Ligand Sequential Replacement on Chromium(III)-Aqua Complexes by l-Alanine and Other Biological Amino Acids: A Kinetic Perspective.

The ligand sequential replacement on chromium(III)-aqua complexes by l-alanine in slightly acidic aqueous solutions (pH range: 3.55-5.61) has been kinetically followed by means of UV-vis spectrophotometry. A two rate constant model has been applied to fit the absorbance-time data, corresponding to the formation ( k1) and decay ( k2) of an intermediate not reactive enough to be in steady state (long-lived intermediate). The kinetic orders of the amino acid were fractional (0.40 ± 0.03 for k1 and 0.40 ± 0.02 for k2). The two steps showed base catalysis, and the activation energies were 60 ± 3 (for k1) and 83 ± 6 (for k2) kJ mol-1. The rate constants for the coordination of the first l-alanine ligand followed the sequence CrOH2+ < Cr(OH)2+ < Cr(OH)3, Cr3+ being almost inactive. This suggests that the increase in the reaction rate with increasing pH was caused by the enhancement of the lability of the Cr(III)-aqua bonds induced by the presence of hydroxo ligands. The activation parameters for a series of ligand substitution on Cr(III)-aqua complexes by organic molecules yielded a statistically significant enthalpy-entropy linear plot with an isokinetic temperature of 296 ± 21 K.


INTRODUCTION
The coordination chemistry of chromium(III) differs from those of other transition metal ions in the rate of the reaction between the metal and its ligands. Whereas chemists are used to see in their laboratories how typical complexes such as tetraamminecopper(II) or diamminesilver(I) ions form in a rather fast way, and kinetic studies of the substitution of coordinated water on Pt(II) and many other metal ions by organic ligands often require the use of rapid reactant mixing techniques as the stopped-flow method, 1 the characteristic kinetic inertness to substitution of the Cr(III) d 2 sp 3 octahedrical complexes 2,3 makes them especially attractive candidates to be employed in kinetic studies affordable by ordinary UV-Vis spectroscopy. For instance, the relatively slow reaction between Cr(III) and ethylenediaminetetraacetic acid (EDTA) 4,5 is selected as an adequate experiment in chemical kinetics for undergraduate students in some university faculties around the world. 6,7 The complexes of Cr(III) are of certain importance in biology. Actually, chromium is nowadays considered by many authors as a necessary nutritional oligoelement 8 because of its participation in the glucose tolerance factor. [9][10][11][12] Although the classification as an essential trace element remains polemical, 13,14 the capacity of chromium to potentiate the action of insulin is well established. 15 On the other hand, L-alanine, the simplest -amino acid presenting optical isomerism, is classified as one of the 10 non-essential biological amino acids for humans, due to their ability to produce it. 16 Given that the amino acid molecules exhibit two functional groups with nitrogen and oxygen atoms capable of acting as electron-pair donors, they can be considered as suitable ligands for vacant-orbital transition metal ions. In particular, the reactions of complexation of Cr(III) by amino acids might be related to the problem of the origin of the first peptides on prebiotic Earth, 17 since transition metal ions have been shown to catalyze the formation of peptide bonds between the amino acid monomers acting as ligands. 18 The substitution reactions on aqua, [19][20][21][22][23][24][25][26] hydroxo, 27 and ammonia 28 complexes of Cr(III) by amino acids have been the subject of several kinetic studies. Although the results of two independent investigations of the Cr(III)-alanine reaction have already been reported, 29,30 the process under a large excess of organic ligand being classified in both cases as a pseudo-first order reaction, some clear-cut deviations from this simple kinetic behavior have been observed. The main objective of the present work will be to search for and eventually find a kinetic model capable of accounting for those deviations.

Materials and Methods.
All the experiments were done using milli-Q quality (Millipore Synergy UV system) water as solvent. The source of metal ions required to carry out the kinetic runs was Cr(NO 3 ) 3 ·9H 2 O (Merck). The source of organic ligands used in most experiments was CH 3 -CH(NH 2 )-COOH (alanine, in its L and DL forms, Sigma-Aldrich).
Other amino acids used were glycine (Merck), as well as L-phenylalanine (Sigma-Aldrich), L-threonine (Sigma-Aldrich), and L-histidine (Fluka). KOH (Merck) and HCl (Sigma-Aldrich) were employed to perform the reactions at an adequate pH range. Actually, the window of accessible pHs was rather narrow, being limited at the bottom by the rate of reaction (too slow under very acidic conditions) and at the top by the eventual precipitation of Cr(OH) 3 . The background electrolyte used to change the ionic strength when necessary was KNO 3 (Merck).

