Rate constants complex reactions

Figure 2.6. Hammett plots for the equilibrium constant of binding of 2.4 to Co, NL, Cu and (open symbols), and for the rate constants of reaction of the metal-ion - 2.4 complex with 2.5 (solid symbols).

In Chapter 2 the Diels-Alder reaction between substituted 3-phenyl-l-(2-pyridyl)-2-propene-l-ones (3.8a-g) and cyclopentadiene (3.9) was described. It was demonstrated that Lewis-acid catalysis of this reaction can lead to impressive accelerations, particularly in aqueous media. In this chapter the effects of ligands attached to the catalyst are described. Ligand effects on the kinetics of the Diels-Alder reaction can be separated into influences on the equilibrium constant for binding of the dienoplule to the catalyst (K ) as well as influences on the rate constant for reaction of the complex with cyclopentadiene (kc-ad (Scheme 3.5). Also the influence of ligands on the endo-exo selectivity are examined. Finally, and perhaps most interestingly, studies aimed at enantioselective catalysis are presented, resulting in the first example of enantioselective Lewis-acid catalysis of an organic transformation in water. 

Table 3.1 summarises the influence of the diamine ligands on the equilibrium constant for binding of 3.8c to the ligand-metal ion complex (K ) and the second-order rate constant for reaction of the ternary complex (ICjat) (Scheme 3.5) with diene 3.9. 

This equation can be generalised to any process within a complex set of chemical reaction pathways to allow for reactions generating A, written with positive rate constants, and reactions removing A, written with negative rate constants for example ... 

Rate constants for reaction of Ca2+aq with macrocycles and with cryptands (281,282,291) reflect the need for conformational changes, considerably more difficult for cryptands than for crown ethers, which may be considerably slower than formation of the first Ca2+-ligand bond. Ca2+aq reacts with crown ethers such as 18-crown-6 with rate constants of the order of 5 x 107M 1 s, with diaza crown ethers more slowly (286,326). The more demanding cryptands complex Ca2+ more slowly than crown ethers (kfslow reaction for cryptands with benzene rings fused to the macrocycle. The dominance of kA over kt in determining stability constants is well illustrated by the cryptates included in Table X. Whereas for formation of the [2,1,1], [2,2,1], and [2,2,2] cryptates kf values increase in order smoothly and gently, the k( sequence Ca[2,l,l]2+ Ca[2,2,l]2+ Ca[2,2,2]2+ determines the very marked preference of Ca2+ for the cryptand [2,2,1] (290). 

The ability of MPO to catalyze the nitration of tyrosine and tyrosyl residues in proteins has been shown in several studies [241-243]. However, nitrite is a relatively poor nitrating agent, as evident from kinetic studies. Burner et al. [244] measured the rate constants for Reactions (24) and (25) (Table 22.2) and found out that although the oxidation of nitrite by Compound I (Reaction (24)) is a relatively rapid process at physiological pH, the oxidation by Compound II is too slow. Nitrite is a poor substrate for MPO, at the same time, is an efficient inhibitor of its chlorination activity by reducing MPO to inactive Complex II [245]. However, the efficiency of MPO-catalyzing nitration sharply increases in the presence of free tyrosine. It has been suggested [245] that in this case the relatively slow Reaction (26) (k26 = 3.2 x 105 1 mol-1 s 1 [246]) is replaced by rapid reactions of Compounds I and II with tyrosine, which accompanied by the rapid recombination of tyrosyl and N02 radicals with a k2i equal to 3 x 1091 mol-1 s-1 [246]. 

Fig. 22 A plot of kohs for methanolysis of 4 x 10 5M methyl /j-nitrophcnyl phosphate (MNPP) vs. [35 2Zn(II)] in the presence of 1 equivalent of CH-jO per ligand showing a saturation behavior, pH = 9.5, T = 25+0.1 °C. Line through the data calculated by NLLSQ fits to a Michaelis-Mentin equation corrected for complex dissociation95 giving a binding constant of A M = 0.37 mmol dm-3 and a maximum rate constant for reaction of the MNPP [(CH3CT) 35 2Zn(II)] complex of kmAK — (4.1 0.1) x 10 2s Reproduced with permission from ref. 95.

Rate constants for reaction of cis-[Pt(NH3)2(H20)Cl]+ with phosphate and with S - and 5/ -nucleotide bases are 4.6xl0-3, 0.48, and 0.16 M-1s-1, respectively, with ring closure rate constants of 0.17 x 10 5 and 2.55x10-5s-1 for subsequent reaction in the latter two cases 220). Kinetic aspects of interactions between DNA and platinum(II) complexes such as [Pt(NH3)3(H20)]2+, ds-[Pt(NH3)2(H20)2]2+, and cis-[Pt(NH3)2(H20)Cl]+, of loss of chloride from Pt-DNA-Cl adducts, and of chelate ring formation of cis-[Pt(NH3)2(H20)(oligonucleotide)]"+ intermediates implicate cis-[Pt(NH3)2(H20)2]2+ rather than cis-[Pt(NH3)2 (H20)C1]+, as usually proposed, as the most important Pt-binder 222). The role of aquation in the overall scheme of platinum(II)/DNA interactions has been reviewed 223), and platinum(II)-nucleotide-DNA interactions have been the subject of molecular modeling investigations 178). 

