Analysis of the titration curve

This analysis is complex, but follows the pattern given for the dibasic acids. The solutions of the final equations have to be found by successive approximation, or else by computer curve fitting to the whole titration curve. In practice, this is how the analysis will be carried out. 

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The liquid Lewis acid VOCl3 was found to completely ionize An-TolCHCI but not Tol2CHCI a detailed analysis of the titration curves as in the case of BC13 also failed. 

No conformational change is detected by analysis of the titration curve. A distinct change in sedimentation coefficient occurs below pH 4, however. (Chari-wood and Ens, 1957.)... 

The complete analysis of the titration curve must include ... 

Analysis of the titration curves for aliphatic and aromatic amino acids, and amino phenols... 

Spectroscopic techniques as well have been used in demonstrating an interaction between CaD and CaT (Mani and Kay, 1990). For fluorescence studies, the sulfhydryl groups in CaD were labeled with acry-lodan. Addition of CaT to labeled CaD in the presence of Ca + produced nearly 50% increase in fluorescence intensity and the emission maximum shifted to 492 nm from 504 nm. Labeled CaD was titrated with CaT. Analysis of the titration curve by curve fitting showed that the best fit was obtained when the molar ratio of CaT to CaD in the complex at saturation was 1 1. A value of (9 2) X 10 M was obtained from the titration. However, there was no evidence of any interaction between CaT and CaD in the absence of Ca2+. 

The scale of operations, accuracy, precision, sensitivity, time, and cost of methods involving redox titrations are similar to those described earlier in the chapter for acid-base and complexometric titrimetric methods. As with acid-base titrations, redox titrations can be extended to the analysis of mixtures if there is a significant difference in the ease with which the analytes can be oxidized or reduced. Figure 9.40 shows an example of the titration curve for a mixture of Fe + and Sn +, using Ce + as the titrant. The titration of a mixture of analytes whose standard-state potentials or formal potentials differ by at least 200 mV will result in a separate equivalence point for each analyte. 

In routine analysis, often a one-dimensional so-called end-point titration can be automatically carried out up to a pre-set pH or potential value and with a previously chosen overall titration velocity in order to avoid overshoot, the inflection point should be sufficiently sharp and the titrant delivery must automatically diminish on the approach to that point in order to maintain equilibrium, and stop in time at the pre-set value. For instance, the Metrohm 526 end-point titrator changes both the dosing pulse length and its velocity by means of a pulse regulator in accordance with the course of the titration curve in fact, the instrument follows the titration two-dimensionally, but finally reports only a one-dimensional result. The Radiometer ETS 822 end-point titration system offers similar possibilities. However, automated titrations mostly represent examples of a two-dimensional so-called eqilibrium titration, where the titration velocity is inversely proportional to the steepness of the potentiometric titration curve hence the first derivative of the curve can usually also be recorded as a more accurate means of determining the inflection... 

In [LJ-control maps the substitution of one ligand by another one results in a change of the range of existence of the manifold intermediates. This change can be expressed by the ligand-property imluced shift of the titration curves identified by the relative position of their inflection points Lq s on the log (lL o/[Ni)Q) scale. These characteristic shifts provide information on the thermodynamic selectivity governed by the association processes only. This type of analysis is designated by . 

R. de Levie, A General Simulator for Add-Base Titrations, J. Chem. Ed. 1999, 76, 987 R. de Levie, Explicit Expressions of the General Form of the Titration Curve in Terms of Concentration, J. Chem. Ed. 1993, 70, 209 R. de Levie, General Expressions for Add-Base Titrations of Arbitrary Mixtures, Anal. Chem. 1996, 68, 585 R. de Levie, Principles ctf Quantitative Chemical Analysis (New York McGraw-Hill, 1997). 

Other methods of refinement of the count of groups exist. The most important one occurs as an adjunct to the semiempirical analysis of the shape of each part of the titration curve, to be discussed in Sections VI, B and VI, C. It is often impossible to achieve a self-consistent interpre-... 

Large sections of protein titration curves are often equally time-independent and reversible, as, for instance, the acid part of the titration curve of (3-lactoglobulin shown in Fig. 2. Any such section of the titration curve will again represent thermodynamic equilibrium and it may be subjected to thermodynamic analysis, as outlined in Sections VI and VII. 

The first detailed analysis of a protein titration curve, according to the semiempirical treatment used for most of the titration curves reviewed in this paper, also involves ovalbumin (Cannan el al., 1941). The first discovery of phenolic groups inaccessible to titration was again made with this protein (Crammer and Neuberger, 1943). 

The titration curve of ribonuclease (Tanford and Hauenstein, 1956b) is reversible between its acid end point and the onset of alkaline denaturation. All titratable groups, which are expected to be present on the basis of amino acid analysis, are found to be titrated in the expected parts of the titration curve, with the exception of the abnormal phenolic groups mentioned above. The amino and imidazole groups appear to have normal pK s, and the neutral and alkaline regions in which they occur are compatible with the same values of w as are required to fit the titration curves of the three normal phenolic groups. 

Rather than resort to purely empirical selection of suitable values of ni and p(/Cint)< for equation 1 it is more usual to begin by fitting experimental data with values of m chosen to conform with the numbers of prototropic groups determined by several more direct and specific methods of examination of titration data. Even where the theoretical analysis of a titration curve is not attempted and exact values of p(Ki t), for each type of group are therefore lacking, the numbers of groups so determined may furnish valuable clues to the internal structure of the protein, especially when they are compared with the results of amino acid analyses. 

From what we have said above, it follows that the acid-base equilibrium in the solutions containing metal cations and oxide ions in different sections of the titration curve is described either by the dissociation constant (in unsaturated solutions) or by the values of solubility product (in saturated solutions). In Refs. [175, 330] we proposed a method based on the analysis of the scatter in the calculated equilibrium parameters corresponding to the titration process. Indeed, in the unsaturated solution section there is no oxide precipitation and the calculated value of the solubility product increases monotonously (the directed shift) whereas the calculated value of the dissociation constant fluctuates about a certain value, which is the concentration-based dissociation constant of the studied oxide. 

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