Complex free ligand concentration

Organic complexes with ligands and free ligand concentration... 

A decrease in coordination number of Ln3+ complexes results, in general, in a decrease in lability. Solvent exchange rates measured on [Ln(TMU)e]3+ are much slower than corresponding values measured on [Ln(DMF)8]3+ (56,257-259) (Table XIX (56,257-259)). The exchange rates, measured in an inert diluent, were found to be independent of free ligand concentration, consistent with a d-activation mode. 

Exchange of complex cations. Complexation of transition metal cations with uncharged ligands such as with amines and with amino acids results in a selectivity enhancement compared to the selectivity of the aqueous metal cation (27, 65-72). Fig. 3 shows an example for the Cu(ethylenediamine) adsorption in montmorillonites of different charge density. Standard thermodynamic data for other cases are given in table IV. In all cases the free ligand concentration in equilibrium solution was... 

Such calculations can be done for a series of free ligand concentrations to generate a family of formation curves of concentration or mole fraction of metal complex species as a function of the concentration of the free ligand. Such curves are shown in Figs. 3.1 and 3.2. These calculations are particularly useful for trace level values of metal as they require only knowledge of the free ligand concentrations and the P . Values of stability constants can be found in Refs. [1,2]. 

The free ligand concentration, [A ], is an important parameter in the formation of metal complexes (see Chapter 3 and section 4.8). In a solvent extraction system with the volumes V and of the aqueous and organic phases, respectively, [A ] is calculated from the material balance ... 

In many extraction systems, Dx is proportional to [L]", where [L] is the free ligand concentration, and the exponent n is determined by the number of ligand molecules per molecule of extracted complex. In these systems, therefore, we may write ... 

Fig. 2.27 GPC spin column ESI-MS determination of MS EC50S. Plot of fraction of known ligand inhibitor non-covalently bound to a fixed amount of kinase protein ([P]o, 5 pM) as a function of initial ligand concentration [L]o. The MS EC50 corresponds to the free ligand concentration [L] when 50% of the initial protein concentration is tied up as protein-ligand complex. At 50% of the...

Li and Wang described a convenient linear plotting protocol that permits one to evaluate stability constants for the formation of reversible metal hgand complexes. Added accuracy is achieved over classical approaches, because their generalized equations quantitatively account for side-reactions of metal ion and/or ligand as well as the difference between the total and free ligand concentration. 

The distribution of M among various mononuclear complexes as a function of free ligand concentration may appear as curves [2] shown in Fig. 3.1. 

When the value of m is obtained experimentally by a technique such as potentiometry, the calculation of free ligand concentration can be done by using the concept of average number of ligands per complex [3] (u)... 

Equation 2 is the 1 1 equilibrium reaction between a metal ion, M, and ligand, L, resulting in the formation of the complex, ML, with charges omitted for simplicity. Equation 3 is the expression for the conditional stability constant, K, the free metal ion concentration, [M], free ligand concentration, [L] (all forms of ligand not associated... 

To take into account the effect of pH on the free ligand concentration in a complexation reaction, it is useful to introduce a conditional or effective formation constant. Such constants are pH-dependent equilibrium constants that apply at a single pH only. For the reaction of Fe with oxalate, for example, we can write the formation constant Ki for the first complex as... 

It is important to note that, for a mononuclear complex, n is a function only of the free ligand concentration [L], and does not depend explicitly upon M, L, or [M]. 

Binding constant of the ai-acid glycoprotein - hemin complex was analyzed using Eq. 6.12 and 6.13, where free ligand concentration was taken into consideration ... 

The binding reaction is in equilibrium when the concentrations of the binding variables such as binding protein/ligand complex, free ligand, and so on are not time dependent an3rmore (after about 3 to 4 Ti see Section 2.3.2). The basis of the analysis of equilibrium binding data is the law of mass action and the retention equations. 

A general titration curve equation can be derived from the mass balance equation for the ligand, i.e., to state that the total ligand concentration is the sum of the bound and free ligand concentrations. By the bound ligand is meant the ligand incorporated into the metal complex(es). Thus, for Ag ... 

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