Acid-base titration inflection points

It has been shown that for most acid-base titrations the inflection point, which corresponds to the greatest slope in the titration curve, very nearly coincides with the equivalence point. The inflection point actually precedes the equivalence point, with the error approaching 0.1% for weak acids or weak bases with dissociation constants smaller than 10 , or for very dilute solutions. Equivalence points determined in this fashion are indicated on the titration curves in figure 9.8. 

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation. 

Before continuing with other examples, it is important to consider how the equivalence point in an acid-base titration is found and what relationship this has with titration curves. As we have said, the inflection point at the center of these curves occurs at the equivalence point, the point at which all of the substance titrated has been exactly consumed by the titrant. The exact position for this in the case... 

In acid-base titrations, pD is pH and pK is pK because [D] = [H+]. This is the reason for the name of the curve, well known from analytical chemistry. The drawback of this plot is that many points are needed in the vicinity of the inflection point. 

A titration such as that of a monobasic weak acid with a strong base or of the last step of a polybasic weak acid usually shows two inflection points, one where the slope of the curve is at a minimum and the other where it is at a maximum. The first inflection point is usually near the 50% neutralization point, but follows it for very weak acids, precedes it for moderately strong acids, and disappears for the strongest acids. The second inflection point precedes the equivalence point the difference amounts to as much as 1 ppt only for very weak adds (K < 10 for 0.1 Af solutions) or highly dilute solutions. The second inflection point disappears for highly dilute or exceedingly weak acids. Automated techniques for end-point detection normally rely on the inflection point signiflcant error therefore may be incurred under certain circumstances. 

We have shown in Chapter 8 that in acid-base titrations the pH of the solution exhibits a large break at the equivalence point. This pH change can easily be monitored with a glass pH electrode. By plotting the measured pH against volume of titrant, one can obtain titration curves similar to those shown in Chapter 8. The end point is taken as the inflection point of the large pH break occurring at the equivalence point this is the steepest part of the curve. 

In this section, we examine acid-base titrations more closely, concentrating on the pH changes that occur during the titration. A plot of the pH of the solution during a titration is known as a titration curve or pH curve. Figure 16.6 v is a pH curve for the titration of HCl with NaOH. Before any base is added to the solution, the pH is low (as expected for a solution of HCl). As the NaOH is added, the solution becomes less acidic because the NaOH begins to neutralize the HQ. The point of inflection in the middle of the curve is the equivalence point. Notice that the pH changes very quickly near the... 

The principal limitation to using a titration curve to locate the equivalence point is that an inflection point must be present. Sometimes, however, an inflection point may be missing or difficult to detect, figure 9.9, for example, demonstrates the influence of the acid dissociation constant, iQ, on the titration curve for a weak acid with a strong base titrant. The inflection point is visible, even if barely so, for acid dissociation constants larger than 10 , but is missing when is 10 k... 

Another situation in which an inflection point may be missing or difficult to detect occurs when the analyte is a multiprotic weak acid or base whose successive dissociation constants are similar in magnitude. To see why this is true let s consider the titration of a diprotic weak acid, H2A, with NaOH. During the titration the following two reactions occur. 

Conductometric titration rests on the marked changes that occur near the titration endpoint in the relation between conductivity and the amount of titrant added (an extreme or inflection point). It is used in particular for the titration of acids with base (and vice versa) in colored and turbid solutions or solutions containing reducing and oxidizing agents (i.e., in those cases where the usual color change of acid-base indicators cannot be seen). 

On the basis of the Henderson equation for titration of acid or base one can prove mathematically that the half-neutralization point represents a true inflection point and that as the titration end-point dpH/dA is maximal or minimal, respectively (the latter is only strictly true for titration of a weak acid with a weak base and vice versa). 

Case C, the titration of a weak acid with a weak base and vice versa, has in fact already been illustrated in Fig. 2.18 by the curves BB and B B are fully valid and for characteristic (3) the initial point is still dependent on the original concentration c however for the further main part of the curve we see a clean symmetry versus the equivalence point, which has become a true inflection point, independent of the concentration and simply determined by the mean value of pKg and pKb, i.e., (p/ia + pKh)/2 or (pifa + pifw - pKa.)/2. It also means that in the simultaneous titration of a polyvalent acid or a series of weak acids of different strength with a strong base and vice versa, (1) the stronger the acid the earlier it is titrated within the series, (2) the initial point and the final end-point of the series are still influenced by the concentration, but (3) the intermediate steps are only determined at the pH of the inflection point by the mean value of the pifas of the subsequent acids and in its steepness by the difference between these pKgs. Therefore, consultation of pKa tables provides the most suitable way of predicting the results of such simultaneous titrations. 

