Equal reactivity

In conclusion, in terms of electrophilic reactivity a methyl group in the 2-position is equally reactive in the two categories of heterocycles (selenazole and thiazole). Of the two positions ortho to nitrogen, only the 2-position is activated. The 5-position is sensitive to electrophilic reagents and resembles more closely the para position of a benzene ring. 

In both the following exercises assume that all the methylene groups in the alkane are equally reactive as sites of free radical chlorination... 

To see why the assumption of equal reactivity is so important to step-growth polymers, recall from Table 1.2 the kind of chemical reactions which produce typical condensation polymers ... 

Not all of the hydrogens in phenol are equally reactive. Under acid conditions the quinoid structure... 

The monomer pair, acrylonitrile—methyl acrylate, is close to being an ideal monomer pair. Both monomers are similar in resonance, polarity, and steric characteristics. The acrylonitrile radical shows approximately equal reactivity with both monomers, and the methyl acrylate radical shows only a slight preference for reacting with acrylonitrile monomer. Many acrylonitrile monomer pairs fall into the nonideal category, eg, acrylonitrile—vinyl acetate. This is an example of a nonideality sometimes referred to as kinetic incompatibiUty. A third type of monomer pair is that which shows an alternating tendency. 

During copolymerization, one monomer may add to the copolymer more rapidly than the other. Except for the unusual case of equal reactivity ratios, batch reactions carried to completion yield polymers of broad composition distribution. More often than not, this is an undesirable result. 

As pointed out by Flory [16], the principle of equal reactivity, according to which the opportunity for reaction (fusion or scission) is independent of the size of the participating polymers, implies an exponential decay of the number of polymers of size / as a function of /. Indeed, at the level of mean-field approximation in the absence of closed rings, one can write the free energy for a system of linear chains [11] as... 

Next, examine each cation s LUMO while displaying the cation as a space-filling model. Assuming that Br preferentially attacks the side of that is both less hindered and permits better overlap with the LUMO, predict the major product obtained from each cation conformer (if the two sides of C+ seem equally reactive, then predict a racemic product mixture). 

It may be unsafe to carry this discussion further until more data are available. Knowledge of the activation parameters would be especially desirable in several respects. Reactivity orders involving different reagents or substrates may be markedly dependent on temperature. Thus, in Table IV both 2- and 4-chloroquinolines appear to be about equally reactive toward sodium methoxide at 86,5°. However, the activation energies differ by 3 kcal/mole (see Section VII), and the relative rates are reversed below and above that temperature. Clearly, such relative rates affect the rs-/ ro- ratios. 

If the alkyl halide contains more than one, equally reactive C-halogen centers, these will generally react each with one aromatic substrate molecule. For example dichloromethane reacts with benzene to give diphenylmethane, and chloroform will give triphenylmethane. The reaction of tetrachloromethane with benzene however stops with the formation of triphenyl chloromethane 7 (trityl chloride), because further reaction is sterically hindered ... 

Problem 18.2 Why do you suppose only symmetrical ethers are prepared by the sulfuric add-catalyzed dehydration procedure What product(s) would you expect if ethanol and 1-propanol were allowed to react together In what ratio would the products be formed if the two alcohols were of equal reactivity ... 

Equal reactivity of functional groups irrespective of the size of the molecule to which the group is attached. 

The concept of equal reactivity of functional groups, Chap. 5. 

One of the main assumptions which have been made in the study of polyesterifications is the concept of equal reactivity of functional groups. It was first postulated by Flory1 who, studying various polyesterifications and model esterifications, found the same orders of reaction and almost the same rate constants for the two systems. He concluded that the reaction rate is not reduced by an increase in the molecular weight of the reactants or an increase in the viscosity of the medium. The concept of equal reactivity of functional groups has been fully and carefully analyzed by Solomon3,135 so that we only discuss here its main characteristics. Flory clearly established the conditions under which the concept of equal reactivity can be applied these are the following ... 

According to Solomon35, there is no example of a system where, these requirements being fulfilled, the concept of equal reactivity is not observed. 

However, there are numerous examples of polyesterifications where the concept of equal reactivity is not observed some examples have been reported and analyzed by Korshak and Vinogradova2315. None of them is at variance with Flory s postulates but this shows that great caution is needed in the use of the concept of equal reactivity. 

The prindple of equal reactivity of functional groups originates in the comparison by Flory of the results obtained for monoesterifications and polyesterifications. This means that it is particularly important to check whether Flory hypotheses are corred and whether the study of a polyesterification must be limited to the last stages of the reaction. 