5
The pH measurements were done by means of a Wave pH-meter provided with a combination electrode (calibrated with buffers at pHs 4.00 and 7.00, Sigma-Aldrich). The kinetic runs were monitored by a periodical measurement of the reacting mixture absorbance either at five different wavelengths with a Shimadzu 160 A UV-Vis spectrophotometer or at a single wavelength with a Shimadzu UV-1201V spectrophotometer. At the end of the reactions, the UV-Vis spectra corresponding to the final reaction products were recorded with the aid of a third spectrophotometer (SI Analytics, UV Line 8100 model).

Kinetic Experiments and Calculations.
In most of the runs, the complexing agent (either L-alanine or other amino acid) was in large excess with respect to the metal ion, Cr(III), acting as limiting reactant (isolation method). The selected wavelength to follow the reactions (leading to the highest difference between the initial and final absorbance readings) was usually that of 530 nm. The absorbances of the reacting mixture were periodically measured (time intervals: 60-360 s) during at least 6 hours, and the final values, along with the UV-Vis spectrum and the pH, were taken 4 days later (higher delay times were not advisable because of the potential contamination by fungal colonies feeding on the amino acid). All the experimental determinations were duplicated. In total, 106 kinetic runs were performed.

Spectrophotometric Monitoring of the Reaction. The stock aqueous solution of
Cr(NO 3 ) 3 (0.3 M, pH 2.01) exhibited a distinct blue color. Addition of an aliquot to an aqueous mixture of L-alanine and KOH resulted usually in precipitation of Cr(OH) 3 , which redissolved rapidly on stirring, yielding a perfectly transparent green solution, whose color shifted gradually to violet as the complexation reaction advanced.
The absorbance of the solution increased at most wavelengths of the UV-Vis spectrum during the course of the reaction, and two absorption peaks shifting gradually toward the left side could be observed (Figure 1). The higher increase of the absorbance was that corresponding to the peak situated at the higher wavelength, thus being the best choice to follow the reaction keeping the experimental errors as low as possible.
In certain kinetic studies, when the reaction has been followed by a spectrophotometric technique determining simultaneously the absorbances at two different wavelengths, a representation of the absorbance at one wavelength, A( 1 ), as a function of the other, A( 2 ), can yield some useful information on the chemical system under study, for instance, the participation of a long-lived intermediate (as opposed to very reactive, steady-state intermediates [31][32][33] ) in the mechanism 5 or the colloidal nature of one of the reaction products. [34][35][36] In the presence of a long-lived intermediate (I), the relationship follows the law: where: In all the experiments corresponding to the Cr(III)-alanine reaction (and also for the other amino acids studied, except in the case of L-histidine), the absorbance-time plots presented a downward-concave curvature, meaning that the reaction rate decreased right from the beginning of the process ( Figure S2, top). This decrease was much faster than expected for a pseudo-first order reaction ( Figure 2). As a consequence, attempted pseudo-first order plots led to nonlinear upward-concave plots ( Figure S2, bottom). However, in the case of Lhistidine, as well in those previously reported for the reactions of Cr(III) with EDTA 5 and Lglutamic acid, 37 sigmoidal (S-shaped) absorbance vs time and autocatalytic-like (bell-shaped) rate vs time plots were found.

Consecutive Steps: A Kinetic Model for the Reaction.
According to the available experimental information, the kinetics of the Cr(III)-alanine reaction seems to follow the simplified mechanism: 12 fast slow where R, I, and P stand for the limiting reactant (the metal ion), the long-lived intermediate (not being reactive enough to be in steady state, the slow step thus being the one corresponding to its decay), and the reaction product, respectively. The exact solutions for the time dependences of the concentrations of these species can be obtained by integration of the corresponding differential equstions, 38 and are the following:  k ) used in the present work. As can be seen in Figure 3, the ratio between the experimental and calculated absorbances during the course of the reaction was much closer to unity when the two rate constant kinetic model was employed, the difference between the two models being especially notable at the beginning of the reaction.

