Empirical kinetic equations

The algebraic relationship between experimentally determined rate constants (k) as a function of factors that affect the reaction rate, such as the concentration of reaction ingredients, including catalysts and temperature, is defined as empirical kinetic equation. The validity of an empirical kinetic equation is solely supported by experimental observations and, thus, its authenticity is beyond any doubt as far as a reliable data fit to the empirical equation is concerned. However, the nature and the values of calculated empirical parameters or constants remain obscure until the empirical kinetic equation is justified theoretically or mechanistically. The experimental determination of the empirical kinetic equations is considered to be the most important aspect of the use of kinetic study in the mechanistic diagnosis of the reactions. The classical and perhaps the most important empirical kinetic equation, determined by Hood in 1878, is Equation 7.8. 

The rate of a reaction is generally affected by all or some of the following factors temperature, reaction medium, the concentration of reactants and cata- 

The Values of Observed Absorbance (Ao, ) at 310 nm as a Function of Reaction Time (t) for Hydrolysis of A/-Methylphthalamic Acid 

Note Data analysis with Equation 7.44 and Equation 7.45. 

---

The following discussion summarizes the arguments for and against the use of simple empirical kinetic equations. 

The problem of calculating reaction rate is as yet unsolved for almost all chemical reactions. The problem is harder for heterogeneous reactions, where so little is known of the structures and energies of intermediates. Advances in this area will come slowly, but at least the partial knowledge that exists is of value. Rates, if free from diffusion or adsorption effects, are governed by the Arrhenius equation. Rates for a particular catalyst composition are proportional to surface area. Empirical kinetic equations often describe effects of concentrations, pressure, and conversion level in a manner which is valuable for technical applications. 

Empirical Kinetic Equation for Coke Formation The experimental observations given in section Vlb(l), (2), and (3) lead to the empirical equation for coke formation... 

A more empirical approach [13] for describing the kinetics of the pyrolytic reactions in solid state is to use a parametric equation that includes formulas for all possible categories of kinetics mechanisms known to occur for the chemical reactions of solid samples. Considering F the mass fraction of the unreacted substance at the time t, the empirical kinetics equation for heterogeneous systems can be expressed in the general form ... 

Recent review of sorption kinetics in soils [796] reports a number of theoretical and empirical kinetic equations that have been used in complex and ill defined systems. 

The different chlorination by-products have been described in detail by Hashimoto (1995). The risk of chlorination by-products in relation to current regulations was discussed, and alternative disinfectants were investigated by Regli et al. (1995). Kronberg (1999) attributes the mutagenic character of DBFs to various chlorohydroxyfuranones (CHFs). The concentrations critical for human health are largely unknown. Main chlorination reaction products of natural waters were summarised by Jiminez et al. (1993) and a model for the THM formation developed. An empirical kinetic equation was established for the formation of THM from HA and hj pochlorite at a different pH. 

The empirical kinetic equation of ethylene oxidation is thus... 

In the very early phase of the kinetic studies on the effects of [micelles] on the reaction rates, it has been observed that an empirical kinetic equation similar to Equation 7.48 with replacement of [M X ] by [Smflj - CMC (where [Smflj and CMC represent total surfactant concentration and critical micelle concentration, respectively) is applicable in many micellar-mediated reactions. But the plots of kobs vs. ([Surf]j - CMC) for alkaline hydrolysis of some esters reveal maxima when surfactants are cationic in nature. - - Similar kinetic plots have also been observed in the hydrolysis of methyl orthobenzoate in the presence of anionic micelles. Bunton and Robinson suggested a semiempirical equation similar to Equation 7.49, which could explain the presence of maxima in the plots of ko s vs. ([Surflj - CMC). In Equation 7.49), J, is an empirical constant. 

Pseudo-first-order rate constants (k bs) for foe nucleophilic reaction of piperidine with phthalimide at different total piperidine concentration ([Piplj) in 100% v/v CH3CN solvent obey the empirical kinetic equation. Equation 7.51,... 

Empirical kinetic equations for dynamic processes such as reaction rates very often form the basis of theoretical developments that show the fine details of the mechanisms of reactions. Perhaps the most classical example of an empirical kinetic equation is Equation 7.8, which was discovered experimentally in 1878. But a satisfactory theoretical justification for Equation 7.8 was provided by Eyring in 1935, which provides the physicochemical meanings of the empirical constants, A and B, of Equation 7.8. Empirical kinetic equations, such as Equation 7.47 to Equation 7.55, obtained as the functions of concentrations of reactants, catalysts, inert salts, and solvents, provide vital information regarding the fine details of reaction mechanisms. The basic approach in using kinetics as a tool for elucidation of the reaetion mechanism consists of (1) experimental determination of empirical kinetic equation, (2) proposal of a plausible reaction mechanism, (3) derivation of the rate law in view of the proposed reaction mechanism (such a derived rate law is referred to as theoretical rate law), and (4) comparison of the derived rate law with experimentally observed rate law, which leads to the so-called theoretical kinetic equation. The theoretical kinetic equation must be similar to the empirical kinetic equation with definite relationships between empirical constants and various rate constants and equilibrium constants used in the proposed reaction mechanism. 

It should be noted that the kinetic approach used to elucidate the fine details of reaction mechanisms may be thought to be the best, and even a necessary, approach, but it is not always sufficient. Additional experimental evidence should be used to strengthen the correctness of the proposed reaction mechanism. Sometimes, two or more alternative mechanisms can lead to the same theoretical rate law or theoretical kinetic equation with, of course, different constant parameters, which means that the empirical kinetic equation cannot differentiate between these alternative mechanisms. Under such circumstances, other appropriate physicochemical approaches are needed to differentiate between alternative reaction mechanisms. An attempt is made in this section of the chapter to give some representative mechanistic examples in which detailed reaction mechanisms are estabhshed based on empirical kinetic equations. 

The theoretical kinetic equation Equation 7.60 is similar to the empirical kinetic equation Equation 7.47 with ROH = CH3OH, a = k2, and P = 2K. ... 

Although all three reaction mechanisms as shown by Scheme 7.4, Scheme 7.5, and Schane 7.6 give theoretical kinetic equations, which are similar to empirical kinetic equations (Equation 7.51), reaction mechanisms represented by Scheme 7.5 and Scheme 7.6 have been ruled out based upon reasons described in details elsewhere. ... 

---