Titration curves for

Examples of titration curves for (a) a complexation titration, (b) a redox titration, and (c) a precipitation titration. 

In the overview to this chapter we noted that the experimentally determined end point should coincide with the titration s equivalence point. For an acid-base titration, the equivalence point is characterized by a pH level that is a function of the acid-base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration. In this section we will learn how to construct titration curves for several important types of acid-base titrations. Our... 

Sketch the titration curve for the titration of 50.0 mb of 0.100 M acetic acid with 0.100 M NaOH. This is the same titration for which we previously calculated the titration curve (Table 9.3 and Figure 9.6). 

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. 

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... 

Titration curve for 50.00 ml of 0.100 M CH3COOH with 0.100 M NaOH showing the range of pHs and volumes of titrant over which the indicators bromothymol blue and phenolphthalein are expected to change color. 

Another method for finding the end point is to plot the first or second derivative of the titration curve. The slope of a titration curve reaches its maximum value at the inflection point. The first derivative of a titration curve, therefore, shows a separate peak for each end point. The first derivative is approximated as ApH/AV, where ApH is the change in pH between successive additions of titrant. For example, the initial point in the first derivative titration curve for the data in Table 9.5 is... 

Titration curves for a weak acid with 0.100 M NaOH—(a) normal titration curve (b) first derivative titration curve ... 

Spectrophotometric titration curves for the titration of an analyte, A, with a titrant, T, to form a product, P, in the presence of a visual indicator. Titration curves are shown for cases where (a) only A absorbs (b) only T absorbs (c) only P absorbs (d) A and T absorb (e) P and T absorb and (f) only the visual indicator absorbs. 

Titration curves for 10 M Mg + with 10 M EDTA using calmagite as an indicator at (a) pH = 9, (b) pH = 10, and (c) pH = 11. The range of pMg and volume of titrant over which the indicator is expected to change color is shown for each titration curve. 

Spectrophotometric titration curve for the complexation titration of a mixture. 

Titration curve for Fe + with Mn04 in 1 M H2SO4 equivalence point is shown by the symbol . 

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. 

The titration curve for a precipitation titration follows the change in either the analyte s or titrant s concentration as a function of the volume of titrant. For example, in an analysis for V using Ag+ as a titrant... 

Titration curve for a mixture of 1 and Cl using AgNOa as a titrant. 

A quantitative analysis for NH3 in several household cleaning products is carried out by titrating with a standard solution of HGl. The titration s progress is followed thermometrically by monitoring the temperature of the titration mixture as a function of the volume of added titrant. Household cleaning products may contain other basic components, such as sodium citrate or sodium carbonate, that will also be titrated by HGl. By comparing titration curves for prepared samples of NH3 to titration curves for the samples, it is possible to determine that portion of the thermometric titration curve due to the neutralization of NH3. 

Calculate or sketch (or both) qualitatively correct titration curves for the following acid-base titrations. 

The following data were collected with an automatic titrator during the titration of a monoprotic weak acid with a strong base. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for this data, and locate the equivalence point for each. 

Schwartz has published some hypothetical data for the titration of a 1.02 X ICr" M solution of a monoprotic weak acid (pXa = 8.16) with 1.004 X ICr M NaOH. " A 50-mL pipet is used to transfer a portion of the weak acid solution to the titration vessel. Calibration of the pipet, however, shows that it delivers a volume of only 49.94 ml. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for these data, and determine the equivalence point for each. How do these equivalence points compare with the expected equivalence point Comment on the utility of each titration curve for the analysis of very dilute solutions of very weak acids. 

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