Reaction of Cr(III) with L-Alanine Kinetic Results. Both rate constants decreased
as the metal ion initial concentration increased, k 1 according to an upward-concave curve, whereas k 2 yielded a straight line ( Figure S3). These decreases were caused by the corresponding decrease in the reacting mixture initial pH, due primarily to the dissociation of hexaaquachromium(III) ion to yield hydroxopentaaquachromium(III) ion. 39,40 In contrast, both rate constants increased as the organic ligand initial concentration increased. The corresponding double-logarithm plots yielded straight lines with slopes 0.40 ± 0.03 in the case of k 1 and 0.40 ± 0.02 in that of k 2 ( Figure 4). This means that the apparent kinetic orders of the amino acid were fractional (non-integer) numbers, thus excluding the possibility of the reaction being of first order as far as the concentration of L-alanine was concerned.
The ionic strength of the medium was changed by the use of KNO 3 as background electrolyte, and its effects on both experimental rate constants have been determined. A plot of the logarithm of each magnitude against I 1/2 / (1 + I 1/2 ) yielded straight lines with the slopes 0.93 ± 0.18 (for k 1 ) and  0.43 ± 0.26 (for k 2 ) M -1/2 ( Figure S4).
The pH of the medium was varied by means of a changing concentration of KOH. An increase of the pH resulted in an increase of both k 1 and k 2 ( Figure 5), indicating the existence of base catalysis in the two cases.
Both experimental rate constants increased with increasing temperature (Table 1), fulfilling the Arrhenius equation ( Figure S5), and yielding an activation energy for the first experimental rate constant considerably lower than that associated with the second (Table 2) .
This result is consistent with the finding that rate constant k 1 was one order of magnitude higher than k 2 .
On the other hand, when the source of organic ligands was changed from L-alanine to a DL-alanine racemic mixture, both the kinetic data (k 1 and k 2 ) and the final UV-Vis spectrum remained unaltered within the experimental error margin ( Figure S6), denoting that the reaction was rather insensitive to the nature of the amino acid optical isomer.

Reactions of Cr(III) with Other Amino Acids: Kinetic Results.
The temperaturedependence kinetic data for the reactions of Cr(III) with four other biological amino acids have been determined, fulfilling in all the cases the Arrhenius equation ( Figure S5) and yielding the activation parameters compiled in Table 2. Whereas the reactions with glycine, Lphenylalanine, and threonine followed the same two rate constant kinetic model developed for that with L-alanine (involving a single long-lived intermediate), the reaction with L-histidine followed a three rate constant kinetic model (involving two long-lived intermediates). These three rate constants were designated as k o , k 1 , and k 2 . Whereas rate constants k 1 and k 2 for Lhistidine correlated well with their counterparts for the other four amino acids ( Figure 6), rate constant k o followed a different pattern. This suggests that the discordant rate constant did not correspond actually to the replacement of an aqua ligand by the amino acid but to the basecatalyzed aquation of an initial Cr(III)-nitrate complex 41,42 (rate constant k o ) instead, the Cr(III)-aqua complex being the one susceptible of reaction with a first amino acid molecule (rate constant k 1 ) followed by a second (rate constant k 2 ).
A representation of the activation enthalpy as a function of the activation entropy for the reactions of Cr(III) with EDTA, 5 L-glutamic acid, 37 and the five amino acids corresponding to the present study yielded a linear plot (Figure 7). It has been shown, however, that at least some of the enthalpy-entropy linear correlations found in the chemical literature are caused by the accumulation of experimental errors. This is so because the standard deviation associated with the enthalpy is directly proportional to that associated with the entropy, the proportionality constant being equal to the mean experimental temperature. [43][44][45][46][47] Nevertheless, there seem to be reliable evidences supporting the physicochemical meaning of some of those correlations. 48,49 In the present case, despite the slope of the plot (isokinetic temperature, T iso = 296 ± 21 K) being almost coincident with the mean experimental temperature (T exp = 298 K), the correlation was statistically significant since, according to the p-test, 50 the probability of it being caused by random experimental errors was relatively low (P = 0.0106).

UV-Vis Spectrum of the Long-Lived
As shown in Figure 8, the spectrum was intermediary between those corresponding to the reactant and product. This result contrasts with the spectra for the long-lived intermediates observed in the reactions of Cr(III) with EDTA 5 or L-glutamic acid, 37 since in the latter two cases the spectrum was very close to that recorded for the reactant. This suggests that they  Table 3. It should be noticed that the ones obtained at infinite initial concentrations (of either metal ion or amino acid) are to be preferred over those obtained at zero initial concentrations, for they are closer to the experimental values in the case of the reactant (the only species for which the spectrum parameters are directly accessible).
A variation of the initial potassium hydroxide concentration had also an effect on the UV-Vis spectrum of the reaction product mixture. As can be observed, an increase of the initial base concentration resulted in a decrease of the wavelengths associated with the two peaks and an increase of the corresponding absorbances ( Figure S8).
The spectroscopic data shown in Figures S7, S8, and 10 indicate that the wavelength for the first visible peak of the final reacting mixture lied in the range 392  409 nm, and for the second in the range 528  548 nm, increasing both with the initial concentration of metal ion and decreasing both with the initial concentrations of either ligand or potassium hydroxide.
The values reported for the number of L-alanine ligands coordinated to each Cr(III) center in the final violet complex are 2 according to some authors 30 and 3 according to others. 29 Actually, the results shown in Figures S7, S8 (22) where L, B, and M stand for ligand, base (potassium hydroxide) and metal, respectively, n is the number of organic ligands coordinated per chromium atom, and K a is the first aciddissociation equilibrium constant of protonated L-alanine (for the carboxyl group, pK a 2.35 at 25.0 ºC). 51,52 The results indicated that the number of hydrogen ions released per chromium atom decreased as the initial concentration of metal ion increased, whereas it increased as the initial concentrations of either L-alanine or potassium hydroxide increased, remaining within the range 0.73 ≤ Number (H + ) ≤ 2.53 ( Figure 11).

