RATE LAW DATA

Reaction rate laws and data can be obtained from the following Web sites  

Standard Reference Database 17, Version 7.0 (Web Version), Release 1.2 

This Web site provides a compilation of kinetics data on gas-phase reactions. 

International Union of Pure and Applied Chemistry (lUPAC) 

This Web site provides kinetic and photochemical data for gas kinetic data evaluation. 

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The most that can be said for relative activities at this stage is that to a good approximation in each period d > d > d Q, and in each group 4d>3d>5d. Only for cobalt has sufficient rate law data been obtained (12,13) to allow future comparisons of absolute activities with respect to CO hydrogenation to oxygenates. 

A plot of PcoPh ch function of P should be a straight line with an intercept of 11a and a slope of bta. From the plot in Figure E5-4.2 we see that the rate law is indeed consistent with the rate law data. 

When collecting rate law data, operate in the reaction-limited region... 

In this chapter we first consider a mathematically tractable model mechanism and demonstrate that, depending upon the relative magnitudes of the rate constants, there are two chemical approximations that may be appropriate for simplifying analysis the preequilibrium and the steady-state assumptions. We then demonstrate how hypotheses based upon these simplifications are used to interpret rate law data and to develop chemically reasonable mechanistic descriptions for gas- and solution-phase reactions. Finally we consider the problem of catalysis, i.c., how addition of trace amounts of an intermediate permits a sluggish or kinetically forbidden reaction to become rapid if a new mechanistic pathway can be created. 

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

The observed rate law depends on the type of catalyst used with promoted iron catalysts a rather complex dependence on nitrogen, hydrogen, and ammonia pressures is observed, and it has been difficult to obtain any definitive form from experimental data (although note Eq. XVIII-20). A useful alternative approach... 

Sequences such as the above allow the formulation of rate laws but do not reveal molecular details such as the nature of the transition states involved. Molecular orbital analyses can help, as in Ref. 270 it is expected, for example, that increased strength of the metal—CO bond means decreased C=0 bond strength, which should facilitate process XVIII-55. The complexity of the situation is indicated in Fig. XVIII-24, however, which shows catalytic activity to go through a maximum with increasing heat of chemisorption of CO. Temperature-programmed reaction studies show the presence of more than one kind of site [99,1(K),283], and ESDIAD data show both the location and the orientation of adsorbed CO (on Pt) to vary with coverage [284]. 

The above rate law has been observed for many metals and alloys either anodically oxidized or exposed to oxidizing atmospheres at low to moderate temperatures—see e.g. [60]. It should be noted that a variety of different mechanisms of growth have been proposed (see e.g. [61, 62]) but they have in common that they result in either the inverse logaritlnnic or the direct logarithmic growth law. For many systems, the experimental data obtained up to now fit both growth laws equally well, and, hence, it is difficult to distinguish between them. 

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 value of the rate constant can be determined by substituting the rate, the [C3H5O], and the [H+] for an experiment into the rate law and solving for k. Using the data from experiment 1, for example, gives a rate constant of 3.31 X 10 s h The average rate constant for the eight experiments is 3.49 X 10-5 M-i s-i ... 

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

These examples illustrate the relationship between kinetic results and the determination of reaction mechanism. Kinetic results can exclude from consideration all mechanisms that require a rate law different from the observed one. It is often true, however, that related mechanisms give rise to identical predicted rate expressions. In this case, the mechanisms are kinetically equivalent, and a choice between them is not possible on the basis of kinetic data. A further limitation on the information that kinetic studies provide should also be recognized. Although the data can give the composition of the activated complex for the rate-determining step and preceding steps, it provides no information about the structure of the intermediate. Sometimes the structure can be inferred from related chemical experience, but it is never established by kinetic data alone. 

Consider the data of Hull and von Ronsenberg in Example 8-3 for mixing in a fluidized bed. Suppose the solids in the fluidized bed were not aeting as a eatalyst, but were aetually reaeting aeeording to a first order rate law (-r) = kC, k = 1.2 min Compare the aetual eonversion with that of an ideal plug flow. 

The second type of behaviour (Fig. 1.89) is much closer to that which one might predict from the regular cracking of successive oxide layers, i.e. the rate decreases to a constant value. Often the oxide-metal volume ratio (Table 1.27) is much greater than unity, and oxidation occurs by oxygen transport in the continuous oxide in some examples the data can be fitted by the paralinear rate law, which is considered later. Destructive oxidation of this type is shown by many metals such as molybdenum, tungsten and tantalum which would otherwise have excellent properties for use at high temperatures. 

