Pseudo-order technique

Use of the isolation or pseudo-order technique. This approach is discussed in Chapter 2, where it was shown how a second-order reaction could be converted to a pseudo-first-order reaction by maintaining one of the reactant concentrations at an essentially eonstant level. The same method may be usefully applied to eomplex reactions. In this way, for example. Scheme XI can be studied under conditions such that it functions as Scheme IX. A corollary that must be kept in mind is that a reaction system that is observed to behave in accordance with (as an example) Scheme IX may actually be more complex than it appears to be, if an unsuspected reactant is present under pseudo-order conditions. 

Application of pseudo-order techniques to rate/concentration data... 

Propagation of errors, 40, 48, 248 Propinquity effect, 263, 365 Protol5Tsis, 147, 148 Proton inventory technique, 302 Proton transfer, 166 direct, 148 extent of, 346 fast, 97, 146, 173 isotope effect in, 296 partial, 395 Proximity effect, 365 Pseudo-first-order rate constant, 23 Pseudo-first-order reaction, 61 Pseudo-order rate constant, 23 Pseudo-order reaction, 23 Pseudo-order technique, 26, 78 Pulse NMR, 170... 

Use cf Integrated Equations 24 The Isolation and Pseudo-Order Techniques Initial Rate Method 28 Fractional Time Methods 29... 

Neretnieks [5] studied the effects of temperature and concentration on surface diffusion, using a pseudo lineeir technique to approximate the slope of isotherm as depicted in Figure 1. An equilibrium point (c=ce2 and q=q 2) was connected to an origin (c=0 and q=0) by a straight line in order to approximate actual slope of the isotherm at Ce2. It is obvious that his pseudo-linear technique offers poor approximation for highly nonhneeu isotherms, which 6ure often found in industrial applications. 

The fundamental research work was subvided into 3 parts [ 6o ] - thermogravimetric analysis (TGA) and differential thermal analysis (PTA) of minute samples (5 50 mg) of the material to be studied. Both techniques yield information on the rate of thermal decomposition, the heat of reaction, the kinetic parameters of this process (pseudo-order and activation energy) and the amount of residue. The analysis of the evolving product has been monitored by means of gas chromatography. High temperature oxidation of the residue allows to compare the reactivity of the carbonized residue. ... 

To siimmorize The initial rale method is essentially an isolation technique but it does not require that any reactants have to be in large excess. In general for a reaction involving two or more reactants, one of these is isolated by arranging that the initial concentrations of the others are held at fixed values during a series of experiments. The main application of the method is for the determination of partial order. Values of pseudo-order rate constants can be determined but with an accuracy that, in turn, depends on how accurately initial rates of reaction can be measured. 

The reaction/mass-transfer technique is based on Danckwerts theory of mass transfer accompanied by a fast pseudo first-order reaction (10) ... 

The isolation experimental design can be illustrated with the rate equation v = kc%CB, for which we wish to determine the reaction orders a and b. We can set Cb >>> Ca, thus establishing pseudo-oth-order kinetics, and determine a, for example, by use of the integrated rate equations, experimentally following Ca as a function of time. By this technique we isolate reactant A for study. Having determined a, we may reverse the system and isolate B by setting Ca >>> Cb and thus determine b. 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

The isolation technique showed that the reaction is first-order with respect to cin-namoylimidazole, but treatment of the pseudo-first-order rate constants revealed that the reaction is not first-order in amine, because the ratio k Jc is not constant, as shown in Table 2-2. The last column in Table 2-2 indicates that a reasonable constant is obtained by dividing by the square of the amine concentration hence the reaction is second-order in amine. For the system described in Table 2-2, we therefore find that the reaction is overall third-order, with the rate equation... 

Proton inventory technique. 21.9-220 Pseudo-first-order kinetics, 16 Pulse-accelerated-flow method. 255 Pulse radiolysis, 266-268 Pump-probe technique. 266... 

For first-order and pseudo first-order reactions of the series type several methods exist for determining ratios of rate constants. We will consider a quick estimation technique and then describe a more accurate method for handling systems whose kinetics are represented by equation 5.3.2. 

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. 

The quantity and quality of experimental information determined by the new techniques call for the use of comprehensive data treatment and evaluation methods. In earlier literature, quite often kinetic studies were simplified by using pseudo-first-order conditions, the steady-state approach or initial rate methods. In some cases, these simplifications were fully justified but sometimes the approximations led to distorted results. Autoxidation reactions are particularly vulnerable to this problem because of strong kinetic coupling between the individual steps and feed-back reactions. It was demonstrated in many cases, that these reactions are very sensitive to the conditions applied and their kinetic profiles and stoichiometries may be significantly altered by changing the pH, the absolute concentrations and concentration ratios of the reactants, and also by the presence of trace amounts of impurities which may act either as catalysts and/or inhibitors. 

LFP-Probe Method. In cases where the radicals of interest do not contain a useful chromophore, the LFP technique can be modified by incorporation of a probe radical reaction that gives a product with a chromophore. The probe reaction can be unimolecular or bimolecular, a constant concentration of probe reagent is employed in the latter case. Formation of the detectable species occurs with an observed first-order or pseudo-first-order rate constant equal to k0. In the presence of another reagent X that reacts with the original radical, the rate constant for formation of detectable species is kohs = k0 + kx [X], and the bimolecular rate constant is determined (as before) by conducting the reaction at varying concentrations of X. Note that the LFP-probe technique is a direct method even though the reactant or product of interest is not monitored. 

The DANTE-Z sequence has been employed successfully as a ID substitute in pseudo 3D experiments [7] and also as a band-selective technique in multidimensional experiments [8] in order to improve the spectral resolution. The efficiency of the DANTE-Z procedure over the simple DANTE sequence is illustrated by the spectra shown in fig. 2. 

As we have seen earlier, even third-order reactions can be reduced to pseudo-first-order reactions by keeping the concentrations of all species except A constant and in great excess compared to A. This technique of using pseudo-first-order conditions is by far the most common technique for determining rate constants. Not only does it require monitoring only one species, A, as a function of time, but even absolute concentrations of A need not be measured. Because the ratio [A]/[A]0 appears in Eq. (T), the measurement of any parameter that is proportional to the concentration of A will suffice in determining k l7, since the proportionality constant between the parameter and [A] cancels out in Eq. (T). For example, if A absorbs light in a convenient... 

The monitoring techniques are used to obtain the absolute rate constants of DPC with other substrates (Q) known to react with triplet carbenes. The experiments are carried out at several reagent concentrations and the experimental pseudo-first-order rate constant, k bs, is plotted against the substrate concentration. It can be shown that feobs is expressed by Eq. 22... 

A variety of pulsed techniques are particularly useful for kinetic experiments (Mclver and Dunbar, 1971 McMahon and Beauchamp, 1972 Mclver, 1978). In these experiments, ions are initially produced by pulsing the electron beam for a few milliseconds. A suitable combination of magnetic and electric fields is then used to store the ions for a variable period of time, after which the detection system is switched on to resonance to measure the abundance of a given ionic species. These techniques allow the monitoring of ion concentration as a function of reaction time. Since the neutrals are in large excess with respect to the ions, a pseudo first-order rate constant can be obtained in a straightforward fashion from these data. The calculation of the rate constant must nevertheless make proper allowance for the fact that ion losses in the icr cell are not negligible. 

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