According to the data, f-BuCl and f-BuBr were equally reactive initiators. Comparable yields were obtained using MeCl and MeBr solvents, particularly at high f-BuX concentration (4.8 x 10-4M). At lower f-BuX concentration (1.2 x 10 4 and 2.4 x 10-4 M), yields were generally lower with f-BuBr than with f-BuCl, and for a given initiator with MeBr than MeCl. Interestingly, f-BuI in conjunction with Et2 AlBr initiated polymerization at —40 °C and —50 °C. However, below —50 °C, polymerization did not take place. Polymerization did not occur also using Mel solvent. 

In dimethoxyethane DME, a more powerful solvating agent than THF, solvation by solvent molecules competes with the intramolecular solvation, increasing the reactivity of ion-pairs. Indeed, the propagation constants of Na+ and Cs+ salts of polymethyl methacrylate are higher in that solvent than in THF, although again both salts are nearly equally reactive 39) as shown in Fig. 5. 

Table I contains the results, some of which have been derived previously (11, 12). These equations are appropriate for the case of equal reactivity of both ends of a difunctional molecule and allow for unequal rate constants for the A-B and A-C reactions. These results are presented here in terms of reaction probabilities, p, (the probability that reactant I has reacted with reactant J) where I,J = A, B or C, and p j = Pj - These should be distinguished from the sequential probabilities of...

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

Complexation with polyaromatic systems has also been observed. For instance, Mlnaphthalenelj, M = Cr (88,183), Mo (183), V (183), or Ti (183) may be synthesized in a solution reactor with the appropriate, metal vapors at liquid-nitrogen temperature. The Cr/naphthalene complex is less stable (dec. 160°C) than CrtCsH ) (m.p. 283-284° C). In fact, the naphthalene ligand is sufficiently labile to allow reaction under mild conditions, to afford CrL (L = CO or Bu NC), or Cr(naphth)Ls [L = PFj, P(OMe)3, or PMea]. The Mo, V, and Ti species are equally reactive. Analogous 1-methylnaphthalene complexes were also isolated (183). In addition, the complexes shown in Fig. 38 were synthesized by reaction, at the temperature of liquid nitrogen, of Cr atoms with 1,4-diphenylbutane (35, 201, 202). Analogous complexes were formed with 1,5-diphenylbutane (202). 

In considering step polymerisation with polyfunctional molecules a number of assumptions are made. They are (i) that all functional groups are equally reactive, (ii) that reactivity is independent of molar mass or solution viscosity, and (iii) that all reactions occur between functional groups on different molecules, i.e. there are no intramolecular reactions. It is found experimentally that these assumptions are not completely valid and tend to lead to an underestimate of the extent of reaction required to bring about gelation. 

Suppose that the reactivity of the A and B endgroups is independent of the chains to which they are attached. This is a form of the equal reactivity assumption that is needed for almost all analytical solutions to polymer kinetic problems. If it is satisfied, we can ignore the details of the polymerization and just concentrate on the disappearance of the endgroups. For a batch system. 

FIGURE 13.3 Molecular weight distributions by number for the equal-reactivity case and the variable-reactivity case of Example 13.4. 

The present section analyzes the above concepts in detail. There are many different mathematical methods for analyzing molecular weight distributions. The method of moments is particularly easy when applied to a living pol5mer polymerization. Equation (13.30) shows the propagation reaction, each step of which consumes one monomer molecule. Assume equal reactivity. Then for a batch polymerization. 

Example 13.5 Determine the instantaneous distributions of chain lengths by number and weight before and after termination by combination. Apply the quasi-steady and equal reactivity assumptions to a batch polymerization with free-radical kinetics and chemical initiation. 

Solution The equal reactivity assumption says that kp and kc are independent of chain length. The quasi-steady hypothesis gives d R /dt = 0. Applying these to a material balance for growing chains of length / gives... 

Consider the pol5merization of two vinyl monomers denoted by X and Y. Each propagation reaction can add either an X or a Y to the growing polymer chain, and it is unrealistic to assume that the monomers have equal reactivities. Furthermore, reaction probabilities can depend on the composition of the polymer chain already formed. We suppose that they depend only on the last member added to the chain. The growing chain to which an X-mer was last added is denoted as IX , and I denotes the catalytic site. There are four propagation reactions to consider ... 

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