Second-order reactions classes

Many second-order reactions follow Class I rate expressions. Among these are the gas-phase thermal decomposition of hydrogen iodide (2HI - H2 + I2), dimerization of cyclopen-tadiene (2C5H6 -> C10H12), and the gas phase thermal decomposition of nitrogen dioxide (2N02 2NO + 02). 

ILLUSTRATION 3.2 USE OF A GRAPHICAL INTEGRAL METHOD FOR DETERMINING THE RATE CONSTANT FOR A CLASS II SECOND-ORDER REACTION... 

Another class of irreversible second-order reactions obeys the rate law r = k[A][B]... 

Oxygen-containing solvents such as water, alcohols or ethers are such poor donors that few complexes with palladium(II) have been isolated. The most important class of complexes of this type consists of those containing water, which are formed as intermediates in the substitution reactions of palladium(II) when carried out in aqueous solution. In these reactions their formation is in competition with the second order reaction of the complex with the incoming ligand. The aqua complexes can also be formed by reaction of halo complexes with silver salts (e.g. N03, C104, BF4) in water. These complexes are acidic, being in equilibrium with hydroxo complexes in neutral or basic media. 

Table 1 covers rate constant data on second order reactions, grouped by class, while Table 2 covers association reactions. Relevant equilibrium constant data are given in Table 3. AU concentrations are measured in molecules cm". Notes on each reaction, as well as related photochemical data, may be found in the reference.

There are two primary classes of second-order reactions. For the first the rate is proportional to the square of the concentration of a single reacting species for the second the rate is proportional to the product of the concentrations of two different species. 

ILLUSTRATION 3.2 Use of a Graphical Integral Method for Determining the Rate Constant for a Class II Second-Order Reaction... 

An analytical method provides the solution in closed form , i.e. a formula can be given for the time evolution of the concentrations. This possibility only exists for a rather limited class of differential equations, even in the special subclass of kinetic differential equations. Methods of how to derive solutions can be found in the book by Kamke (1959) or in problems books like those by Filippov (1979), Matveev (1983), or Krasnov et al. (1978). The special case of kinetic differential equations is treated by Rodiguin Rodiguina (1964) who published the explicit solution for many first order reactions, and by Szabo (1969), who collected results for second order reactions too (together with realistic chemical examples). 

In general, the reaction between a phenol and an aldehyde is classified as an electrophilic aromatic substitution, though some researchers have classed it as a nucleophilic substitution (Sn2) on aldehyde [84]. These mechanisms are probably indistinguishable on the basis of kinetics, though the charge-dispersed sp carbon structure of phenate does not fit our normal concept of a good nucleophile. In phenol-formaldehyde resins, the observed hydroxymethylation kinetics are second-order, first-order in phenol and first-order in formaldehyde. 

However, the E2C mechanism has been criticized, and it has been contended that all the experimental results can be explained by the normal E2 mechanism. McLennan suggested that the transition state is that shown as 18. An ion-pair mechanism has also been proposed. Although the actual mechanisms involved may be a matter of controversy, there is no doubt that a class of elimination reactions exists that is characterized by second-order attack by weak bases. " These reactions also have the following general characteristics (1) they are favored by good leaving groups (2) they are favored by polar aprotic solvents (3) the reactivity order is tertiary > secondary > primary, the opposite of the normal E2 order (p. 1319) (4) the elimination is always anti (syn elimination is not found), but in cyclohexyl systems, a diequatorial anti elimination is about as favorable as a diaxial anti elimination (unlike the normal E2 reaction, p. 1302) (5) they follow Zaitsev s rule (see below), where this does not conflict with the requirement for anti elimination. 

The structure of the reactions in Equation (6.1) is typical of an immense class of industrially important reactions. It makes little difference if the reactions are all second order. Thus, the reaction set... 

The present paper tests the assumed original and enhancement mechanisms with rates and conversions for a broad range of contaminants measured under a fixed mass concentration (50 mg/m ) feed condition. The plots compared are reaction rates vs. (1) dark adsorption, Ot. (2) second order rate constant for (OH ) (TCE absent) or (Cl ) (TCE present), and (3) the product of these gas phase second order rate constant times the reactant dark coverage. Where a second order gas phase rate constant was not available, we estimated its value from correlations of kci vs. koH for tke same class of compounds. 

For Class II second-order rate expressions of the form of equation 3.1.10, the rate can be expressed in terms of the extent of reaction per unit volume as... 

Class II second-order rate expressions are one of the most common forms one encounters in the laboratory. They include the gas phase reaction of molecular hydrogen and iodine (H2 + I2 -> 2HI), the reactions of free radicals with molecules (e.g., H -f Br2 -> HBr -f Br), and the hydrolysis of organic esters in nonaqueous media. 

Frost and Schwemer have developed a time-ratio technique based on equations 5.4.21 and 5.4.16 in order to facilitate the calculation of second-order rate constants for the class of reactions under consideration. Data for A/A0 versus t at various values of k are presented in Table 5.2, and time ratios are given in Table 5.3. The latter values may be used to determine k by using various time ratios from a single kinetic run if one recognizes that (tf/rf) = t1/t2). Once k has been determined, Table 5.2 may be used to determine the t values at a given A/A0 and k. Equation 5.4.18 may then be used to determine... 

This paper is about a reinterpretation of the cationic polymerizations of hydrocarbons (HC) and of alkyl vinyl ethers (VE) by ionizing radiations in bulk and in solution. It is shown first that for both classes of monomer, M, in bulk ([M] = niB) the propagation is unimolecular and not bimolecular as was believed previously. This view is in accord with the fact that for many systems the conversion, Y, depends rectilinearly on the reaction time up to high Y. The growth reaction is an isomerization of a 7t-complex, P +M, between the growing cation PB+ and the double bond of M. Therefore the polymerizations are of zero order with respect to m, with first-order rate constant k p]. The previously reported second-order rate constants kp+ are related to these by the equation... 

LFP-Clock Method. In this method, rate constants for the radical clock reactions are measured directly by LFP, and the clocks are used in conventional competition kinetic studies for the determination of second-order rate constants. The advantages are that the clock can be calibrated with good accuracy and precision in the solvent of interest, and light-absorbing reagents can be studied in the competition reactions. The method is especially useful when limited kinetic information is available for a class of radicals. 

In most chemical reactions the rates are dominated by collisions of two species that may have the capability to react. Thus, most simple reactions are second-order. Other reactions are dominated by a loose bond-breaking step and thus are first-order. Most of these latter type reactions fall in the class of decomposition processes. Isomerization reactions are also found to be first-order. According to Lindemann s theory [1, 4] of first-order processes, first-order reactions occur as a result of a two-step process. This point will be discussed in a subsequent section. 

Using a different convention, a simple metal in contact with its cations is also commonly termed an electrode of the first kind, or a class I or first-order electrode, while an electrode covered with an insoluble salt, e.g. AgCI I Ag for determining u(Cr), is termed an electrode of the second kind, or a class II or second-order electrtxle. In this latter convention, inert electrodes fur following redox reactions (cf. Chapter. 4) are somewhat confusingly termed redox electrodes. 

However, the E2C mechanism has been criticized, and it has been contended that all the experimental results can be explained by the normal E2 mechanism.66 McLennan has suggested that the transition state is that shown as 18.w An ion-pair mechanism has also been proposed.70 Although the actual mechanisms involved may be a matter of controversy, there is no doubt that a class of elimination reactions exists that is characterized by second-order attack by weak bases.71 These reactions also have the following general characteris-... 

---