Free ligand concentrations calculations

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 ... 

Figure 4. Observed ratio of borate diesters to borate monoesters, scaled by Ilf versus the global free ligand concentration. Standard errors are shown based on multiple fits to individual nB NMR spectra. As the free ligand concentration is also calculated (by difference) from the MB NMR spectra, standard errors are given for this variable as well. The dashed line is the best fit from the model which gives Rg = 88.5 A. For these samples,/was always between 0.2 and 0.6. 

In Figure 5 we plot the ratio of borate esters to borate anion as a function of global free ligand concentration. The borate anion concentration was calculated from the free boron concentration (Bj) observed with 1 B NMR and the pH ... 

Since M is known, the value of m can be obtained by integrating the curve involving n vs. log a. The free ligand concentration a can be calculated from the values of h and a, using the relationship... 

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)... 

The values of pL = — log[L], where [L] is free ligand concentration have been calculated using equation (3.23)... 

The use of conditional constants greatly simplifies calculations because Cj is often known or readily computed, whereas the free ligand concentration is not as easily... 

Free ligand concentrations In our experimental media were calculated using equations of the form ... 

With the aid of the equilibrium constants determined in the different solutions, Gaizer et al. calculated how the concentrations of the complexes in the solutions vary with the change in the concentration of the free ligand. Figure 8.1 was constructed from the results. It can be seen that, whereas the complexes of composition MA and MA3 predominate over a wide free ligand concentration... 

The calculation of stability constants is based on the fact that measurement of total ligand concentration at any point within column allows a determination of the amount bound to protein, since the cross-sectional areas of Vq and V, can be known frcm Independent experiments (ref. 34). When M is totally excluded the free ligand concentration can be calculated frcm equation... 

It is well known that pH measurements during the titration with alkali of a solution of a chelating agent, in the presence and in the absence of metal ions, can be used for calculating the free ligand concentration [A], the number of units bound per metal ion n, and the stability constants, 3 , of the metal-ligand complexes [23, 24]. 

The Bjerrum complex formation curves of the metal chelates are obtained by plotting n, the number of monomer units per bound metal ion as calculated from the potentiometric titrations, against pA = -log[ j, [A] being the free ligand concentration (Figure 3). 

Csilibrsition. Quantitative binding analysis requires knowing the concentration of FLPEP, which can be determined for a stock solution of FLPEP by absorption spectroscopy. The quenching by the antibody is essentially quantitative, and the relative amounts of free and bound ligand are calculated from the relative fluorescence intensity. 

In these equations, [X] is the concentration of free ligand. With these five expressions that give the fraction of the free metal ion and the fraction in each complex, it is possible to vary [X] and calculate the fraction of the metal ion in each complex environment. 

The concentration of bound ligand is calculated from the difference between total and free ligand and the data are analysed as above. 

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