Complication rates

In Section 1.2 we distinguished between elementary and complex reactions. We now make a distinction between simple and complicated rate equations. A simple rate equation has the form of Eq. (1-11). A complicated rate equation has a form different from Eq. (1-11) it may be a sum of terms like that in (1-11), or it may have quantities in the denominator. We have seen that there is no necessary relationship between the complexity of the reaction and the form of the experimental rate equation. Simple rate equations are treated in Chapter 2 and complicated rate equations in Chapter 3. 

This ability to reduce the reaction order by maintaining one or more concentrations constant is a veiy valuable experimental tool, for it often permits the simplification of the reaction kinetics. It may even allow a complicated rate equation to be transformed into a simple rate equation. 

In Chapter 1 we distinguished between elementary (one-step) and complex (multistep reactions). The set of elementary reactions constituting a proposed mechanism is called a kinetic scheme. Chapter 2 treated differential rate equations of the form V = IccaCb -., which we called simple rate equations. Chapter 3 deals with many examples of complicated rate equations, namely, those that are not simple. Note that this distinction is being made on the basis of the form of the differential rate equation. 

There is no general explicit mathematical treatment of complicated rate equations. In Section 3.1 we describe kinetic schemes that lead to closed-form integrated rate equations of practical utility. Section 3.2 treats many further approaches, both experimental and mathematical, to these complicated systems. The chapter concludes with comments on the development of a kinetic scheme for a complex reaction. 

This procedure constitutes an application of the steady-state approximation [also called the quasi-steady-state approximation, the Bodenstein approximation, or the stationary-state hypothesis]. It is a powerful method for the simplification of complicated rate equations, but because it is an approximation, it is not always valid. Sometimes the inapplicability of the steady-state approximation is easily detected for example, Eq. (3-143) predicts simple first-order behavior, and significant deviation from this behavior is evidence that the approximation cannot be applied. In more complex systems the validity of the steady-state approximation may be difficult to assess. Because it is an approximation in wide use, much critical attention has been directed to the steady-state hypothesis. 

Many reactions with complicated rate laws proceed by bimolecular steps. The complexity often arises from attendant equilibria. Several instances have been cited where no clear-cut choice could be made between algebraically compatible alternatives. Thus, do Cr2+, Fe3+, and Cl- react via CrCl+ and Fe3+ orCr2+ and FeCl2+ Does the first term in Eq. (6-33) correspond to CrOH+ and Fe3+ or Cr2+ and FeOH2+ Does the iodide-peroxide reaction necessarily imply that H302+ reacts with I- could not H202 and HI be responsible The answers to these questions will not be found strictly from the kinetics. Other experiments must be devised. Some have been mentioned previously, and two more will be cited here. 

More complicated rate expressions are possible. For example, the denominator may be squared or square roots can be inserted here and there based on theoretical considerations. The denominator may include a term k/[I] to account for compounds that are nominally inert and do not appear in Equation (7.1) but that occupy active sites on the catalyst and thus retard the rate. The forward and reverse rate constants will be functions of temperature and are usually modeled using an Arrhenius form. The more complex kinetic models have enough adjustable parameters to fit a stampede of elephants. Careful analysis is needed to avoid being crushed underfoot. 

The organo-corrinoids show similar behavior, but also additional complications. Rate constants have been determined 84) for the attack of mercury(II) acetate on various organocobalt cobinamides (X = H2O or absent) and cobalamins (X = 5,6-dimethylbenziminazole). The first complication, which has to be born in mind when comparing the cobinamides with the cobalamins or DMG complexes, is that the organocobin-amides are partly (R = vinyl and methyl) or wholly (R = Et, -Pr, t-Pr,... 

Decompressive hemicraniectomy was indirectly compared with moderate hypothermia (33°C) in a series of 36 patients from Georgiadis et al. They found a lower mortality rate for the patients who underwent hemicraniectomy (47% vs. 12%), as well as a lower complication rate. However, this was not a randomized study, and there was no comparison arm of patients who did not undergo either experimental therapy. 

Prestwood and Wahl, in a report of a more detailed study conducted at an ionic strength of 3.68 M (C104 ) and temperatures in the range 10 to 50 °C, have presented results consistent with a more complicated rate expression... 

---