Finding the End Point

The equivalence point in a titration is defined by the stoichiometry of the reaction. The end point is the abrupt change in a physical property (such as pH) that we measure to locate the equivalence point. Indicators and pH measurements are commonly used to find the end point in an acid-base titration. 

Choose an indicator whose color change comes as close as possible to the theoretical pH of the equivalence point. 

In Section 9-6, we learned that an indicator is an acid or base whose various proton-ated species have different colors. For the weak-acid indicator HIn, the solution takes on the color of HIn when pH pA Hin 1 and has the color of In when pH pA Hin + 1. In the interval pATnin - 1 pH pA Hin + 1, a mixture of both colors is observed. 

If you dump half a bottle of indicator into your reaction, you will introduce a different indicator error. Because indicators are acids or bases, they consume analyte 

One of the most common indicators is phenolphthalein, which changes from colorless in acid to pink in base  

As in acid-base titrations, indicators and electrodes are commonly used to find the end point of a redox titration. 

A redox indicator is a compound that changes color when it goes from its oxidized to its reduced state. The indicator ferroin changes from pale blue (almost colorless) to red. 

To predict the potential range over which the indicator color will change, we first write a Nemst equation for the indicator. 

As with acid-base indicators, the color of In( reduced) will be observed when 

Putting these quotients into Equation 16-14 tells us that the color change will occur over the range 

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To find the end point we monitor some property of the titration reaction that has a well-defined value at the equivalence point. Eor example, the equivalence point for a titration of ITCl with NaOlT occurs at a plT of 7.0. We can find the end point. 

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. 

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... 

Finding the End Point by Monitoring Temperature The reaction between an acid and a base is exothermic. Heat generated by the reaction increases the temperature of the titration mixture. The progress of the titration, therefore, can be followed by monitoring the change in temperature. 

Finding the End Point with a Visual Indicator Most indicators for complexation titrations are organic dyes that form stable complexes with metal ions. These dyes are known as metallochromic indicators. To function as an indicator for an EDTA titration, the metal-indicator complex must possess a color different from that of the uncomplexed indicator. Furthermore, the formation constant for the metal-indicator complex must be less favorable than that for the metal-EDTA complex. 

Finding the End Point Potentiometrically Another method for locating the end point of a redox titration is to use an appropriate electrode to monitor the change in electrochemical potential as titrant is added to a solution of analyte. The end point can then be found from a visual inspection of the titration curve. The simplest experimental design (Figure 9.38) consists of a Pt indicator electrode whose potential is governed by the analyte s or titrant s redox half-reaction, and a reference electrode that has a fixed potential. A further discussion of potentiometry is found in Chapter 11. 

Initial attempts at developing precipitation titration methods were limited by a poor end point signal. Finding the end point by looking for the first addition of titrant that does not yield additional precipitate is cumbersome at best. The feasibility of precipitation titrimetry improved with the development of visual indicators and potentiometric ion-selective electrodes. 

Students measured the concentration of HC1 in a solution by titrating with different indicators to find the end point.13... 

A problem with using derivatives to find the end point is that titration data are least accurate right near the end point, because buffering is minimal and electrode response is sluggish. A Gran plot uses data from before the end point (typically from 0.8 Vc or 0.9 Ve up to Vc) to locate the end point. 

The beauty of a Gran plot is that it enables us to use data taken before the end point to find the end point. The slope of the Gran plot enables us to find Ka. Although we derived the Gran function for a monoprotic acid, the same plot (VbIO-PH versus Vb) applies to polyprotic acids (such as H6A in Figure 11-6). 

I. Finding the end point from pH measurements. Here are data points around the second apparent end point in Figure 11-6 ... 

Finding the End Point with a pH Electrode 11-33. What is a Gran plot used for ... 

Data for the titration of 100.00 mL of a weak acid by NaOH are given below. Find the end point by preparing a Gran plot, using the last 10% of the volume prior to Ve. 

Prepare a second derivative graph to find the end point from the following titration data. 

Select indicators from Table 16-2 that would be suitable for finding the end point in Figure 16-3. What color changes would be observed ... 

To measure the total oxidizing power of chromium in the material, a crystal was dissolved in 2.9 M HC104 at 100°C, cooled to 20°C, and titrated with standard Fe2+, using Pt and Ag AgCl electrodes to find the end point. Chromium oxidized above the +3 state should oxidize an equivalent amount of Fe2+ in this step. That is, Cr4+ would consume one Fez+, and each atom of Cr6+ in Cr20 - would consume three Fe2+ ... 

Gran plot A graph such as the plot of Vb 10 ph versus Vb used to find the end point of a titration. Vb is the volume of base (titrant) added to an acid being titrated. The slope of the linear portion of the graph is related to the dissociation constant of the acid. 

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