Acid-base titration equivalence point

More precisely, the color change of an indicator signals the end point of the titration, which if the proper indicator is chosen lies very near the equivalence point. Acid-base titrations are discussed in more detail in Section 17.3. 

Equivalent Weights Acid-base titrations can be used to characterize the chemical and physical properties of matter. One simple example is the determination of the equivalent weighf of acids and bases. In this method, an accurately weighed sample of a pure acid or base is titrated to a well-defined equivalence point using a mono-protic strong acid or strong base. If we assume that the titration involves the transfer of n protons, then the moles of titrant needed to reach the equivalence point is given as... 

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... 

Sketching an Acid—Base Titration Curve To evaluate the relationship between an equivalence point and an end point, we only need to construct a reasonable approximation to the titration curve. In this section we demonstrate a simple method for sketching any acid-base titration curve. Our goal is to sketch the titration curve quickly, using as few calculations as possible. 

Where Is the Equivalence Point We have already learned how to calculate the equivalence point for the titration of a strong acid with a strong base, and for the titration of a weak acid with a strong base. We also have learned to sketch a titration curve with a minimum of calculations. Can we also locate the equivalence point without performing any calculations The answer, as you may have guessed, is often yes ... 

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. 

Earlier we noted that an acid-base titration may be used to analyze a mixture of acids or bases by titrating to more than one equivalence point. The concentration of each analyte is determined by accounting for its contribution to the volume of titrant needed to reach the equivalence points. 

Scale of Operation In an acid-base titration the volume of titrant needed to reach the equivalence point is proportional to the absolute amount of analyte present in the analytical solution. Nevertheless, the change in pH at the equivalence point, and thus the utility of an acid-base titration, is a function of the analyte s concentration in the solution being titrated. 

Accuracy When working with macro-major and macro-minor samples, acid-base titrations can be accomplished with relative errors of 0.1-0.2%. The principal limitation to accuracy is the difference between the end point and the equivalence point. 

In practice, however, any improvement in the sensitivity of an acid-base titration due to an increase in k is offset by a decrease in the precision of the equivalence point volume when the buret needs to be refilled. Consequently, standard analytical procedures for acid-base titrimetry are usually written to ensure that titrations require 60-100% of the buret s volume. 

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. 

Potcntiomctric Titrations In Chapter 9 we noted that one method for determining the equivalence point of an acid-base titration is to follow the change in pH with a pH electrode. The potentiometric determination of equivalence points is feasible for acid-base, complexation, redox, and precipitation titrations, as well as for titrations in aqueous and nonaqueous solvents. Acid-base, complexation, and precipitation potentiometric titrations are usually monitored with an ion-selective electrode that is selective for the analyte, although an electrode that is selective for the titrant or a reaction product also can be used. A redox electrode, such as a Pt wire, and a reference electrode are used for potentiometric redox titrations. More details about potentiometric titrations are found in Chapter 9. 

As pointed out in Chapter 4, an acid-base indicator is useful in determining the equivalence point of an acid-base titration. This is the point at which reaction is complete equivalent quantities of acid and base have reacted. If the indicator is chosen properly, the point at which it changes color (its end point) coincides with the equivalence point To understand how and why an indicator changes color, we need to understand the equilibrium principle involved. 

In acid-base titrations the end point is generally detected by a pH-sensitive indicator. In the EDTA titration a metal ion-sensitive indicator (abbreviated, to metal indicator or metal-ion indicator) is often employed to detect changes of pM. Such indicators (which contain types of chelate groupings and generally possess resonance systems typical of dyestuffs) form complexes with specific metal ions, which differ in colour from the free indicator and produce a sudden colour change at the equivalence point. The end point of the titration can also be evaluated by other methods including potentiometric, amperometric, and spectrophotometric techniques. 

A. Internal oxidation-reduction indicators. As discussed in Sections 10.10-10.16, acid-base indicators are employed to mark the sudden change in pH during acid-base titrations. Similarly an oxidation-reduction indicator should mark the sudden change in the oxidation potential in the neighbourhood of the equivalence point in an oxidation-reduction titration. The ideal oxidation-reduction indicator will be one with an oxidation potential intermediate between... 

Titrations can be carried out in cases in which the solubility relations are such that potentiometric or visual indicator methods are unsatisfactory for example, when the reaction product is markedly soluble (precipitation titration) or appreciably hydrolysed (acid-base titration). This is because the readings near the equivalence point have no special significance in amperometric titrations. Readings are recorded in regions where there is excess of titrant, or of reagent, at which points the solubility or hydrolysis is suppressed by the Mass Action effect the point of intersection of these lines gives the equivalence point. 

An analogous effect on the sharpness at the equivalence point as for an acid-base titration (cf., eqn. 2.30) may not be overlooked in the case of curve II because... 

