Substitution, first order

These reactions follow first-order kinetics and proceed with racemisalion if the reaction site is an optically active centre. For alkyl halides nucleophilic substitution proceeds easily primary halides favour Sn2 mechanisms and tertiary halides favour S 1 mechanisms. Aryl halides undergo nucleophilic substitution with difficulty and sometimes involve aryne intermediates. 

A more convincing approach leads to an adaptive method based on the symmetric second order scheme (9). As a first step, we have to introduce a first order scheme substituting p of the previous section. In what follows, we use the following pair of schemes ... 

Time derivatives in expansion (2.113) can now be substituted using the differential equation (2.112) (Donea, 1984 The first order time derivative in expansion (2.113) is substituted using Equation (2.112) as... 

The value for the pseudo-first-order rate constant is determined by solving equation 13.6 for k and making appropriate substitutions thus... 

The first mechanistic studies of silanol polycondensation on the monomer level were performed in the 1950s (73—75). The condensation of dimethyl sil oxanediol in dioxane exhibits second-order kinetics with respect to diol and first-order kinetics with respect to acid. The proposed mechanism involves the protonation of the silanol group and subsequent nucleophilic substitution at the siHcone (eqs. 10 and 11). 

Higher than first order for monomer, such as the 3/2 power suggests that VP is involved in initiation (17). If the efficiency of initiation is a function of the monomer concentration, then f = P [M], and substituting in equation 2 gives... 

A well-known example of non-prototropic tautomerism is that of azolides (acylotropy). The acyl group migrates between the different heteroatoms and the most stable isomer (annular or functional) is obtained after equilibration. In indazoles both isomers are formed, but 2-acyl derivatives readily isomerize to the 1-substituted isomer. The first order kinetics of this isomerization have been studied by NMR spectroscopy (74TL4421). The same publication described an experiment (Scheme 8) that demonstrated the intermolecular character of the process, which has been called a dissociation-recombination process. 

Substituted 2-haloaziridines are also known to undergo a number of reactions without ring opening. For example, displacement of chlorine in (264) with various nucleophilic reagents has been found to occur with overall inversion of stereochemistry about the aziridine ring (65JA4538). The displacements followed first order kinetics and faster rates were noted for (264 R = Me) than for (264 R = H). The observed inversion was ascribed to either ion pairing and/or stereoselectivity. 

Successive Substitutions Let/(x) = 0 be the nonlinear equation to be solved. If this is rewritten as x = F x), then an iterative scheme can be set up in the form Xi + = F xi). To start the iteration an initial guess must be obtained graphically or otherwise. The convergence or divergence of the procedure depends upon the method of writings = F x), of which there will usually be several forms. However, if 7 is a root of/(x) = 0, and if IF ( 7)I < I, then for any initial approximation sufficiently close to a, the method converges to a. This process is called first order because the error in xi + is proportional to the first power of the error in xi for large k. 

Substitution of Eq. (14-61) into Eq. (14-62) and integration lead to the following relation for an extremely slow first-order reaction in an absorption tower ... 

To find the effectiveness under poisoned conditions, this form of the modulus is substituted into the appropriate relation for effec tiveness. For first-order reaction in slab geometry, for instance,... 

The points that we have emphasized in this brief overview of the S l and 8 2 mechanisms are kinetics and stereochemistry. These features of a reaction provide important evidence for ascertaining whether a particular nucleophilic substitution follows an ionization or a direct displacement pathway. There are limitations to the generalization that reactions exhibiting first-order kinetics react by the Sj l mechanism and those exhibiting second-order kinetics react by the 8 2 mechanism. Many nucleophilic substitutions are carried out under conditions in which the nucleophile is present in large excess. When this is the case, the concentration of the nucleophile is essentially constant during die reaction and the observed kinetics become pseudo-first-order. This is true, for example, when the solvent is the nucleophile (solvolysis). In this case, the kinetics of the reaction provide no evidence as to whether the 8 1 or 8 2 mechanism operates. 

Chlorination generally exhibits second-order kinetics, first-order in both alkene and chlorine. The reaction rate also increases with alkyl substitution, as would be expected for an electtophilic process. The magnitude of the rate increase is quite large, as shown in Table 6.3. 

Fig. 8.4. Logarithm of the first-order rate constants for the hydrolysis of substituted benzylidene-l,l-dimethyl-ethylamines as a fiinction of pH. [Reproduced fiom J. Am. Chem. Soc. 85 2843 (1963) by permission of the American Chemical Society.]...

The table below gives first-order rate constants for reaction of substituted benzenes with w-nitrobenzenesulfonyl peroxide. From these data, calculate the overall relative reactivity and partial rate factors. Does this reaction fit the pattern of an electrophilic aromatic substitution If so, does the active electrophile exhibit low, moderate, or high substrate and position selectivity ... 

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. 

The unit of the veloeity eonstant k is see Many reaetions follow first order kineties or pseudo-first order kineties over eertain ranges of experimental eonditions. Examples are the eraeking of butane, many pyrolysis reaetions, the deeomposition of nitrogen pentoxide (NjOj), and the radioaetive disintegration of unstable nuelei. Instead of the veloeity eonstant, a quantity referred to as the half-life iyj is often used. The half-life is the time required for the eoneentration of the reaetant to drop to one-half of its initial value. Substitution of the appropriate numerieal values into Equation 3-33 gives... 

Substituting Equation 3-197 into the integrated first order reaetion Equation 3-33 gives the eorresponding equations expressed in terms of the solution absorbanee ... 

Equation 6-74 is a first order differential equation substituting Equations 6-70 and 6-78 for the temperature, it is possible to simulate the temperature and time for various eonversions at AX = 0.05. Table 6-4 gives the eomputer results of the program BATCH63, and Eig-ure 6-7 shows profiles of both fraetional eonversion and temperature against time. The results show that for the endodiermie reaetion of (-i-AH[ /a) = 15.0 keal/gmol, die reaetor temperature deereases as eonversion inereases with time. 

Also, for the first order reaetion, A —> produets, the rate expression is (-r ) = kC. Substituting the rate expression, the Arrhenius equation, and Equation 6-118 into Equation 6-116 yields... 

The half-life tvi is defined to be the time required for the reactant concentration to decay to one-half its initial value. To find tvi for a first-order reaction we use Eq. (2-6) with the substitutions Ca = c°/2 and t = finding... 

If (A i[X ]/A 2[Y ]) is not much smaller than unity, then as the substitution reaction proceeds, the increase in [X ] will increase the denominator of Eq. (8-65), slowing the reaction and causing deviation from simple first-order kinetics. This mass-law or common-ion effect is characteristic of an S l process, although, as already seen, it is not a necessary condition. The common-ion effect (also called external return) occurs only with the common ion and must be distinguished from a general kinetic salt effect, which will operate with any ion. An example is provided by the hydrolysis of triphenylmethyl chloride (trityl chloride) the addition of 0.01 M NaCl decreased the rate by fourfold. The solvolysis rate of diphenylmethyl chloride in 80% aqueous acetone was decreased by LiCl but increased by LiBr. ° The 5 2 mechanism will also yield first-order kinetics in a solvolysis reaction, but it should not be susceptible to a common-ion rate inhibition. 

---