Observed pseudo-first-order rate

Herein k js is the observed pseudo-first-order rate constant. In the presence of micelles, analogous treatment of the experimental data will only provide an apparent second-order rate constant, which is a weighed average of the second-order rate constants in the micellar pseudophase and in the aqueous phase (Equation 5.2). 

The effect of micelles of SDS, CTAB and C12E7 on the apparent second-order rate constants of the Diels-Alder reaction between nonionic 5.1a, anionic 5.1 f and cationic 5.1g with 5.2 is reported in Table 5.1. These apparent rate constants are calculated from the observed pseudo-first-order rate constants by dividing the latter by the overall concentration of 5.2. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Assuming complete binding of the dienophile to the micelle and making use of the pseudophase model, an expression can be derived relating the observed pseudo-first-order rate constant koi . to the concentration of surfactant, [S]. Assumirg a negligible contribution of the reaction in the aqueous phase to the overall rate, the second-order rate constant in the micellar pseudophase lq is given by ... 

When the dienophile does not bind to the micelle, reaction will take place exclusively in the aqueous phase so that the second-order rate constant of the reaction in the this phase (k,) is directly related to the ratio of the observed pseudo-first-order rate constant and the concentration of diene that is left in this phase. 

As the second step in Scheme 5-1 is much faster than the first, the observed pseudo-first-order rate constant ( obs) is related to kx in Scheme 5-1 as described by Scheme 5-7. The second term in this equation arises from the fact that k x cannot... 

Under photostationary conditions, the slopes of the linear plots of the consumption of dissolved oxygen are the observed pseudo-first order rate constant of the chemical quenchers, k hs (Criado et al., 2008), and the rate constant for the reactive quenching of 1O2 by GA is calculated with eqn. 12. 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

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. 

In the 1988-1999 period, almost all absolute kinetic studies of carbenic reactions employed LFP with UV detection. Carbenes that contain a UV chromophore (e.g., PhCCl) are easily observed, and their decay kinetics during reaction can be readily followed by LFP.11 However, alkyl, alkylhalo, and alkylacyloxycarbenes are generally transparent in the most useful UV region. To follow their kinetics, Jackson et al. made use of the ylide method, 12 in which the laser-generated carbene (2) is competitively captured by (e.g.) pyridine, forming a chromophoric ylide (3, cf. Scheme 1). The observed pseudo first order rate constants (kobs) for the growth of ylide 3 at various concentrations of pyridine are monitored by UV spectroscopy, and obey Eq. 1. 

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. 20 A plot of the observed pseudo-first-order rate constants (kobs) for the methanolysis of HPNPP (4 x 10 5moldm ) as a function of [35 2Zn(II)] in the presence of 1 equivalent of added CH30 per complex giving jpH = 9.5, T = 25 + 0.1 °C. Dotted line is presented as a visual aid directed through all actual data collected at 280 nm ( ) or 320 nm (O) which are the wavelengths for disappearance of HPNPP and appearance of /j-nitrophenol solid line is a linear fit of the data corrected for inhibition by triflate counterions at 280 nm ( ) or 320 nm ( ). Reproduced with permission from ref. 95.

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.

The effects of micelles of cetyltrimethylammonium bromide (CTABr), tetradecyl-trimethylammonium bromide (TTABr) and sodium dodecyl sulfate (SDS) on the rates of alkaline hydrolysis of securinine (223) were studied at a constant [HO ] (0.05 m). An increase in the total concentrations of CTABr, TTABr and SDS from 0.0 to 0.2 M causes a decrease in the observed pseudo-first-order rate constants (kobs) by factors of ca 2.5, 3, and 7, respectively. The observed data are explained in terms of pseudophase and pseudophase ion-exchange (PIE) models of micelles. Cationic micelles of CTABr speed attack of hydroxide ion upon coumarin (224) twofold owing to a concentration effect. ... 

The kinetic form depends upon the complexity of the reaction. Whenever only one adduct is formed from a given substrate, the observed pseudo first-order rate constant Aobs is given by Eq. (8), where k( is the second-order rate... 

In the subsequent, thermodynamically controlled process the more stable adduct At becomes predominant through a reequilibration via the starting substrate. The observed pseudo first-order rate constant is given by Eq. (10).46... 

Quantitative studies for the formation of adducts from 5-membered heteroaromatic rings and methoxide ion have usually been carried out in methanolic solution and, in some cases (pyrrole derivatives), in Me2SO-MeOH 2 1 (v/v). Data have been obtained by allowing the substrates to react with a measured excess of MeO" and by following the increase in absorbance of the adduct. The observed pseudo first-order rate constant for the attainment of the equilibrium is found to obey the relation given in Eq. (23),... 

The most general kinetic form for the observed pseudo first-order rate constant (Arobs) is given by Eq. (24), which involves two-term expressions for both the forward and reverse reactions,... 

Average observed pseudo-first-order rate constants for the hydrolysis of the three methoxy groups of SiQAC in aqueous solution... 

The observed pseudo-first order rate constants as a function of pressure for benzophenone triplet in supercritical C02 at 33°C and isopropanol mole fraction of 0.0025. 

Observed, pseudo-first-order rate constant... 

The second-order rate constants, obtained from the linear plots of the observed pseudo-first-order rate constants against oxyMb or oxyHb concentrations, are pH... 

Figure 16. Inhibition of the reaction between p-nitrophenyl acetate and HSA by inorganic anions. Solutions of each anion, triethanolamine, and 3.5 X 10 5M HSA were prepared at the appropriate concentrations and pH 8.1. Logarithms of the observed pseudo-first-order rate constants are plotted vs. a function of ionic strength, jjl, for triethylammonium phosphate (O), fluoride (D), sulfate (%), chloride (M), iodide (A), and perchlorate ( A).

Note, however, that the exchange rate constants in the rate matrix are not necessarily rate constants for elemental chemical reactions. The observed pseudo-first-order rate constants in R are dependent on the fractional populations at various sites and are often made up of several elemental rate constants. The rate constants for the elemental steps of a chemical reaction must therefore be derived from the observed rate constants with a given mechanism in mind. Considerations for interpreting the measured magnetization transfer rates have been discussed (38) for both intra- (46) and intermodular systems (32). In the following section we show a few examples. 

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