Pseudo-first-order kinetics, deviation

In mild alkaline conditions, highly methylated pectin was demethylated following a (pseudo)-first order kinetics with respect to the concentration of methoxylated galacturonate moieties. Investigation in this pH range, where the initial concentration of methylesters was higher than the initial concentration of OH ions, was complicated by the necessity to use a buffer. This led to deviations from the theoretical behavior as the concentration of OH ions still varied in proportions which could not be neglected in the equations of the kinetics. However these deviations could be accounted for be the pH variation, and the pH variation itself predicted from the amount of liberated methanol. The constant we found was similar to previously reported data (Scamparini Bobbio, 1982). 

Pseudo-first order kinetics was assumed to interpret the experimental data. Fig. 5.4-36 shows that the fit of the experimental data using first order-kinetics is acceptable. However, a systematic deviation is observed in the curve obtained at 110 C. This indicates inadequacy of the first-order kinetics, which is inappropriate from the view of theory. On the other hand, the kinetic equation seems to describe the... 

The fact that sometimes a type of saturation kinetics and sometimes pseudo first-order kinetics were observed indicates that the reaction involves two steps (1) formation of the catalyst-substrate complex and (2) dissociation of the product from the intermediate complex with the associated formation of either the now oxidized or reduced complex form (Scheme 4.4). Actually, The reaction between a reduced molybdenum centre and an oxygen-donating substrate has been proposed to proceed via a transition state where the substrate oxygen atom binds directly to the molybdenum atom . It has to be considered that the initial condition [S]o [E]o together with the circumstance that the en me will not be recycled but consumed are both responsible for the deviating behaviour. 

The sensitivity of resonance fluorescence by F atoms was, however, sufficient for kinetic studies to be made of the rapid titration reaction of F with Brj, v/z. F + Bri - BrF + Br. It was necessary to make corrections both for nonlinearity of fluorescence intensity with [F] and for deviations from pseudo-first-order kinetic conditions, both due to the relatively high F P atom concentrations used (>1 X 10 cm" ). The final rate constant for the F + Br2 reaction was (1.4 0.5) X 10" ° at 298 K, in fair agreement with results from the (similarly difficult) mass spectrometric study of Appelman and Oyne [A = (3.1 0.9) X 10" >]. 

The deviation of the kinetics from the simple pseudo first order kinetics observed for the hydrolysis is certainly related to the differences in size and nucleophilicity of the attacking nucleophile. Similar to the induction period observed for the hydrolysis of NHS esters in SAMs of NHS-C15 on gold. 

Continuous-flow e.s.r. studies have been made on the oxidation of vanadium(iv) by hydrogen peroxide.Both the VO + ion and the intermediate complex formed, [OVOO] +, have been monitored over a wide range of initial V, H2O2, and H+ concentrations. In the presence of excess H2O2, a mechanism accounting for the deviation from pseudo-first-order kinetics may be represented as... 

Figure 8.14 The reaction of A and B, with B greatly in excess is a second-order reaction, but it follows a kinetic rate law for a first-order reaction. We say it is pseudo first-order reaction. The deviation from linearity at longer times occurs because the concentration of B (which we assume is constant) does actually change during reaction, so the reaction no longer behaves as a first-order reaction...

Kinetic analysis revealed that this reaction is pseudo-first order in dienophile at low conversions (200). At higher conversions, the rate deviates from a linear relationship, suggestive of product inhibition. Indeed, addition of product to the reaction at the start resulted in a decrease in rate by 18%. A number of competitive inhibitors were identified in this study. Particularly interesting was the observation that the matched chiral dienophile product was less effective as an inhibitor than the mismatched product. The authors suggest that the sterically matched complex (where the ligand bulk and imide chirality is on the same side of the complex) is thermodynamically less stable than the mismatched complex. 

The rate laws (8.29) and (8.30), with [Cr(II)]t ,a[ in excess, lead to oxidation by Co(C204)j and Ij" showing initially pseudo zero-order kinetics. As the concentration of the oxidant decreases however, Arjfoxid] S and some deviation from linearity for the plot occurs and eventually becomes first-order, although this may be near to the completion of reaction. With Co(edta) in deficiency, the reaction is pseudo first-order. 

In a number of works [124-126], the model of monodisperse micelles has been used to determine the diffusivity of the micelles Joos and van Hunsel [127] have used this model to interpret experimental data for kinetics of adsorption obtained by the drop-volume method. These authors have demonstrated that the data can be fitted by means of a simpler expression for and R , which are linear with respect to the concentration see also Refs. 77, 128, and 129. In fact, every reaction mechanism reduces to a reaction of pseudo-first-order for small deviations from equilibrium see, for example, Ref. 130, Sec. 5. 

If the first-order or pseudo-first-order rate constant for a reaction under a specific reaction condition is 0.035 sec-, then such a reaction is completed almost 50% within 20 sec — an average minimum time to obtain first data point on the vs. t plot in a conventional UV-visible spectrophotometric technique. In order to test reliable and satisfactory fit of observed kinetic data for such reactions to Equation 7.24, the experimentally determined kinetic data (A b, vs. t) for a typical kinetic run on the nucleophilic substitution reaction of pyrrolidine with phenyl salicylate are shown in Table 7.7 in which the rate of reaction remains strictly first order for the reaction period of 53 half-lives. 3 The observed kinetic data in Table 7.7 have been treated with Equation 7.24 using the nonlinear least-squares technique. The kinetic parameters (k, S pp, and AJ calculated using different reaction time ranges (t to ts3, where subscripts n and 53 represent half-lives of the reaction and n < 53) with n = 0.8, 1.8, 2.4, and 3.6, are summarized in Table 7.7. The extent of reliability of the data fit to Equation 7.24 is evident from the values of and standard deviations associated with the calculated kinetic parameters (Table 7.7). A similar calculation has been carried out on kinetic data of Table 7.1 using Equation 7.25, and the results obtained are summarized in Table 7.8. 

---