Theory of Acid-Base Titrations

Indicators are either very weak organic acids or bases which always exists in two tautomeric forms. One of the tautomers is in the non-electrolytic forms and scarcely ionises but the other is an electrolyte and hence ionisable. 

Let HIn be the non-ionisable tautomeric form and HIn be the ionisable form of phenolpthalein where In represents the indicator ion. The colour of HIn and In-are the same but different from HIn. In aqueous solution there would exist two equilibrium. 

In acid solution the dissociation will be supressed and the whole of the indicator ion shall remain in imdissociated form i.e. as HIn and HIn, which have different colours. The indicators will be applicable only if the equilibrium constant of 4.6.14.1 is small so that the undissociated 

Log Yj may be evaluated with extended Debye-Huckel law, but for most purposes, it is small and can be neglected, so that 

It is seen that at a given pH, indicator will exist in a definite ratio of concentrations of ionised and non-ionised form. Both the forms are present in any pH, but human eye can discern the colour distinctly when one predominates. It has been found that the acid colour, namely 

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Hydrogen was recognized as the essential element in acids by H. Davy after his work on the hydrohalic acids, and theories of acids and bases have played an important role ever since. The electrolytic dissociation theory of S. A. Arrhenius and W. Ostwald in the 1880s, the introduction of the pH scale for hydrogen-ion concentrations by S. P. L. Sprensen in 1909, the theory of acid-base titrations and indicators, and J. N. Brdnsted s fruitful concept of acids and conjugate bases as proton donors and acceptors (1923) are other land marks (see p. 48). The di.scovery of ortho- and para-hydrogen in 1924, closely followed by the discovery of heavy hydrogen (deuterium) and... 

The utility of acid-base titrimetry improved when NaOH was first introduced as a strong base titrant in 1846. In addition, progress in synthesizing organic dyes led to the development of many new indicators. Phenolphthalein was first synthesized by Bayer in 1871 and used as a visual indicator for acid-base titrations in 1877. Other indicators, such as methyl orange, soon followed. Despite the increasing availability of indicators, the absence of a theory of acid-base reactivity made selecting a proper indicator difficult. 

The Bronsted-Lowry theory of acids and bases referred to in Section 10.7 can be applied equally well to reactions occurring during acid-base titrations in non-aqueous solvents. This is because their approach considers an acid as any substance which will tend to donate a proton, and a base as a substance which will accept a proton. Substances which give poor end points due to being weak acids or bases in aqueous solution will frequently give far more satisfactory end points when titrations are carried out in non-aqueous media. An additional advantage is that many substances which are insoluble in water are sufficiently soluble in organic solvents to permit their titration in these non-aqueous media. 

This example shows also that the proton theory, in addition to being valid for aprotic solvents, also works for amphiprotic solvents, and so represents a more general theory. How in an acid-base titration the theory works out can be followed from the titration of a certain amount of HC1 gas introduced into pyridine as an aprotic solvent ... 

Potentiometric acid-base titrations are particularly useful for the analysis of mixtures of acids or poly-protic acids (or bases) because often, discrimination between the endpoints can be made. An approximate numerical value for the dissociation constant of a weak acid or base can be estimated from potentiometric titration curves. In theory, this quantity can be obtained from any point along the curve, but it is most easily derived from the pH at the point of halfneutralization. 

The first point to be made concerning acids and bases is that so-called acid-base theories are in reality definitions of what an acid or base is they are not theories in the sense of valence bond theory or molecular orbital theory. In a very real sense, we can make an acid be anything we wish the differences between the various acid-base concepts are not concerned with which is right but which is most convenient to use in a particular situation. All of the current definitions of acid-base behavior are compatible with each other. In fact, one of the objects in the following presentation of many different definitions is to emphasize their basic parallelism and hence to direct the students toward a cosmopolitan attitude toward acids and bases which will stand them in good stead in dealing with various chemical situations, whether they be in aqueous solutions of ions, organic reactions, nonaqueotis titrations, or other situations. 

Thus the change of the concentration of free base of one order of magnitude will produce an increase of potential of 59 millivolts at 25°, i.e., the increase of base concentration from 1CH to 10 mol per liter will produce the same effect on the potential as the change from 10-3 to lO2 mol per liter. A plot of E against the volume of added base will be very closely of the form given in Fig. 2 (o). A more adequate discussion of the theory of the acid-base titration, including the ionization equilibrium of water, is given later in this chapter. 

