Rate Constants Kij Research Articles

A New Chiral N,N‘,O-Donor Heteroscorpionate Ligand. Structures of Ni2+, Cu2+, Zn2+ Complexes and Study of Solution Equilibria by Means of 1H NMR/UV−Vis Titrations and EXSY NMR Spectroscopy

The N,N',O-heteroscorpionate ligand 1-(4-methoxy-3,5-dimethyl-pyridin-2-yl)-2-methyl-1-pyrazol-1-yl-propan-2-ol (LOH) was prepared in two high-yield steps. Complexes [M(LOH)2][MCl4] (M2+ = Cu2+ and Zn2+) and [M(LOH)2]Cl2 (M2+ = Ni2+ and Cu2+) were prepared and characterized by X-ray crystallography. The speciation in solution (methanol:water 95:5) of the M2+/LOH systems was investigated by means of spectrophotometric (Ni2+ and Cu2+) and 1H NMR (Zn2+) titrations. The beta1 and beta2 global formation constants for the [M(LOH)]2+ and [M(LOH)2]2+ species were obtained and are in agreement with the Irving-Williams series: Ni2+< Cu2+> Zn2+. The Zn2+/LOH system was studied by means of quantitative 1H-1H EXSY spectroscopy (300 K, mixing time = 0.2-0.8 s), which allows the description of the equilibria occurring between five octahedral [Zn(LOH)2]2+ structural isomers and tetrahedral [Zn(LOH)Cl]Cl species. Exchange constants kijex and associated rate constants kij suggest that two types of interconversion occur: octahedral-octahedral (faster) and octahedral-tetrahedral (slower). DFT calculations (B3LYP/6-311+G(d)) were employed to evaluate the relative stability of the [Zn(LOH)2]2+ isomers, which are comparable for the five complexes with a maximum energy difference of 6.3 kJ/mol.

Rate and Equilibrium Constants for Reactions Transferring a Dimethylcarbamoyl Group between Pyridines

We have studied 18 reactions, including four identity reactions, involving transfer of a dimethylcarbamoyl group with N-acylpyridinium bonds to pyridine and its 4-substituted derivatives in acetonitrile solutions at 298 K. The rate constants kij varied within the range 0.4 to 10−6 L/mol·s; the equilibrium constants Kij varied from 107 to 10−5. The rate and equilibrium for exchange of carbamoyl groups are described satisfactorily by the Bronsted equation. We have shown that all the reactions occur according to a forced concerted SN2 mechanism. The structure of the transition state and its position on the reaction coordinate for identity transfer are considered using a More O'Ferrall-Jencks diagram.

Indirect Determination of Self-Exchange Electron Transfer Rate Constants

Second-order rate constants kij(obsd) measured at 25 °C in acetonitrile by stopped-flow spectrophotometry for forty-four electron transfer (ET) reactions among fourteen 0/+1 couples [three aromatic compounds (tetrathiafulvalene, tetramethyltetraselenafulvalene, and 9,10-dimethyl-9,10-dihydrophenazine), four 2,3-disubstituted 2,3-diazabicyclo[2.2.2]octane derivatives, six acyclic hydrazines, and the bridgehead diamine 1,5-diazabicyclo[3.3.3]undecane] and seventeen compounds and forty-seven reactions from a previous study (J. Am. Chem. Soc. 1997, 119, 5900) [three p-phenylenediamine derivatives, four ferrocene derivatives, and ten tetraalkylhydrazines] are discussed. When all 91 kij(obsd) values are simultaneously fitted to Marcus's adiabatic cross rate formula kij(calcd) = (kiikjjKijfij)1/2, ln fij = (ln Kij)2/4 ln(kiikjj/Z2), best-fit self-exchange rate constants, kii(fit), are obtained that allow remarkably accurate calculation of kij(obsd); kij(obsd)/kij(calcd) is in the range 0.5−2.0 for all 91 reactions. The average difference without regard to sign, |ΔΔGij|, between observed cross reaction activation free energy and that calculated using the kii(fit) values and equilibrium constants is 0.13 kcal/mol. The ΔGii(fit) values obtained range from 2.3 kcal/mol for tetramethyltetraselenafulvalene0/+ to 21.8 kcal/mol for tetra-n-propylhydrazine0/+, corresponding to a factor of 2 × 1014 in kii(fit). The principal factor affecting kii(fit) for our data appears to be the internal vertical reorganization energy (λv), but kii(fit) values also incorportate the effects of changes in the electronic matrix coupling element (V). Significantly smaller V values for ferrocenes and for hydrazines with alkyl groups larger than methyl than for aromatics and tetramethylhydrazine are implied by the observed ΔGii(fit) values.

