Bjerrum method

Knowing K1K2 and K4 the forward and reverse rate constants can be obtained. K K2 was obtained by the Bjerrum method [19] or the diffusion theory [20] of Eigen. The forward and reverse rate constants were determined using the relationship... 

Bjerrum Method. In the method of Bjerrum, one plots e/[M]t versus [L]t for various constant values of [Mjj, where t denotes total concentration of the designated form. A line drawn horizontally on the graph intersects the experimental curves at points whose coordinates show the composition of the so-called corresponding solutions which have a given value of e/[M]t. For complexes of the type ML (n = 1, 2, 3,...), the solutions also have the same value of n. The value of n (an average number of ligands bonded to the central group) may be obtained at various concentrations of L when the total concentrations of such solutions are known. For detailed description, see references [16, 17]. 

An illustration of the Bjerrum method for calculating the formation constants for a complex between Cu and 5-sulphosalicycUc acid (H3L) is... 

Method 1 (Lund and Bjerrum, 1931). The procedure depends upon the reactions ... 

The book is organized into eight chapters. Chapter 1 describes the physicochemical needs of pharmaceutical research and development. Chapter 2 defines the flux model, based on Fick s laws of diffusion, in terms of solubility, permeability, and charge state (pH), and lays the foundation for the rest of the book. Chapter 3 covers the topic of ionization constants—how to measure pKa values accurately and quickly, and which methods to use. Bjerrum analysis is revealed as the secret weapon behind the most effective approaches. Chapter 4 discusses experimental... 

J. Bjerrum (1926) first developed the theory of ion association. He introduced the concept of a certain critical distance between the cation and the anion at which the electrostatic attractive force is balanced by the mean force corresponding to thermal motion. The energy of the ion is at a minimum at this distance. The method of calculation is analogous to that of Debye and Hiickel in the theory of activity coefficients (see Section 1.3.1). The probability Pt dr has to be found for the ith ion species to be present in a volume element in the shape of a spherical shell with thickness dr at a sufficiently small distance r from the central ion (index k). 

In the preceding section, we have described two methods that are frequently used to determine the composition of complexes in solution. We will now turn our attention to a consideration of the simultaneous equilibria that are involved in complex formation. The widely used approach described here is known as Bjerrum s method, and it was described by Jannik Bjerrum many years ago. 

An initial step in data analysis is to develop an equation that represents the experimental data reasonably. Although previous sections dealt with this issue, the approach assumed that certain species are formed. Two alternatives to this procedure are discussed here, both yielding the approximate stoichiometry of the complexes formed in the system. The most elementary is referred to as Job s method, while the ligand number method, developed by J. Bjerrum, is slightly more advanced. 

Because the ions in electrolyte solutions are often more or less associated, Eq. (7.5) is useful in analyzing conductivity data. The experimental data for A and c are subjected to computer analysis, by applying the least-squares method, and optimum values of such parameters as A°°, KA and a are obtained. Sometimes the ion parameter a (i.e. the distance of closest approach) is replaced by the Bjerrum s distance q in Section 2.6. In this case, the parameters obtained from Eq. (7.5) are of two kinds, A°° and KA. 

The overall stability constants of several metals in solution have been determined by many workers34 employing Bjerrum s technique, pH titration and distribution and potentiometric methods. It has been shown by Irving and Williams,35 as well as by Mellor and Maley,36 that the stability of chelates of bivalent 3d metals increases regularly from Mn2+ to Cu2+ and decreases from... 

Since Bjerrum s [7] introduction of the concept of ion pairing in 1926, a variety of analytical methods has been employed to study the structure and energetics of ion pairs. Szwarc s Book deals with the development of the ideas up to 1972 [3a]. It is also a guiding reference for the different spectroscopic methods that have been employed in the examination of ion pairs. 

Gruen and Marcelja considered that the electric and polarization fields are not proportional in the vicinity of a surface and that while the electric field has the ion concentrations as its source, the source of the polarization field is provided by the Bjerrum defects. The coupled equations for the electric and polarization fields were derived through a variational method. Attard et al.14 contested the Gruen—Marcelja model because, to obtain an exponential decay of the repulsion, the nonlocal dielectric function was assumed to have a simple monotonic dependence upon the wavelength (eq 33 in ref 13). This was found to be inconsistent with the exact expression for multipolar models.14 In addition, the characteristic decay length for polarization (denoted in eq 18, ref 13) is inversely proportional to the square of the (unknown) concentration of Bjerrum defects in ice. While at large concentrations of Bjerrum defects the disordered ice becomes similar to water and the traditional Poisson—... 

This method has been developed by Bjerrum (4) and is now extensively employed for the determination of complex formation constants (8, 25,... 

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