Titration curves acid-base, figure

The end point in a titration is a little different from the end of a reaction. What is desired is to know when all the add is titrated. This happens when the titration curve, shown in Figure 10.1, reaches its maximum slope. This change occurs at a pH of 7 for a typical strong acid-base titration), but occurs at pH... 

When an indicator is used in a titration, the range of pH values at which its endpoint occurs must include, or be close to, the equivalence point. Some representative acid-base titration curves, shown in Figures 8.11, 8.12, and 8.13, will illustrate this point. 

The example used here is the determination of the protonation constants of 3,2,3-tet (1,5,8,12-tetraazadodecane, H2N(CH2)3NH(CH2)2NH(CH2)3NH2). The tetraprotonated amine was titrated with standard base. It can be seen from the titration curve shown in Figure 22-7 that while one proton is much more acidic... 

The weaker the acid, the more pronounced these differences become. To illustrate this consider the family of titration curves shown in FIGURE 17.11. Notice that as the acid becomes weaker (that is, as becomes smaller), the initial pH increases and the pH change near the equivalence point becomes less marked. Furthermore, the pH at the equivalence point steadily increases as K decreases, because the strength of the conjugate base of the weak acid increases. It is virtually impossible to determine the equivalence point when pK is 10 or higher because the pH change is too small and gradual. 

Titration of a weak base (such as 0.100 MNH3) with a strong acid solution (such as 0.100 M HCl) leads to the titration curve shown in FIGURE 17.15. In this example, the equivalence point occurs at pH 5.28. Thus, methyl red is an ideal indicator but phenolphthalein would be a poor choice. 

The opposite of a weak acid-strong base titration is the titration of a weak base (NH3) with a strong acid (HCl). This titration curve, shown in Figure 19.9, has the same shape as the weak acid-strong base curve, but it is inverted. 

FIGURE 16.7 Titration Curve Strong Base + Strong Acid This curve represents the titration of 25.0 mL of 0.100 M NaOH with 0.100 M HCl. 

Automatic titrators that are electronically equipped to compute the first and second derivative of pH with respect to time, and hence reagent flow, can automatically locate the equivalence point. The first derivative, which is the slope of the titration curve, reaches a maximum at the equivalence points. The second derivative changes sign at the equivalence points. A plot of first derivative helps in the control system design because it is indicative of the pH process sensitivity. Figure 3-2a shows a plot of the first derivatives for the weak acid and weak base titration curv e in Figure 3-le. For more information on automatic titrators, consult Reference 3.3. 

The titration curve in Figure 9.1 is not unique to an acid-base titration. Any titration curve that follows the change in concentration of a species in the titration reaction (plotted logarithmically) as a function of the volume of titrant has the same general sigmoidal shape. Several additional examples are shown in Figure 9.2. 

This approach can be used to sketch titration curves for other acid-base titrations including those involving polyprotic weak acids and bases or mixtures of weak acids and bases (Figure 9.8). Figure 9.8a, for example, shows the titration curve when titrating a diprotic weak acid, H2A, with a strong base. Since the analyte is... 

Figure 9.8b shows a titration curve for a mixture consisting of two weak acids HA and HB. Again, there are two equivalence points. In this case, however, the equivalence points do not require the same volume of titrant because the concentration of HA is greater than that for HB. Since HA is the stronger of the two weak acids, it reacts first thus, the pH before the first equivalence point is controlled by the HA/A buffer. Between the two equivalence points the pH reflects the titration of HB and is determined by the HB/B buffer. Finally, after the second equivalence point, the excess strong base titrant is responsible for the pH. 

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 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... 

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. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

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. 

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. 

Titration is the analytical method used to determine the amount of acid in a solution. A measured volume of the acid solution is titrated by slowly adding a solution of base, typically NaOH, of known concentration. As incremental amounts of NaOH are added, the pH of the solution is determined and a plot of the pH of the solution versus the amount of OH added yields a titration curve. The titration curve for acetic acid is shown in Figure 2.12. In considering the progress of this titration, keep in mind two important equilibria ... 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

FIGURE 2.15 A buffer system consists of a weak acid, HA, and its conjugate base, A. The pH varies only slightly in the region of the titration curve where [HA] = [A ]. The unshaded box denotes this area of greatest buffering capacity. Buffer action when HA and A are both available in sufficient concentration, the solution can absorb input of either H or OH, and pH is maintained essentially constant. 

Buffers are solutions that tend to resist changes in their pH as acid or base is added. Typically, a buffer system is composed of a weak acid and its conjugate base. A solution of a weak acid that has a pH nearly equal to its by definition contains an amount of the conjugate base nearly equivalent to the weak acid. Note that in this region, the titration curve is relatively flat (Figure 2.15). Addition of H then has little effect because it is absorbed by the following reaction ... 

The titration of a solution of a weak acid with a solution of a strong base is shown graphically in Figure 18-4. This titration curve has four distinct regions, each characterized by different major species ... 

The principles that describe the titration of a weak acid also describe the titration of a weak base with hydronium ions. The titration curve for a weak base is shown in Figure 18-6. 

C18-0146. The figure beiow shows the titration curves for 50.0-mL samples of weak bases A, B, and C. The titrant was 0.10 M HCl. (a) Which is the strongest base (b) Which base has the largest p (c) What are the initial concentrations of the three bases (d) What are the approximate p K- values of the conjugate acids of the three bases (e) Which of the bases can be titrated quantitatively using indicators Explain your answers, and identify an appropriate indicator for each base that can be titrated successfully. 

Attention is secondly focused on Figure 6.5 (B) which represents the titration curve of a weak acid against a strong base. The poor dissociation of the weak acid is reflected in the initial conductivity being low. The addition of alkali results in the formation of highly ionized sodium acetate and the conductance of the solution begins to increase. 

Figure 6.8 shows the Bjerrum plots for an weak acid (benzoic acid, pKa 3.98, log So — 1.55, log mol/L [474]), a weak base (benzydamine, pKa 9.26, log So —3.83, log mol/L [472]), and an ampholyte (acyclovir, pKa 2.34 and 9.23, log So — 2.16, log mol/L I/40N ). These plots reveal the pKa and pA pp values as the pcH values at half-integral % positions. By simple inspection of the dashed curves in Fig. 6.8, the pKa values of the benzoic acid, benzydamine, and acyclovir are 4.0, 9.3, and (2.3, 9.2), respectively. The pA pp values depend on the concentrations used, as is evident in Fig. 6.8. It would not have been possible to deduce the constants by simple inspection of the titration curves (pH vs. volume of titrant, as in Fig. 6.7). The difference between pKa and pA pp can be used to determine log So, the intrinsic solubility, or log Ksp, the solubility product of the salt, as will be shown below.

FIGURE 5.1 Acid-base titration curves (a) 0.10 M HCI (strong acid) titrated with 0.10 M NaOH (strong base), (b) 0.010 M HCI titrated with 0.010 M NaOH, and (c) 0.10 M acetic acid (weak acid) titrated with 0.10 M NaOH. 

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