Acid—base titrations

Titrations are procedures in which one reactant is slo dy added into a solution of another reactant, while equihbrium concentrations along the way are monitored, aoo (Section 4.6) There are two main reasons to do titrations (1) you want to know the concentration of one of the reactants or (2) you want to know the equilibrium constant for the reaction. 

To understand why titration curves have certain characteristic shapes, we will examine the curves for three kinds of titrations (1) strong acid-strong base, (2) weak acid-strong base, and (3) polyprotic acid-strong base. We will also briefly consider how these curves relate to those involving weak bases. 

Acid-base titration of the enzyme ribonuclease. The isoionic point is the pH of the pure protein with no ions present except H+ and OH. The isoelectric point is the pH at which the average charge on the protein is 0. [C. I Tanford and J. D. Hauenstein, Hydrogen Ion Equilibria of Ribonuclease. J. Am. Chem. Soc. 1956, 78.5287.] 

If tyrosine is buried deep inside the protein, it is not readily accessible and a high concentration of OH is required to remove the proton from the phenol group. 

Ribonuclease is an enzyme with 124 amino acids. Its function is to cleave ribonucleic acid (RNA) into small fragments. A solution containing pure protein, with no other ions present except H+ and OH- derived from the protein and water, is said to be isoionic. From this point near pH 9.6 in the graph, the protein can be titrated with acid or base. Of the 124 amino acids, 16 can be protonated by acid and 20 can lose protons to added base. From the shape of the titration curve, it is possible to deduce the approximate pATa for each titratable group.1-2 This information provides insight into the environment of that amino acid in the protein. In ribonuclease, three tyrosine residues have normal values of pATa(=10) (Table 10-1) and three others have pA a 12. The interpretation is that three tyrosine groups are accessible to OH, and three are buried inside the protein where they cannot be easily titrated. The solid line in the illustration is calculated from pA a values for all titratable groups. 

Theoretical titration curves for enzymes can be calculated from known crystal structures and first principles of electrostatics. Key amino acids at the active site have significantly perturbed pK values and unusual regions in which they are partially protonated over a wide pH region.3 In principle, such titration calculations can identify the active site of a protein whose structure is known, but whose function is not. 

From an acid-base titration curve, we can deduce the quantities and pK.d values of acidic and basic substances in a mixture. In medicinal chemistry, the pATa and lipophilicity of a candidate drug predict how easily it will cross cell membranes. We saw in Chapter 10 that from pKa and pH, we can compute the charge of a polyprotic acid. Usually, the more highly charged a drug, the harder it is to cross a cell membrane. In this chapter, we learn how to predict the shapes of titration curves and how to find end points with electrodes or indicators. 

The titration of an acid solution with a standard solution of alkali will determine the amount of alkali which is equivalent to the amount of acid present (or vice versa). The point at which this occurs is called the equivalence point or end-point. For example, the titration of hydrochloric acid with sodium hydroxide can be expressed as follows  

If both the acid and alkali are strong electrolytes, the resultant solution will be neutral (pH 7). If on the other hand either the acid or alkali is a weak electrolyte the resultant solution will be slightly alkaline or acidic, respectively. In either case, detection of the end-point requires accurate measurement of pH. This can be achieved either by using an indicator dye, or by measuring the pH with a glass electrode (described in Chapter 7). 

Typical acid-base indicators are organic dyes that change colour at or near the equivalence or end-point. They have the following characteristics  

Selected common indicators together with their pH ranges and colour changes are shown in Table 22.1. Ejcamples for thymol blue and phenolphthalein are shown in Fig. 22.1. 

Indicator pH. range Colour in acid Colour in aljcalma 

Indicator pH range Colour in acid solution Colour in alkaline solution 

A plot of pH against the volume of alkali added (mL) is known as a neutralization or titration curve (Fig. 22.2). The curve is generated by a potentiometric titration in which pH is measured after each addition of alkali (or add). The significant feature of the curve is the very sharp and sudden change in pH near to the equivalence point of the titration. For a strong acid and alkali this will occur at pH 7. If either the acid or base concentration is unknown, a preliminary titration is necessary to find the approximate equivalence point followed by a more accurate titration as described on p. 146. The ideal pH range for an indicator is 4.5-9.5. 

An important application for acid-base equilibria is the analytic method called titration. With the help of titration, it is possible to investigate the composition of an initial solution using the equivalence point. Moreover, it can also be used to 

If the proton potential is plotted as a function of the added volume of the titrator (or any other quantity dependent upon the added amount, such as the amount of protons), one obtains a so-called titration curve. 

Experiment 13. Add-base titration-. One possibility would be for example the titration of a sodium hydroxide solution with hydrochloric acid. A suitable sensor for these and other aqueous solutions would be a glass electrode that will be discussed in more detail in Sect. 22.7. 

