Partial rate factors definition

The partial rate factors for phenylation of protonated and nonprotonated 4-substituted p5n idines indicate a small but definite... 

Because the rate of substitution varies with position, in a benzene derivative it is more informative and frequently more useful to talk about partial rate factors than about relative rates. A partial rate factor is defined as the rate at one particular position in the benzene derivative relative to the rate of substitution at one position in benzene. Let us, for example, calculate the para and meta partial rate factors (pf and mf, respectively) for bromination of toluene with bromine in aqueous acetic acid. Toluene brominates 605 times faster than benzene under these conditions. The product is 66.8 percent p-, 0.3 percent m-, and 32.9 percent o-bromotoluene. Attack at the para position of toluene occurs 0.668 x 605 times as fast as attack at all six positions of benzene but (0.668 x 605 x 6 = 2420) times as fast as at one position of benzene. Therefore pfCH for bromination of toluene under these conditions is 2420. There are only three times as many total carbons in benzene as meta carbons in toluene. Therefore mfca3 = 0.003 x 605 x 3 = 5.5. The definitions of the partial rate factors for monosubstituted benzenes (—R) are given in Equations 7.78-7.80. 

According to the definition, the partial rate factors express the ratio of the rate constant of a particular substitution reaction at a given site to the rate constant of a single site in an unsubstituted benzene nucleus. To illustrate, this principle would predict that the partial rate factor for position 6 in 4-hydroxy-3-methoxytoluene is equal to the product /wOH X fPOMe X... 

Starting with the definition of partial rate factor, derive an expression relating p to the rate of substitution para to G in CeHsG. 

The rate-controlling step is the elementary reaction that has the largest control factor (CF) of all the steps. The control factor for any rate constant in a sequence of reactions is the partial derivative of In V (where v is the overall velocity) with respect to In k in which all other rate constants (kj) and equilibrium constants (Kj) are held constant. Thus, CF = (5 In v/d In ki)K kg. This definition is useful in interpreting kinetic isotope effects. See Rate-Determining Step Kinetic Isotope Effects... 

Special attention of investigators dealing with gradient elements is paid to the study of interconnection of RID with their optical and other properties. It is shown that optical characteristics of selfocs are also definitely influenced by factors such as fractional composition of the reaction mixture after obtaining the gel-polymeric matrix, conversion degree, nature of diffusate, the ratio of monomer diffusion rate and the rate of its copolymerization in partially polymerized matrix, etc. [2, 14, 29, 33, 56, 57],... 

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