Determination of the kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine in water at different pH values: A striking example of the determination of intimately intricate kinetic and equilibrium constants

Apparent kinetic constants of the reversible opening of a triazolo‐1,4‐thienodiazepine were determined by UV‐spectrophotometry and by polarography in water at several pH values assuming as a hypothesis a stationary state for the carbinolamine intermediate. Both the apparent kinetic constants, k_f and k_r, exhibited a maximum for the values H₀ = −0.25 and pH = 6.07. A possible determination of the elementary kinetic constants of the several acido‐basic species which may be involved in the opening and closing process according to the pH and pKa values was studied and is discussed. The results are consistent with the hypothesis that both the opening of the diazepine cycle and the closing of the opened form proceed through a mechanism suggesting that the protonated form of the carbinolamine function of the intermediate is involved. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 826–834, 1999     

Structure–Reactivity Relationship in the Frustrated Lewis Pair (FLP)‐Catalyzed Hydrogenation of Imines

The autoinduced, frustrated Lewis pair (FLP)‐catalyzed hydrogenation of 16‐benzene‐ring substituted N‐benzylidene‐tert‐butylamines with B(2,6‐F₂C₆H₃)₃ and molecular hydrogen was investigated by kinetic analysis. The pK_a values for imines and for the corresponding amines were determined by quantum‐mechanical methods and provided a direct proportional relationship. The correlation of the two rate constants k₁ (simple catalytic cycle) and k₂ (autoinduced catalytic cycle) with pK_a difference between imine and amine pairs (ΔpK_a) or Hammett's σ parameter served as useful parameters to establish a structure–reactivity relationship for the FLP‐catalyzed hydrogenation of imines.     

Reactions of Substituted Phenylnitromethane Carbanions with Aromatic Nitro Compounds in Methanol: Carbanion Reactivity,Kinetic, and Equilibrium Studies

The feasibility of carrying out nucleophilic addition from electron‐deficient heteroaromatics has been addressed through a detailed investigation of the interaction of a two 7‐substituted‐nitrobenzofurazan (R = OMe 2a ; R = Cl 2b ) with a series of substituted‐nitroaryl anions (X = 4‐NO₂ 1a ; X = 3‐NO₂ 1b ; X = 4‐CN 1c ; X = 4‐Br 1d ), all reactions first lead to the quantitative formation of the σ‐adducts 3a–d and 4a–d arising from covalent addition of the nucleophile to the C‐5 carbon. The rate and equilibrium constants for the formation of σ‐adducts 3a–d and 4a–d (k₅, K ₅ ) together with the rate constants for their decomposition (k_?5) have been determined in methanol at 25°C, allowing a determination of intrinsic rate constants, k₀ = 0.03, the lower k₀ value reflects the very strong salvation by methanol of the negative charge on the nitro group. The discovery of a linear correlation between the E and pK_a^MeOH parameters allows a calibration of the electrophilicity power of 2a and 2b , E = ?11.67 and ?10.29, respectively. Applying the general approach to nucleophilicity/electrophilicity recently developed by Mayr et al. through the relationship log k = s(E + N), a successful ranking of our nitroaryl anions 1a–d on the general nucleophilicity scale (N) has been carried out. The N values of 1a–d are found to cover a range from 15.78 to 16.69. The results are compared with previously reported data in water and DMSO.     

Structure‐Reactivity Relationships as Probes to Acetylcholinesterase Inhibition Mechanisms by Aryl Carbamates. II. Hammett‐Taft Cross‐Interaction Correlations