At first, the proton potential changes only slightly as titrator is continuously added. However, as the point is approached where a stoichiometrically equivalent amount of hydrochloric acid (in this case 10 mmol) has been added to the sodium hydroxide solution, a drastic increase of proton potential occurs. At the equivalence point, there is no proton deficiency anymore, and the proton reservoir is completely filled. There is only an aqueous solution of Na and Cl ions that has almost no influence upon the proton potential which is then equal to the neutral value of —40 kG of pure water. If we continue to add hydrochloric acid to the neutralized 

7 Consequences of Mass Action Acid-Base Reactions 

The discussion of acid-base titrations in Chapter 4 focused on stoichiometry. Here, the emphasis is on the equilibrium principles that apply to the acid-base reactions involved. It is convenient to distinguish between titrations involving— 

Titrating a solution of HCI with NaOH using phenolphthalein as the indicator. 

As pointed out in Chapter 13, strong acids ionize completely in water to form H30+ ions strong bases dissolve in water to form OH- ions. The neutralization reaction that takes place when any strong acid reacts with any strong base can be represented by a net ionic equation of the Bronsted- Lowry type  

The equation just written is the reverse of that for the ionization of water, so the equilibrium constant can be calculated by using the reciprocal rule (Chapter 12). 

The enormous value of K means that for all practical purposes this reaction goes to completion, consuming the limiting reactant, H+ or OH-. 

At the equivalence point, when all the HCI has been neutralized by NaOH, a solution of NaCl, a neutral salt, is present. The pH at the equivalence point is 7. 

Chemists study acid-base reactions quantitatively through titrations. In any titration, one solution of known concentration is used to determine the concentration of another solution through a monitored reaction. 

Moles of (originally in flask) = moles of OH (added from buret) 

The end point of the titration occurs when a tiny excess of OH ions changes the indicator permanently to its color in base. In calculations, we assume this tiny excess is insignificant, and therefore the amount of base needed to reach the end point is the same as the amount needed to reach the equivalence point. 

Finding the Concentration of Acid from an Acid-Base Titration 

Problem You perform an acid-base titration to standardize an HCI solution by placing 50.00 mL of HCI in a flask with a few drops of indicator solution. You put 0.1524 M NaOH into the buret, and the initial reading is 0.55 mL. At the end point, the buret reading is 33.87 mL. What is the concentration of the HCI solution  

By this time you know that a strong acid solution contains H and a solution of strong base contains OH ions. As we saw earlier, when a strong acid and a strong base are mixed, the H and OH react to form H2O  

This reaction is called a neutralization reaction because if equal amounts of H+ and OH are available for reaction, a neutral solution (pH = 7) will result. 

Why can a strong add-strong base titration be called a neutralization reaction What is meant by a neutral solution  

The Titration of a Strong Acid with a Strong Base 

Determine the volume of 0.100 M NaOH needed to titrate 50.0 mL of 0.200 M HNO3. 

An acid-base titration is a procedure that is used where a base of known concentration is added to an acid of unknown concentration (or vice-versa) in order to determine the concentration of the unknown. In addition, it is possible to determine the of the acid being titrated (or of the base) as well as an appropriate indicator. Acid-base titrations are often the topic of AP exam questions and are frequently used in the laboratory questions. You should know about titrations from a conceptual level, be able to perform calculations for titrations, and know how to properly perform one in the laboratory. We ll begin with the conceptual explanation of titrations. 

One of the most common titrations of this type is the titration of hydrochloric acid, HCl, with sodium hydroxide, NaOH. If you remember from Chapter 10, this is a neutralization reaction. However, you should also remember from Chapter 11 that in order for a complete neutralization to occur, the reaction must use appropriate stoichiometric ratios. When we first look at the process, we will do so with two solutions of known concentration, but you will see that this process can be used to determine the concentration of one of the solutions. 

For the titration of a weak base with a strong acid, the effect is fairly similar. The main difference is that the pH will be lower than 7 at the equivalence point. As the hydrogen ions in the acid neutralize the hydroxide from the base, the concentration of the conjugate acid from the base will increase. If you recall, the conjugate acids of weak bases will 

Of considerable difference with the titrations of weak acids and weak bases are the buffering effects of the conjugate salts. The titration curves all contain a buffering region near the equivalence point where most of the solution consists of the conjugate base (for a weak acid titration a conjugate acid for a weak base titration)  

Arrhenius acids increase the concentration of H+ ions in solution, while Arrhenius bases increase the concentration of OH in solution. The strongest acids and bases are Arrhenius acids and bases. Br0nsted-Lowry acids donate protons in solution. Br0nsted-Lowry bases accept protons in solution. The definitions for Br0nsted-Lowry acids and bases are more broad and allow for the consideration of many more substances than either of the other two definitions. 

