Potentiometric titrations stability equilibria from

Complex stability constants are often determined by pH-potentiometric titration of the ligand in the presence and absence of the metal ion (129). This method works well when equilibrium is reached rapidly (within few minutes), which is usually the case for linear ligands. For macrocyclic compounds, such as DOTA and its derivatives, complex formation is slow, especially at pH-s where the formation is not yet complete, therefore a batch method is used instead of direct titration (130,131). A few representative examples of stability constant data mainly collected from Ref. (132), on MRI relevant Gdm complexes are presented in Table IV. 

The pAj value for anhydrous quinazoline obtained using a rapid reaction apparatus is 1.95 at 20°C, as compared to the equilibrium pAf, value of 3.51 and to the pA, value of 7.77 for the hydrated species. The equilibrium pK value obtained by potentiometric titration or by spectrophotometry is a composite value arising from equilibrium between a stable hydrated cation and a stable anhydrous neutral species. Quinazoline in aqueous solution is a much stronger base (pAT = 3.51) than pyrimidine (pAT = 1.31) because its cation is stabilized as a covalent 3,4-hydrate. Most quinazoline derivatives in which the cation is capable of hydration are stronger bases than the corresponding pyrimidines. Substituents at the 4-position interfere with the covalent addition of water making the pK. values of 4-substituted quinazolines comparable with the pAf, values of the corresponding 4-substitiited pyrimidines (e.g., 4-methylquinazoline has pK 2.52, as compared to pK of 2.0 for 4-methylpyrimidine). The pAT values of several substituted quinazolines have been compiled. ... 

The following entry defines the commonly used stability constants (stepwise, overall, conditional, association, dissociation, and pK) and relates the values to a rigorous thermodynamic definition of equilibrium constants. In addition, the article briefly outlines experimental techniques (potentiometric titration, spectroscopic methods involving ultraviolet/visible, infrared, Raman, fluorescence. and nuclear magnetic resonance spectroscopy), together with the numerical methods and computer programs that can be used to derive stability constants from such experimental data. 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

The interpretation of the titration data given by the authors starts from the premise that Zr(OH)2 is the main hydrolysis species. Moreover, as in [99VEY], the implicit assumption is made that all Zr is bound to carbonate complexes, i.e. a very high formation constant is assumed a priori. Therefore, the stability constant ( "4 = 8.0 x 10 °) derived by [80MAL/CHU] for the formation reaction Zr(C03)j" + CO " = Zr(C03)4, had to be rejected. We re-interpreted the potentiometric data on the base of full equilibrium calculations and using the Zr hydroxo, chloride and sulphate stability constants selected in this review (see below). 

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