The acidity or basicity of a solution is frequently an important factor in chemical reactions. The use of buffers of a given pH to maintain the solution pH at a desired level is very important. In addition, fundamental acid-base equihbria are important in understanding acid-base titrations and the effects of acids on chemical species and reactions, for example, the effects of complexation or precipitation. In Chapter 6, we described the fundamental concept of equilibrium constants. In this chapter, we consider in more detail various acid-base equilibrium calculations, including weak acids and bases, hydrolysis, of salts of weak acids and bases, buffers, polyprotic acids and their salts, and physiological buffers. Acid-base theories and the basic pH concept are reviewed first. 

Integration of Cooperativities Due to Apolar-Polar and Charge-Charge Repulsion into Acid-Base Titration Theory... 

The theory of indicators, pK values (as a measure of acid strength) and the choice of indicators for acid-base titrations is discussed in Chapter 18. 

T. A. Khudyakova and A. P. Kreshkov, J. Electroanal. Chem., 29, 181 (1971). The theory of conductimetric and acid-base titrations in nonaqueous solutions. 

J. A. Riddick, Anal. Chem., 24, 41 (1952). Acid-base Titrations in Nonaqueous Solvents. Extensive survey of theory and practice. 

The theory of titrations between weak acids and strong bases is dealt with in Section 10.13, and is usually applicable to both monoprotic and polyprotic acids (Section 10.16). But for determinations carried out in aqueous solutions it is not normally possible to differentiate easily between the end points for the individual carboxylic acid groups in diprotic acids, such as succinic acid, as the dissociation constants are too close together. In these cases the end points for titrations with sodium hydroxide correspond to neutralisation of all the acidic groups. As some organic acids can be obtained in very high states of purity, sufficiently sharp end points can be obtained to justify their use as standards, e.g. benzoic acid and succinic acid (Section 10.28). The titration procedure described in this section can be used to determine the relative molecular mass (R.M.M.) of a pure carboxylic acid (if the number of acidic groups is known) or the purity of an acid of known R.M.M. 

The pyridinium ion (acid 2) as the analyte can be titrated with quaternary ammonium hydroxide (base 3) as it concerns the determination of H+ of the Brensted acid pyridinium, a potentiometric measurement of the pH titration curve and its inflection point is most obvious. In the aprotic, but protophilic, solvent pyridine no stronger acid can exist (see reactions 4.37 and 4.38) than the pyridinium ion itself hence there is a levelling effect but in theory only on the acid side. 

Although the ester mechanism is not yet generally accepted, the evidence accumulating since it was first put forward is in its favour, and the evidence which is alleged to be against it, or which has been interpreted in terms of ion-pairs in place of the ester, is certainly compatible with the ester theory [13, 14,15]. We note in passing an interesting application of the polymerisation of styrene by perchloric acid it was used as an indicator-reaction in the enthalpy titration of weak bases [16]. 

Myosin is another protein to which the theory of Linderstr0m-Lang in its present form is not applicable, since in myosin the ratio of molecular length to width is 100/1—far from the sphericity on which the theory is based. Thus experimental values of the parameter w cannot be easily interpreted quantitatively. Myosin is soluble in the presence of salt on the alkaline side of its isoionic point only, and thus should behave as a soluble protein above pH 5.7 to 5.8 and as an insoluble one below this. Mihdlyi (1950) has studied the effect of salt on the titration of myosin and reports that its insolubility in acid in the presence of greater than 0.05 M KCl does not affect the reversibility of the titration nor are there any obvious discontinuities in his titration curves, shown in Fig. 4. The data for basic solutions appear to be affected by salt very much as those of other soluble proteins, and reach an apparent limiting curve at a fairly low ionic strength (0.15). In acid solution where the protein is insoluble, however, the effect of salt closely resembles that for wool, except that the displacements of the parallel central portions of the curves are somew hat less than for wool, consistent with a lower affinity of myosin for chloride ion. The slopes of these portions of the curves are within 10 % of those observed for... 

In this chapter we have applied the methods of chapter 4 to ionic equilibria other than those between acids and bases. Of course, complexation, extraction, solubility, precipitation, and redox equilibria may also involve acid-base equilibria, which is why we treated acid-base equilibria first. The examples given here illustrate that the combination of exact theory with the computational power of a spreadsheet allows us to solve many problems that occur in quantitative chemical analysis, and to analyze experimental data accordingly. Even quite complicated titrations, such as the multi-component precipitation titrations, the von Liebig titration, and redox titrations involving many species and complicated stoichiometries, can be handled with ease. 

Textbooks of analytical chemistry should be consulted for further details concerning the ionization of weak acids and bases and the theory of indicators, buffer solutions, and acid-alkali titrations. 

We can detect the end point by measuring either pCl or pAg with an appropriate electrode and a potentiometer. We discuss this in Chapter 13. It is more convenient if an indicator can be employed. The indicator theory for these titrations is different from that for acid-base indicators. The properties of the indicators do not necessarily depend on the concentration of some ion in solution, that is, on pCl or pAg. 

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