In a titration, the equivalence point is the point at which chemically equivalent amounts of reactants have reacted, whereas the end point is the point at which an indicator changes color and a titration should be stopped. So, a chemist needs to be careful when choosing an indicator in an acid-base reaction, to be certain that the pH at which the indicator changes color is close to the pH at the equivalence point of the titration. 

In an acid-base titration you may either add acid to base or base to acid. This addition continues until there is some indication that the reaction is complete. Often a chemical known as an indicator will indicate the endpoint of a titration reaction, the experimental end of the titration. If we perform the experiment well, the endpoint should closely match the equivalence point of the titration, the theoretical end of the reaction. All the calculations in this section assume accurate experimental determination of the endpoint, and that this value is the same as the equivalence point. 

An acid-base titration is a laboratory procedure that we use to determine the concentration of an unknown solution. We add a base solution of known concentration to an acid solution of unknown concentration (or vice versa) until an acid-base indicator visually signals that the endpoint of the titration has been reached. The equivalence point is the point at which we have added a stoichiometric amount of the base to the acid. 

The addition of titrant from the buret must be stopped at precisely the correct moment—the moment at which the last trace of substance titrated is consumed by a fraction of a drop of titrant added, so that the correct volume can be read on the buret. That exact moment is called the equivalence point of the titration. In order to detect the equivalence point, an indicator is often used. An indicator is a substance added to the reaction flask ahead of time in order to cause a color change at or near the equivalence point, i.e., to provide a visual indication of the equivalence point. For example, the use of a chemical named phenolphthalein as an indicator for a titration in which a strong base is used as the titrant and an acid as the substance titrated would give a color change of colorless to pink in the reaction flask near the equivalence point. The color change occurring near, not exactly at, the equivalence point is usually not a concern. The reason will become clear in a later discussion. The point of a titration at which an indicator changes color, the visual indication of the equivalence point, is called the end point of the titration. As we will see, equivalence points can be determined in other ways too. 

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... 

The equivalence point of an acid—base titration is the point at which the moles of H+ from the acid equals the moles of OH- from the base. The endpoint is the point at which the indicator changes color, indicating the equivalence point. 

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. 

In an acid-base titration, you carefully measure the volumes of acid and base that react. Then, knowing the concentration of either the acid or the base, and the stoichiometric relationship between them, you calculate the concentration of the other reactant. The equivalence point in the titration occurs when just enough acid and base have been mixed for a complete reaction to occur, with no excess of either reactant. As you learned in Chapter 8, you can find the equivalence point from a graph that shows pH versus volume of one solution added to the other solution. To determine the equivalence point experimentally, you need to measure the pH. Because pH meters are expensive, and the glass electrodes are fragile, titrations are often performed using an acid-base indicator. 

For example, one indicator, called methyl red, is red when the pH is below 4.2, and yellow when the pH is above 6.2. The point in a titration at which an indicator changes colour is called the end-point. The colour change occurs over a range of about 2 pH units, but the pH of a solution changes rapidly near the equivalence point. Often a single drop of base causes the shift from colour 1 to colour 2. For methyl red, the end-point occurs over the pH range 4.2 to 6.2. Therefore, this indicator is used when an acid-base titration results in a moderately acidic solution at equivalence. Figure 9.3 shows the colours and end-points of various indicators. 

For the titration of a strong base with a weak acid, the equivalence point is reached when the pH is greater than 7. The half equivalence point is when half of the total amount of base needed to neutralize the acid has been added. It is at this point that the pH = pK of the weak acid. In acid-base titrations, a suitable acid-base indicator is used to detect the endpoint from the change of colour of the indicator used. An acid-base indicator is a weak acid or a weak base. The following table contains the names and the pH range of some commonly used acid-base indicators. 

The pH at the equivalence point in the titration of any strong base (or acid) with strong acid (or base) will be 7.00 at 25°C. 

As we will soon discover, the pH is not 7.00 at the equivalence point in the titration of weak acids or bases. The pH is 7.00 only if the titrant and analyte are both strong. 

The pH at the equivalence point in this titration is 9.25. It is not 7.00. The equivalence-point pH will always be above 7 for the titration of a weak acid, because the acid is converted into its conjugate base at the equivalence point. 

The pH is always higher than 7 at the equivalence point In the titration of a weak acid with a strong base. 

Why does an acid-base titration curve (pH versus volume of titrant) have an abrupt change at the equivalence point ... 

Equations 16-9 and 16-10 are analogous to the Henderson-Hasselbalch equation of acid-base buffers. Prior to the equivalence point, the redox titration is buffered to a potential near E+ = formal potential for Fc 1 Fe2+ by the presence of Fe 1 and Fe2+. After the equivalence point, the reaction is buffered to a potential near E+ = formal potential for Ce4+ Ce3+. [R. de Levie Redox Buffer Strength, J. Chem. Ed. 1999, 76, 574.]... 

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