Third-order rate law

It is clear from figure A3.4.3 that the second-order law is well followed. Flowever, in particular for recombination reactions at low pressures, a transition to a third-order rate law (second order in the recombining species and first order in some collision partner) must be considered. If the non-reactive collision partner M is present in excess and its concentration [M] is time-independent, the rate law still is pseudo-second order with an effective second-order rate coefficient proportional to [Mj. 

Empirically, one indeed finds a third-order rate law... 

However, the postulated trimolecular mechanism is highly questionable. The third-order rate law would also be consistent with mechanisms arising from consecutive bimolecular elementary reactions, such as... 

The reaction rates of toluene and benzene with i-propyl chloride in nitromethane fit a third-order rate law ... 

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. 

As before, the mechanism gives rise to an overall third-order rate law, in agreement with experiment. Although this procedure is much simpler than the steady-state approach, it is less flexible it is more difficult to extend to more complex mechanisms and it is not so easy to establish the conditions under which the approximation is valid. 

Figure 12. Extent of dissolution and re-precipitation between aqueous Fe(III) and hematite at 98°C calculated using Fe-enriched tracers. A. Percent Fe exchanged (F values) as calculated for the two enriched- Fe tracer experiments in parts B and C. Large diamonds reflect F values calculated from isotopic compositions of the solution. Small circles reflect F values calculated from isotopic compositions of hematite, which have larger errors due to the relatively small shifts in isotopic composition of the solid (see parts B and C). Curves show third-order rate laws that are fit to the data from the solutions. B. Tracer experiment using Fe-enriched hematite, and isotopically normal Fe(lll). C. Identical experiment as in part B, except that solution Fe(lll) is enriched in Te, and initial hematite had normal isotope compositions. Data from Skulan et al. (2002).

In the oxidation of Fe(II)P + (5) by excess O2 there is a second-order loss of Fe(II). The second-order rate constant Ar is linearly dependent on [Oj] with a zero intercept for the [O2] plot. An overall third-order rate law therefore holds. 

The rate data for individual runs can be used to derive independent estimates of k7 + kg, and these are shown in Table II. Both rate constants for an assumed second-order and third-order rate law are shown. The second-order rate constants show the smaller deviation from constancy, but the total change in concentration of the reactants is relatively small so that the order cannot be definitely proved at present. 

Johnston and Slentz231 found the reaction to be third order to % atm at 25°C. Briner, Pfeiffer, and Malet57 studied the reaction at temperatures down to 80°K, at which temperature the rate constant was about two orders of magnitude smaller than that predicted by eq. (d). Kassel241 explained this by showing that the pressures in their experiments were too great for the third-order rate law to be applicable at this temperature. 

According to reaction (559) these reactions can occur by an oxidation reaction of platinum(II). With one-electron oxidants, the intermediate formation of platinum(III) complexes occurs. The best early example of this type of reaction is in the oxidation of PtCi - and Pt(en)2+ by IrIVCl - in the presence of free chloride ion. The presence of platinum(III) intermediates has been inferred from the rate law.2036 For the oxidation of platinum(II) by gold(III) the kinetic data are consistent with a mechanism requiring a complementary two-electron transfer,2037 with a rate independent of chloride ion. For the substituted pyridine derivatives PtCkLj (L = substituted pyridine) however, the third-order rate law is found with first-order dependencies on PtCl I, Aum and Cl-.2038 Comparisons have been made with the amine complexes PtC L (L = NH2R).2039... 

With a variety of different mechanisms available, it is not surprising that the characteristics of hydrochlorination depend on the reaction conditions. Thus, in nitromethane, a medium that gives extensive Wagner-Meerwein shifts during hydrochlorination, olefins react according to the third-order rate law,... 

An important example of an association reaction is the formation of ozone in the stratosphere from atomic and molecular oxygen O + O2 + M —> O3 + M. At low pressures, a third-order rate law is found with rate constants given in the table below for M = N2 [J. Phys. Chem. Ref. Data 26, 1329 (1997)]. 

Reactions of phosphonium salts with hydroxide probably involve a pentacoordinated intermediate, since a third-order rate law is observed (Aksnes and Bergesen, 1966). Reaction via several intermediates was... 

Hypobromous acid, HOBr, is found to be a poorer brominating agent than Bra at pll 3 (aqueous solutions). However, at higher concentrations of strong acids a third-order rate law is observed/... 

Several workers have chosen to interpret their results in terms of an overall third-order rate law, and reported a third-order rate coefficient. Kaufman attempted to measure the recombination rate in a discharge flow system and obtained an upper limit of 5 x 10 l. mole", sec for the rate coefficient of the overall reaction written as... 

Mechanisms resulting in second-order or third-order rate laws ... 

In Scheme 8.11 the products formed upon treatment of CpFe(CO)2R with HgX2 (X = Cl, Br, or I) seem to depend on the nature of R. The stereochemistry of the liberated organic group, moreover, also depends on the structure of R. The scheme takes into account the involvement of HgX2 in the first two steps of the mechanism, giving an observed third-order rate law of... 

Although bromination, iodochlorination and iodobromination of unsaturated compounds in aprotic solvents are generally described as following a third-order rate law, chlorination was always found to obey, in the presence of radical inhibitors, second-order kinetics . However, it has been recently shown , through kinetic studies on chlorine addition to... 

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