Pseudounimolecular reactions

As mentioned in Section 4, the analysis of rate data resulting from unimolecular reactions is considerably easier than the analysis of such data for bimolecular reactions, and the same is true for pseudounimolecular reactions. Kinetic probes currently used to study the micellar pseudophase showing first-order reaction kinetics are almost exclusively compounds undergoing hydrolysis reactions showing in fact pseudofirst-order kinetics. In these cases, water is the second reactant and it is therefore anticipated that these kinetic probes report at least the reduced water concentration (or better water activity in the micellar pseudophase. As for solvatochromic probes, the sensitivity to different aspects of the micellar pseudophase can be different for different hydrolytic probes and as a result, different probes may report different characteristics. Hence, as for solvatochromic probes, the use of a series of hydrolytic probes may provide additional insight. 

The rates of the reaction of the OH radical with benzene derivatives are generally studied from the build-up of the transient species (OH adducts) at the absorption maxima under pseudounimolecular reaction conditions at concentrations < 10" mol dm" and the second-order rate constants were evaluated from the plots of versus [solute]. The OH radical is reactive towards arenes with diffusion-controlled... 

Assuming further a steady-state concentration C for the cyclic intermediate and a pseudounimolecular reaction (42), the mole fractions of reactant and product may be expressed as Eq. (1) ... 

In these circumstances, where routine kinetic measurements are uninformative and direct measurements of the product-forming steps difficult, comparative methods, involving competition between a calibrated and a non-calibrated reaction, come into their own. Experimentally, ratios of products from reaction cascades involving a key competition between a first-order and a second-order processes are measured as a function of trapping agent concentration. Relative rates are converted to absolute rates from the rate of the known reaction. The principle is much the same as the Jencks clock for carbenium ion lifetimes (see Section 3.2.1). However, in radical chemistry Newcomb prefers to restrict the term clock to a calibrated unimolecular reaction of a radical, but such restriction obscures the parallel with the Jencks clock, where the calibrated reaction is a bimolecular diffusional combination with and the unknown reaction a pseudounimolecular reaction of carbenium ion with solvent. Whatever the terminology, the practical usefulness of the method stems from the possibility of applying the same absolute rate data to all reactions of the same chemical type, as discussed in Section 7.1. 

Single-substrate enzymes (see) display first order kinetics. The rate equation for such a unimolecular or pseudounimolecular reaction is v = -d[S]/dt = k[S]. The reaction is characterized by a half-life tv, = In2/ k = 0.693/k, where k is the first-order rate constant. The relaxation time, or the time required for [S] to fall to (1/e) times its initial value is x t= 1/k = tv,/ln 2. 

Most of the pseudounimolecular hydrolytic probe reactions involve water-catalyzed pH-independent hydrolysis of activated esters, amides, or acid chlorides " " (Scheme 9). The hydrolysis of these probes occurs via a dipolar... 

As the reasons for rate retardations have been discussed for pseudounimolecular probe reactions already, we focus on the reported increased bimolecular rate constants. Two main reasons for increases in bimolecular rate constants come to the fore (1) dehydration of the reactive counterions and (2) charge delocalization during the activation process leading to the transition state. An intriguing third reason (although, admittedly, not strictly equating to an increased bimolecular rate constant) is (3) the increase in local counterion concentration as a result of comoving counterions. We will discuss these three effects in order. 

If some of the reactant or product species are present in excessive quantities, then the fractional changes in their concentrations over the entire duration of the reaction may be immeasurably small. In such cases the concentrations of the reactants present in excess remain approximately constant and may be absorbed into the rate constant fe. A measurement of the order of the reaction from concentration-time plots then does not reveal the dependence of the rate on the concentrations of the overabundant species the measurement yields the pseudo molecularity of the reaction, that is, the sum of the orders with respect to the species that are not present in excess. Thus a number of higher-order reactions are found to be pseudounimolecular under certain conditions. This observation provides the basis for the isolation method of determining the order of a complex reaction with respect to a particular reactant in this method, the apparent overall order (pseudo-molecularity) of the reaction is measured under conditions in which all of the reactants except the one of interest are present in excess. 

However, with unhindered alcohols (in carbon tetrachloride) such as methanol and ethanol, there is a competition between the dissociation pathway and a pathway involving direct attack of the alcohol on the dimer (Eqs. 4.24, 4.25). The reaction when carried out under pseudounimolecular conditions (with excess ROH) at several different concentrations, and plotted versus [ROH], linear plots are realized. The rate constants for the dissociation pathways k ) and the direct attack pathway (k ) can be evaluated from these plots. 

In neutral aqueous solutions protonation reaction of ArO can be neglected, since its pseudounimolecular rate constant ( calculated as a product of the diffusion rate constant... 

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