Rate laws continued elementary

To verify that Eq. (2.4) is indeed elementary, one can employ experimental conditions that are dissimilar from those used to ascertain the rate law. For example, if the k values change with flow rate, one is determining nonmechanistic or apparent rate coefficents. This was the case in a study by Sparks et al. (1980b), who studied the rate of potassium desorption from soils using a continuous flow method (Chapter 3). They found the apparent desorption rate coefficients ( d) increased in magnitude with flow rate (Table 2.1). Apparent rate laws are still useful to the experimentalist and can provide useful time-dependent information. 

Equipped with this principle, let us now continue the derivation of the rate law for SN reactions. The approximation [carbenium ion] = 0 must be replaced by Equation 2.6. Let us now set the left-hand side of Equation 2.6, the change of the carbenium ion concentration with time, equal to the difference between the rate of formation of the carbenium ion and its consumption. Because the formation and consumption of the carbenium ion are elementary reactions, Equation 2.7 can be set up straightforwardly. Now we set the right-hand sides of Equations 2.6 and 2.7 equal and solve for the concentration of the carbenium ion to get Equation 2.8. With this equation, it is possible to rewrite the previously unusable Equation 2.5 as Equation 2.9. The only concentration term that appears in Equation 2.9 is the concentration of the alkylating agent. In contrast to the carbenium ion concentration, it can be readily measured. 

This irreversible reaction has an elementary rate law and is carried out in aqueous ethanol. Therefore, like almost all liquid-phase reactions, the density remains almost constant throughout the reaction. It is a general principle that for most liquid-phase reactions, the volume V for a batch reaction system and the volumetric flow rate v for a continuous-flow system will not change appreciably during the course of a chemical reaction. 

In solution kinetics an important distinction between solvent and reactants must be maintained. The solvent is continually interacting with the reactants if such interactions were incorporated in the mechanistic model all solution mechanisms would perforce be multimolecular. By considering the solvent as a medium and not as a participant in the reaction (unless, of course, solvent actually takes part in a reaction step), the problem of mechanism is greatly simplified. In this sense isomerizations, rearrangements, and conformational changes, like the chairi chair2 interconversion in cyclohexane, are first-order reactions for which the empirical rate law is a direct indication of the only important elementary step. Most solution reactions proceed via bimolecular steps. There are countless examples for which only one such step is needed and for which the rate law reflects that process. 

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