DALTON FULL PAPER J. Chem. Soc., Dalton Trans., 1998, 3565–3576 3565 Kinetics and mechanisms of the complexation of aqueous lanthanide ions by 4-(2-pyridylazo)resorcinol † Yanlong Shi,a Edward M. Eyring *a and Rudi van Eldik *b a Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA b Institute for Inorganic Chemistry, University of Erlangen-Nürnberg, 91058 Erlangen, Germany Received 24th July 1998, Accepted 14th August 1998 Three kinetic steps were observed for the complexations of Eu31 and UO2 21 by PAR [4-(2-pyridylazo)resorcinol] or PAN [1-(2-pyridylazo)-2-naphthol] in diVerent buVered solutions. The first step can be assigned to the co-ordination of the nitrogen donor from the pyridine moiety of the ligand based on the dependencies of [Eu31], pH, pressure, nature and concentration of the buVer.The rate-determining step is the release of water molecules from the co-ordination sphere of the lanthanide ion. Variations in the rate of the first step with diVerent lanthanide ions indicated that a co-ordination number changeover is involved in this lanthanide series.For the second step the formation of a “hydroazone–Ln31 chelate” intermediate accounts for all of the observed kinetic behaviors. The kinetic investigations of the third step show that there is a deprotonation preequilibrium preceding the transition state of the final product with two chelated 5-membered rings involved. Surprisingly, the rate constants of the three steps for the complexation of UO2 21 by PAR are very close to those for 18-crown-6 and diaza-18-crown-6 reacting with uranyl ion.The diVerences in the kinetics between PAR and PAN can be related to the diVerence in their structures. The fifteen trivalent lanthanide, or f-block, ions ranging from La3 to Lu31 represent the most extended series of chemically similar metal ions. The progressive filling of the 4f orbitals from La31 to Lu31 is accompanied by a smooth decrease in the cation radius rM with increasing atomic number because of the increasingly strong nuclear attraction for the electrons in the diVuse f orbitals (the lanthanide contraction).In an ideal situation, smooth variation of rate parameters with radii might be expected. However, the solution chemistry of the lanthanides displays more interesting variation than a simple linear correlation of rate and/or thermodynamic parameters with shrinking cation radius.1,2 A changeover in the co-ordination number of the lanthanide complexes from nine to eight near the middle of the series 3–6 gives rise to kinetics for the complexation or solvent exchange of lanthanide ions in solution that has been studied extensively using high-pressure NMR relaxation techniques. 7–13 Interest in these kinetic phenomena has increased with the development of some lanthanide complexes as contrast agents in magnetic imaging (MRI).14–16 Another signifi- cant feature of lanthanide element behavior in aqueous solution is the very high stability of the trivalent state although cerium(IV) and, in strongly reducing solutions, divalent samarium, europium and ytterbium can be formed.17,18 A third important characteristic is the strongly ionic character of lanthanide bonding. Thus, the lanthanides are typically “hard acids”.The kinetics of complexation is normally quite fast for Ln31 cations reacting with simple ligands compared to the rates of complexation for analogous complexes of the transition metal ions in the same oxidation state.The kinetics of complexation of Ln31(aq) by many monodentate or multidentate ligands has been studied using fast kinetic techniques. The ligands include NO3 2 (ultrasonic relaxation),19,20 SO4 22 (ultrasonic relaxation),21,22 acetate (ultrasonic relaxation),23 picolinic acid (pyridine-2-carboxylic acid) (pulse-radiolytic pH-jump),24 † Supplementary data available: rate constants as a function of buVer concentration for the Eu31–PAR reaction.For direct electronic access see http://www.rsc.org/suppdata/dt/1998/3565/, otherwise available from BLDSC (No. SUP 57431, 2 pp.) or the RSC Library. See Instructions for Authors, 1998, Issue 1 (http://www.rsc.org/dalton). murexide (E-jump),25 methyl red (pulse-radiolytic pH-jump),26 anthranilate (temperature-jump),26 malonate (ultrasonic relaxation), 27 oxalate (pressure-jump),28 arsenazo III [3,6-bis- (o-arsonophenylazo)-4,5-dihydroxynaphthalene-2,7-disulfonic acid] (stopped-flow) 13 and acyclic aminopolycarboxylates, such as EDTA (ethylenedinitrilotetraacetate) and DTPA [carboxymethyliminobis( ethylenenitrilo)tetraacetate].18,29 The rate of complexation is aVected either by the size of the central ion or by the nature of the ligand.However, the complexations of Ln31 by cyclic aminopolycarboxylates, such as DOTA (1,4,7,10-tetraazacyclododecane-N,N9,N0,N--tetraacetic acid), are slower and susceptible to study by traditional UV/VIS spectrophotometric techniques.18,30–39 The rate-determining step of the complexation of Ln31 by cyclic aminocarboxylates is proton loss from the ligand and the rearrangement of the intermediate.The rate of complexation is also aVected by the ring size of the ligands. The well known analytical reagents PAR [4-(2-pyridylazo) resorcinol] and PAN [1-(2-pyridylazo)-2-naphthol], like arsenazo III, have been studied extensively for the colorimetric determination of lanthanides and uranium(VI) 40 since they form stable, intensely colored complexes with a molar absorptivity of (3–8) × 104 M21 cm21. The compound PAR has been used widely in analytical chemistry because both it and the lanthanides and uranium(VI) complexes are water soluble, thus simplifying the analysis since no expensive, or toxic, organic solvents are required. Although the IR spectra,41,42 Raman spectra,43 acid–base equilibria 44,45 and HMO (Hückel molecular orbital) quantum calculations 45 of PAR and PAN, and some structural chemistry 46–49 and stability constants 50–52 of their lanthanide complexes have been investigated, neither bonding information N N N HO N N N HO OH PAR PAN3566 J.Chem. Soc., Dalton Trans., 1998, 3565–3576 between the lanthanide ion and the ligand nor kinetic studies have been reported for the complexation of lanthanides by PAR and PAN. However, some kinetics of the complexation of transition metal ions by PAR and PAN has been reported.53–66 DiVerences between transition metal ions and lanthanide or actinide ions make it interesting to study the complexation kinetics of lanthanide ions and uranium(VI) with PAR and PAN.We have sought a clear understanding of the nature of the diVerent contributions to the complexation kinetics and mechanism (e.g., ligand geometry, size of the central metal ion, pH, buVer, pressure, etc.). In the present paper, we mainly focus on the complexation of Eu31 by PAR and PAN, under diVerent buVer environments in the pH range of 1.8–8.1 using either conventional or high-pressure stopped-flow spectrophotometric techniques.In addition, we also studied the kinetics and mechanism of the complexation of other lanthanide(III) ions and UO2 21 by PAR for comparison. Experimental Materials The compounds PAR, PAN and Sudan Orange G [4-(phenylazo) resorcinol] were obtained from Aldrich and recrystallized from methanol, LaCl3?6H2O, CeCl3?7H2O, PrCl3?6H2O, NdCl3? 