Substituted phenyl‐N‐butyl carbamates ( 1 ) and p‐nitrophenyl‐N‐substituted carbamates ( 2 ) are characterized as “pseudo‐pseudo‐substrate” inhibitors of acetylcholinesterase. Since the inhibitors protonate in pH 7.0 buffer solution, the virtual inhibition constants (K_i's) of the protonated inhibitors can be calculated from the equation, ‐logK_i' = ‐logK_i ‐ pK_a + 14. The ‐logK_i' and logk_c values for acetylcholinesterase inhibitions by carbamates 1 correlate with the Hammett equation (log(k/k₀) = ρσ); moreover, those by carbamates 2 correlate with the Taft equation (log(k/k₀) = ρ* σ*). With modified Hammett‐Taft cross‐interaction variations, multiple linear regressions of the ‐logK_i' and logk_c values of carbamates 1 and 2 give good correlations, and the cross‐interaction constants (ρ_XR) are 0.5 and 0.0, respectively. The ρ_XR value of 0.5 indicates that the carbamate O‐C(O)‐N‐R geometries for the transition states that lead to enzyme‐carbamate tetrahedral intermediates are all pseudo‐trans conformations. Therefore, the carbamate moiety of the inhibitors stretches along the active site gorge of the enzyme but does not bind in the acyl binding site pocket of the enzyme. Overall, the carbamate O‐C(O)‐N‐R geometries for carbamates 1 and 2 , protonated carbamates 1 and 2 , and the tetrahedral intermediate are all retained in pseudo‐trans conformations. The ρ_XR value of 0.0 suggests that the transition states that lead to the carbamyl enzymes are breaking C‐O bonds and are excluding the leaving groups, substituted phenols.     

Schiff bases of pyridoxal and polyallylamine. The formation rate determining step

The apparent rate constants of formation (k₁) and hydrolysis (k₂) of the Schiff bases formed between pyridoxal and polyallylamine has been fitted to a kinetic scheme that involve the different protonated species in the reaction medium and the individual rate constants of formation (k₁ⁱ) and hydrolysis (k₂ⁱ). The (k₁ⁱ) values precludes an acid catalyzed intramolecular process. The effects of hydrophobic medium due to the presence of the macromolecule on the reaction is also discussed. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 1–6, 1998.     

Influence of the stereochemical configuration on the radical polymerization of methacrylic monomers: cis‐ and trans‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate

The synthesis of two new isomeric monomers, cis‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate (CCDM) and trans‐(2‐cyclohexyl‐1,3‐dioxan‐5‐yl) methacrylate (TCDM), starting from the reaction of glycerol and cyclohexanecarbaldehyde, is reported. The process involved the preparation of different alcohol acetals and esterification with methacryloyl chloride of the corresponding cis and trans 5‐hydroxy compounds of 2‐cyclohexyl‐1,3‐dioxane. The radical polymerization reactions of both monomers, under the same conditions of temperature, solvent, monomer, and initiator concentrations, were studied to investigate the influence of the monomer configuration on the values of the propagation and termination rate constants (k_p and k_t ).The values of the ratio k_p /k_t ^1/2 were determined by UV spectroscopy by the measurement of the changes of absorbance with time at several wavelengths in the range 275–285 nm, where an appropriate change in absorbance was observed. Reliable values of the kinetics constants were determined by UV spectroscopy, showing a very good reproducibility of the kinetic experiments. The values of k_p /k_t ^1/2, in the temperature interval 45–65 °C, lay in the range 0.40–0.50 L^1/2/mol^1/2s^1/2 and 0.20–0.30 L^1/2/mol^1/2s^1/2 for CCDM and TCDM, respectively. Measurements of both the radical concentrations and the absolute rate constants k_p and k_t were also carried out with electron paramagnetic resonance techniques. The values of k_p at 60 °C were nearly identical for both the trans and cis monomers, but the termination rate constant of the trans monomer was about three times that of the cis monomer at the same temperature. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3883–3891, 2000     

Structure‐Reactivity Relationships as Probes to Acetylcholinesterase Inhibition Mechanisms by Aryl Carbamates. I. Steady‐State Kinetics

