The reaction order approach

The common theoretical approach to the determination of the LSV and CV response to reactions coupled to charge transfer is to set up and 

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If the monomer is the trne reacting species and the reaction of the monomer with an electrophile is fast enough compared to the monomer-aggregate eqnilibrinm, then the rate should be independent of the electrophile concentration. This was indeed fonnd for the reaction of BuLi with methyl trifluoroacetate in diethyl ether the reaction was extremely fast (18.5 s at — 28 °C) and was 0th order with respect to the ester concentration. Reaction of benzonitrile with BuLi in diethyl ether was slower, bnt the rate increased with increasing the benzonitrile concentration and reached a maximnm valne similar to that (7 X 10 s at —82°C) with methyl trifinoroacetate and the reaction order approached 0. Thus, the rate-determining step for the reaction of benzonitrile changed with its concentration. 

Thus, the reaction order approach involves the analysis of plots or correlations of logi>c vs. log CA or log Cx in order to determine Raib and Rx from which rate laws can be formulated for the process in question. In the event that the rate-determining step does not change as the concentration of reagents is changed, both z and x are obtained as the slopes of linear plots or correlations. This is the case for the simple reaction mechanisms such as those illustrated in Table 16. Any curvature in the log—log plots indicates complications which could be due to... 

Rate constants can be assigned by curve fitting to find the value of n, in CA units, and then application of the theoretical relationships corresponding to either of the limiting cases. An example of the application of the reaction order approach is treated in a following section. 

The reaction order approach for the LSV response to simple reaction mechanisms, eqns. (49)—(51), has already been described. These equations are applied directly to experimental data and rate laws are derived before a mechanism or a theoretical model is considered. Since RA and RB are separable during LSV analysis, the changes in RB as a function of CA can be observed directly from djf p/d log v [72], When RB is changing with changes in CA, this slope will not be linear over large intervals but will appear to be linear over small intervals of v. For the reaction order analysis, CA was defined as the concentration when RB is half-way between the limiting values, usually 1 and 2, i.e. 1.5. In terms of n, multiples of CA, there are again three distinct cases which must be satisfied by f(n). They are n = 1 (,RB = 1.5), n < 1 (RB = 1) and n> 1 (RB = 2). These requirements are satisfied by eqn. (65) and illustrates how RB varies with n. 

Apparent activation energies and kinetic isotope effects using the reaction order approach... 

It is convenient at this juncture to introduce a concept that, in electro analytical chemistry, sometimes is referred to as the reaction order approach. Consider first the half-life-time, t1/2> which in conventional homogeneous kinetics refers to the time for the conversion of half of the substrate into product(s). From basic kinetics, it is well known that t /2 is independent of the substrate concentration for a reaction that follows a first-order rate law and that 1/t j2 is proportional to the initial concentration of the substrate for a reaction that follows a second-order rate law. Similarly, in electro analytical chemistry it is convenient to introduce a parameter that reflects a certain constant conversion of the primary electrode intermediate. In DPSCA, it is customary to use ti/2 (or to.s), which is the value of (f required to keep the value of Ri equal to 0.5. The reaction orders (see Equation 6.30) are then given by Equations 6.35 and 6.36, where Ra/b = a + b, and Rx = x (in reversal techniques such as DPSCA, in which O and R are in equilibrium at the electrode surface, it is not possible to separate the... 

The rate law necessary for making a mechanistic proposal is conveniently determined by DCV using the reaction order approach introduced in Section 6.7.1. Usually, the value of v required to keep R/ equal to 0.5 is used and referred to as U /2 (or v0.5). The relationships between v /2 and the reaction orders of Equation 6.30 are given by Equations 6.44 and 6.45... 

The advantages of the reaction order approach is that experimental data are treated directly without making any mechanistic assumptions and the... 

It should be pointed out that all of the rate expressions were derived using the steady state approximation on an appropriate intermediate and represent limiting cases of the complete rate laws. These approximations are always used in the theoretical calculations, but the reaction order approach does not require such approximations since experimental data are treated directly. 

Table 1. Equations for calculating rate constants for simple reaction mechanisms based on the reaction order approach for DPSC [137],...

Eqn. (2) seems to be generally suitable for describing the initial rate of priopion-aldehyde decomposition. According to this equation, the reaction order approaches f at high pressures and low temperatures. (Note the activation energies )... 

The rate law necessary for making a mechanism suggestion is conveniently determined by DCV. The procedure, sometimes referred to as the reaction order approach, is based on measurements of the sweep rate necessary to maintain a certain constant conversion of B as a function of CX, and Cx if relevant. Usually the sweep rate necessary to... 

As was discussed in section 1.7.9 one also may transform the high pressure dissociation rate constant by equation (1.81) into a high pressure recombination rate constant, i.e. into the recombination rate constant for the region where the reaction order approaches two. To do this one must combine the equilibrium constant (equation (1.83)) with equation (1.99) ... 

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. 

Experimental tests of this mechanism can determine the reaction order with respect to each component and verify the molecularities assumed, but are unable to separate even the factors k K, let alone measure / and as long as the assumption of pre-equihbrium remains vaUd. Better time resolution in the experiment captures the approach of [i] toward equihbrium and, consequently, violates that assumption. 

Pb(IV) EtOH + ROOH products and the reaction order with respect to peroxide approaches unity. 

The fractional life approach is most useful as a means of obtaining a preliminary estimate of the reaction order. It is not recommended for the accurate determination of rate constants. Moreover, it cannot be used for systems that do not obey nth order rate expressions. 

For a reaction of the type shown in (74) with hydroxide ion in excess, the expected variation of the time constant (t-1) for the first-order approach to equilibrium after a temperature perturbation is given by (75). Thus a plot of reciprocal relaxation time (t 1) against hydroxide ion concentration is... 

Where r is the rate of reaction in kmol/m (Ni)/h and the partial pressures, p, are in MPa. The reaction order with respect to steam was very sensitive to temperature, decreasing from —0.6 at 450°C, to —0.2 at 550°C. The steam-surface interactions weaken with increasing temperature, hence the reaction order with respect to steam approaches zero due to weak adsorption at high temperatures. 

A very low reaction order, with respect to i-Cg, suggests a strong adsorption of i-Cg molecules on the Ni surface. Rostrup-Nielsen " also noticed a retarding effect of aromatics and higher hydrocarbons on the reaction rate. Due to the presence of % electrons, aromatics can strongly adsorb onto the catalyst surface and cause the reaction order to approach zero. 

As Haber and Weiss (1934) suggested, at lower H202 concentrations and fixed Fe2+ the oxidation reaction approaches second order however, when the ratio of H202 Fe2+ increases, the reaction kinetic approaches zero order and the reaction process depends on the competition between hydroxyl radicals and superoxide radicals. If an excess of hydrogen peroxide is present, then the reactions as shown in Equation (6.123) and Equation (6.124) for 2,4-dinitrotoluene are dominant. The amount of H202 was used up quickly in this study, indicating the importance of Equation (6.123). At concentrations of Fe2+ greater than 600 mg/L, the DRE of BTX reached a maximum value at approximately 82% for benzene and toluene and 73% for xylene. 

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