6H2O, SmCl3?6H2O and DyCl3?6H2O from Aldrich, EuCl3? 6H2O, GdCl3?6H2O, ErCl3?6H2O, YbCl3?6H2O and LuCl3? 6H2O from Strem and TbCl3?6H2O from Alfa.All these lanthanides were used as received (purity >99.9%); HoCl3?6H2O and YbCl3?6H2O were prepared from Ho2O3 (Strem) and Yb2O3 (Sigma) and UO2(ClO4)2?6H2O (Alfa) was used as received. N9- 2-Hydroxyethylpiperazine-N-3-propanesulfonic acid (HEPPS), MES [2-(morpholino)ethanesulfonic acid] and Tris [tris- (hydroxymethyl)aminomethane] were obtained from ICN Biochemicals.Imidazole (Eastman Kodak) was recrystallized from benzene. Succinic acid, sodium salt (A. R.) was from Aldrich. Acetate buVer solution was prepared by treating acetic acid (J. T. Baker) with sodium hydroxide. Succinate buVer solution was made by mixing succinic acid dipotassium salt (Eastman Kodak) with perchloric acid (Fisher Scientific). The pH of HEPPS, MES and Tris buVer solutions was adjusted with NaOH.Distilled water was purified using a Barnstead “EPure” purification system. 1,4-Dioxane (spectrophotometric grade) was from Aldrich. Stock solutions of the lanthanides and ligands were prepared by weight; NaClO4 (Aldrich) was used to maintain the ionic strength. All glassware was first treated with an EDTA solution and then cleaned with successive detergent, ammonia, and distilled water rinses. The pH was adjusted by adding HClO4 (Fisher Scientific, ACS reagent) or NaOH solutions (Aldrich).Instrumentation Spectrophotometric measurements were made with a Hewlett- Packard 8452A diode array spectrophotometer equipped with a thermostatted cell holder. pH-Metric measurements were made with an Orion Research 701 A Digital Ionanalyzer equipped with glass and calomel combined electrodes. Kinetic studies Kinetic measurements were made either at atmospheric pressure on a Durrum stopped-flow spectrophotometer or on a home-made, high pressure stopped-flow system 67 for pressures up to 1000 bar. n-Heptane was used as the pressurizing medium.An Edmund Scientific f/3.9 monochromator (1 nm per division) and a Hamamatsu photomultiplier tube (R376) were employed in all kinetic measurements. Transmitted light intensity versus time signals were recorded on a Tektronix (model 7D20) storage oscilloscope and transferred to a PC, on which data were fitted with the On Line Instrument System (OLIS) KINFIT (Bogart, GA) programs.Several experimental traces were averaged in the determination of each rate constant. The complexation of Ln31 or UO2 21 by PAR or PAN was studied at 25 8C. Constant temperature was maintained with a Forma Scientific model 2006 constant temperature bath and circulator system for the ambient Durrum D-110 Stopped- Flow Spectrophotometer, and a Brinkmann Instrument Lauda K-2/RD constant temperature apparatus for the high-pressure stopped-flow spectrophotometer at 25.0 8C.Temperature control precision was ±0.1 8C. All kinetic data were measured after not less than 1 h of temperature equilibriation. Experimental rate constants reported in the Results section are the average of at least 5 replicate determinations. The optimum observation wavelength of 502 nm was determined from preliminary observations on a HP 8452A spectrophotometer. Calculations All experimental runs for the three consecutive kinetic steps were best described by a single exponential.Observed pseudo- first-order rate constants were obtained from a least-squares fit of at least 3 half-lives of the reactions. Volumes of activation were obtained by a fit of the natural logarithm of the observed pseudo-first-order rate constants using eqn. (1). Here k0 denotes ln k = ln k0 2 (DV‡P/RT) (1) the rate constant at ambient pressure. Errors reported in the Tables correspond to one standard deviation. Results and discussion Structure, acid–base equilibria and tautomeric equilibria of PAR The visible spectra of 4-(2-pyridylazo)resorcinol were studied by Geary et al.44 as a function of pH from 1.0 to 13.0 and the chromophoric species were identified as follows: protonated form (A), lmax = 420 nm, e = 14 750 dm3 mol21 cm21, pH 1.06 and 1.52; free base form (B), lmax = 392 nm, e = 15 240 dm3 mol21 cm21, pH 3.19, 4.35 and 5.56; monoionic form (C), lmax = 414 nm, e = 23 100 dm3 mol21 cm21, pH 7.56–13.56; diionic form (D), lmax = 502 nm, e = 17 800 dm3 mol21 cm21, pH 12.96 and 13.56.The relationship among all the species is summarized in Scheme 1. Zhao et al.45 suggested that there are five forms for PAR in aqueous alcohol solution. The equilibria are: H4L21 2H1 Ka1 H3L1 2H1 Ka2 H2L 2H1 Ka3 HL2 2H1 Ka4 L22. The pKa values are pKa1 = 22.30, pKa2 = 3.00, pKa3 = 5.58 and pKa4 = 12.03, respectively. They found that the H3L1 is present in a hydrazone form (see Scheme 1); H2L exists in both the hydrazone and azo forms.The results 45 are in agreement with those obtained by Drozdzewski 43 from resonance Raman spectra. The anions HL2 and L22 exist in the azo forms, and are consistent with the result of Geary et al. shown in Scheme 1. Bonding and stability constants of the LnIII–PAR complexes When a 1 × 1024 mol dm23 PAR solution is mixed with a 1 × 1023 mol dm23 Eu31 solution at pH 4.35 in 0.1 mol dm23 acetate buVer using a tandem cuvette the lmax immediately shifts from 390 to 502 nm.This indicates that complexation of Eu31 (aq) by PAR does take place and raises the question what the structure of the formed complex could be. N N O O Sudan Orange G H HJ. Chem. Soc., Dalton Trans., 1998, 3565–3576 3567 Scheme 1 lmax and pKa values, measured in water solution, cited from ref. 44; lmax* and pKa* values, measured in water–alcohol solution, cited from ref. 45. + N N N OH2 + O H H [H2PAR]2+ N N N OH O H+ H H+ PAR N N N O HO PAR H lmax = 470, 401 nm* lmax = 494 nm* + N N N OH O H H N N N OH O H N N N O– –O N N N O– O H lmax = 420 nm lmax = 392 nm, lmax* = 393 nm lmax = 502 nm lmax* = 493, 430 nm lmax = 414 nm, lmax* = 413 nm H+PAR PAR PAR2– PAR– –H+, pKal* = –2.30 –H+ pKal = 2.35 pKa2* = –3.00 pKa2 = 7.01 pKa3* = 5.58 –H+ pKa3 = 13.0 pKa4* = 12.0 –H+ In order to study