From enzyme kinetics, 4‐nitrophenyl‐N‐substituted carbamates 1 are characterized as pseudo‐substrate inhibitors of acetylcholinesterase. However, the activity of the carbamyl enzyme does not recover in the presence of a competitive inhibitor, edrophonium. Therefore, carbamates 1 should be called as the “pseudo‐pseudo‐substrate” inhibitors of the enzyme. Moreover, the ‐logK_i, logk_c, and logk_i values are linearly correlated with Taft‐Ingold equation, log (k/k_o) = ρ*σ* + δ E_s. A three‐step AChE inhibition mechanism by carbamates 1 is proposed. The first step is the pre‐equilibrium protonations of carbamates 1 with ρ* value of ?1.4 from pK_a‐σ*‐correlation. The second step is the enzyme‐carbamates 1 tetrahedral intermediate formation from nucleophilic attack of the active site Ser200 on the protonated carbamates 1 . The ρ* value for the ‐logK_i‐σ*‐E_s‐correlation indicates that the true ρ* value for the second step is 0.5 [= ?0.9 ‐ (‐1.4)]. The δ value of 0.56 for the ‐logK_i‐σ*‐E_s‐correlation indicates that carbamates 1 with bulky substituents retarded the formation of enzyme‐inhibitor tetrahedral intermediates. The third step (k_c step) is the carbamylation step and is the carbamyl enzyme conjugate formation from the enzyme‐carbamates 1 tetrahedral intermediate. The ρ* value of 0.21 for the logk_c‐correlation indicates that the transition state for the carbamylation step is more negative charge than the enzyme‐carbamates 1 tetrahedral intermediate. Moreover, the k_c step is insensitive to substituent effects since there is a cancellation of electronic demands for bond‐making and bond‐breaking components, like S_N2 reactions. The δ value of 0.00 for the logk_c‐correlation indicates that the k_c step is independent of substituent steric effect. Therefore, the product of this step carbamyl enzyme conjugate is as crowded as the enzyme‐carbamates 1 tetrahedral intermediate and is likely bound to the leaving group, p‐nitrophenol.     

Theoretical Study of Firefly Luciferin pKa Values—Relative Absorption Intensity in Aqueous Solutions

Ground‐state vibrational analyses of firefly luciferin and its conjugate acids and bases are performed. The Gibbs free energies obtained from these analyses are used to estimate pK_a values for phenolic hydroxy and carboxy groups and the N–H⁺ bond in the N‐protonated thiazoline or benzothiazole ring of firefly luciferin. The theoretical pK_a values are corrected using the experimental values. The concentrations of these chemical species in solutions with different pH values are estimated from their corrected pK_a values, and the pH dependence of their relative absorption intensities is elucidated. With the results obtained we assign the experimental spectra unequivocally. Especially, the small peak near 400 nm at pH 1–2 in experimental absorption spectra is clarified to be due to the excitation of carboxylate anion with N‐protonated thiazoline ring of firefly luciferin. Our results show that the pK_a values of chemical species, which are contained in the aqueous solutions, are effective to assign experimental absorption spectra.     

Tautomerization of Phenols,Part III,The Anthrone−Anthrol Equilibrium in Aqueous Solution

The equilibrium between 10H‐anthr‐9‐one and 9‐anthrol favors the ketone, which ionizes as a carbon acid in aqueous base. Rates of equilibration were measured over the pH range 1 – 13 in aqueous solution (25°, ionic strength I=0. M ). Five independent thermodynamic and kinetic parameters were determined by analysis of the pH‐rate profile: the equilibrium constant of enolization, pK_E=2.17, the ionization quotient of anthrol, pQ=7.84, and the rate constants of enolization catalyzed by acid, k=2.2⋅10⁻⁴ M ⁻¹ s⁻¹, base, k=51.0 M ⁻¹ s⁻¹, and water, k=1.21⋅10⁻⁵ s⁻¹. Structure‐reactivity relationships strongly support the view that pH‐independent enolization of anthrone in water proceeds by rate‐determining ionization of the C‐acid.     

Kinetic study on solute permeation at the interface of molecular aggregates by partial filling capillary electrophoresis

Moment analysis method using partial filling CE was developed for the kinetic study on solute permeation at the interface of spherical molecular aggregates. Moment equations for partial filling CE were developed by classifying CE systems into five categories according to the migration velocities of solute and molecular aggregate. The method was applied to the study on the dissolution of electrically neutral solutes into SDS micelles. Elution peaks were measured by partial filling CE while changing the concentration of SDS and the filling ratio of SDS micellar zone to the capillary (ϕ_M). Partition equilibrium constants (K_p) and rate constants of interfacial solute permeation of SDS micelles (k_in and k_out) were determined from the first absolute and second central moments of the elution peaks by using the moment equations. Their values were comparable irrespective of ϕ_M and were almost the same as those previously measured by complete filling CE. The positive correlation of K_p with the hydrophobicity of the solutes was explained in terms of the change in k_in and k_out. It was demonstrated that the moment analysis method using partial filling CE is effective for studying solute permeation kinetics at the interface of spherical molecular aggregates.     

