Pseudo-first-order rate constants for

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.

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. 

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 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... 

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. 

Fig. 6. The variation of the pseudo first-order rate constant for release of p-nitro-phenolate ion from p-nitrophenyl acetate at pH 10.6 with the concentration of added cycloheptaamylose (VanEtten et al., 1967a).

In a few cases, a direct comparison of the effects of cyclohexa-, cyclo-hepta-, and cyclooctaamylose toward the same substrate can be made. Pertinent data are presented in Table V. It should be noted that the rate constants presented in this Table are pseudo first-order rate constants for the appearance of phenol in the presence of 0.01 M cycloamylose. They are not the maximal rate constants k2 for appearance of phenol from the fully... 

Pseudo first-order rate constant for the appearance of pheno-late ion in the presence of 0.01 M cydohexaamylose. 

Pseudo first-order rate constants for acylation of the catalyst in the presence of equivalent concentrations of 12 or 13. 

Scheme 3 leads to Eq. (6) for the pseudo-first-order rate constant for demetalation of lm at a given pH when the concentration of total iron (Mt) is much less than that of L and P. 

The next difficulty in comparing the predictions of Eq. (1) with experiment is that experimental values are reported in terms of either second-order rate constants for the gas-phase experiments or pseudo-first-order rate constants for the solution experiments. According to Eq. (1), neither pure reaction order is correct nor should the apparent rate constant depend on the concentration or... 

Spectroscopically invisible carbenes can be monitored by the ylide method .92 Here, the carbene reacts with a nucleophile Y to form a strongly absorbing and long-lived ylide, competitively with all other routes of decay. Although pyridine (Py) stands out as the most popular probe, nitriles and thiones have also been used. In the presence of an additional quencher, the observed pseudo-first-order rate constant for ylide formation is given by Eq. 2.92,93 A plot of obs vs. [Q] at constant [Y ] will provide kq. With Q = HX, complications can arise from protonation of Y and/or the derived ylides. The available data indicate that alcohols are compatible with the pyridine-ylide probe technique. 

Here the alkene and pyridine will compete for the carbene at a constant concentration of pyridine the observed pseudo first order rate constant for ylide formation will increase with increasing alkene concentration. A plot of kobs vs. [alkene] will be linear with a slope of kad, which is the rate constant for the carbene/alkene addition reaction affording cyclopropane 5 (Scheme 1). 

Fig. 14 Plots of observed pseudo-first-order rate constants for the methanolysis of increasing and equimolar [La3 + ] = [32, HPNPP] at 25 °C and pH 5.0 (iV,jV-dimethylaniline buffer, , right axis) or pH 6.7 (2,6-lutidine buffer, , left axis). Lines through the data computed from fits to a standard one-site binding model. Reproduced from ref. 81 with permission.

Fig. 23 A plot of the observed pseudo-first-order rate constant for the methanolysis of 0.04mM HPNPP ( , left axis) catalyzed by 0.2mM35 2Zn(II) or 0.04mM methyl /j-nitro-phenyl phosphate (O, right axis) catalyzed by 0.4 mM 35 Zn(II) as a function of the [CH30-]/ [35 Zn(II)] ratio at 25 + 0.1 °C. Experiments done by pH jump method starting at a [CH30-]/ [35 Zn(II)] ratio of 1.0 (vertical dashed line, (pH = 9.5) and adding acid (left) or base (right). Reproduced with permission from ref. 95.

Samples 1-4 correspond to VPO treated in steam for 92, 312h, in N2 and activated base catalysts, respectively, k, are pseudo-first-order rate constants for the disappearance of butane. The constants are measured in a microreactor on a larger amount ( 1 g) of catalyst at 633 K. k (intrinsic) are based on the BET surface area. 

Let us recall that the pseudo-first order rate constant for this process is very large (ka x 1015 s 1) whereas the subsequent steps of de-excitation occur with much... 

Fast spectroscopy was also used to probe the reactivity of PBN +. The 266 nm laser excitation of peroxydisulfate ion in aqueous solution at room temperature gives the powerful oxidant SOr, which oxidizes PBN in an exergonic reaction (by about 0.8 eV, see Tables 1 and 5) with k = 3 X 109 dm3 mol-1 s 1. The pseudo-first-order rate constant for the decay of PBN + by reaction with water to give HO-PBN" was 2 x 106 s 1, a relatively slow reaction (k = 3.6 x 104 dm3 mol-1 s-1 at ambient temperature). 

Fig. 16.12 Pseudo-first-order rate constants, for the transformation of CFBr - 6.5pM) in suspensions of goethite (25Fe(II)j j of ImM at 25 °C ionic strength = 20mM) as a function of solution pH ( ). The contact time of Fe(II) with iron oxide before addition of CFBr3 was >24 hours. Also shown are k values for the control experiments in the absence of goethite ( ). The precipitate formed in the pH 8.9 control (arrow) was identified as a form of green rust. Reprinted with permission from Pecher K, Haderline SB, Schwarzenbach RP (2002) Reduction of polyhalogenated methanes by surface-bound Fe(ll) in aqueous suspensions of iron oxides. Environ Sci Technol 36 1734-1741. Copyright 2002 American Chemical Society...

In which kg Is the pseudo-first-order rate constant for OP hydrolysis In the absence of PB. With PB In great excess. In buffered solution, kg and [HO2 ] are constant. Then pseudo-first-order kinetics result and we get equation (8),... 

Figure 2. Kinetic plot of pseudo-first-order rate constant for reaction of paraoxon (kohc) versus concentration of added sodium perborate at 27.5 oc avvarious pH in 0.1 mol dm borate buffer.

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