry and rate law for the oxidation of a-hydroxyacetophenone by Cu(II) acetate to be, respectively,... 

Such coincidence of stoichiometry and rate law is fairly uncommon, the former is commonly no guide at all to the latter, which can only be obtained by experiment. Thus for the base catalysed bromination... 

Reaction mechanism a postulated sequence of elementary reactions that is consistent with the observed stoichiometry and rate law these are necessary but not sufficient conditions for the correctness of a mechanism, and are illustrated in Chapter 7. 

Combining the mole balance, stoichiometry, and rate law, we have... 

E Related material This problem uses the mole balances developed in Chapter 1 for a batch reactor and the stoichiometry and rate laws... 

Example 6-4 Stoichiometry and Rate Laws for Multiple Reactions... 

Given the reaction stoichiometry and rate laws, a desired objective and system constraints, what is the optimal reactor network structure What is the flow pattern of this network Where should mixing or segregatation occur in this network Where should heating and cooling be applied in this network ... 

Given the reaction stoichiometry and rate laws for an isothermal system, a simple representation for targeting of reactor networks is the segregated-flow model (see, e.g., Zwietering, 1959). A schematic of this model is shown in Fig. 2. Here, we assume that only molecules of the same age, t, are perfectly mixed and that molecules of different ages mix only at the reactor exit. The performance of such a model is completely determined by the residence time distribution function,/(f). By finding the optimal/(f) for a specified reactor network objective, one can solve the synthesis problem in the absence of mixing. 

Edwards, J.O., Green, E.F., Ross, J. (1968). From stoichiometry and rate law to mechanism. Journal of Chemical Education, 45, 381-385. 

Empirical Stoichiometry and Rate Law Model Stoichiometry and Rate Law... 

Cl(III) in excess CIO2 is observed Br appears to catalyze the decomposition of HCIO2. The stoichiometry and rate law are difficult to define. However, at concentrations in the narrow range [CKllDJo 2 x 10" M, [Br"] 5 x 10" M, a clock reaction... 

A > B to relate conversion and catalyst weight. Recall our mole balance stoichiometry. "i rate law, and ... 

The term reaction mechanism is part of the everyday language of chemists, yet it conveys different things to different people. The IUPAC Gold book (www.goldbook.iupac.org) defines the mechanism of a reaction as A detailed description of the process leading from the reactants to the products of a reaction, including a characterization as complete as possible of the composition, structure, energy and other properties of reaction intermediates, products and transition states. An acceptable mechanism of a specified reaction (and there may be a number of such alternative mechanisms not excluded by the evidence) must be consistent with the reaction stoichiometry, the rate law and with all other available experimental data, such as the stereochemical course of the reaction. On the basis of Occam s razor (Section 3.7.4), one should always choose the simplest mechanism that is consistent with all available evidence. 

The order of a reaction depends on the number of species and the number of times each species appears in the rate law. Often, the order of a reaction is equal to the number of particles that collide in the rate-determining step of the reaction. Later, however, we shall have examples in which the order of a reaction is less than the number of particles involved in the rate-determining step. From this discussion it should be apparent that the rate law for a reaction cannot be determined ifom stoichiometry. The rate law for the reaction A A may contain a variety of species not included in the chemical reaction also, it need not include A or A. If one can determine experimentally the rate law for a reaction, one may learn which species are involved in the ratedetermining step and hence obtain vital information about the reaction mechanism. 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Several important points about the rate law are shown in equation A5.4. First, the rate of a reaction may depend on the concentrations of both reactants and products, as well as the concentrations of species that do not appear in the reaction s overall stoichiometry. Species E in equation A5.4, for example, may represent a catalyst. Second, the reaction order for a given species is not necessarily the same as its stoichiometry in the chemical reaction. Reaction orders may be positive, negative, or zero and may take integer or noninteger values. Finally, the overall reaction order is the sum of the individual reaction orders. Thus, the overall reaction order for equation A5.4 isa-l-[3-l-y-l-5-l-8. 