Hydrogen bond interactions at the TiO2 surface: Their contribution to the pH dependent photo-catalytic degradation of p-nitrophenol

We have obtained pK_a values of p-nitrophenol–TiO₂ by measuring the adsorption equilibrium constants of p-nitrophenol (PNP) on the TiO₂ surface at different pH values. These values have been obtained from Langmuir isotherms and from a plot of 1/rate vs. 1/[PNP]_o obtained during TiO₂ catalyzed solar light photo-degradation of PNP. Two limit equilibrium constants are readily obtained depending on the solution pH: at pH 5 at which the TiO₂ surface is mainly positively charged and at pH 8 when it is negatively charged. With these and other adsorption equilibrium constants and the PNP pK_a value in solution, thermodynamic cycles are established in order to obtain the PNP pK_a when it is adsorbed on positively charged, neutral and negatively charged TiO₂ surfaces. From these pK_a values useful information on the PNP–TiO₂ interaction is readily obtained. For instance, the PNP nitro group interacts with the TiO₂ surface via a hydrogen bond, arising from the complex of water molecules with the Ti⁴⁺ ions on its surface. The weaker the hydrogen bond donor, the stronger the oxygen nitro group basicity. Therefore, pK_a changes on the phenolic hydroxyl group result from these interactions. Linear free energy correlations, maximum PNP adsorption capacity values (Q_L) and FTIR ATR, spectrum support this proposal. A k_obs vs. pH degradation profile of p-nitrophenol is also provided.     

Nucleophilicities of Para‐Substituted Phenoxide Ions in Water and Correlation Analysis

Second‐order rate constants for the reactions of 2‐aryl‐4,6‐dinitrobenzotriazole 1‐oxides 1a‐d with some 4‐X‐substituted phenoxide ions 2a‐d (X = OCH₃, H, Cl, and CN) have been measured in aqueous solution at 20°C. The pK_a values for the σ‐complexation processes of a series of benzotriazole 1a‐d measured in water have been used to determine their electrophilicity parameters E according to the correlation E = –3.20 – 0.662 pK_a (F. Terrier, S. Lakhdar, T. Boubaker, and R. Goumont, J Org Chem, 2005 , 70, 6242–6253). For these reactions, plots of log k versus the electrophilicity parameters E of the benzotriazoles 1a‐d were linear, allowing to derive the nucleophilicity parameters N and s for phenoxide ions as defined by the Mayr equation log k₁ (20°C) = s (E + N) (H. Mayr, M. Patz. Angew Chem, Int Ed Engl 1994 , 33, 938–957). The N values are found to cover a range of nucleophilicity from 6.85 to 10.22, going from 4‐cyanophenoxide 2d for the least reactive ion to 4‐methoxyphenoxide 2a for the most reactive nucleophile. Good linear correlations were found between the nucleophilicity parameters N of phenoxide ions 2a‐d and the pK_a values of their conjugate acids (N = –3.05 + 1.25 pK_a) and the constants of the substituents X (N = 9.21 – 2.51).     

Luminescence Color Tuning of PtII Complexes and a Kinetic Study of Trimer Formation in the Photoexcited State

We investigated the luminescence properties and color tuning of [Pt(dpb)Cl] (dpbH=1,3‐di(2‐pyridyl)benzene) and its analogues. An almost blue emission was obtained for the complex [Pt(Fmdpb)CN] (FmdpbH=4‐fluoro‐1,3‐di(4‐methyl‐2‐pyridyl)benzene), modified by the introduction of ?F and ?CH₃ groups to the dpb ligand and the substitution of ?Cl by ?CN. As the concentration of the solution was increased, the color of the emission varied from blue to white to orange. The color change resulted from a monomer–excimer equilibrium in the excited state. A broad emission spectrum around 620 nm was clearly detected along with a structured monomer emission around 500 nm. Upon further increases in concentration, another broad peak appeared in the longer wavelength region of the spectrum. We assigned the near‐infrared band to the emission from an excited trimer generated by the reaction of the excimer with the ground‐state monomer. The emission lifetimes of the monomer, dimer, and trimer were evaluated as τ_M=12.8 μs, τ_D=2.13 μs, and τ_T=0.68 μs, respectively, which were sufficiently long to allow association with another Pt^II complex and dissociation into a lower order aggregate. Based on equilibrium constants determined from a kinetic study, the formation of the excimer and the excited trimer were concluded to be exothermic processes, with ΔG*_D=?24.5 kJ mol^?1 and ΔG*_T=?20.4 kJ mol^?1 respectively, at 300 K.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Lanthanide(III) Complexes of 2‐[4,7,10‐Tris(phosphonomethyl)‐1,4,7,10‐tetraazacyclododecan‐1‐yl]acetic Acid (H7DOA3P): Multinuclear‐NMR and Kinetic Studies