Chromium(III) Speciation.
The kinetics of the reaction between Cr(III) and Lalanine resembles that of other similar processes, such as the complexations of the same metal ion by EDTA 5 or the -amino acids L-glutamic acid, 26,37 DL-leucine, 25 and DL-lysine, 26 in that all of them exhibit base catalysis. It is precisely this pH dependence that offers the main clue to elucidate the mechanism involved in the reaction.
Trivalent chromium finds itself in slightly acidic aqueous solutions in the form of several species in equilibrium, from hexaaquachromium(III) ion to dissolved (either monomolecular or colloidal) chromium(III) hydroxide, passing through the monohydroxo and dihydroxo complexes: where x = 0  2. Although the corresponding equilibrium constants were not known with exactitude for some time, 53 a recent publication has reported experimental values for them that can be considered as reliable (for the successive dissociations of the hexaaqua complex: pK a,1 3.52, pK a,2 5.78, pK a,3 7.88). 54 Since, according to the kinetic model developed in the present work, rate constant k 1 should be considered as the ratio between the initial values of the reaction rate and the concentration of the inorganic (limiting) reactant, it must be correlated with the initial pH of the reacting mixtures. Unfortunately, given the slow response of the pH meter to yield accurate measurements, the only pH data experimentally accessible with a high degree of confidence are those corresponding to an equilibrium state (pH ∞ ). However, the initial pH for each kinetic run could be theoretically calculated from the first and second acid-dissociation equilibrium constants of hexaaquachromium(III) ion 54 A BASIC program was developed in order to find the best set of values k 1,x (x = 0  3) minimizing the difference between the calculated (k 1,cal ) and experimental (k 1,exp ) rate constants. However, a k 1,exp vs. k 1,cal plot yielded a downward-concave curve (Figure 12, top). Therefore, a second trial was made (considering now negligible the contribution corresponding to x = 0) with a function of the type: 3 (3  (25) yielding the results k 1,1 = 1.77 M -1 s -1 , k 1,2 = 128 M -1 s -1 , k 1,3 = 3.07  10 4 M -1 s -1 , and K = 9.66  10 4 M -1 , with an excellent concordance between k 1,cal and k 1,exp (Figure 12, bottom). We can see that, according to these data, the reactivity of the chromium species toward L-alanine increases following the sequence two sequences, each with its own slow rate-determining step, the activation energy associated with the first sequence being the lower of the two ( Figure 13). Thus, according to the available experimental data, the mechanism that can be proposed for the complexation of Cr(III) by L-alanine consists of two elementary step sequences. The first leads from the reactants to the long-lived intermediate: where x = 1, 2, or 3, depending on the particular reacting Cr(III) species, and RH stands for the zwitterionic form of the amino acid. The experimental results suggest that the presence of OH  ligands in the reactant complex renders the Cr(III)-H 2 O chemical bonds more labile. The breakage of one of those bonds (as in eq 26) has been postulated to be a requirement for the formation of the Cr(III)-EDTA complex. 7 Then, a competition between hydroxide ion (eq 27), water (eq 28) and the organic ligand (eq 29) for the vacant coordination site of the pentacoordinated metal ion takes place. In the last reaction the organic ligand suffers a conversion from monodentate (RH) to bidentate (R) and a water molecule is released, leading to the formation of the long-lived intermediate (eq 30).
Assuming that the penta-coordinated intermediate is reactive enough to be in steady state, the following expressions can be obtained for the parameters appearing in eq 25: Assuming again that the penta-coordinated intermediate is reactive enough to be in steady state, the following expression can be obtained for the second experimental rate constant:  Given enough time ( at t =  ), the following equilibria might be reached: The correspondence between the complexes appearing in eqs 39 -41 and those seen before in eqs 12 and 13 is shown in Table 4.
The number of hydrogen ions released to the medium during the course of the reaction (per chromium atom belonging to the violet complex) can then be estimated as: