Second order reaction significant excess

A kinetic study of nitrous acid-catalyzed nitration of naphthalene with an excess of nitric acid in aqueous mixture of sulfuric and acetic acids (Leis et al. 1988) shows a transition from first-order to second-order kinetics with respect to naphthalene. (At this acidity, the rate of reaction through the nitronium ion is too slow to be significant the amount of nitrous acid is sufficient to make one-electron oxidation of naphthalene as the main reaction path.) The reaction that initially had the first-order in respect to naphthalene becomes the second-order reaction. The electron transfer from naphthalene to NO+ has an equilibrium (reversible) character. In excess of the substrate, the equilibrium shifts to the right. A cause of the shift is the stabilization of cation-radical by uncharged naphthalene. The stabilized cation-radical dimer (NaphH)2 is just involved in nitration ... 

For the analysis of second order reactions carried out under condition (c), when the concentrations of the two reactants are not equal but neither is significantly in excess of the other, the following general equation has to be solved ... 

The rate of reduction of Tl(III) by Fe(II) was studied titrimetrically by John-son between 25 °C and 45 °C in aqueous perchloric acid (0.5 M to 2.0 M) at i = 3.00 M. At constant acidity the rate data in the initial stages of reaction conform to a second-order equation, the rate coefficient of which is not dependent on whether Tl(III) or Fe(II) is in excess. The second-order character of the reaction confirms early work on this system . A non-linearity in the second-order plots in the last 30 % of reaction was noted, and proved to be particularly significant. Ashurst and Higginson observed that Fe(III) retards the oxidation, thereby accounting for the curvature of the rate plots in the last stages of reaction. On the other hand, the addition of Tl(l) has no significant effect. On this basis, they proposed the scheme... 

In a semi-quantitative stopped-flow study, based only on yields of chlorine dioxide, (15) was found to be faster than (16), with (17) always occurring but of most significance for low concentrations of chlorous acid. With excess sodium chlorite, the yield of chlorine dioxide could be in excess of that predicted by (15) so that catalysis (by CI2 or by HCIO) of a chlorite reaction seems probable. Reactions (15) and (16) are both approximately second order. The mechanism, suggested to be consistent with Dodgen and Taube s results , involves the steps... 

Gunnarsson et al. 166) have measured the rate of reduction of T q)es 1 and 3 Cu2+ in the presence of excess EDTA by several substrates, including ascorbate, l oth reactions were found to be well behaved second-order processes in which no saturation was observed even when substrate was present at a concentration several-fold greater than its steady state Km value. The rate of reduction of Types 1 and 3 were identical suggesting either a complete equihbration between the two electron acceptors or identical rates of reduction by substrate. When less than stoichiometric amounts of substrate (ascorbate) were present, however, the two chromophores were reduced at significantly different rates 172). 

Using the above equation, we can calculate the rate constant k for various values of AG, shown in Table 2.2. The half-life of a unimolecular reaction is equal to (In 2) k or 0.693/, and a reaction is 97% complete after five half-lives. Table 2.2 uses the formula ln(c7c) = kt to relate the rate constant, k, and the original concentration, c°, to the concentration, c, at time t seconds for a unimolecular reaction. Reactant concentrations are very important in a bimolecular reaction. If reactant B in a bimolecular reaction is in large excess, then its concentration will not change significantly over the course of the reaction and can be considered a constant, making the reaction pseudo-first order. We can then use the above formula to calculate the concentration of A at time t by substituting the pseudo-first-order rate constant, k = [B]. 

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