The protonation constants of 2‐[4,7,10‐tris(phosphonomethyl)‐1,4,7,10‐tetraazacyclododecan‐1‐yl]acetic acid (H₇DOA3P) and of the complexes [Ln(DOA3P)]^4? (Ln=Ce, Pr, Sm, Eu, and Yb) have been determined by multinuclear NMR spectroscopy in the range pD 2–13.8, without control of ionic strength. Seven out of eleven protonation steps were detected (pK =13.66, 12.11, 7.19, 6.15, 5.77, 2.99, and 1.99), and the values found compare well with the ones recently determined by potentiometry for H₇DOA3P, and for other related ligands. The overall basicity of H₇DOA3P is higher than that of H₄DOTA and trans‐H₆DO2A2P but lower than that of H₈DOTP. Based on multinuclear‐NMR spectroscopy, the protonation sequence for H₇DOA3P was also tentatively assigned. Three protonation constants (pK_MHL, pK_MH2L, and pK_MH3L) were determined for the lanthanide complexes, and the values found are relatively high, although lower than the protonation constants of the related ligand (pK , pK , and pK ), indicating that the coordinated phosphonate groups in these complexes are protonated. The acid‐assisted dissociation of [Ln(DOA3P)]^4? (Ln=Ce, Eu), in the region c_H+=0.05–3.00 mol dm^?3 and at different temperatures (25–60°), indicated that they have slightly the same kinetic inertness, being the [Eu(H₂O)₉]³⁺ aqua ion the final product for europium. The rates of complex formation for [Ln(DOA3P)]^4? (Ln=Ce, Eu) were studied by UV/VIS spectroscopy in the pH range 5.6–6.8. The reaction intermediate [Eu(DOA3P)]* as ‘out‐of‐cage’ complex contains four H₂O molecules, while the final product, [Eu(DOA3P)]^4?, does not contain any H₂O molecule, as proved by steady‐state/time‐resolved luminescence spectroscopy.     

Thermal dimerization kinetics of 3‐(p‐bromo‐phenyl)‐pyridazinium benzoyl methylid in solutions

3‐(p‐Bromo‐phenyl)‐pyridazinium‐benzoyl methylid (BPPBM) participates in solution at 3 + 3 dipolar thermal dimerization that can be spectrally monitored by the extinction in its visible intramolecular charge transfer (ICT) band. The attenuation of ICT band intensity shows the decrease of the BPPBM concentration with the increasing of dimer concentration. The complex kinetics of light‐assisted dimerization process was studied taking into account that the thermodynamic equilibrium is reached after more than 24 h. On the basis of general order of reaction theory, we found that the dimerization reaction must be described as a multistep mechanism. The rate constants of the dimerization reactions in ethanol (k = 0.00897 s^?1) and benzene (k = 0.00774 s^?1) solutions were correlated with the BPPBM and dimer structural features established by using the HyperChem 5.02 simulation program package. A kinetic mechanism of 3 + 3 dipolar thermal dimerization for the studied ylid is proposed. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 230–239, 2008     

Anilinolysis of reactive aryl 2,4‐dinitrophenyl carbonates: Kinetics and mechanism

The reactions of a series of anilines with phenyl 2,4‐dinitrophenyl ( 1 ), 4‐nitrophenyl 2,4‐dinitrophenyl ( 2 ), and bis(2,4‐dinitrophenyl) ( 3 ) carbonates are subjected to a kinetic investigation in 44 wt% ethanol–water, at 25.0 ± 0.1°C and an ionic strength of 0.2 M. Under amine excess pseudo‐first‐order rate coefficients (k_obs) are obtained. Plots of k_obs against free amine concentration at constant pH are linear, with slopes k_N. The Brønsted plots (log k_N vs. anilinium pK_a) for the anilinolysis of 1 – 3 are linear, with slope (β) values of 0.52, 0.61, and 0.63, respectively. The values of these slopes and other considerations suggest that these reactions are ruled by a concerted mechanism. For these reactions, the k_N values follow the reactivity sequence: 3 > 2 > 1 . Namely, the reactivity increases as the number of nitro groups attached to the nonleaving group increases. Comparison of the reactions of this work with the stepwise pyridinolysis of carbonates 1 – 3 indicates that the zwitterionic tetrahedral intermediate (T^±) formed in the pyridinolysis reactions is destabilized by the change of its pyridino moiety by an isobasic anilino group. This is attributed to the superior leaving ability from the T^± intermediate of anilines, relative to isobasic pyridines, which destabilize kinetically this intermediate. The k_N values for the anilinolysis of carbonates 1 – 3 are similar to those found in the reactions of these carbonates with secondary alicyclic amines. With the kinetic data for the anilinolysis of the title substrates and 4‐methylphenyl and 4‐chlorophenyl 2,4‐dinitrophenyl carbonates, a multiparametric equation is derived for log k_N as a function of the pK_a of the conjugate acids of anilines and nonleaving groups. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 191–197, 2011     

