Quantitative Analysis by Using Bands Decomposition

Mixtures of components, that caimot be physically separated but whose molar fractions can be changed under a number of factors are considered as undefined. Such mixtures cannot be analyzed by means of classical spectrophotometric analysis (lack of calibration as shown above) and tautomeric mixtures are a typical example. Therefore, there are two approaches to treat tautomeric mixtures presented as a set of spectra with different tautomeric ratios direct quantitative analysis based on overlapping band decomposition or nonlinear optimization based on existing physical relations between the tautomeric constant and the external factor causing the shift in the equilibrium. The first one is the only option to analyze changes caused by the solvent or by salt addition. Both could be used to estimate the effects of temperature, acidity, or concentration and a critical comparison is available in Section 2.2.3 in this respect 

As has been mentioned several times in this book, the individual tautomers, being physically inseparable, can be measured only as an overall spectral envelop, where the molar fraction of each of them determines the extent of its contribution. The logical question which follows is when it is impossible to have their individual spectra measured experimentally, can their contributions to the spectrum of the 

3) See the assumptions made in Section 2.2.3 about salt effect. 

For the first time, such an approach was used by Metzler and collaborators [20] who studied the two-component tautomeric equilibrium between the neutral form (37b, Chapter 1) and the dipolar ion (37a, Chapter 1) of 3-hydroxypyridine in water and water/methanol binary mixtures at various temperatures. Very similar is the procedure used by Reeves et al. [21] for the analysis of the keto-enol tautomerism of 4-phenylazo-l-naphthol-2,4 -disulfonate VSzquez Segura and collaborators [22] in the case of 5 -deoxypyridoxal and Vilanova et al. [23] for the analysis of tautomeric members of vitamin Bg family. In all these cases, the individual bands belonging to tautomers are mathematically resolved using a suitable band-shape function (in this case log-normal [18]), and the corresponding spectral areas I are calculated. The tautomeric constant Kj. is then given as 

This problem has been solved following the physical reality-the individual spectrum of each tautomer might consist of overlapping bands, which have to be taken into account [9, 26]. The approach is based on Eq. (2.16), where the partial spectrum of each tautomeric form is presented as a superposition of its individual bands, described by a Gaussian band-shape function F [17]  

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