Theoretical rate equations

However, one of the postulates of transition state theory is that the rate of reaction is equal to the product of the transition state species concentration and the frequency of their conversion to products, so the theoretical rate equation is... 

Two conditions must be met if the proton transfer step is to be slow and rate-determining (a) k must be smaller than the rate coefficient of a diffusion-controlled reaction, and (b) fe i must be smaller than ku. The first condition is fulfilled in most proton transfer processes to or from carbon. It may be met also in a proton transfer among oxygen, sulfur, or nitrogen atoms if either the acidity of the proton donor or the basicity of the acceptor is extremely low. The second condition, e.g. <1kn, can be fulfilled if the intermediate is sufficiently unstable with respect to decomposition toward the products. In several examples, ku and ft, are of the same order of magnitude, e.g. k [ ku, and the proton transfer step is partially rate-determining. For these cases, the theoretical rate equation must be derived with the aid of the stationary state method Vol. 2, pp. 352-354). 

These workers are mainly concerned with developing a theoretical rate equation for mixing, and interpreting this equation. No experimental data are given. 

A descriptor rate constant for solid-state degradation can be obtained once a theoretical rate equation has been derived and the data have been tested to see if they conform to the proposed model. However, for solid-state degradation in which the factors affecting the degradation mechanism have not been elucidated, because of the complexity involved, often an apparent constant (or constants) obtained by fitting the observed degradation curve to an empirical equation or equations is utilized. Such constants and the empirical relationships themselves can sometimes be used for stability prediction purposes. This section first discusses various theoretical equations used to describe the solid-state stability of drugs and introduces an empirical equation that can often describe the data adequately. 

Although the theoretical rate equations indicate that a higher concentration leads to a faster reaction, there are some practical limits to reactant concentration. The solubility of the reactant in the synthesis solvent restricts the upper limit of the concentration. There is also the possibility of the occurrence of undesired side reactions with highly concentrated or reactive reagents. This is particularly true for the deblock reaction. For instance, when higher concentrations of acid are used in the deblock reaction in oligonu-... 

This equation is an example of a rate equation and, more explicitly, it is the theoretical rate equation for the elementary reaction described by Equation 4.1. The quantity theory is the theoretical rate constant for the elementary reaction it has a value that is independent of the concentrations of reactants A and B. 

For an elementary reaction involving two reactant species A and B, a simple collision model predicts a theoretical rate equation of the form... 

This prediction is also borne out experimentally (cf. Table 4.1) since the experimental rate equation is of exactly the same form in other words the partial order of reaction with respect to each reactant is 1 and overall the reaction is second-order. In the case of a unimolecular reaction, the situation is more complicated since a single reactant particle has to become energized or activated by collisions, either with other reactant particles or other bodies that are present, in order for reaction to occur. However, although we shall not go into detail, a theoretical treatment shows that under most circumstances the rate of reaction will be directly proportional to the concentration of the single reactant species so that the theoretical rate equation can be written... 

The derivation of the form of the theoretical rate equation using a simple collision model is more complex in this type of case but it turns out that the equation is of the expected form... 

Elementary reactions may be unimolecular, bimolecular or, very rarely, termolecular. An important feature of these reactions is that the experimental overall order of reaction is the same as the molecularity. This means that the theoretical rate equation for a reaction that is proposed to be elementary can be written down on the basis of the stoichiometry. 

J The theoretical rate equation for the first step, which is bimolecular, is... 

What are the theoretical rate equations for the forward and reverse reactions in Step 1 (Label the rates of reaction as J and 7 i, respectively.)... 

Discuss the meaning of the terms elementary reaction and molecularity , and write down the form of the theoretical rate equation for a chemical reaction that is thought to be elementary. (Question 7.1)... 

J What is the theoretical rate equation predicted by this mechanism ... 

Since both substrate and reagent are involved in this elementary step the theoretical rate equation will involve a concentration term from both substrate and reagent... 

What is the theoretical rate equation predicted by this mechanism if (a) the first step is rate-limiting and (b) the second step is rate-limiting ... 

We have now determined the theoretical rate equations for each of our possible mechanisms. The next step is to compare them with experimental rate equations. 

J The only mechanism that generates a theoretical rate equation that is first-order is a two-step dissociative mechanism with the first step rate-limiting. 

The Sn reaction between bromomethane and sodium hydroxide in methanol at 25 °C follows second-order kinetics with the experimental rate Equation 4.1. The concerted and two-step associative mechanisms both generate a theoretical rate equation of this form, so it s at this point that we have to use other information to discriminate between these two mechanisms. 

In order to relate the theoretical rate equations to experiments, it is useful to derive some general consequences without intra-ducing any restrictive assumptions. Such assumptions can be additionally introduced to obtain more restricted relations which are, however, also independent of the particular model used to describe a given type of chemical reaction. 

Assuming a steady state with respect to the concentration of Intermediate radicals and atoms, theoretical rate equations were derived and those were found to be Identical with the experimental equations (see Table I and Table II-A) for the relatively low hydrogen partial pressures of up to < 73 bar. In further testing the applicability of this mechanism under more extended experimental conditions. It was found that the kinetics of the toluene formation was different at a hydrogen partial pressure of 230 bar. At the latter hydrogen pressure a rate equation of... 

Table II Thermal hydrocracking of indan theoretical rate equations according to the c< ring opening chain reaction.

The many different factors that can influence the rate of dissolution of silica particles in addition to the surface area have been reviewed by O Connor and Greenberg (217). The temperature, degree of crystallinity, previous mechanical and heat treatment, and previous treatments with water, alkali, or acid all had their effects. They found that the theoretical rate equations for dissolution hold only if the silica is completely dispersed as individual particles and that in aggregated or flocculated materia not all the surface area is available to solution. They formulated the rate of solution as follows ... 

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