Acid-base titrations determining equivalence point

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... 

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. 

Perhaps the most obvious limitation imposed by Ks is the change in pH during a titration. To see why this is so, let s consider the titration of a 50 mb solution of 10 M strong acid with equimolar strong base. Before the equivalence point, the pH is determined by the untitrated strong acid, whereas after the equivalence point the concentration of excess strong base determines the pH. In an aqueous solution the concentration of H3O+ when the titration is 90% complete is... 

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. 

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... 

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. 

Figure 6.3 A schematic pH curve for the titration of a strong acid with a strong base. At the equivalence point, the amount of alkali added is the same as the amount of acid in solution initially, allowing for an accurate calculation of the acid s concentration. Note how the end point is determined by extrapolating the linear regions, and drawing a third parallel line between them...

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. 

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. 

Any titration involves the progressive change of the activities (or concentrations) of the titrated and titrating species and, in principle, can be done potentiometrically. However, for an accurate determination it is necessary that there is a fairly rapid variation in equilibrium potential in the region of the equivalence point. Useful applications are redox, complexation, precipitation, acid-base titrations, etc. From the titration curve it is possible to calculate values of the formal potentials of the titrated and titrating species, as explained below. 

Fig. 13.2. Methods for determining the equivalence point of a potentiometric titration curve (including acid-base titrations), (a) First derivative (b) Second derivative (c) Gran plot for titration of a strong acid with a strong base Vx is the initial volume of acid and V the volume of base added.

An acid-base titration is a procedure that is typically used to determine the concentration of an unknown acid or base solution. In a titration, a strong or base or known concentration is added to a base or acid of unknown concentration. An indicator solution is typically utilized to mark the equivalence point, or the point at which the stoichiometric amounts of acid and base are equivalent. 

Acid-base titrations are an example of volumetric analysis, a technique in which one solution is used to analyze another. The solution used to carry out the analysis is called the titrant and is delivered from a device called a buret, which measures the volume accurately. The point in the titration at which enough titrant has been added to react exactly with the substance being determined is called the equivalence point, or the stoichiometric point. This point is often marked by the change in color of a chemical called an indicator. The titration procedure is illustrated in Fig. 4.18. 

There are two common methods for determining the equivalence point of an acid—base titration ... 

One common laboratory activity, which makes use of the information that we have covered in this chapter, is an acid-base titration reaction. A titration reaction is a neutralization reaction carried out using a solution with a known concentration (called a standard solution), in order to find the concentration of an unknown solution. By determining the volume of the standard solution required to neutralize a specific volume of the unknown solution, we can mathematically determine the concentration of the unknown. An indicator is used to signal the time when neutralization occurs, which is called the end point or the equivalence point of the titration. 

We find two types of titration errors in acid/base titrations. The first is a determinate error that occurs when the pH at which the indicator changes color differs from the pH at the equivalence point. This type of error can usually be minimized by choosing the indicator carefully or by making a blank correction. 

Analytically useful acid-base titration curves are characterized by a rather fast pH change near the equivalence point. This suggests that the location of the equivalence point might be determined experimentally from that of the maximum in its first derivative, d(pH)/dVfo, or the zero-crossing of its second derivative, d2(pH)/dVj,2. The advantage of such an approach is that it does not rely on any particular theoretical model, but instead exploits the characteristic feature of the titration curve, i.e., its fast pH change in the region around the equivalence point. The method does not even require that the pH meter is carefully calibrated. 

In order to titrate an unknown widi a standard solution, there must be some way to determine when the equivalence point of die titration has been reached. In acid-base titrations, dyes known as acid-base indicators are used for this purpose. For example, the dye known as phenolphthalein is colorless in acidic solution but is pink in basic solution. If we add phenolphthalein to an unknown solution of add, the solution will be colorless, as seen in Figure 4.19(a) . We can dien add standard base from a buret until the solution barely turns from colorless to pink, as seen in Figure 4.19(b). This color change indicates that die acid has been neutralized and the drop of base that caused the solution to become... 

In acid-base titration, a solution of known concentration (say, a base) is added gradually to a solution of im-known concentration (say, an acid) with the goal of determining the unknown concentration. The point at which the reaction in the titration is complete is called the equivalence point. 

As we saw in Chapter 4, a titration is commonly used to determine the amount of acid or base in a solution. This process involves a solution of known concentration (the ti-trant) delivered from a buret into the unknown solution until the substance being analyzed is just consumed. The stoichiometric (equivalence) point is often signaled by the color change of an indicator. In this section we will discuss the pH changes that occur during an acid-base titration. We will use this information later to show how an appropriate indicator can be chosen for a particular titration. 

Acid-Base Titration In an add-base titration, an acid (or base) of known concentration is added to a base (or acid) of unknown concentration. The two reactants are combined until they are in exact stoichiometric proportions (moles of H = moles of OH ), which marks the equivalence point of the titration. In titration, since you know the moles of H (or OH ) that you added, you can determine the moles of OH (or H ) in the unknown solution. 

We cover acid-base titrations and indicators in more detail in Chapter 16. In most laboratory titrations, the concentration of one of the reactant solutions is unknown, and the concentration of the other is precisely known. By carefully measuring the volume of each solution required to reach the equivalence point, we can determine the concentration of the unknown solution, as demonstrated in Example 4.14. 

An acid-base titration is a laboratory procedure in which a reaction is carried to its equivalence point—the point at which the reactants are in exact stoichiometric proportions titrations are useful in determining the concentrations of unknown solutions. 

---