Complex-formation titrations equilibrium

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. 

As has been mentioned previously, the approach to equilibrium can often be slow for macrocyclic complex formation indeed, equilibrium may take days, weeks or even months to be established. This may give rise to experimental difficulties in conventional titration procedures. Under such circumstances, it is usually necessary to carry out batch determinations in which a number of solutions, corresponding to successive titrations points, are prepared and equilibrated in sealed flasks. The approach to equilibrium of each solution can then be monitored at will. 

Calorimetric titrations show that Al2Br0 forms 1 1 AlBrj adducts with a-bromo-,a,a-dibromo-, and a,a,a-tribromo-acetophenone and RCOPh (R = Me, Pr or PhCH2). Heats of complex formation and equilibrium constants were determined. 

Complex stability constants are most often determined by pH-potentiometric titration of the ligand in the presence and absence of the metal ion.100 This method works well when equilibrium is reached rapidly (within a few minutes), which is usually the case for linear ligands. For macrocyclic compounds, such as DOTA and its derivatives, complex formation is very slow, especially for low pH values where the formation is not complete, therefore a batch method is... 

Complexes, see also specific type in solution, structures, see X-ray diffraction n-Complexes, 4 178-184 Complex formation constant, outersphere, 43 46, 55 electrovalent interaction in, 3 269-270 Compressibility coefficient of activation, 42 9 Comproportionation constants, class II mixed-valence complexes, 41 290-292 Comproportionation equilibrium, 41 280-281 Compton effect, 3 172 Conantokins, calcium binding, 46 470-471 Concanavalin A, 36 61, 46 308 Concensus motif, 47 451 Concentration-proportional titrations of poly-metalates, 19 250, 251, 254 Condensation... 

In textbooks of computational chemistry you will invariably find examples calculating the pH = - lg [H+]/(mol/l)> in weak acid - strong base or strong acid - weak base solutions. Indeed, these examples are important in the study of acids, bases and of complex formation, as well as for calculating titration curves. Following (ref. 24) we consider here the aquous solution that contains a weak tribasic acid H A and its sodium salts NaH, Na HA and Na A in known initial concentrations. The dissociation reactions and equilibrium relations are given as follows. 

The method of continuous variation can be carried out with many separate solutions, as in Table 19-1. However, a titration is more sensible. Figure 19-9a shows a titration of EDTA with Cu2+. In Figure 19-9b, the abscissa has been transformed into mole fraction of Cu2+(= [moles of Cu2+]/[moles of Cu2+ + moles of EDTA]) instead of volume of Cu2+. The sharp maximum at a mole fraction of 0.5 indicates formation of a 1 1 complex. If the equilibrium constant is not large, the maximum is more curved than in Figure 19-9b. The curvature can be used to estimate the equilibrium constant.7... 

EDTA (ethylenediaminetetraacetic acid) (H02CCH2)2NCH2CH2N-(CH2C02H)2, the most widely used reagent for complexometric titrations. It forms 1 1 complexes with virtually all cations with a charge of 2 or more, effective formation constant Equilibrium constant for formation of a complex under a particular stated set of conditions, such as pH, ionic strength, and concentration of auxiliary complexing species. Also called conditional formation constant. 

In the case of the purely aliphatic ligand 2,2,6,6-tetrakis(amino-methyl)-4-azaheptane (12), complex formation with copper appears to proceed in two steps, as elucidated by titration experiments with the fully protonated ligand (12 5 HC1). Three and two protons from (Hr,12) + are sequentially abstracted, and the predominant species after full deprotonation appears to be a dinuclear complex in which two copper(II) ions are coordinated, each in square planar fashion, by the l,3-diaminoprop-2-yl units of two molecules of pentaamine ligand, thus forming a macrocyclic complex of composition [Cu2(12)2]4+ (23). The UV/vis spectral data show an interesting solvent dependence, suggesting an equilibrium between [Cu2(12)2]4 + and two equivalents of mononuclear complex [Cu(12)]2+ under suitable conditions. ESR spectroscopic data are also compatible with the formulation of a dinuclear species. Further addition of base to an aqueous solution of [Cu2(12)2]4+ gives the mononuclear hydroxo complex [(12)Cu(OH)]+, as inferred from the UV/vis spectroscopic data. 

