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Here, KA(BH+) denotes the acid dissociation constant of a basic coloured indicator B (for the theory, see Section 1.4.7). If a given indicator is half dissociated, the value of Ho is equal to the decadic logarithm of its acidity constant times 1. For practical measurements an indicator may be used only in the range of its colour transition, i.e. at most in the range of the ratio cB/cBH+ from 10 to 10"1. For a larger interval of Ho values several indicators have to be used. In view of the term containing activity coefficients, the acidity function depends on the ionic type of the indicator. The definition of Ho is combined with the assumption that the ratio YB/YBH+ is constant for all indicators of the same charge type (in the present case the base is electroneutral; hence the index 0 in // 0 ). Thus, the acidity function does not depend on each individual indicator but on the series of indicators. The acidity function is determined by successive use of a range of indicators. Hammett and Deyrup started with / -nitroaniline, the pKAx of which in a dilute aqueous solution is 1.11 (the solvolysis constant has been identified with the acidity constant). Since in a dilute aqueous solution, = 7B YBH+ ~ 1 > the acidity function for the aqueous media goes over to the pH scale. By means of p-nitroaniline, the acidity constant of another somewhat more acidic indicator is obtained under conditions such that both forms of each indicator are present at measurable concentrations. Then Ho as well as the pKAl of the other indicator is determined by using Eq. (1.4.40). By means of this indicator, values of Ho not accessible with / -nitroaniline may be reached. The Ho scale is further extended by using a third indicator and its pKA3 is determined in the same way (see Fig. 1.11). The concentration ratios are determined photometrically in the visual or ultraviolet region. Figure 1.12 shows the dependence of Ho on the composition of the H2SO4-H2O mixture and was obtained as indicated above. 1.4.7 Acid-base indicators The interest in colour indicators has recently increased as they are used for the direct determination of pH (acid-base indicators) and free calcium ions (fluorescent derivatives based on the calcium chelator EGTA as metallochromic indicators) in biological systems at cellular level.
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Fig. 1.12 Acidity function H() for the mixture H 2 SO 4 -H 2 O as a function of the composition. (According to L. P. Hammett and M. A. Paul)
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While the role of acid-base indicators in acidimetric titrations has been surpassed by more advanced, automatic, potentiometric methods various metallochromic indicators are still in use in complexometric analysis. Here we shall deal only with acid-base indicators. According to the early view of Ostwald, acid-base indicators are weak acids or bases, the undissociated form of which differs in colour from the ionic form. For example, the molecule of an indicator HI dissociates in water according to the equation HI + H2O = H 3 O + + I" (1.4.41) The equilibrium constant of this reaction in a dilute solution is fH3O+][I-] (1.4.42) [HI] whence [HI] showing the dependence of the ratio [I ]/[HI] on pH. pH = pKi + log (1.4.43)
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67 In a later conception due to Hantzsch, an indicator possesses two tautomeric forms differing in colour, and at least one form functions as an acid or base. If both tautomeric forms are capable of dissociation their ions also differ in colour. However, the ions and molecules of the same form show identical light absorption because such a small variation of the structure of a molecule as the dissociation of a proton cannot cause a large change in molecular property such as light absorption. For example, phenolphthalein does not absorb visible light in the acid and neutral region, but at pH > 8.2 one of its hydroxyl groups becomes ionized and, at the same time, a tautomeric change takes place: )H
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