Spectrophotometric studies of the formation of charge transfer complex of iron(III) with N,N′-bis(2-pyridylmethylidene)-1,2-diiminoethane di-Schiff base ligand in methanol

The complex formation reaction between N,N′-bis(2-pyridylmethylidene)-1,2-diiminoethane (BPIE) di-Schiff base ligand as an electron donor and iron(III) chloride as an electron acceptor have been studied spectrophometrically in methanol at 28°C. The values of equilibrium constants, K and molar absorptivities, ε were obtained from the Benesi–Hildebrand, Scott and Foster–Hammick–Wardley equations. The results indicate the formation of 1?:?1 charge transfer complex. The absorption band energy of the complex, E _CT, the ionization potential of the BPIE Schiff base ligand, I ^D, and the Gibbs energy changes of the above reaction, ΔG ⁰, were calculated. Finally, the kinetics of the complex formation reaction were studied and was found to be second-order in each reactant. The values of the rate constants of the forward and reverse reactions k ₁ and k _?1 were determined.     

Nucleophilic substitution reactions of diethyl 4‐nitrophenyl phosphate triester: Kinetics and mechanism

The reactions of diethyl 4‐nitrophenyl phosphate ( 1 ) with a series of nucleophiles: phenoxides, secondary alicyclic (SA) amines, and pyridines are subjected to a kinetic study. Under excess of nucleophile, all the reactions obey pseudo‐first‐order kinetics and are first order in the nucleophile. The nucleophilic rate constants (k_N) obtained are pH independent for all the reactions studied. The Brønsted‐type plot (log k_N vs. pK_a nucleophile) obtained for the phenolysis is linear with slope β=0.21; no break was found at pK_a 7.5, consistent with a concerted mechanism. The Brønsted‐type plots for the SA aminolysis and pyridinolysis are linear with slopes β=0.39 and 0.43, respectively, also suggesting concerted processes. The concerted mechanisms for the latter reactions are proposed on the basis of the lack of break in the Brønsted‐type plots and the instability of the hypothetical pentacoordinate intermediates formed in these reactions. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 708–714, 2011     

Early stages of the hydrolysis of chromium(III) in aqueous solution-XII. Kinetics of cleavage of the trimer and tetramer in acidic solution

The kinetics of cleavage of the hydrolytic trimer and tetramer of chromium(III) have been studied in acidic solution and at elevated temperatures using spectrophotometric methods. For both reactions, the variation in absorbance with time was consistent with the presence of two consecutive rate-determining processes. The two reactions were concluded to proceed according to: Product analyses and consideration of the stability constants for these oligomers indicated that their overall cleavage reactions were irreversible under the conditions studied. However, it was unclear whether the initial step in tetramer cleavage was irreversible or not. The dimer was identified as an intermediate in the cleavage of the trimer. Each of the bridge-cleavage processes (k₁ and k₂) occurred via acid-dependent pathways, involving protonation processes in addition to bridge-cleavage processes, while only some of them displayed acid independent pathways. The acid dependence of the rate constants and associated parameters at 298 K are: (i) for trimer cleavage k₁ = k_b [H⁺], where the dimer to monomer was found to be the rate-determining step at higher temperatures (≈350 K), while cleavage of the trimer to dimer and monomer becomes rate determining at lower temperature (≈ 300 K). This change in the rate-determining step is attributable to the much higher value for k₁ compared with k₂. Possible mechanisms for trimer and tetramer cleavage are discussed and their rates compared to previously studied cleavage reactions of Cr^III oligomers.