the bonding between PAR and Eu31, we used Sudan Orange G to react with Eu31 as a function of pH.We found that the metal complex absorbed at almost the same wavelength as the ligand itself at diVerent pH values below 7.For example, when [Sudan Orange G] = 1 × 1024 mol dm23 at pH 5.4 in 0.05 mol dm23 acetate buVer lmax is 374 nm for free Sudan Orange G, and lmax is still at 374 nm after mixing with aqueous 1 × 1023 mol dm23 Eu31 solution (1 : 1 v/v). The role of the pyridine nitrogen atom of PAR in the colorimetric reaction with Eu31 ion is evident from these results. The fact that there is no shift in lmax on chelation by the benzene analogue of PAR, Sudan Orange G, must mean that the nitrogen atom from the pyridine moiety of PAR is involved in the bonding to Eu31.To test which one of the nitrogen atoms of the azo group participates in the bonding, Geary et al.44 found that when the copper(II) ion reacts with 2-(o-hydroxyphenyliminomethyl)- pyridine, the complex absorbs at a wavelength of 395 nm at pH values above 8.50. This represents a shift of 15 nm away from the maximum wavelength of the ligand at this pH.This shift is considerably less than the shift for the copper or europium complexes of PAR, yet the co-ordinating system is the same as in the PAR system except that the azo nitrogen nearest the heterocycle is replaced by a CH]] group. The removal of this nitrogen has a profound eVect on the color reaction with metal ions, and it seems clear that in PAR the azo nitrogen farthest from the heterocycle must play a greater role in the chromophoric reaction than its neighbors.This conclusion is further supported by the visible spectra of the metal complexes of 2-(salicyclideneamino)pyridine.44 This ligand gave strongly absorbing red complexes of transition N C H N HO 2-(o-hydroxyphenyliminomethyl)pyridine metal ions similar to those with PAR. For example, the main peak of the ligand at 350 nm at pH 4.88 is shifted to 453 nm at this pH in the presence of copper(II). These results demonstrate that in the Eu31–PAR complex the chromophoric reaction is due to co-ordination by the pyridine nitrogen, the azo nitrogen farthest from the heterocycle, and the o-hydroxyl group, even though there is an “intramolecular hydrogen bonding” as shown in free PAR. The partial coordination of Eu31(aq) by PAR can decrease the pKa values for the deprotonation of both the o- and the p-hydroxyl groups, and therefore the deprotonation takes place at much lower pH.The sensitivity of the color reaction of this ligand with metal ions is therefore explained by the combination of a pseudophenanthroline system and o,o9-disubstituted azo dyestuV.The stability constants of Ln31–PAR have been measured by Ohyoshi 51,52 using UV/VIS spectrophotometry. Both Ln31– PAR2 and Ln31–PAR22 complexes form in the pH range 5–6. The stability constants, log K (Ln31–PAR2) and log K (Ln31– PAR22), range from 3.78 ± 0.02 (Ce) to 4.39 ± 0.02 (Lu), and from 9.61 ± 0.06 (Ce) to 10.70 ± 0.05 (Lu), respectively. The acidity of the Ln31–PAR2 complexes parallels the order of stability of the Ln31–PAR22 complexes.In an attempt to elucidate the co-ordination structure of the N N C H HO 2-salicylideneaminopyridine N N N O OH PAR with "intramolecular hydrogen bonding" H3568 J. Chem. Soc., Dalton Trans., 1998, 3565–3576 PAR complexes, extraction studies of the 1 : 2 Ni–PAR complexes were carried out by Hoshino et al.68 They suggested that in the chelation of Ni(PAR2)2?2H2O and [Ni(PAR22)2]22 the PAR2 and PAR22 are acting as bidentate and terdentate ligands, respectively.They suggested that the basic change in the chelate structure from Ni(PAR2)2?2H2O to [Ni(PAR22)2]22 and deprotonation of the PAR2 ligand both cause a substantial increase in the absorptivity (from 3.73 × 104 to 8.08 × 104 dm3 mol21 cm21). Although the 1 : 1 lanthanide–PAR complexes differ in type from the Ni–PAR complexes, a considerable increase in the absorptivity [from (0.95–1.15) × 104 to 3.0 × 104 dm3 mol21 cm21] was similarly observed with increasing pH.The Ln31–PAR22 complexes may have a more stable chelate structure which gives rise to a larger diVerence in stability than for the Ln31–PAR2 complexes. Based on all the information given above it appears that the structures of the 1 : 1 Eu31–PAR2 and Eu31–PAR22 complexes are those shown below. Overview of the observed kinetics All kinetic runs were made with at least a 10-fold excess of Eu31. The reaction of aqueous Eu31 with PAR occurs in two steps in succinate buVered solution when pH < 2.65. Three steps were observed at 502 nm on diVerent timescales when pH > 2.65. The first is much faster than the second and third with a half-life of 2 ms to 100 s, depending upon pH, Eu31 concentration, amine buVer concentration, the nature of the amine buVer, pressure, and the nature of the lanthanide ions and UO2 21.A typical kinetic trace is shown in Fig. 1(a). The first step is assigned to the complexation of Eu31(aq) by the nitrogen atom from pyridine since the kinetics traces could be obtained when the pH was as low as 1.80 at a rate which depended on the pH.Fig. 1(b) is a typical kinetic trace for the second step showing that the absorbance at 502 nm decreases with increasing time with a half-life of ca. 500 ms. The second step is independent of pH, Eu31 concentration, amine buVer concentration, the nature of the amine buVer and the choice of the lanthanide ions, but the rate increases with increasing pressure. We assign the second step to the formation of the “hydrazone–Eu31 chelate” intermediate of a “phenanthroline style”.In the third slowest step the absorbance at 502 nm increases with increasing time. A typical kinetic trace for this step at pH 7.55 in HEPPS buVer solution is shown in Fig. 1(c). The third step depends on pH, amine buVer concentration, the nature of the amine buVer and pressure, but is independent of the concentration of Eu31.This step is attributed to the formation of the final 1 : 1 complex, Eu31–PAR22, shown above. Kinetic studies of the first step Eu31 Concentration dependence. Table 1 presents the rate constants k1 for the first step of the reaction of Eu31 with PAR as a function of Eu31 concentration either in a pH 2.08 succinate buVer or a pH 4.35 acetate buVer. The plots (Fig. 2) of k1 versus [Eu31] in both succinate and acetate buVers are linear with no significant intercept. The rate constants calculated from the slopes are 6.15 × 101 and 4.12 × 104 dm3 mol21 s21 in succinate and acetate buVers, respectively.The large diVerence is attributed not only to the diVerence in pH but also to the nature of the buVers used (see EVect of pH). This kinetic behavior suggests that the first step follows the Eigen–Wilkins mechanism depicted in Scheme 2 69 where A represents H2O, acetate or other buVer molecules which are involved in the co-ordination N N N HO O– 1:1 Eu3+-PAR–complex Eu3+ N N N –O O– Eu3+ 1:1 Eu3+-PAR2–complex to Eu31.From Scheme 2, d[product]/dt = k1[b] but d[b]/dt = 2k1[b] 2 k210[b] 1 k10[a] = 0, [b] = k10[a]/(k1 1 k210) and d- [product]/dt = k1k10[a]/(k1 1 k210) = {K19k1k10[Eu(H2O)8(A)x1]- [PAR]}/(k1 1 k210), but [PAR] = Ka1[H1PAR]/[H1]. Thus, d[product]/dt = {Ka1K19k1k10[Eu(H2O)8(A)x1][H1PAR]}/{(k1 1 k210)[H1]} where K19 = k19/k219. This rate law is consistent with the dependence on Eu31 concentration shown in Table 1 and Fig. 2, and also agrees with the observed eVect of pH discussed below. EVect of pH. Measurements made in succinate and acetate buVer solutions covered the pH range 1.80–5.40. All runs were made at a constant ionic strength of [NaClO4] = 0.1 mol dm23 and a constant concentration of 0.05 mol dm23 of the basic component of the buVer. Table 2 presents the observed rate Fig. 1 Typical kinetic traces recorded for the first (a), second (b) and third step (c) of the reaction of Eu31(aq) with PAR at ambient pressure and 25.0 8C in 0.01 mol dm23 HEPPS buVer solution (pH 7.55, [Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23).J.Chem. Soc., Dalton Trans., 1998, 3565–3576 3569 constants as a function of pH in either succinate buVer or acetate buVer at ambient pressure and 25.0 8C. Fig. 3 is a linear plot of k1 versus 1/[H1] (k1 increases with increasing 1/[H1]) that proceeds through the origin in the succinate buVer in the pH range 1.80–3.31.The rate constants of the first step in acetate buVered solution in the pH range 3.61–5.40 (see Table 2) are much faster, and are independent of the pH or 1/[H1]. Although the acetate anion forms only weak complexes with lanthanide cations, for Fig. 2 Plots of k1 versus Eu31 concentration for the first step of the reaction of Eu31 with PAR at ambient pressure and 25.0 8C ([Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23): n, pH 4.35, [acetate] = 0.05 mol dm23; h, pH 2.08, [succinate] = 0.05 mol dm23.Scheme 2 [Eu(H2O)8(A)]x+ + PAR(aq) [Eu(H2O)8(A)]x+ • [PAR(aq)] [Eu(H2O)8(A)x+----PAR(aq)] [Eu(H2O)7(A)x+----PAR(aq)] + H2O product H+PAR(aq) k1¢ k–1¢ k1¢¢ k–1¢¢ k1 Ka1 –H+ a b Table 1 Rate constants as a function of concentration of Eu31 for the three steps of the reaction of Eu31 (aq) with PAR at 25.0 8C and ambient pressure ([PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23) [Eu31]/mol dm23 10k1/s21 10k2/s21 10k3/s21 pH 2.08 (succinate 0.05 mol dm23) 0.001 0.002 0.003 0.004 0.005 0.50 ± 0.02 1.42 ± 0.01 2.12 ± 0.13 2.53 ± 0.19 3.02 ± 0.14 3.90 ± 0.15 3.76 ± 0.09 3.68 ± 0.15 3.84 ± 0.10 3.59 ± 0.08 3.79 ± 0.09 3.58 ± 0.11 3.81 ± 0.12 3.72 ± 0.05 3.65 ± 0.11 pH 4.35 (acetate 0.05 mol dm23) 0.001 0.002 0.003 0.005 0.010 50 ± 3 89 ± 7 127 ± 6 204 ± 8 420 ± 12 10.1 ± 0.4 9.82 ± 0.2 9.53 ± 0.4 9.95 ± 0.3 9.30 ± 0.2 18.5 ± 0.4 19.0 ± 0.6 17.8 ± 0.6 18.9 ± 0.2 17.6 ± 0.5 example, log b1 ª 1.9 for EuAc21,16 the concentration of acetate is very large compared with the other species present.Therefore, the Ac2 involvement in co-ordination must be considered. Calculations from the thermodynamic equilibrium data indicate that the concentration of EuAc21 is about 40% of that of Eu31(aq) in solutions of pH 4.5 when [HAc] 1 [Ac2] @ [Eu31].70 Some kinetic studies 71–73 indicate that the catalytic eVect results from a trans labilization eVect by co-ordinated acetate and involves the attack by a solvent water molecule on the metal–carbon bond for the heterolysis reaction of (a-hydroxyalkyl)chromium(III). The co-ordinated acetate accelerates dissociation of water molecules from the inner coordination sphere of the metal ions, resulting in kinetic diVerences with reactions in unbuVered or other buVered solutions. 13,74 No protonated pyridine nitrogen exists in the acetate buVered pH range (3.61–5.40) since the pKa1 is as low as 2.35,44 thus [PAR]tot = [PAR], and k1 is independent of pH in acetate buVer.Pressure dependence. The pressure dependence for the first Fig. 3 Plot of k1 versus [H1]21 for the first step of the reaction of Eu31 with PAR at ambient pressure and 25.0 8C in 0.05 mol dm23 succinate buVered solution ([Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23). Table 2 Rate constants as a function of pH for the first step of the reaction of Eu31(aq) with PAR* pH 10k1/s21 [succinate] = 0.05 mol dm23 1.80 2.08 2.30 2.65 2.89 3.31 0.07 ± 0.06 0.83 ± 0.04 1.90 ± 0.16 5.00 ± 0.04 8.96 ± 0.13 21.2 ± 0.5 [acetate] = 0.05 mol dm23 3.62 4.14 4.35 4.58 5.02 5.40 48.9 ± 1.3 50.2 ± 1.3 50.2 ± 1.8 48.5 ± 1.7 46.9 ± 1.1 49.6 ± 2.3 * Experimental conditions: [Eu31] = 1 × 1023 mol dm23; [PAR] = 1 × 1024 mol dm23; 25.0 8C; [NaClO4] = 0.1 mol dm23.3570 J.Chem. Soc., Dalton Trans., 1998, 3565–3576 Table 3 Rate constants as a function of pressure for the three steps of the reaction of Eu31(aq) with PAR in diVerent buVer solutions at 25.0 8C and [Eu31] = 1 × 1023 mol dm23 and [NaClO4] = 0.1 mol dm23 10k1/s21 DV‡ 1/cm3 mol21 P/bar 1 50 250 500 750 1000 pH 2.65 [succinate] = 0.05 [PAR] = 1 × 1024 0.50 ± 0.04 0.49 ± 0.03 0.44 ± 0.04 0.40 ± 0.04 0.36 ± 0.02 0.33 ± 0.02 pH 4.35 [acetate] = 0.05 [PAR] = 5 × 1025 — 25.7 ± 1.4 23.0 ± 2.3 20.7 ± 0.4 12.6 ± 0.4 10.1 ± 0.3 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 50.2 ± 1.8 47.3 ± 2.6 40.0 ± 1.9 32.7 ± 2.2 25.0 ± 0.6 19.8 ± 1.4 pH 2.65 [succinate] = 0.05 [PAR] = 1 × 1024 110.1 ± 0.7 pH 4.35 [acetate] = 0.05 [PAR] = 5 × 1025 125.4 ± 3.8 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 122.8 ± 0.56 k2/s21 102k3/s21 DV‡ 2/cm3 mol21 DV‡ 3/cm3 mol21 P/bar 1 50 250 500 750 1000 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 1.01 ± 0.08 1.02 ± 0.11 1.23 ± 0.07 1.39 ± 0.12 1.67 ± 0.05 1.91 ± 0.08 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 1.85 ± 0.12 1.92 ± 0.19 2.25 ± 0.12 2.40 ± 0.14 2.70 ± 0.20 2.96 ± 0.24 pH 7.10 [imidazole] = 0.05 [PAR] = 1 × 1024 — 29.4 ± 2.5 35.4 ± 2.0 40.3 ± 3.4 48.1 ± 3.5 55.3 ± 4.5 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 215.9 ± 0.6 pH 4.35 [acetate] = 0.05 [PAR] = 1 × 1024 211.2 ± 0.9 pH 7.10 [imidazole] = 0.05 [PAR] = 1 × 1024 215.9 ± 0.8 step of the reaction of Eu31 with PAR was studied at diVerent pH values, PAR concentrations and in diVerent buVers at 25.0 8C.The k1 values as a function of pressure under diVerent reaction conditions are summarized in Table 3.Fig. 4 clearly shows a linear relationship between ln k1 and pressure, from which it follows (see