Bjerrum’s method

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. 

Most of the studies on the RE(III) complexes with neutral and basic amino acids have shown that complexation takes place when pH > 6, and that RE(OH)3 precipitation forms if the pH > 8, and experiments done at pH < 7 or 7.5 are considered to be free of significant hydrolysis. However, a few studies did show that protonated complex species form at pH < 2, and the hydrolysis of RE(III) starts at pH < 6 [126,135,136]. The large discrepancies among the data could be a result of different experimental conditions [concentrations of the RE(III) and the ligands, the RE L ratios] and various computing models used, as all of the experiments and the calculations are based on Bjerrum s method [142]. More detailed and systematic studies are thus definitely needed for the solution chemistry of RE(III)-amino acid complexes. 

The extraction equilibrium is therefore dictated by the concentration of the neutral salt, ML2, in the aqueous phase. That concentration can be calculated from the known initial concentrations of the metal salt and of the ligand and from the stepwise stability constants of ail metal complexes present, by using Bjerrum s method [6]. 

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. 

Later Bjerrum s theory was supported by the work of Kraus [138], who showed importance of the dielectric constant, and Atherton [139], who demonstrated the existence of ion pairs using electron spin resonance spectroscopy. The formation of ion pairs may be studied by various methods conductance studies, UV-visible spectrometry, IR spectrophotometry, partition, distribution, or solvent extraction. The lifetime of ion pairs was determined to be at least 10 sec, which is equivalent to about 10 molecular vibrations, demonstrating that ion pairs can be considered as independent species [140]. Today, the ion-pair formation as independent species is widely accepted. 

I. Bjerrum s Wedge Method. —rectangular glass box is divided into two wedge-shaped compartments by the insertion of a sheet of glass... 

Procedures for preparing most of these salts were originally submitted by Dr. McReynolds, who was impressed by the simplicity of Dr. Bjernim s method. Shortly after the manuscript for VoL II had been sent to the publisher, similar procedures for three of these salts were submitted by Dr. Bjerrum. Inasmuch as the method was developed by Dr. Bjerrum and war conditions prevented bis submittii the procedures at an earlier date, the editors have taken the liberty of combining the two sets of directions and presenting them as a joint effort of the two men. 

In the same year as BJerrum s thesis was published, Leden (20) described a method based on the measurement of electrode potentials for the determination of the stability constants of the halogeno complexes of cadmlum(II) based on the measurement of electrode potentials. This method essentially solved the problem raised by Jaques. VHiile BJerrum s book was published in English (taking into account that Denmark was under German occupation, this was a brave deed), Leden s paper was published in German and his thesis two years later in Swedish (21). 

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... 

Studies on ionic hydration and complex formation reactions in solution in the 1960 s quite actively proceeded in Europe, especially in northern Europe. J. Bjerrum, a son of N. Bjerrum in Denmark, established a method for determination of stepwise formation constants of complexes with simple monodentate ligands in solution by the spectrophotomeffic method, which was soon modified to the method by potentiometry. Sillen in Sweden extended the method to polynuclear complex formation reactions and Schwartzenbach in Switzerland, who is a pioneer of chelate chemistry, applied this method to multidentate ligand complexes... 

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