The overall effect of complex formation is to remove a hydrated metal ion from the mixture of ions in solution by displacing the equilibrium in favour of the complex, cf. the similar process in the formation of water in acid-base titrations and precipitation reactions. 

We will use standard electrode potentials throughout the rest of this text to calculate cell potentials and equilibrium constants for redox reactions as well as to calculate data for redox titration curves. You should be aware that such calculations sometimes lead to results that are significantly different from those you would obtain in the laboratory. There are two main sources of these differences (1) the necessity of using concentrations in place of activities in the Nernst equation and (2) failure to take into account other equilibria such as dissociation, association, complex formation, and solvolysis. Measurement of electrode potentials can allow us to investigate these equilibria and determine their equilibrium constants, however. 

Complex formation of the alkali ions with murexide in methanol was studied quantitatively by spectrophotometric titration with Li+, Na+, and K+. (For Rb+ and Cs+ only qualitative measurements could be obtained since these complexes tend to precipitate). Fig. 8 shows the shift of the absorption maximum upon titration with Na+. The well defined isosbestic point is a good indication for a simple 1 1 complexation equilibrium. In so much as the spectral shift (upon complexation) is a criterion of the strength of the complexes. Fig. 9 indicates that the absolute complex stability parallels monotonically the sequence of ionic sizes. (Both /lAmax and Ae are largest for the smallest ion). In the alkali ion series Li+ forms the strongest and Cs+ the weakest complexes. This monotonic size dependence of the charge density is also expressed in the energy values for the desolvation (—zlHuydr. for Li+= 120 kcal and for Cs+ 60 kcal) (77). 

Important solution reactions are well known from the study of quantitative analysis in analytical chemistry. These include acid-base reactions, redox reactions, and complex formation reactions. Often the reaction is so fast that the system is considered to come instantaneously to equilibrium, for example, in the acid-base reaction involved in a titration. In fact, any of these reactions has a finite rate whose kinetics can be determined using modern experimental techniques. 

The heat that is measured at each injection step after reaching equilibrium is proportional to the increment of complex formation at each step (Figure 11). As the reaction in the cell approaches saturation, the increment diminishes until eventually only the heat of dilution is measured (used for baseline correction in data analysis). At the end of the titration, an isotherm is constructed by plotting the net heat after equilibrium (peak area) versus the calculated molar ratio of the two reactants in the cell at the end of each titration step. The equilibrium constant K, the reaction stoichiometry, and the enthalpy AH can then be determined by fitting an appropriate model to the isotherm (see Figure 11). 

If auxiliary chemical reactions are involved in concentration determinations using ion-selective electrodes (end point titration, standard addition or subtraction, indirect procedures), extreme caution is required with variable sample temperatures. This is because in addition to the electrochemical effects discussed, purely chemical phenomena may become problematic (temperature dependence of equilibrium constants, solubility products, complex formation constants and activity coefficients). With the low sample flow rates commonly encountered (a few ml/minute), thermostating the solution and sample cell with the help of a quickly responding proportional controller (Orion, Series 1,000) presents no problem. 

The kinetics of reactions of NO with ferri- and ferro-heme proteins and models under ambient conditions have been studied by time-resolved spectroscopic techniques. Representative results are summarized in Table I (22-28). Equilibrium constants determined for the formation of nitrosyl complexes of met-myoglobin (metMb), ferri-cytochrome-c (Cyt111) and catalase (Cat) are in reasonable agreement when measured both by flash photolysis techniques (K= konlkQff) and by spectroscopic titration in aqueous media (22). Table I summarizes the several orders of magnitude range of kon and kQs values obtained for ferri- and ferro-heme proteins. Many k0f[ values were too small to determine by flash photolysis methods and were determined by other means. The small values of kQ result in very large equilibrium constants K for the... 

You can see from the example that a metal-EDTA complex becomes less stable at lower pH. For a titration reaction to be effective, it must go to completion (say, 99.9%), which means that the equilibrium constant is large—the analyte and titrant are essentially completely reacted at the equivalence point. Figure 12-9 shows how pH affects the titration of Ca2+ with EDTA. Below pH 8, the end point is not sharp enough to allow accurate determination. The conditional formation constant for CaY2" is just too small for complete reaction at low pH. 

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