Metal-ligand titration curve

The formation of metal complexes is indicated by the considerable shift along the volume axis of the metal-ligand titration curve as compared to the ligand titration curve. The study assumes a negligible extent of hydrolysis of M(III), and the formation of polynuclear... 

The calculation that we just did was oversimplified because we neglected any other chemistry of such as formation of MOH, M(OH)2(a ), M(0H )2(5), and M(0H)3. These species decrease the concentration of available and decrease the sharpness of the titration curve. Mg " is normally titrated in ammonia buffer at pH 10 in which Mg(NH3) also is present. The accurate calculation of metal-EDTA titration curves requires full knowledge of the chemistry of the metal with water and any other ligands present in the solution. 

Figure 12 [115] shows a series of complex formation titration curves, each of which represents a metal ion-ligand reaction that has an overall equilibrium constant of 1020. Curve A is associated with a reaction in which Mz+ with a coordination number of 4 reacts with a tetradentate ligand to form an ML type complex. Curve B relates to a reaction in which Mz+ reacts with bidentate ligands in two steps, first to give ML complexes, and finally close to 100% ML2 complexes in the final stages of the titration. The formation constant for the first step is 1012, and for the second 108. Curve C refers to a unidentate ligand that forms a series of complexes, ML, ML2. .. as the titration proceeds, until ultimately virtually 100% of Mz+ is in the ML4 complex form. The successive formation constants are 108 for ML, 106 for ML2, 104 for ML3, and 102 for ML4 complexes. 

Example 2.4 Shift in the Alkali metric Titration Curve of an Oxide in the Presence of an Adsorbable Metal Ion or Ligand... 

As we have seen, the net surface charge of a hydrous oxide surface is established by proton transfer reactions and the surface complexation (specific sorption) of metal ions and ligands. As Fig. 3.5 illustrates, the titration curve for a hydrous oxide dispersion in the presence of a coordinatable cation is shifted towards lower pH values (because protons are released as consequence of metal ion binding, S-OH + Me2+ SOMe+ + H+) in such a way as to lower the pH of zero proton condition at the surface. 

In Fig. 3.5 we illustrated generally that an alkalimetric or acidimetric titration curve of a hydrous oxide dispersion becomes displaced by the adsorption of a metal ion or, - in opposite direction - by the adsorption of an anion (ligand). 

Effect of ligands and metal ions on surface protonation of a hydrous oxide. Specific Adsorption of cations and anions is accompanied by a displacement of alkalimetric and acidimetric titration curve (see Figs. 2.10 and 3.5). This reflects a change in surface protonation as a consequence of adsorption. This is illustrated by two examples ... 

Fig. 10. NMRD curves of free Gd (O) and its complexes with calix[4]arenes2(0) (at the maximum of the relaxivity titration curve), 3 ( ) (at the maximum of the relaxivity titration curve), 4 (A) (ligand to metal ratio = 2) in anhydrous acetonitrile at 25° C (63,66,67).

To obtain information on the coupling of the various intermediates one has to analyze the relationship between the corresponding titration curves. Scheme 3.4-3 shows typical steady-state curves for the (1) stepwise twofold association of ligand L with metal complex M, (2) association of L with two metal complexes M and N at equilibrium and (3) association of L to two metal complexes M and N being not at equilibrium (kinetically separated). From these three types of coupling most of the partial maps can be easily interpreted. 

The greater the effective formation constant, the sharper is the EDTA titration curve. Addition of auxiliary complexing agents, which compete with EDTA for the metal ion and thereby limit the sharpness of the titration curve, is often necessary to keep the metal in solution. Calculations for a solution containing EDTA and an auxiliary complexing agent utilize the conditional formation constant K" = aM aY4- Kt, where aM is the fraction of free metal ion not complexed by the auxiliary ligand. 

A difference plot, also called a Bjerrum plot, is an excellent means to extract metal-ligand formation constants or acid dissociation constants from titration data obtained with electrodes. We will apply the difference plot to an acid-base titration curve. 

Figure 1 Titration curves for H,edta. Curve 1 H4edta curve 2 H4edta + lithium curve 3 H4edta + magnesium curve 4 H4edta + copper. The quantity a is in moles of strong base per mole H4edta. Total ligand and metal concentration ...