A disadvantage inherent in the reduced time method of analysis, as discussed by Sharp et al. [70] Geiss [488] and others [30,33] is that it involves the comparison of curves. An alternative, and widely used, method of preliminary identification of the rate law providing the most satisfactory fit to a set of data is through a plot of the form... 

Although individual runs for the first set of experiments follow the second-order rate law, the observed second-order rate coefficients, k, are strongly dependent on the initial amine concentrations, with the rate increasing regularly as the amine concentration increases. Nevertheless, for all of the measurements, a plot of k versus the initial amine concentration is linear, and the data can be fitted withegn.(4), with k equal to 1.87 x 10-4 l.mole-1. sec-1 and k" equal to 5.63 x 10-412. mole-2. sec-1. 

Rather than the use of instantaneous or initial rates, the more usual procedure in chemical kinetics is to measure one or more concentrations over the timed course of the reaction. It is the analysis of the concentrations themselves, and not the rates, that provides the customary treatments. The concentration-time data are fitted to an integrated form of the rate law. These methods are the subjects of Chapters 2, 3, and 4. 

Generally, to do this one guesses the rate law or mechanism and tests the data against its predictions. The initial supposition of the mechanism may be made on the basis of precedents in the literature, the results of an earlier trial, or the appearance of the raw data. 

Let us now assume that these matters have been attended to properly. At this stage we can but assume that the reaction orders were correctly identified and correct mathematical procedures followed. During the course of the work, the investigator should make the occasional quick calculation to show the values are roughly correct. (Does the rate constant yield the correct half-time ) Also, one should examine the experimental data fits to see that the data really do conform to the selected rate equation. Deviations signal an incorrect rate law or complications, such as secondary reactions. 

Kinetic data for the reaction between PuOi- and Fe2+, given in Table 2-4, are fitted to the integrated rate law for mixed second-order kinetics. The solid curve represents the least-squares fit to Eq. (2-34). left and (2-35). right. 

These plots illustrate the variations of [A] (left axes, open squares) and of absorbance (right axes, filled squares) during the conversion of A(e = 1000) to P( = 7000) for data following zeroth-order (left), halforder (center), and three-halves-order rate laws. 

If concentrations are known to —1-2 percent, a minimum of 10-fold excess over the stoichiometric concentration is required to evaluate k to within a few percent. The origins of error have been discussed.14,15 If the rate law is v = fc[A][B], with [B]o = 10[AJo, [B1 decreases during the run to 0.90[A]o. The data analysis provides k (the pseudo-first-order rate constant). To obtain k, one divides k by [B]av- If data were collected over the complete course of the reaction,... 

Better yet, a least-squares analysis of k versus [B]av is carried out. The order with respect to [A], the limiting reagent, is established from the fit of the data to a chosen rate law. Experiments over a range of [A]o are a preferable way to show the order in LA], At constant [B], will be the same regardless of [A]o if the rate is first-order with respect to [A],... 

Wilkinson s method allows the evaluation of the reaction order from data taken during the first half-life. This, as we saw, was not possible from treatment by the integrated rate law. Note, however, that relatively small errors in [A] can lead to a larger error in E at small conversions.17... 

Second-order kinetics, (a) Derive expressions for the half-time and lifetime of A if the rate law for its disappearance is v = fc[A]2 (b) calculate t]/i and t for the data presented in Section 2.2 (c) calculate the second half-life, t /i(2), i.e., the time elapsed between 50 percent and 75 percent completion, for the same reaction (d) compare fj/2(l) and fi/>(2), and contrast this result with that from first-order kinetics. 

The reaction follows a mixed second-order rate law. The progress was monitored spec-trophotometrically at 723 nm, where Np4+ has a maximum absorption. The following data refer to an experiment with [Np3+]o = 1.53 x 10-4 M, [Fe3+]o = 2.24 x 10-4 M (taken at 298.0 K, [H+] = 0.400 M, and ionic strength = 2.00 M). Calculate the rate constant either taking the end point value as 0.351 or, if a suitable program is available, allowing it to be found in the calculation. 

The reaction follows first-order kinetics when studied at constant [Melm] and [CO]. Formulate the rate law and calculate any constants from the following data obtained at 23 °C in benzene with [CO] = 3.17 X 10 3 M ... 

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