A rate law is determined experimentally and the rate constant evaluated empirically. There is no necessary connection between the stoichiometry of a reaction and the form of the rate law. 

The result of the steady-state condition is that the overall rate of initiation must equal the total rate of termination. The application of the steady-state approximation and the resulting equality of the initiation and termination rates permits formulation of a rate law for the reaction mechanism above. The overall stoichiometry of a free-radical chain reaction is independent of the initiating and termination steps because the reactants are consumed and products formed almost entirely in the propagation steps. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

Example treats a reaction of this kind. The experimental rate law for the reaction of H2 gas with Br2 gas depends on the square root of the Bf2 concentration, and the reaction also is first order in H2 H2+Br2 2HBr Rate =. "[H2] [Br2] Despite the simple 1 1 stoichiometry of the overall reaction, this experimental rate law cannot be explained by a simple mechanism. For the first step of the mechanism for this reaction to be rate-determining, it would have to include a half-molecule of Bf2. There is no... 

Is this mechanism satisfactory A satisfactory mechanism must meet three criteria. It must be made up entirely of reasonable elementary steps, it must give the correct stoichiometry of the reaction, and it must predict the experimental rate law. 

The postulation of the +4 oxidation state of cobalt is necessary to account for the retarding influence of Pb(II). The existence of a dimeric species of Co(II) acetate is required by the rate law and is confirmed by spectrophotometric and solubility measurements. The existence of ionic species of the reactants is inferred by the rate increase on addition of sodium acetate, an observation which cannot be attributed to a salt effect because sodium perchlorate produces a rate decrease. On this scheme an explanation of the effect of water on the stoichiometry is that the step... 

The stoichiometry and the rate law for the oxidation by alkaline ferricyanide are, respectively (EDTA = H4Y) ... 

Cr(II) reduction of benzaldehyde in aqueous acidic ethanol also yields largely hydrobenzoin although other products were characterised, e.g. hydrobenzoin monoethyl ether, and a 1 1 stoichiometry is preserved. The rate law in ethanol acidified both with HCIO4 and HCl is complex for example, in HCl-ethanor°°,... 

However both groups agree on the stoichiometries, which are all of the type 2 Cr(n) 1 reductant molecule, and on the rate laws, which are generally... 

Tracing a kinetic redox path is a matter of redistributing mass among the basis entries, adding mass, for example, to oxidized basis entries at the expense of reduced entries. The stoichiometry of the mass transfer is given by the kinetic reaction 17.3, and the transfer rate is determined by the associated rate law (Eqn. 17.9, 17.12, or 17.21). 

I of reaction as a reaction path). The important consequence is that the maximum / number of steps in a kinetics scheme is the same as the number (R) of chemical equations (the number of steps in a kinetics mechanism is usually greater), and hence stoichiometry tells us the maximum number of independent rate laws that we must obtain experimentally (one for each step in the scheme) to describe completely the macroscopic behavior of the system. 

In this expression, both (—rA) and V vary and must be related to /A, through the rate law and an equation of state incorporating the stoichiometry, respectively for the equation of... 

A stoichiometric analysis based on the species expected to be present as reactants and products to determine, among other things, the maximum number of independent material balance (continuity) equations and kinetics rate laws required, and the means to take into account change of density, if appropriate. (A stoichiometric table or spreadsheet may be a useful aid to relate chosen process variables (Fj,ch etc.) to a minimum set of variables as determined by stoichiometry.)... 

In line with the stoichiometry Al H = 1 1 at the edge surface and Al H = 1 3 at the gibbsite surface and in accordance with Eqs. (5.12b) and (5.17b) the proton promoted rate law indicates a first order reaction 0 = 1) with respect to protons bound to the edge surface and a third order dependence (j = 3) with respect to the mol fraction of protons bound to the gibbsite surface. 

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