Pseudo reaction order

Negligible dissolution of solid in the gas-liquid film This represents a relatively simple situation where no solid dissolves in the gas-liquid film Fj. The following steps are involved diffusion of gas A through the film dissolution of solid B and diffusion and simultaneous reaction of B with dissolved A in film Fj. The last step can occur in regime 3 (fast reaction, pseudo-order), regimes 3-4 (fast reaction, with depletion), or regime 4 (instantaneous reaction). The first two cases are sketched in Figure 12.8a and the third in 12.8b. The conditions and rate equations for the three cases are summarized in Table 12.5. 

Pseudo-Order Reactions and the Method of Initial Rates Unfortunately, most reactions of importance in analytical chemistry do not follow these simple first-order and second-order rate laws. We are more likely to encounter the second-order rate law given in equation A5.11 than that in equation A5.10. 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

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. 

Fast reaction, pseudo-first order < Ha < E = tanh Ha... 

If the forward reaction is pseudo first order and the reverse reaction second order, then, as discussed in Sections 1.4.4 and 1.4.5 in Volume 3, the rate equation may be written as ... 

Isopropylbenzene (A) is alkylated with propylene (P) using HF catalyst. The mono (B), di (C), tri (D) and tetra (E) derivatives are formed. Relative specific rates are given by Rodiguin Rodiguina (Consecutive Chemical Reactions, 1964) for the case of a large excess of propylene which makes the reactions pseudo first order. The relative specific rates used here are kx = 1.0, k2 = 0.5, k3 = 0.3 and k4 0.2. The system of linear differential... 

This reaction appears to be first order because the cerium ions are in excess, so the concentration does not really change. We look at pseudo-order reactions on p. 387. 

We will need to look further at this equation when thinking about kinetic situations in which one of the reactants is in great excess (the so-called pseudo order reactions described in Section 8.4). 

A pseudo-order reaction proceeds with all but one of the reactants in excess. This ensures that the only concentration to change appreciably is that of the minority reactant. 

How in practice, then, do we determine kinetic parameters for pseudo-order reactions such as these ... 

Worked Example 8.17 The following kinetic data were obtained for the second-order reaction between osmium tetroxide and an alkene, to yield a 1,2-diol. Values of k are pseudo-order rate constants because the 0s04 was always in a tiny minority. Determine the second-order rate constant k2 from the data in the following table ... 

Figure 8.15 The rate constant of a pseudo-order reaction varies with the concentration of the reactant in excess graph of k (as V) against [alkene]0 (as V). The data refer to the formation of a 1,2-diol by the dihydrolysis of an alkene with osmium tetroxide. The gradient of the graph yields k2, with a value of 3.2 x 10 2 dm3 mol-1 s-1...

The reactions, in which molecularity and order are different due to the presence of one of the reactant in excess, are known as pseudo-order reactions. The word (pseudo) is always followed by order. For example, inversion of cane sugar is pseudo-first order reaction. 

Table 23.1 HMF formation kinetics in isothermal heating as a function of treatment temperature, first order reaction pseudo rate constant and regression coefficients...

When a = b = 1 in (1.42) the overall reaction is second-order. Even a quite small excess of one reagent (here B) can be used and pseudo first-order conditions will still pertain. As the reaction proceeds, the ratio of concentration of the excess to that of the deficient reagent progressively increases so that towards the end of the reaction, pseudo first-order conditions certainly hold. Even if [B] is maintained in only a two-fold excess over [A], the error in the computed second-order rate constant is 2% for 60% conversion. ... 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

For reactions between ions of like charge, the term in xrc (1 + kR) 1 should be multiplied by a number 0.6—0.9, whereas for unlike charges, this number is 0.3—0.6 depending on R. Certainly, eqn. (58) is not the appropriate correction term. In eqn. (57), the ionic relaxation time for univalent ions is Tjon = 1/(477[rc Dn), where n is the electrolyte concentration. This is also the characteristic time for reaction (pseudo first-order decay time) of a univalent species reacting with one or other ion of the... 

A more detailed LSV study [58, 89] resulted in the conclusion that the kinetics, under all conditions, could not be described by the simple eCej, scheme. It was proposed that the reaction order in anthracene anion radical (AN- ) varies between 1 and 2 and the reaction order in phenol is greater than 1. A complex mechanism was also indicated from DCV measurements [89]. At a phenol concentration of 10 mM, values of dEpj d log v were in all cases close to that expected for a reaction second order in An-, i.e. 19.5mV decade-1 under the conditions of the experiments. The process is fast enough under these conditions for it to be expected to fall well within the KP zone. That this is the case was indicated by the fact that d p/dlog v was linear over a reasonably wide range of v (10— 1000 mV s-1). The highest value of the slope, observed at a phenol concentration of 100mM, was still significantly lower than 29.3 mV decade -1 predicted for a pseudo-first-order reaction. 

The rate of product formation will be directly proportional to [A] but inversely proportional to [Br ]. By using an excess of Br so that its initial concentration [Br ]0 does not change appreciably over the course of the reaction, pseudo-first-order behavior can be achieved with /cobs = k2Keq/[Br ]0. 

The reaction is catalysed by acids, but during the experiment quoted [acid] remains constant, and reaction is being carried out under pseudo-order conditions. 

Toluene is both a reactant and the solvent, and so the toluene will always be in excess, and again reaction is carried out under pseudo-order conditions. 

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