Rate Laws—First Order

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. 

Silverman and Dodson made the first detailed isotopic study of this exchange system using the separation afforded by the addition of 2,2 -dipyridyl at pH 5, followed by the precipitation of the ferric iron with either ammonia or 8-hydro-xyquinoline. Dodson , using this separation method, had previously obtained an overall rate coefficient of 16 l.mole" sec at 23 °C for 0.4 M perchloric acid media. The exchange in perchlorate and perchlorate-chloride media was found to conform to a rate law, first order with respect to both total ferrous and ferric ion concentrations, with an observed rate constant (k bs) dependent on the hydrogen-ion concentration, viz. 

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. 

In the presence of antimony pentachloride, titanium tetrachloride, stannic chloride, and tellurium tetrachloride, the decomposition reaction follows a second-order rate law, first order with respect to each component. Equation 3 is in accordance with these results. With antimony trichloride and... 

Kinetics and rate law First order Rate = kfalkyl halide] (Section 8.8) Second order Rate = fcfalkyl halide][nudeophile] (Section 8.3)... 

The first-order rate law is but one of many possibilities, and an interesting comparison can be made between several of the simpler rate laws using a pseudo half life. Consider the case where two measurements of pesticide residue in soil are made 1 year apart and assume, further, that one half of the added pesticide has disappeared during that year—that is, the pesticide shows a half life of 1 year for this specific concentration. In Figure 2, the path of disappearance of one concentration unit is plotted on semilog paper according to a pseudo half life of 1 year and four possible rate laws first-order, second-order, one-half-order, and zero-order—that is, whether the rate of decomposition is proportional to the concentration, the square of the concentration, the square root of the concentration, or independent of the concentration. 

In such a case reaction 3 or 3 could be rate-determining and give a rate law first order in adsorbed alcohol. Since, however, the dehydrogenation reactions are facilitated by metal catalysts, particularly the transition metals, it is just as likely that the surface reaction proceeds via free radical species with moderately strong bonding to the metal atoms in the surface. By denoting metal atoms in the surface by M, such a mechanism could be represented by... 

Mole balance Rate law First-order dX dt AO Second-order... 

One-electron reduction of NO to HNO is unique because of the spin issues involved. Sequential electron-proton transfer would generate 3NO as an intermediate, and protonation of this species to give UNO is slow.112 These kinetic considerations add to the overall thermodynamic effects favoring H-atom transfer mechanisms. Despite these expectations, evidence in favor of H-atom transfer to NO is quite sparse. NO has been argued to act as a H-atom acceptor in its reaction with hydroxylamine.113 This reaction has a rate law first order in [NO] and first order in [H2NO ], and HNO is inferred as an intermediate. NO also abstracts a hydrogen atom from hyponitrous acid, HONNOH.114 As Table 9.10 shows, NO is now considered to be a very weakhydrogen atom acceptor, so the reports of its reactivity in this mode may bear reexamination. 

Reduction of [IrCls] by a variety of agents has been cited. The reduction of [IrXs] " (Cl, Br) by 2-thiouracil and 2-thiopyrimidine follows second-order rate laws, first-order with respect to both the concentration of the oxidant and the reductant. A pH-rate profile as well as activation parameters have been presented, and a free radical mechanism proposed." Reduction in aqueous alcoholic solution by aquated electrons, hydrogen and alkyl radicals was investigated by pulse radiolysis, and found to result in the production of [IrClg] " A kinetic examination of reaction (123) in aqueous solution shows that this outer-sphere electron transfer reaction proceeds by parallel paths first and second order in substrate (SCN ). The kinetics of the oxidation of hydrazine by [Ir(Cl)4(H20)2], [Ir(Cl)5(H20)], [IrClef , as well as [IrBrsf , in aqueous acidic perchlorate solution have been investigated." ... 

Knowledge Required (1) The meanings of the terms rate law, first order, and second order. (2) The algebraic form of the rate equation. 

Mono-, bis-, and tris-sulfito complexes of Fe(III), produced from the reaction of Fe(III)aq and S(IV) oxides, undergo two successive redox reactions and produce Fe(II), SOJ , and 8206 . The mechanistic aspects of the reported data are discussed in reference to the suggested complex formation mechanism and results previously reported. Rate constants for the oxidation of S2OI by [PtCl ] " follow the expected second-order rate law, first order in both S2OI and Pt(IV). While the influence of pH is small, the rate does depend on the nature and concentration of the added cation in the order Cs > Rb > > Na" > Li". The reduction of... 

The insertion of O2 into the Pd- H bond of 1 was readily monitored by H and P H NMR spectroscopy, and the reaction was found to proceed with a second-order rate law, first order in [1] and first order in [O2]. No experimental evidence for a radical process was found the rates were reproducible and no effects of light or radical inhibitors on the reaction were observed. A kinetic isotope effect (KIE) of kjj/kp = 5.8(5), measured using the analogous palladium deuteride complex, (tBupcp)pdD, implicated the breaking of the Pd-H bond in the rate-determining step of the reaction. 

Integrated Rate Laws Zero-Order Integrated Rate Law First-Order Integrated Rate Law Second-Order Integrated Rate... 

Ligand exchange between [VO(acac)2] and C-labelled acacH in CH2CI2 solution has a second-order rate law, first-order in [VO(acac>2] and first-order with respect to the enol form of acacH at 240 K, 10 A =7.1 s, A = 11.2... 

Rate law First order in entering ligand Typically zero order in entering ligand... 

Having clarified what is meant by the term oxidative addition, it is clear that the description is purely stoichiometric and can cover a range of mechanistic pathways. The factors which increase the nucleophilicity of the site (i.e. a relatively low oxidation state and electron-releasing ligands) are the same factors which favour its behaviour as a reductant. As shown by the example in Scheme 1, although a reaction may stoichiometrically resemble a nucleophilic pathway of the form of (1), this cannot be assumed and the simple second-order rate law (first-order in both reactants) cannot distinguish between the two mechanisms. 

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