Rate expressions experimental determination

This approach can be used with other simple rate expressions to determine a representative value of the reaction rate constant. Moreover, the experimental plan on which this technique is based will provide data over such a range of fraction conversions that it is readily adapted to various graphical techniques. Illustration 3.4 indicates how this approach is used to determine a reaction rate constant. 

The developments so far are based on the premise that intrinsic rate expressions are available. As discussed in Chapter 3, these rate expressions are determined from the kinetic data obtained under experimental conditions that ensure negligible transport effects. Various criteria of negligible transport effects have been developed to provide guidance on the experimental conditions and these were summarized in Chapter 3 without derivation. Consider these criteria in light of the understanding gained in this chapter. In view of the fact that external transport effects usually... 

These relative rate data per position are experimentally determined and are known as partial rate factors They offer a convenient way to express substituent effects m elec trophilic aromatic substitution reactions... 

The slope of a concentration-time curve to define the rate expression can be determined. However, experimental studies have shown the reaction cannot be described by simple kinetics, but by the relationship ... 

Rate constants (fifth column) usually correspond to one of the temperatures reported in the original papers and may be either experimentally determined values or those calculated from the activation parameters. In the preparation of the present review, the author has normalized a number of rate constants at arbitrary temperatures to permit direct comparisons with other data these normalized values and temperatures are tabulated (in italics) with the hope that they will offer additional useful information. The rate constants are usually expressed in liter x mole x sec when the values are followed by the symbol (A i) the units are sec. and dH are in kcal/mole JS is in eu. 

As we have seen, rate expressions for reactions must be determined experimentally. Once this has been done, it is possible to derive a plausible mechanism compatible with the observed rate expression. This, however, is a rather complex process and we will not attempt it here. Instead, we will consider the reverse process, which is much more straightforward. Given a mechanism for a several-step reaction, how can you deduce the rate expression corresponding to that mechanism ... 

Sometimes the rate expression obtained by the process just described involves a reactive intermediate, that is, a species produced in one step of the mechanism and consumed in a later step. Ordinarily, concentrations of such species are too small to be determined experimentally. Hence they must be eliminated from the rate expression if it is to be compared with experiment. The final rate expression usually includes only those species that appear in the balanced equation for the reaction. Sometimes, the concentration of a catalyst is included, but never that of a reactive intermediate. 

This result is experimentally indistinguishable from the general form, Equation (10.12), derived in Example 10.1 using the equality of rates method. Thus, assuming a particular step to be rate-controlling may not lead to any simplification of the intrinsic rate expression. Furthermore, when a simplified form such as Equation (10.15) is experimentally determined, it does not necessarily justify the assumptions used to derive the simplified form. Other models may lead to the same form. 

Mechanism I is a three-step process in which the first step is rate-determining. When the first step of a mechanism is rate-determining, the predicted rate law is the same as the rate expression for that first step. Here, the rate-determining step is a bimolecular collision. The rate expression for a bimolecular collision is first order in each collision partner Rate = j i[03 ][N0 j Mechanism I is consistent with the experimental rate law. If we add the elementary reactions, we find that it also gives the correct overall stoichiometry, so this mechanism meets all the requirements for a satisfactory one. 

Mechanism II begins with fast reversible ozone decomposition followed by a rate-determining bimolecular collision of an oxygen atom with a molecule of NO. The rate of the slow step is as follows Rate = 2[N0][0 This rate expression contains the concentration of an intermediate, atomic oxygen. To convert the rate expression into a form that can be compared with the experimental rate law, assume that the rate of the first step is equal to the rate of its reverse process. Then solve the equality for the concentration of the intermediate ... 

By applying the machinery of statistical thermodynamics we have derived expressions for the adsorption, reaction, and desorption of molecules on and from a surface. The rate constants can in each case be described as a ratio between partition functions of the transition state and the reactants. Below, we summarize the most important results for elementary surface reactions. In principle, all the important constants involved (prefactors and activation energies) can be calculated from the partitions functions. These are, however, not easily obtainable and, where possible, experimentally determined values are used. 

The value of this ratio is characteristic of the reaction order. Table 3.1 contains a tabulation of partial reaction times for various rate expressions of the form r = kCAn as well as a tabulation of some useful ratios of reaction times. By using ratios of the partial reaction times based on experimental data, one is able to obtain a quick estimate of the reaction order with minimum effort. Once this estimate is in hand one may proceed to use a more exact method of determining the reaction rate parameters. 

Since the problem of deriving a rate expression from a postulated set of elementary reactions is simpler than that of determining the mechanism of a reaction, and since experimental rate expressions provide one of the most useful tests of reaction mechanisms, we will now consider this problem. 

What rate expression results from this mechanism Is this expression consistent with the experimentally determined rate expression ... 

This form is consistent with the experimentally determined rate expression. 

The various theories can provide useful insight into the way in which reactions occur, but we must again emphasize that they must be regarded as inadequate substitutes for experimental rate measurements. Experimental work to determine an accurate reaction rate expression is an essential prerequisite to the reactor design process. 

The problem of determining the mathematical form of the rate expression for a chemical reaction is one that involves a combination of careful experimental work and sound judgment in the analysis of the data obtained thereby. In many cases the analytical techniques discussed in Section 3.3 are directly applicable to studies of reversible reactions. In other cases only minor modifications are necessary. 

In this subsection we have treated a variety of higher-order simple parallel reactions. Only by the proper choice of initial conditions is it possible to obtain closed form solutions for some of the types of reaction rate expressions one is likely to encounter in engineering practice. Consequently, in efforts to determine the kinetic parameters characteristic of such systems, one should carefully choose the experimental conditions so as to ensure that potential simplifications will actually occur. These simplifications may arise from the use of stoichiometric ratios of reactants or from the degeneration of reaction orders arising from the use of a vast excess of one reactant. Such planning is particularly important in the early stages of the research when one has minimum knowledge of the system under study. 

It has been suggested that the rate limiting step in the mechanism is the chemisorption of propionaldehyde and that the hydrogen undergoes dissociative adsorption on nickel. Determine if the rate expression predicted by a Hougen-Watson model based on these assumptions is consistent with the experimentally observed rate expression. 

The resulting expression for [B2] is substituted into the expression for reaction rate, and we see that the experimentally determined rate law is not recovered. 

To determine Km and Vmax, experimental data for cs versus t are compared with values of cs predicted by numerical integration of equation 10.3-3 estimates of Km and Vmax are subsequently adjusted until the sum of the squared residuals is minimized. The E-Z Solve software may be used for this purpose. This method also applies to other complex rate expressions, such as Langmuir-Hinshelwood rate laws (Chapter 8). 

The obvious challenge in the interpretation of the data is to find a suitable explanation for the independence of the third term of the rate law, Eq. (102), on the concentrations of HSO3 and 02. The rate expression determined experimentally could be modeled quantitatively by combining the following propagation steps with the uncatalyzed reaction mechanism ... 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

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