Table 3) that all DV‡ 1 values are positive. The DV‡ 1 values in acetate buVered solution (>120 cm3 mol21) are much larger than those found in succinate buVered solution (110.1 cm3 mol21). In general the pKa values of buVers depend on pressure, typically for HAc H1 1 Ac2, DV ª 212 cm3 mol21. It means that the buVer becomes more acidic (increase in Ka) with increasing pressure. In our system this will not aVect the data in the acetate buVer since we found no pH dependence in this range.However, at lower pH in succinate buVer, a part of the observed DV‡ 1 could be due to the Fig. 4 Plots of ln k1 versus pressure for the first step of the reaction of Eu31 with PAR at 25.0 8C under diVerent reaction conditions ([Eu31] = 1 × 1023 mol dm23 and [NaClO4] = 0.1 mol dm23): h, pH 4.35, [PAR] = 1 × 1024 mol dm23, [acetate] = 0.05 mol dm23; s, pH 4.35, [PAR] = 5 × 1025 mol dm23, [acetate] = 0.05 mol dm23; ,, pH 2.66, [PAR] = 1 × 1024 mol dm23, [succinate] = 0.05 mol dm23.pressure dependence of the buVer, i.e. a lowering in pH due to an increase in Ka, which will slow down the reaction and show up as a positive DV‡ value. These DV‡ 1 values demonstrate that when other reaction conditions are held constant the ratedetermining step is the release of water molecules from the first co-ordination sphere. In succinate buVered solution an Id mechanism apparently prevails, whereas in acetate buVered solution a D mechanism controls the first step because of the “acetate eVect” mentioned above.Influence of buVer. Since weak organic acids are frequently used as buVers, their ability to complex lanthanide cations should not be ignored. The stability constant, log bn, of the lanthanide cation with the buVering anion increases with the pKa of the buVer acid. Acetate buVer is a typical example.In neutral solutions buVers are often amine compounds. Complexation by these buVers may be of less concern. Thus our measurements of buVer concentration dependence were made in MES, HEPPS and Tris buVers over the 6.15–8.1 pH range. In this pH range the pyridinium ion of the ligand is completely dissociated (even in acetate buVer as discussed above). The rate of the first step is pH-independent and is subject to specificand general-base catalysis so that k1 = k0 1 kOH[OH2] 1 kb[B].Fig. 5 shows typical plots of k1 as a function of buVer base concentration. The linear plot for the MES buVers at pH 6.15 is evidence of general-base catalysis by this buVer when [MES] < 0.1 mol dm23. The non-linear plot of k1 vs. [B2] at pH 7.55 with HEPPS buVer suggests that specific interaction with this buVer obscures any base catalysis. The same phenomenon was observed by Reeves 55 for the complex formation of NiIIsulfonated 1-(2-pyridylazo)-2-naphthol (b-PAN) in HEPES buVer [N9-(2-hydroxyethyl)-N-piperazineethanesulfonic acid].Reeves noted that absorption of b-PAN in a pH 6.89 HEPES buVer ([HEPES] = 0.01 mol dm23) in the absence of NiII has a significantly higher absorptivity than the curve for a MES buVer of the same pH and [B2]. The interaction is apparently between the buVer and the dye and not with the metal ion. Similar evidence for a specific dye–buVer interaction between piperazine buVer and a cyano keto azo dye ligand has been observed.60 In the linear plot (Fig. 5) for the Tris buVer k1 decreases with increasing Tris buVer concentration. This could be due to the multiple complexation equilibria between the buVer and Eu31.J. Chem. Soc., Dalton Trans., 1998, 3565–3576 3571 This kind of complexation between NiII and Tris has been reported.75 The log b1 for Eu(Tris)31 is ca. 2.5. For [Tris] = 0.005 mol dm23, [EU(Tris)31] would be 60% larger than [Eu31]. In addition, the formation of the hydrolysed europium species Eu(OH)n 32n, at such high pH causes a decrease in reactive europium concentration that cannot be neglected.DiVerent Ln31. The second order rate constants for the first step of the reaction of Ln31 with PAR, k1/dm3 mol21 s21, in logarithmic form, as a function of diVerent lanthanide ions, and versus reciprocal metal ionic radius in 0.05 mol dm23 MES buVer at pH 6.15, ambient pressure and 25.0 8C ([Ln31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23), are given in Fig. 6. For comparison, the complex-formation rate constants of aqueous Ln31 ions with some other ligands are also given in Fig. 6. The rates of complexation not only depend on the metal ion but also on the nature of the incoming ligand. The rate constants k1 are seen to reach a maximum around samarium for our Ln31–PAR system. The same trends were observed for the complexations of lanthanide ions by sulfate,22 acetate 23 and CyDTA.30 Other workers 12,13,76,77 have concluded that there is probably a change in co-ordination number (CN) occurring from Sm31 to Gd31.This may explain the observed change along the lanthanide series in the rate of almost all the complexations included in Fig. 6, as well as by sulfate and acetate. These results suggest a very easy substitution pathway for these ions, due to the almost identical energies of the octa- and nona-co-ordinated species. Moreover, the observation of an associative water-exchange 12 or complex-formation 13 mechanism on the octahydrated heavy Ln31 ions (the smallest of the series according to their ionic radii) leads to the presumption of a larger co-ordination number for the lighter elements, thus reinforcing the idea of a co-ordination number change in the middle of the series.The co-ordination numbers of the Ln31 ions in water have been the subject of substantial debate,78–80 but it is now established from neutron scattering,76,81 X-ray scattering,82 extended X-ray absorption fine structure (EXAFS),5 density 83 and spectrophotometric 6 studies that the lighter La31–Nd31 ions are predominantly nine-co-ordinate, Pm31–Gd31 exist in equilibria between eight- and nine-co-ordinate states, and the heavier Tb31–Lu31 are predominantly eight-co-ordinate.5,6,76,81–83 The systematic decrease in k1 for L = PAR, oxalate and murexide shown in Fig. 6, and the decreasing water exchange Fig. 5 Plot of the rate constant as a function of the concentration of buVer base in MES (s, pH 6.15), HEPPS (h, pH 7.55), and Tris (,, pH 8.10) for the first step of the reaction of aqueous Eu31 with PAR. rate,12,84 as the ionic radius decreases from Gd31 to Yb31, is consistent with increasing steric crowding, hindering the entry of the incoming ligand and dominating the variation of k1.The corresponding increase in surface charge density might be expected to provide an increased electrostatic attraction between the entering ligand and Ln31, and thereby accelerate