Formation curve concept

The diagram n as a function of the decimal antilogarithm of the ligand activity (concentration) of the free ligand after complexation (here pCl) is known as the formation curve. The mathematical study of the formation curve permits us to determine the equilibrium constants, A l, K2, K3, K4, etc. (see Sect. 24.3). The formation curve concept is due to J. Bjerrum. It can be extended to other phenomena in solution. 

The concept of a formation curve presents great interest when there is formation of polynuclear complexes. The study of its evolution as a function of the total concentration of the metallic ion permits us to detect the presence of polynuclear complexes. We have already seen (Chap. 24, Sects. 24.6 and 24.7) that when no polynuclear complex is formed, the curve is independent of the total concentration in the metallic ion. Inversely, this is no longer the case when there are polynuclear complexes. For the example of the hydroxo complexes of ferric ion, the curve formation is the curve n as a function of [OH ] or n as a function of pH. By definition,... 

Based upon the concepts of the adsorption of the anode reaction product, the share of the anodic curve, on which the carbamide oxidation processes is reflected as a wave, can be explained. It may be assumed that the adsorption of the reaction product inhibits the direct oxidation of carbamide. To verify this conclusion, the anode was polarized to the electrolysis product formation potential, and the reverse sweep was stopped before the electrolysis product was reduced at the electrode. Then the carbamide oxidation process was completely inhibited on the subsequent forward sweep, and the curve exhibited only a current increase at the chlorine ion oxidation potential. 

The concept of categorizing carcinogens into threshold carcinogens and non-threshold carcinogens is a pragmatic approach that simplifies the reality of dose-response relationships. The observed dose-response curve for tumor formation in some cases represents a single rate-determining step however, in many cases it may be more complex and represent a superposition of a number of dose-response curves for the various steps involved in the mmor formation. It is therefore more realistic to assume that there is a continuum of shapes of dose-response relationships which cannot be easily differentiated by data and information usually available. 

As it was for acid-base titrations, the concept of relative precision (Section 3-7) is useful for comparing the steepness of titration curves in the immediate vicinity of the end point. For the formation of a precipitate of symmetrical charge type (m = n), with activity coefficients assumed to be unity. 

Theories dealing with the photophysics of excimer formation and decay involving the "isolated monomer" and "energy migration" concepts have been developed in order to explain the complex fluorescence decay curves observed for polymer systems (5.). Application of these fluorescence decay laws continues to be a topic of interest as will be demonstrated in chapters throughout this book. 

Following the approach introduced by Ya. Frenkel, let us apply the concepts of particle size distribution to the analysis of the kinetics of the formation of new phase nuclei during phase transitions. Equation (IV. 13), describing the particle size distribution, yields the particle concentration distribution curve with respect to particle radii, n(r) when applied to metastable system (Ap = p. -pr<0 also assuming that the interfacial tension is independent of particle size distribution). The particle radii distribution curve contains a minimum (Fig. IV-8). The shape of the curve indicates that the formation of large particles only occurs in a... 

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