Rate law second-order

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is... 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

A simple kinetic order for the nitration of aromatic compounds was first established by Martinsen for nitration in sulphuric acid (Martin-sen also first observed the occurrence of a maximum in the rate of nitration, occurrii for nitration in sulphuric acid of 89-90 % concentration). The rate of nitration of nitrobenzene was found to obey a second-order rate law, first order in the concentration of the aromatic and of nitric acid. The same law certainly holds (and in many cases was explicitly demonstrated) for the compounds listed in table 2.3. 

First-order nitrations. The kinetics of nitrations in solutions of acetyl nitrate in acetic anhydride were first investigated by Wibaut. He obtained evidence for a second-order rate law, but this was subsequently disproved. A more detailed study was made using benzene, toluene, chloro- and bromo-benzene. The rate of nitration of benzene was found to be of the first order in the concentration of aromatic and third order in the concentration of acetyl nitrate the latter conclusion disagrees with later work (see below). Nitration in solutions containing similar concentrations of acetyl nitrate in acetic acid was too slow to measure, but was accelerated slightly by the addition of more acetic anhydride. Similar solutions in carbon tetrachloride nitrated benzene too quickly, and the concentration of acetyl nitrate had to be reduced from 0-7 to o-i mol 1 to permit the observation of a rate similar to that which the more concentrated solution yields in acetic anhydride. 

Kinetic studies of these reactions reveal that they follow a second order rate law Rate = [Aryl halide] [Nucleophile]... 

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 gas decomposition reaction with stoichiometry 2A —> 2B -i- C follows a second order rate law rj(mol / m s) = kC, where C is the reactant concentration in mol/m. The rate constant k varies with the reaction temperature according to the Arrhenius law ... 

Since the reaction is carried out in a batch system of constant volume, the rate expression for a second order rate law is... 

Although individual runs for the first set of experiments follow the second-order rate law, the observed second-order rate coefficients, k, are strongly dependent on the initial amine concentrations, with the rate increasing regularly as the amine concentration increases. Nevertheless, for all of the measurements, a plot of k versus the initial amine concentration is linear, and the data can be fitted withegn.(4), with k equal to 1.87 x 10-4 l.mole-1. sec-1 and k" equal to 5.63 x 10-412. mole-2. sec-1. 

Presto, a third-order rate law This multiplication should not be taken as representing a chemical event or as carrying such implications it is only a valid mathematical manipulation. Other similar transformations can be given,2 as when one multiplies by another factor of unity derived from the acid ionization equilibrium of HOC1. (The reader may show that this gives a second-order rate law.) These considerations illustrate that it is the rate law and not the reaction itself that has associated with it a unique order. 

The reaction follows a mixed second-order rate law. The progress was monitored spec-trophotometrically at 723 nm, where Np4+ has a maximum absorption. The following data refer to an experiment with [Np3+]o = 1.53 x 10-4 M, [Fe3+]o = 2.24 x 10-4 M (taken at 298.0 K, [H+] = 0.400 M, and ionic strength = 2.00 M). Calculate the rate constant either taking the end point value as 0.351 or, if a suitable program is available, allowing it to be found in the calculation. 

Calculate t p, Re, and k, assuming a second-order rate law for exchange. Also calculate the expected value of tip in a similar experiment but with 5.0 x 10-3 M Fe2+. 

In the next two sections, we concentrate on first- and second-order rate laws, but the techniques can be used for other reaction orders, too. 

As we have seen for first- and second-order rate laws, each integrated rate law can be rearranged into an equation that, when plotted, gives a straight line and the rate constant can then be obtained from the slope of the plot. Table 13.2 summarizes the relationships to use. 

Mechanism II for the decomposition of NO2 predicts that the reaction should have a second-order rate law ... 

Students who have taken calculus will recognize that Equation results from integration of the second-order rate law. 

Moser and Gratzel reported that the absorption signals of Ij could be seen immediately after a laser flash on an I -containing a-Fe203 sol. The quantum yield was 80%. In a subsequent reaction, 1 disappeared according to a second order rate law 2 Ij 21 - - I2. The authors pointed out that single crystals and polycrystalline... 

Equation 1.13 reduces to the second-order rate law, shown in equation 1.12, when K[ L ] first-order rate law, equation 1.14,... 

The associative (A or SA 2) will give the simple second-order rate law shown in equations 1.19 and 1.20 if the higher coordination number intermediate concentration remains small, resulting in the rate dependence shown in equation 1.21. 

We may compare these results with a second-order rate law which exhibits Arrhenius temperature dependence ... 

Mechanistic interpretation of activation volumes on square-planar complexes is complicated by the geometry. The sterically less crowded complexes may have loosely bound solvent molecules occupying the axial sites above and below the plane. Replacing them in the formation of a five-coordinate transition state or intermediate may result by compensation in relatively small volume effects. It is therefore difficult to distinguish between Ia and A mechanisms from the value of the activation volume. Nevertheless, the AV values are negative and together with the second-order rate laws observed, point to an a-activation for those solvent exchange reactions. 

Reaction of the binuclear complex [(bpy)Pd(p-OH)2Pd(bpy)]2+ with dl-methionine (met) obeys a simple second-order rate law (Aif = 46kJmol-1 AS = —101J K-1 mol-1). The mechanism suggested is rate-determining associative attack of the methionine-sulfur to give... 

Subsequent to a photolytic flash of low energy, the decay of [CIO] follows the second-order rate law expected for removal by (9). At high flash energies the reaction... 

In contrast, in protic solvents and at low bromine concentration, the addition process is characterized by a second order rate law (first order in bromine), Scheme 2, path b. In this case, due to the ability of the solvent to provide a specific electrophilic solvation to the leaving bromide ion, the reaction occurs via an SN1 -like unimolecular ionization of the 1 1 it complex to form a bromonium or P-bromocarbenium bromide ion pair. It is worth noting that protic solvents can also give nucleophilic assistance, depending on their specific solvent properties. 

The time-dependent decrease in the concentration of particles (N = number of particles per cubic centimeter) in a monodisperse suspension due to collisions by Brownian motion can be represented by a second-order rate law... 

C—The 2 exponent means this is a second-order rate law. Second-order rate laws give a straight-line plot for 1 /[A] versus t. 

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