the co-ordination rate, but this is evidently not important here.The k1 values shown in Fig. 6, and the other rate constants of aqueous Ln31 complexations by H2O,5,12 NO3 2,19,20 SO4 22,21,22 acetate,23 picolinic acid,24 methyl red,26 malonate,27 arsenazo III,13 and acyclic aminopolycarboxylates, such as EDTA and DTPA,18,29 vary by several orders of magnitude for the same metal ion. The ligands do not have the same steric properties and electronic charge and will have very diVerent outer-sphere parameters.However, the diVerence in the k1 values is probably due to various other factors as well, such as diVerences in experimental reaction conditions and measurement methods. It should also be recalled that the ligands in Fig. 6 are all weak bases, and competition may occur between protonation and metal bond formation on the ligand basic sites. This is exempli- fied by monoprotonated CyDTA complexation on the lanthanide ions where the complexation rate constants (ª3 dm3 mol21 s21 at 25.0 8C) are governed by the final deprotonation step of the ligand.In many studies 19–29 only one step was observed for the complexations of Ln31 by various multidentate ligands on a short timescale because of limitations of the kinetic techniques, such as ultrasonic relaxation and NMR. Subsequent slower reaction steps were not observed. An advantage of the stopped-flow technique is the relatively slower accessible timescales permitting a more complete kinetic picture of the complexation of aqueous Ln31 by multidentate ligands.Based on the information given above, Scheme 3 provides a reasonable description of the first step of the complexation of aqueous Eu31 by PAR in diVerent buVered solutions. Comparison between PAR and PAN. Owing to the low solubility of PAN in aqueous solution, a water–1,4-dioxane (3 : 1 v/v) mixed solvent was used to compare the kinetics of complexation of Eu31(aq) by PAN and PAR.The rate constant, k1 (see Fig. 6 Comparison of the complex-formation rate constants k1 (second order rate constant) for some reactions of Ln31 ions with different ligands in water, versus reciprocal metal ionic radius: e, L = anthranilate, see ref. 27; n, L = murexide, see refs. 25 and 26; h, L = oxalate, see ref. 29; ,, L = CyDTA (cyclohexane-1,2-diyldinitrilotetraacetate), see ref. 31; s, L = PAR, this work.3572 J.Chem. Soc., Dalton Trans., 1998, 3565–3576 Table 4), for the first step of the complexation of aqueous Eu31 by PAR is 12 times greater than for PAN under the same reaction conditions. Scheme 1 shows that PAR exists as the monoanion PAR2 at pH 6.15 in MES buVer; PAN is a neutral molecule at the same pH. The negative charge on PAR gives rise to a higher electron density on the nitrogen atom of the pyridine moiety through conjugation. Consequently, the first complexation step takes place at a faster rate for PAR than for PAN.In addition, the k1 value (71.5 ± 0.9 s21) for PAR obtained in the water–1,4-dioxane mixed solvent is smaller than in pure water (126 ± 2 s21) under the same reaction conditions. Cusumano61 also observed that rate constants for the complexation of nickel(II) by PAR and PAN in diVerent non-aqueous solvents depend strongly on the nature of the solvent. Comparison between Eu31 and UO2 21. Although the number of actinide elements is the same as the number of lanthanide elements, the availability of the former and their chemical characteristics have so far largely restricted the study of their ligand substitution mechanisms to dioxouranium(VI), the ionic form of uranium most amenable to such studies in solution.Commonly observed solvated species have the stoichiometry [UO2- (solvent)5]21, for example, [UO2(H2O)5]21, characterized by two oxo ligands bound in axial sites with average axial U–O distances in the range 1.71–1.75 Å.Five water molecules occupying the equatorial plane have an average equatorial distance of 2.45 Å (see structure below). In solution the two oxo atoms undergo slow exchange, whereas the equatorial solvent molecules experience fast exchange. Thus the [UO2(solvent)5]21 system oVers the opportunity to study solvent exchange in a single plane of a solvated metal ion.2,85–87 Kinetic data of the complexations of UO2(aq)21 and Eu31(aq) by PAR in 0.1 mol dm23 acetate buVer at pH 4.35 are summarized in Table 5.The k1 value for the complexation of Scheme 3 + N N N OH O H H N N N OH O H H+ PAR PAR N N N OH O H [Eu(H2O)8(A)]x+ [Eu(H2O)7(A)]x+ + H2O k1 k–1 + –H+ pKa1 [H2O)7(A)Eu]x+ k A = H2O, x = 3 A = acetate, x = 2 O U O H2O H2O OH2 OH2 OH2 2+ UO2(H2O)5 2+ Table 4 Rate constants for the three steps of the complexation of Eu31(aq) by PAR or PAN in MES buVered, water–1,4-dioxane (3 : 1 v/v) at pH = 6.15, ambient pressure and 25.0 8C ([Eu3] = 1 × 1023 mol dm23, [L] = 1 × 1024 mol dm23 (L = PAR or PAN), [MES] = 0.05 mol dm23 and [NaClO4] = 0.1 mol dm23) L PAR PAN lmax/nm 502 532 k1/s21 71.6 ± 0.90 5.89 ± 0.30 10k2/s21 1.85 ± 0.12 4.58 ± 0.12 102k3/s21 7.01 ± 0.73 1.01 ± 0.10 UO2 21 by PAR is about the same as that of the Eu31–PAR system.This suggests that the first step of the UO2 21 complexation by PAR follows the same mechanism proposed for the lanthanides (see Schemes 2 and 3), even though there are two oxo ligands bound in the axial sites on UO2 21.Fux et al.87 found that the rate constants of the observed first step of the complexation of UO2 21 by 18-crown-6 and diazo-18-crown-6 in propylene carbonate are 930 ± 50 and 23 ± 1 s21, respectively. The mechanism is very similar to our mechanism proposed in Scheme 2. Comparing our rate constant k1 with those found by Fux et al.87 for reactions with UO2 21, we found that: k1(18- crown-6, in propylene carbonate, 930 s21) > k1(PAR, in water, 46.7 s21) > k1(diazo-18-crown-6, in propylene carbonate, 23 s21). Our k1 value is much closer to that for the complexation of UO2 21 by the nitrogen atom in diazo-18-crown-6, which means that the complexation of UO2 21 by an oxygen donor is faster and stronger than that by a nitrogen donor.This is attributed to the “hard acid” character of UO2 21. Kinetic studies of the second step In a typical kinetic trace shown in Fig. 1(b) for the observed second step the absorbance at 502 nm decreases with increasing time with a half-life of ca. 500 ms. Mochizuki et al.88 observed a similar phenomenon in the complexation of Co21 and Ni21 by PAN in aqueous 1,4-dioxane. They proposed that the absorbance decrease is caused by the formation of the insoluble neutral intermediate [CoII(PAN2)2]0, and the slowest step, namely, the absorbance increase with increasing time is due to the formation of the soluble final product [CoIII- (PAN2)2]1. If the same process holds true for our Ln31–PAR (or PAN) system, the intermediates should be [LnII(PAR22)]0 or [LnII(PAR2)2]0, and [LnII(PAN2)2]0, respectively.However, if it is kept in mind that for our kinetic studies aqueous Ln31 ions were always in excess concentration and only samarium, europium and ytterbium have 12 oxidation states,70 it is obvious that the suggestion by Mochizuki et al.88 cannot apply to our Ln31–PAR (or PAN) system. We propose that the formation of the “hydrazone–Ln31 chelate” intermediate (see the structure below) is more reasonable because it destroys the whole conjugated structure which is the basis of many azo dyes.It therefore becomes interesting to explore whether the formation of a “hydrazone–Mn1 chelate” intermediate is a common phenomenon during multi-step complexations of metal cations by many azo dyes. Eu31 Concentration dependence. The rate constants for the second step of the reaction of Eu31 with PAR, k2, as a function of Eu31 concentration, either in a pH 2.08 succinate buVer or a pH 4.35 acetate buVer, are summarized in Table 1.One sees that k2 is independent of Eu31 concentration either in succinate N N N O OH(O–) H [(H2O)5(A)Eu]x+ Hydrogen bonding H2O "Hydrazone-Eu3+ chelate" Table 5 Rate constants for the three steps of the complexations of UO2 21(aq) and Eu31(aq) by PAR in acetate buVer at pH 4.35, ambient pressure and 25.0 8C ([M] = 1 × 1023 mol dm23, M = UO2 21 or Eu31; [PAR] = 1 × 1024 mol dm23, [acetate] = 0.1 mol dm23 and [NaClO4] = 0.1 mol dm23) M UO2 21 Eu31 1021k1/s21 4.67 ± 0.10 5.02 ± 0.18 k2/s21 0.94 ± 0.40 1.00 ± 0.03 102k3/s21 0.74 ± 0.50 1.85 ± 0.11J.Chem. Soc., Dalton Trans., 1998, 3565–3576 3573 or acetate buVers which suggests that “intramolecular ring closure” must be rate-determining. pH Dependence. Measurements made in acetate buVer solutions covered the pH range 3.61–5.40. All runs were made at a constant ionic strength of [NaClO4] = 0.1 mol dm23 and a constant (0.05 mol dm23) concentration of the basic component of the buVer.The observed rate constants as a function of pH in acetate buVered solution at ambient pressure and 25.0 8C are shown in Table 6. The k2 values are independent of pH. This result is consistent with the formation of a “hydrazone–Eu31 chelate” intermediate proposed above which does not involve any deprotonation or acid–base equilibrium. Pressure dependence. The pressure dependence for the second step of the reaction of Eu31 with PAR was studied in 0.05 mol dm23 acetate buVer at 25.0 8C (see Table 3).The plots of ln k2 versus pressure yield a DV‡ 2 value 215.9 ± 0.6 cm3 mol21. The negative sign suggests that the rate-determining process of the second step has an associative character. This result is also consistent with the intermediate formation of the “hydrazone–Eu31 chelate” proposed above, which will involve a ring compact transition state.Influence of buVer. The k2 values as a function of buVer concentration in MES (pH 6.15), HEPPS (pH 7.55) and Tris (pH 8.10) buVers at ambient pressure and 25.0 8C over the concentration range of 0.01–0.10 mol dm23 are given in SUP 57431. In all three buVers the rate constants are independent of buVer concentration. Absence of a buVer eVect in this step suggests that the mechanism does not involve complex formation between the buVer and Eu31 species. The k2 values obtained from MES and HEPPS are very similar.On the other hand, the values obtained with Tris buVer (higher pH) are smaller. The diVerence is probably caused by a decrease in concentration of the reactive Eu31 species at such a high pH (8.10) in the Tris buVer due to hydrolysis to form Eu(OH)n 3 2 n as mentioned before. Comparison between PAR and PAN. Measurements were made under the same reaction conditions as for the first step except for the timescale. Table 4 indicates that the k2 value (0.458 s21) for the complexation of Eu31 by PAN is larger than that for PAR (0.185 s21).The extra benzene ring of the Eu31– PAN intermediate may make it more stable than the Eu31–PAR intermediate because of further conjugation. N N N O O– H Eu H2O N N N O H Eu H2O Eu3+-PAR hydrazone chelate Eu3+-PAN hydrazone chelate Table 6 Rate constants as a function of pH for the second step of the reaction of Eu(aq)31 with PAR in acetate buVer ([acetate] = 0.05 mol dm23) solution at ambient pressure and 25.0 8C ([Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23) pH 3.62 4.14 4.35 4.58 5.02 5.40 k2/s21 1.01 ± 0.04 1.03 ± 0.03 1.00 ± 0.03 0.99 ± 0.05 0.96 ± 0.04 1.02 ± 0.05 Comparison between Eu31 and UO2 21.Table 5 shows that the k2 value for the complexation of UO2 21 (0.94 s21) by PAR is about the same as that of the Eu31–PAR system (1.00 s21). This suggests that the second step of the UO2 21 complexation by PAR follows the same pathway as for the lanthanides.Desolvation and formation of the “UO2 21–PAN hydrazone intermediate” must be completed within the equatorial plane. The two axial U]] O bonds do not aVect the complexing process. Again, it is interesting to compare our k2 value for the complexation of UO2 21 by PAR with observed rate constants for the complexation of uranyl ion by 18-crown-6 or diazo-18-crown-6.86 Our k2 value is close to that of the UO2 21–diazo-18-crown-6 system (1.3 s21) and smaller than that of the UO2 21–18-crown-6 system (18 s21).Fux et al.87 proposed that the rate-determining rearrangement reaction in the UO2L “external” complex consists of metal and ligand cavity desolvations with a simultaneous rotation of the uranyl group to give the UO2L “exclusive” complex. DiVerent Ln31. Measurements were carried out under the same reaction conditions as for the first step except for the timescale. All the k2 values for the complexation of the lanthanides from Sm31 to Lu31 by PAR are close to 2.0 s21, and parallel the stability constants for Ln31–PAR2.The second step was not observed for the complexation of La31, Ce31, Pr31 and Nd31 by PAR. Our observations here are consistent with the work by Merbach and co-workers.7–12,76,80,84,85 Based on the above, the second step of the complexation of aqueous Eu31 by PAR is adequately represented by Scheme 4. Kinetic studies of the third step pH and Eu31 Concentration dependence.pH Dependence studies were carried out in succinate, acetate, imidazole, MES, HEPPS and Tris buVered solutions covering the pH range 1.80–8.80. All runs were made at a constant ionic strength of [NaClO4] = 0.1 mol dm23 and a constant 0.05 mol dm23 concentration of the basic component of the buVer. The observed rate constants as a function of pH in all buVered solutions at ambient pressure