Formation kinetics for eight tetraaza macrocycles of the cyclam type reacting with copper(II) have been analyzed in terms of rate constants for reaction with [Cu(OH)3] and with [Cu(OH)4]2. There is a detailed discussion of mechanism and of specific steric effects (292). Complex formation from cyclam derivatives containing -NH2 groups on the ring -CH2CH2CH2- units proceeds by formation followed by kinetically-distinct isomerization. The dramatic reactivity decreases consequent on... 

Relative reactivies of the species Zn2+, Zn(OH)+, Zn(OH) s, and Zn(OH)4 have been established for the reaction of zinc(II) with tetrad-methyl-4-pyridyl)porphyrins in basic solution (319). The rate constant for reaction of a typical zinc finger peptide with Zn2q has been estimated as 2.8 x 107 M-1 s 1, for dissociation of this complex 1.6 x 104 s 1 (282). 

The dependence of rate constants for approach to equilibrium for reaction of the mixed oxide-sulfide complex [Mo3((i3-S)((i-0)3(H20)9] 1+ with thiocyanate has been analyzed into formation and aquation contributions. These reactions involve positions trans to p-oxo groups, mechanisms are dissociative (391). Kinetic and thermodynamic studies on reaction of [Mo3MS4(H20)io]4+ (M = Ni, Pd) with CO have yielded rate constants for reaction with CO. These were put into context with substitution by halide and thiocyanate for the nickel-containing cluster (392). A review of the chemistry of [Mo3S4(H20)9]4+ and related clusters contains some information on substitution in mixed metal derivatives [Mo3MS4(H20)re]4+ (M = Cr, Fe, Ni, Cu, Pd) (393). There are a few asides of mechanistic relevance in a review of synthetic Mo-Fe-S clusters and their relevance to nitrogenase (394). 

From Eyring, the rate constant of reaction k depends on a pseudo equilibrium constant AT, relating to the formation of a transition-state complex, TS. Clearly, AT will always be virtually infinitesimal. 

The rate constants characterizing reactions of the uncomplexed ion pairs are given subscript 1, those of the complexed ion-pairs subscript 2. 

One can set up to do this using the competition between dimerization and halogen atom abstraction from RX to form the rhodium(III) halide complex. As a function of [RX], the product ratio is quite easily evaluated. From that, one can get the rate constant ratio but, knowing independently the rate constant for dimerization, it is possible to extract from those data rate constants for reactions of the rhodium(II) complex with these organic halides. The rate constants obtained are listed in Table I. 

Study of the relative rate constants for reactions of a series of similar complexes A with reagents B and C may reveal deviations by a particular complex of the series A from the general pattern and therefore suggest it is reacting by an anomalous mechanism. This rarely occurs, but a general correlation suggests a common mechanism for the reactions. 

The rate constant for one reaction may have to be correlated with the equilibrium constant not for that reaction but for a related one. Rate constants for reactions of metal complexes... 

There have been extensive studies of the influence of an entering ligand on its rate of entry into a Pt(ll) complex.The rate constants for reaction of a large number and variety of ligands with trans-Pt(py)2C 2 have been measured (Table 4.13). The large range of reactivities is a feature of the associative mechanism and differentiates it from the behavior of octahedral complexes. The rate constants may be used to set up quantitative relationships. For a variety of reactions of Pt complexes in different solvents (Sec. 2.5.4) ... 

R. van Eldik, J. Asano and W. J. LeNoble, Chem. Rev. 89, 549 (1989) — Compilation of AV values. Collections of rate constants for reactions of radicals and metal complexes excited states are cited in Refs. 143-148 and 358 in Chap. 3. 

A number of rate constants for reactions of transients derived from the reduction of metal ions and metal complexes were determined by pulse radiolysis [58]. Because of the shortlived character of atoms and oligomers, the determination of their redox potential is possible only by kinetic methods using pulse radiolysis. In the couple Mj/M , the reducing properties of M as electron donor as well as oxidizing properties of as electron acceptor are deduced from the occurrence of an electron transfer reaction with a reference reactant of known potential. These reactions obviously occur in competition with the cascade of coalescence processes. The unknown potential °(M /M ) is derived by comparing the action of several reference systems of different potentials. 

In a series of reports published over the last 10-15 years, Mayr and co-workers obtained second-order rate constants for reactions of carbocations and other electrophiles such as metal-7i complexes with a series of nucleophiles, especially 7t-nucleophiles where a C C bond is formed. An impressive body of reactivity data has been accumulated, and, including data from other groups, correlated by the following equation. 

O rate constant for reaction between [Co(III)(en)2(PNVl)CllCl2 and Fe(ll)edta, A rate constant for reaction between monomeric [Co(IIlXen)2(NEI)CllCli and Fe(II)edta, intrinsic viscosity of PVMI-Co complex solution, PVNI = poly(N-vinyl-2-methylimidazole),... 

The solubilized substrate MA is the analog of the complex ES in Reaction (E), and the product P is formed in the micelle with the rate constant km. The product can also form from the substrate without involving the micelle A 0 is the rate constant for the last process. The experimental (subscript exp) rate constant for Reaction (G) is then a weighted sum of the two constants km and k0 ... 

The rate constant for reaction of the excited intermediate C (n) to form products D and E, which goes through the activated complex corresponding to a critical energy with m vibrational quanta was given by Eq. 10.188 as... 

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