In the use of potentiometry for the evaluation of stability constants for complex ions, the expressions can become extremely complicated if multiequilibria are present. For a simple one-to-one complex a direct potentiometric titration curve again provides die most satisfactory route to an accurate evaluation of the constant. The curve looks similar to that for an acid-base titration, and the appropriate point to pick is the half-equivalence point. If the complex is extremely stable, then die amount of free metal ion at this point on die dtration curve (ligand titrated with metal ion) is sufficiently low that it can be disregarded. If not, it must be handled in a way similar to the first point on the titration curve for phosphoric acid. Assuming that it is a stable complex, at the first half-equivalence point the concentration of complexed metal ion will be equivalent to that of the free ligand. The potential will give a direct measure of the free metal ion and allow the stability constant for the complex to be evaluated at the half-equivalence point ... 

The ligand interchange reaction between metal S-diketonates and edta was utihzed to establish the amount of metal -diketonate by conductometry in DMF or DMSO. The -diketonates studied were of Co(ll), Cu(ll), Mn(ll), Fe(III) and Cr(III). The combination ratios of the metal /3-diketonate with edta were 4 1, 2 1 and 1 1. Presence of less than 1% H2O, inorganic acids or organic solvents did not affect the inflection points in the conductometric titration curves . 

In the case of a polyprotic acid for which the individual ionizations are well separated (ideally, by at least 3 log units), values for the individual constants can be calculated from data points in the appropriate regions of the titration curve. If the individual ionizations overlap, the Bjerrum fi (n-bar) method may be used. This mathematical approach was introduced by Bjerrum for the calculation of stability constants of metal-ligand complexes, but it can also be applied to the determination of proton-ligand equilibrium constants. 

Acid-base titrations of humic substances reflect the nature of the different p/Tfl values, hence the smeared out appearance of these titration curves. While no unique equivalence points are observed, different p regions of carboxylic and phenolic groups can be discerned. Similarly, in metal titrations, metal ions are bound differently by the different ligand groups. The extent of metal-ion binding depends on the ratio of metal ions to humic substances, [M7]/ [L7-]. In titrating humic or fiilvic acids with metal ions (at fixed pH), the metal is bound first to the highest affinity sites. 

F ure 9.21. The net charge at the hydrous oxide surface is established by the proton balance (adsorption of or OH and their complexes) at the interface and specifically bound cations or anions. This charge can be determined from an alkalimetric-acidi-metric titration curve and from a measurement of the extent of adsorption of specifically adsort)ed ions. Specifically adsorbed cations (anions) increase (decrease) the pH of the point of zero charge (pzc) or the isoelectric point but lower (raise) the pH of the zero net proton condition (pznpc). Addition of a ligand, at constant pH, increases surface protonation while the addition of a metal ion (i.e., specifically adsorbed) lowers surface protonation. (Adapted from Hohl et al., 1980.)... 

Figure 5.4. Titration curve of one ligand complexing the metal M (a) with a 1 1 stoichiometric ratio (b) plot of the transformed titration data.

The labile metal concentration, [M ], is evaluated during titration by the peak current, ip, obtained after each addition. Sensitivity, S, represents the slope of the titration curve measured at high values of titrant added, where organic ligands have been saturated. The titration curve becomes thus a straight line (Figure 5.4a) ... 

Substituting the equation (24) in the metal mass balance, equation (20), for all the i ligands, the theoretical equation of the titration curve is obtained (104) ... 

Figure 5.5. Plot of the transformed titration curve of one sample containing two ligands complexing the metal M.

Figure 17-1 Titration curves for complexometric titrations. Titration of 60.0 raL of a. solution that is 0.020 M in metal M with (A) a 0.020 M solution of the tetradentate ligand D to give MD as the product (B) a 0.040 M. solution of the bidentate ligand B to give MB2 and (C) a 0.080 M solution of the unidentate ligand A to give MA4. The overall formation constant for each product is I O ".

Titration curves of HS fluorescence quenching versus concentration of added metal quencher have been used to obtain the CC values of HS ligands and the stability constants of HS-metal complexes (Saar and Weber, 1980, 1982 Underdown et al., 1981 Ryan et al., 1983 Weber, 1983 Dobbs et al., 1989 Grimm et al., 1991 Hernandez et al., 2006 Plaza et al., 2005, 2006). Two fluorescence techniques, lanthanide ion probe spectroscopy (LIPS) and fluorescence quenching of HSs by Cu-+, have been used in conjunction with a continuous distribution model to study metal-HS complexation (Susetyo et al., 1991). In the LIPS technique, the HS samples are titrated by Eu-+ ions, and the titration plot of the ratio of the intensities of two emission lines of Eu + is used to estimate the amount of bound and free species of the probe ion. In the other technique, titration curves of fluorescence intensity quenched by Cu versus the logarithm of total added Cu2+ are used. 

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