Experimental Design in Global Compartmental Analysis of Reversible Intramolecular Two-State Excited-State Processes with Added Quencher

Although reversible intramolecular two-state excited-state processes without a priori information are unidentifiable, bounds on the excited-state rate constants kij can be specified when a quencher is used [Van Dommelen et al. J. Phys. Chem. 1993, 97, 11738]. These limits can be obtained by a scanning procedure consisting of a series of global compartmental analyses of a fluorescence decay surface in which one of the rate constants kij is held fixed at different preset values. The theory requires that the rate constants of quenching (kQ1, kQ2) for the two excited species have different values. In the present paper, computer-generated fluorescence decay surfaces are used to investigate the criteria under which reliable estimates of the bounds on the rate constants kij can be obtained. If the values of kQ1 and kQ2 are substantially different, reliable estimates are obtained. If kQ1 and kQ2 are nearly equal in value, the quality of the estimates of the bounds depends on the combinations of the values of the rate constants kij. It may happen that no reliable limits for the rate constants can be obtained so that another quencher is required. A test procedure based on a limited number of decay traces is described which allows one to assess the appropriateness of the quencher for the given excited-state process.

Kinetic Studies of the Oxygen Exchange of Chromate and Arsenate Ions with Water. Catalysis by Tellurate and Tellurite Ions

Abstract The oxygen exchange reaction of the chromate ions with water is catalyzed by the tellurate and tellurite ions. The catalytic reaction rate (RC), which is defined as the increase in the rate of the chromate-oxygen exchange upon the addition of Te(VI) or Te(IV), was studied by an 18O tracer method. The catalytic process has been interpreted in terms of the rapid reversible condensation of the Cr(VI) with Te(VI) or Te(IV) species to form hetero-poly anions. As exemplified for the Cr(VI)–Te(VI) reaction system, the rate law is given as the sum of kinetic terms: RC = ∑kij[Cr(VI)]i × [Te(VI)]j where [Cr(VI)]i and [Te(VI)]j denote the concentration of the various ionic species of the chromate and tellurate ions, respectively, and kij is the rate constant of the elementary reaction between (Cr(VI))i and (Te(VI))j. The catalytic rates were analyzed according to the rate law in order to obtain the rate constants kij. The catalytic reaction system As(V)–Te(IV) was also studied. The values of kij obtained for various catalytic systems were compared with each other.

Pre- and post-gel size distributions in (ir)reversible polymerisation

A class of irreversible coagulation processes can be modelled by Smoluchowski's coagulation equation with rate constants Kij=A+B(i+j)+Cij (non-negative A, B and C). For C not=0 a gelation transition occurs. The authors obtain explicit solutions for the size distribution ck(t) with ck(0)= delta k1. Next, they construct and solve the equations for reversible polymerisation by incorporating break-up processes in the kinetic equation with a unimolecular fragmentation rate Fij= lambda NiNjKij/Ni+j. The degeneracy factors Nk obey (k-1)Nk=1/2 Sigma KijNiNj with i+j=k and N1=1, and the strength parameter lambda =exp(g/kBT), where the binding energy g to - infinity for irreversible coagulation. Explicit results are only given for Flory's polymerisation models RAf and BRAf-1. In the vicinity of the gel point the authors verify the scaling hypothesis and calculate critical exponents.

Studies of Radical Alternating Copolymerization. I. Quantitative Determination of the Relative Reactivities between Free Comonomers and a Complex between Them; A Theoretical Treatment in Terms of Frontier Molecular Orbital Interactions. Application to Radical Maleic Anhydride-Vinyl Acetate Alternating Copolymerization

Abstract A simple quantitative determination of the ratio β1 of rate constants kij corresponding to the addition of a complex or a free monomer on a same growing chain in alternating copolymerization was determined. The application of this method to the case of alternating maleic anhydride (A)-vinyl acetate (D) copolymerization give for β1 = kAC/kAD and for β2 = kDC/kDA (C refers to the complex) the respective values of 7 and 0. A complex was more reactive than A but less reactive than D toward a growing chain. In order to explain these reactivities, a frontier molecular orbital treatment was proposed. A good qualitative correlation with experimental results was obtained.

The volumes of some compartment systems with sampling and loss from one compartment.

If the concentrationc 1(t)=∑ i=1 n A i exp (−α i t) for one compartment, one presumes a linear catenaryn-compartment system without sinks and loss only from the same compartment, then the volumesV i , rate constantsk ij , and concentrationsc i (t) in each compartment can be determined in terms of theA i 's,A i ′s, α i ′s, the dose injectedD o and the partition coefficientsr ij =k ij /k ji . If the concentration would become uniform at equilibrium, then the total volume of distribution may be determined without knowledge ofr ij or restriction to catenary configuration.