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. 

The slope of the tangent to the curve at the inflection point where oc = is thus inversely proportional to the number of electrons n. The E-oc curves are similar to the titration curves of weak acids or bases (pH-or). For neutralization curves, the slope dpH/doc characterizes the buffering capacity of the solution for redox potential curves, the differential dE/da characterizes the redox capacity of the system. If oc — for a buffer, then changes in pH produced by changes in a are the smallest possible. If a = in a redox system, then the potential changes produced by changes in oc are also minimal (the system is well poised ). 

The problem the analyst has is to choose indicators that change color close enough to an equivalence point so that the accuracy of the experiment is not diminished, which really means at any point during the inflection point. (Refer to Section 4.2 for the definitions of equivalence point and end point.) It almost seems like an impossible task, since there must be an indicator for each possible acid or base to be titrated. Fortunately, there are a large number of indicators available, and there is at least one available for all acids and bases, with the exception of only the extremely weak acids and bases. Figure 5.5 lists some of these indicators and shows the pH ranges over which they change color. 

Figure 5.11 represents the titration curve of sodium carbonate titrated with a strong acid. Notice that there are two inflection points. This is because sodium carbonate is a dibasic base—there are two hydrogen ions accepted by the carbonate. On the way to the first inflection point, hydrogen ions are accepted by the carbonate to form bicarbonate ... 

In the process of a weak acid or weak base neutralization titration, a mixture of a conjugate acid-base pair exists in the reaction flask in the time period of the experiment leading up to the inflection point. For example, during the titration of acetic acid with sodium hydroxide, a mixture of acetic acid and acetate ion exists in the reaction flask prior to the inflection point. In that portion of the titration curve, the pH of the solution does not change appreciably, even upon the addition of more sodium hydroxide. Thus this solution is a buffer solution, as we defined it at the beginning of this section. 

Define monoprotic acid, polyprotic acid, monobasic base, polybasic base, titration curve, and inflection point. 

Direct potentiometric titration with alkali gave rather flat curves without distinct inflection points 26, 44). Villars 26) concluded that no chemical groups of distinct acidities were present. However, very often the potential becomes constant only several hours after the addition of alkali. Therefore, it was attempted in my laboratory 45-47) to differentiate the acid groups by neutralization with bases of different basicities. The samples were agitated for at least 16 hours with 0.06 N solutions of four bases NaHCOs, NajCO., NaOH, and Na ethoxide. The... 

In titrations involving 1 1 stoichiometry of reactants, the equivalence point is the steepest point of the titration curve. This is true of acid-base, complexometric, and redox titrations as well. For stoichiometries other than 1 1, such as 2Ag+ + CrO —> Ag2Cr04(s), the curve is not symmetric near the equivalence point. The equivalence point is not at the center of the steepest section of the curve, and it is not an inflection point. In practice, conditions are chosen such that titration curves are steep enough for the steepest point to be a good estimate of the equivalence point, regardless of the stoichiometry. 

The complete titration curve in Figure 11-1 exhibits a rapid change in pH near the equivalence point. The equivalence point is where the slope (dpH/dVf) is greatest (and the second derivative is 0, which makes it an inflection point). To repeat an important statement, the pH at the equivalence point is 7.00 only in a strong-acid-strong-base titration. If one or both of the reactants are weak, the equivalence point pH is not 7.00. 

The strength of the basic compounds pKb in engine oil estimated in glacial acetic acid is from 11 to 12.5 units in water scale (see Fig. 6.6). Also, it has been proved that 2,4,6-trimethylpyridine, pKb(H20) = 6.68, applied as a reference in the ASTM D664 emf technique to obtain the inflection point on the badly developed titration curves, is too strong of a base (Pawlak, 1980) and should be replaced by the base having pKb(H20) about 11, e.g., 2-chloroaniline, pyrazole, or 3-acetyl-pyridine. 

A correlation between reaction rates, molecular stmcture of the humic or fulvic acid, and content of reactive sites is more difficult to demonstrate. It has been hypothesized that the hydroquinone or quinone is the main reactive site for electron transfer during dechlorination reactions. Phenolic acidity, as based on the inflection point during titration of organic matter, is indicative of the hydroquinone content within humic materials. Published information indicates that the quinone content of humic acids is generally higher than for fulvic acid (Stevenson, 1994). 

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