and 25.0 8C are given in Table 7. Fig. 7 shows that a plot of k3 versus pH has a typical “titration curve” from pH 4 to 7.This demonstrates that there must be a deprotonation Fig. 7 Plot of k3 versus pH for the third step of the reaction of Eu31 with PAR at ambient pressure and 25.0 8C in diVerent buVer solutions ([Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23, [NaClO4] = 0.1 mol dm23 and [buVer] = 0.05 mol dm23). BuVers: s, succinate; h, acetate; n, HEPPS; , imidazole; e, MES; ,, Tris.3574 J. Chem. Soc., Dalton Trans., 1998, 3565–3576 Scheme 4 N N N O OH(O–) H [(H2O)6(A)Eu]x+ Hydrogen bonding N N N O OH(O–) H [(H2O)5(A)Eu]x+ H2O N N N O OH(O–) H [(H2O)7(A)Eu]x+ Hydrogen bonding N N N O OH(O–) H [Eu(H2O)5(A)x+ k2 slow fast –H2O –H2O fast 'Hydrazone-Eu3+" intermediate pre-equilibrium prior to the rate -determining step for the third step of the complexation of aqueous Eu31 by PAR.The preequilibrium should be the deprotonation of o-hydroxyl with the hydrogen bonding shown. An approximate value of the pKa for the pre-equilibrium, i.e. 5.4, can be deduced from the data of Table 7/Fig. 7. Rate constants k3 for the third step of the reaction of Eu31 with PAR as a function of Eu31 concentration either in a pH 2.08 succinate buVer or a pH 4.35 acetate buVer are given in Table 1. They are seen to be independent of the Eu31 concentration either in succinate or acetate buVers, which means that an “intramolecular rearrangement” or “intramolecular ring closure” is the rate-determining step. Pressure dependence.The pressure dependence for the third step of the reaction of Eu31 with PAR was studied either in 0.05 mol dm23 acetate buVer at pH 4.35 or in 0.05 mol dm23 imidazole buVer (pH 7.10) at 25.0 8C. The k3 values as a function of Table 7 Rate constants as a function of pH for the third step of the reaction of aqueous Eu31 with PAR in diVerent buVer solutions at ambient pressure and 25.0 8C ([Eu31] = 1 × 1023 mol dm23, [PAR] = 1 × 1024 mol dm23 and [NaClO4] = 0.1 mol dm23) BuVer Succinate Acetate MES Imidazole HEPPS Tris pH 2.65 3.31 3.61 4.14 4.35 4.58 5.02 5.40 5.40 5.70 5.95 6.15 6.21 6.50 6.81 7.10 7.55 7.20 7.60 8.00 8.10 8.40 8.80 102k3/s21 0.37 ± 0.02 0.64 ± 0.03 0.68 ± 0.03 1.54 ± 0.09 1.85 ± 0.11 2.64 ± 0.18 5.74 ± 0.27 14.0 ± 0.9 15.0 ± 1.2 24.0 ± 1.2 26.0 ± 0.2 27.8 ± 2.2 28.2 ± 3.0 28.4 ± 1.3 28.6 ± 2.4 29.4 ± 2.3 30.6 ± 2.7 30.0 ± 1.5 29.6 ± 2.4 30.4 ± 1.5 29.8 ± 1.7 30.6 ± 2.6 30.6 ± 3.0 pressure are summarized in Table 3.The plots of ln k3 versus pressure indicate that the DV‡ 3 value in 0.05 mol dm23 acetate buVer at pH 4.35 is 211.2 ± 0.9 cm3 mol21 and the DV‡ 3 value in 0.05 mol dm23 imidazole buVer at pH 7.10 is 215.9 ± 0.8 cm3 mol21.These DV‡ values suggest that the rate-determining process in the third step of the complexation, like the second step described above, is dominated by an associative character and a compact transition state. Influence of buVer. The k3 values as a function of buVer concentrations in MES (pH 6.15), HEPPS (pH 7.55) and Tris (pH 8.10) buVered solutions at ambient pressure and 25.0 8C over the concentration range of 0.01–0.10 mol dm23 are given in SUP 57431. They show that in HEPPS and Tris buVers the observed rate constants for the third step of the complexation are independent of the concentrations of the buVers used.The absence of a buVer eVect in the third step suggests that the mechanism does not involve complex formation between the buVers and “hydrazone–Eu31 chelate” or the following “azo– Eu31, pseudo-phenanthroline style” chelate species.The k3 values obtained in both HEPPS and Tris are very close. However, the k3 values obtained from MES buVer (lower pH) decrease with increasing concentration of the MES buVer. We do not know the cause of this diVerence. Correlating with the pH-dependent studies shown in Fig. 7, we found that in MES buVered solution at pH 6.15 the k3 value does not reach the saturation value. Probably, the higher the concentration of the MES buVer, the more diYcult is the deprotonation of the o-hydroxyl because of intramolecular hydrogen bonding, and therefore the smaller are the k3 values.DiVerent Ln31. Kinetic measurements were performed under the same reaction conditions as for the first and the second steps except for the timescale. All the k3 values for the complexation of the lanthanides by PAR are close to 0.25 s21. Thus the third step of the complexation of aqueous Ln31 by PAR is not aVected by the nature of the lanthanide. Comparison between PAR and PAN.Table 4 indicates that the k3 value (0.01 s21) for the complexation of Eu31 by PAN is smaller than that by PAR (0.07 s21). The two negative charges due to deprotonation of both the o- and p-hydroxyl groups of N N N O O– H [Eu(H2O)5(A)]x+ N N N –O O– [Eu(H2O)6(A)]x+ + H+J. Chem. Soc., Dalton Trans., 1998, 3565–3576 3575 PAR at pH 6.15 in MES buVer make the co-ordination by the o-oxyl anion of PAR22 much easier than by PAN2 which has only one negative charge as a result of deprotonation.Therefore, the third step of the complexation of Eu31 by PAR is faster than that of PAN. Comparison between Eu31 and UO2 21. Table 5 shows that the k3 value for the complexation of UO2 21 (0.0074 s21) by PAR is smaller than that of the Eu31–PAR system (0.0185 s21). This means that the third step for UO2 21 complexation by PAR is slowed down by the two axial U]] O bonds.In order to complete the slowest step, namely, the co-ordination of the UO2 21–PAR intermediate from the second step by the o-oxyl anion of PAR, the two axial U]] O bonds must rotate to some degree. The formation of the transition state cannot be completed within the equatorial plane. The k3 value of the UO2 21–PAR system is also smaller than that in the third observed step of the complexation of UO2 21 by either 18-crown-6 (0.022 s21) or by diazo-18-crown-6 (0.283 s21).87 On the basis of the above kinetic results for the third step of the complexation of aqueous Eu31 by PAR we propose the mechanism depicted in Scheme 5.Acknowledgements Financial support by the Department of Energy, OYce of Basic Energy Sciences (Y. S. and E. M. E.) and by the Volkswagen Foundation (R. v. E.) is gratefully acknowledged. References 1 S. F. Lincoln, Adv. Inorg. Bioinorg. Mech., 1983, 4, 217. 2 S. F. Lincoln and A. E. Merbach, in Advances in Inorganic Chemistry, ed. A.G. Sykes, Academic Press, San Diego, 1995, vol. 42. 3 L. Helm and A. E. Merbach, Eur. J. Solid State Inorg. Chem., 1991, 28, 245. 4 A. Habenschuss and F. H. Spedding, J. Chem. Phys., 1980, 73, 442. 5 T. Yamaguchi, M. Nomura, H. 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