First-order rate constant for

The operation of the nitronium ion in these media was later proved conclusively. "- The rates of nitration of 2-phenylethanesulphonate anion ([Aromatic] < c. 0-5 mol l i), toluene-(U-sulphonate anion, p-nitrophenol, A(-methyl-2,4-dinitroaniline and A(-methyl-iV,2,4-trinitro-aniline in aqueous solutions of nitric acid depend on the first power of the concentration of the aromatic. The dependence on acidity of the rate of 0-exchange between nitric acid and water was measured, " and formal first-order rate constants for oxygen exchange were defined by dividing the rates of exchange by the concentration of water. Comparison of these constants with the corresponding results for the reactions of the aromatic compounds yielded the scale of relative reactivities sho-wn in table 2.1. 

Since the first-order rate constant for nitration is proportional to y, the equilibrium concentration of nitronium ion, the above equations show the way in which the rate constant will vary with x, the stoichiometric concentration of dinitrogen tetroxide, in the two media. An adequate fit between theory and experiment was thus obtained. A significant feature of this analysis is that the weak anticatalysis in pure nitric acid, and the substantially stronger anticatalysis in partly aqueous nitric acid, do not require separate interpretations, as have been given for the similar observations concerning nitration in organic solvents. 

Ratio of first order rate constant for solvolysis in indicated solvent to that for solvolysis in acetic acid at 25 C... 

The first order rate constant for ethanolysis of the allylic chloride 3 chloro 3 methyl 1 butene is over 100 times greater than that of tert butyl chloride at the same temperature... 

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.]...

Fig. 8.P3I. Plot of the pseudo-first-order rate constants for hydrolysis of thioesters A (O), B ( ), C (A), D (A) as a fiinction of pH at 50°C and ionic strength 0.1 (KCI). Lines are from fits of the data to = kon(K /H+)) + (k KJK + [//+])) where koH is the hydroxide term and is the intramolecular assistance term for B and C and from linear regression for A and D. Reproduced from problem reference 31 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 ... 

These are pseudo-first-order rate constants for the alkaline hydrolysis of ethyl / -nitrobenzoate at 25°C. 

Give an expression for the pseudo-first-order rate constant for Meisenheimer complex formation. 

Fig. 1. First-order rate constants for the hydrolysis of 4-(2-methylpropenyl)morpholine in aqueous phosphate buffers at 25° as a function of the concentration of H2P04 ions. pH values 7.30 o 6.30 a 6.00 5.79 (15).

Fig. 3. First-order rate constants for the hydrolysis of l-(2-methylpropenyl)pyrrolidine in acetate buffers (24.8°). pH values o, 4.41 A, 4.94 (23).

Quantitative structure-reactivity analysis is one of the most powerful tools for elucidating the mechanisms of organic reactions. In the earliest study, Van Etten et al. 71) analyzed the pseudo-first-order rate constants for the alkaline hydrolysis of a variety of substituted phenyl acetates in the absence and in the presence of cyclodextrin. The... 

Table 9. Pseudo-first-order rate constants for the release of p-nitrophenol in the reactions of optically active esters in a CTAB micelle...

The first-order rate constant for the decomposition of a certain drug at 25°C is 0.215 month1. 

A plot of the first-order rate constant for equilibration in reaction (3-23) is shown as a function of [Co(edta)2 ]. the reagent present in large excess. The plot is linear as expected from Eq. (3-23). Data, from Ref. 1. are given in Table 3-1. 

A Hammett plot (a) of the apparent first-order rate constants for semicarbazone formation at pH 3.9, where a change in the RCS occurs, and (b) of the denitrosation of A-methyl-A-nitrosoanilines, where the mechanism changes. Data are from Refs. 9 and 10. 

If the equilibrium is suddenly displaced, the results obtained in Chapter 3 show that the re-equilibration process will follow first-order kinetics. It is customary in this field to refer to r, the relaxation time, which is defined as reciprocal of the first-order rate constant for re-equilibration. In this case, we have... 

The overall catalytic rate constant of SNase is (see, for example, Ref. 3) kcat — 95s 1 at T = 297K, corresponding to a total free energy barrier of Ag at = 14.9 kcal/mol. This should be compared to the pseudo-first-order rate constant for nonenzymatic hydrolysis of a phosphodiester bond (with a water molecule as the attacking nucleophile) which is 2 x 10 14 s corresponding to Ag = 36 kcal/mol. The rate increase accomplished by the enzyme is thus 101S-1016, which is quite impressive. 

Thus, we may write the pseudo first-order rate constant for disappearance of CD4 as n(CH5 iD -+) = 4.40 X 10 4 sec.-1 Appropriate rate equations are... 

It is of substantial interest to note that, c.s the temperature of the reaction mixture is increased to —33-5°, ion 19 is converted quantitatively back to 18. At that temperature the first-order rate constant for the reversion has been calculated to be 8-0 x 10 sec , which corresponds to a free enthalpy barrier AG ) of 17-4 kcal/mol. 

Table 11.1. First-order rate constants for hydrogenation of pentenes.

The successive equilibria are characterized by K12 and K23, respectively, and when Kl2 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of M2+ and 1/ (considered as spherical species) in M OH2 Um x) +, e is the solvent dielectric constant, and zM and zL are the charges of Mm+ and Lx, respectively (20). Frequently, it is only possible to characterize kinetically the second equilibrium of Eq. (2), and the overall equilibrium is then expressed as in Eq. (4) (which is a general expression irrespective of mechanism). Here, the pseudo first-order rate constant for the approach to equilibrium, koba, is given by Eq. (5), in which the first and second terms equate to k( and kh, respectively, when [Lx ] is in great excess over [Mm+]. When K0[LX ] <11, koba - k,K0[Lx ] + k.it and when K0[LX ] > 1, fc0bs + k l. Analogous expressions apply when [Mm+] is in excess. 

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