A solution of the strong base sodimn hydroxide can be used as the standard solution in a titration, but it must first be standardized, because sodium hydroxide in solution reacts with carbon dioxide in the air, making its concentration unstable over time. We can standardize the sodium hydroxide solution by titrating it against an acid solution of accurately known concentration. The acid often chosen for this task is a monoprotic acid called potassium hydrogen phthalate (BCHP), for which the molecular formula is KHC8H4O4. KHP is a white, soluble sohd that is commercially available in highly pure form. The reaction between KHP and sodium hydroxide is 

To standardize a solution of NaOH with KHP, a known amount of KHP is transferred to an Erlenmeyer flask and some distilled water is added to make up a solutiom Next, NaOH solution is carefully added to the KHP solution from a burette until all the acid has reacted with the base. This point in the titration, where the acid has been completely neutralized, is called the equivalence point. It is usually signaled by the endpoint, where an indicator causes a sharp change in the color of the solution. In acid-base titrations, indicators are substances that have distinctly different colors in acidic and basic media. One commonly used indicator is phenolphthalein, which is colorless in acidic and neutral solutions but reddish pink in basic solutions. At the equivalence point, all the KHP present has been neutralized by the added NaOH and the solution is still colorless. However, if we add just one more drop of NaOH solution from the buret, the solution will be basic and will immediately turn pink. Sample Problem 4.15 illustrates just such a titration. 

Student Annotation Standardization in this context is the meticulous determination of concentration. 

Student Annotation Note that KHP is a monoprotic acid, so it reacts in a 1 1 ratio xvith hydroxide ion. 

Student Annotation The endpoint in a titration is used to approximate the equivalence point. A careful choice of indicators, which we will discuss in Chapter 16, helps make this approximation reasonable. Phenolphthalein, although very common, is not appropriate for every acid-base titration. 

There are a few main types of titrations a strong acid titrated with a strong base (or a strong base titrated with a strong acid) a weak acid titrated with a strong base a weak base titrated with a strong acid and a polyprotic acid titrated with a strong base. Each one of these produces characteristic results and will need to be discussed separately. For the solutions of weak acids and bases, the process is complicated by the common-ion effect. 

The way that this procedure is typically done is to obtain a sample of strong base that has been standardized (the exact concentration determined) and place it into a buret. Frequently, questions appear on the test that deal with the procedures for titrations. One procedural question that has come up more than once involves the cleaning of the buret prior to the 

Strategy Using the mass given and the molar mass of KHP, determine the number of moles of KHP. Recognize that the number of mole.s of NaOH in the volume given is equal to the number of moles of KHP. Divide moles of NaOH by volume (in liters) to get molarity. 

Because moles of KHP = moles of NaOH, then moles of NaOH = 0.003495 mol. 

Solution The molar masses of Cl and AgCl are 35.45 g and 143.4 g, respectively. Therefore, the percent hy mass of Cl in AgCl is given by 

Because the original compound also contained this amount of Cl ions, the percent by mass of Cl in the compound is 

Practice Exercise A sample of 0.3220 g of an ionic compound containing the bromide ion (Br ) is dissolved in water and treated with an excess of AgN03. If the mass of the AgBr precipitate that forms is 0.6964 g, what is the percent by mass of Br in the original compound  

Note that gravimetric analysis does not establish the whole identity of the unknown. Thus, in Example 4.9 we still do not know what the cation is. However, knowing the percent by mass of Cl greatly helps us to narrow the possibilities. Because no two compounds containing the same anion (or cation) have the same percent composition by mass, comparison of the percent by mass obtained from gravimetric analysis with that calculated from a series of known compounds would reveal the identity of the unknown. 

Quantitative studies of acid-base neutralization reactions are most conveniently carried out using a technique known as titration. In titration, a solution of accurately known concentration, called a standard solution, is added gradually to another solution of unknown concentration, until the chemical reaction between the two solutions is complete. If we know the volumes of the standard and unknown solutions used in the titration, along with the concentration of the standard solution, we can calculate the concentration of the unknown solution. 

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Table8.23 Indicators for Aqueous Acid-Base Titrations 8.116...

Table 11.27 Primary Standards for Aqueous Acid-Base Titrations Table 11.28 Titrimetric (Volumetric) Factors...

Titrimetric (Volumetric) Factors for Acid-Base Titrations... 

Titrimetric (volumetric) factors for acids and bases are given in Table 11.28. Suitable indicators for acid-base titrations may be found in Tables 8.23 and 8.24. 

The %w/w Na2C03 in soda ash can be determined by an acid-base titration. The results obtained by two analysts are shown here. Determine whether the difference in their mean values is significant at a = 0.05. 

The accuracy of a standardization depends on the quality of the reagents and glassware used to prepare standards. For example, in an acid-base titration, the amount of analyte is related to the absolute amount of titrant used in the analysis by the stoichiometry of the chemical reaction between the analyte and the titrant. The amount of titrant used is the product of the signal (which is the volume of titrant) and the titrant s concentration. Thus, the accuracy of a titrimetric analysis can be no better than the accuracy to which the titrant s concentration is known. 

In this experiment the overall variance for the analysis of potassium hydrogen phthalate (KHP) in a mixture of KHP and sucrose is partitioned into that due to sampling and that due to the analytical method (an acid-base titration). By having individuals analyze samples with different % w/w KHP, the relationship between sampling error and concentration of analyte can be explored. 

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. 

The utility of acid-base titrimetry improved when NaOH was first introduced as a strong base titrant in 1846. In addition, progress in synthesizing organic dyes led to the development of many new indicators. Phenolphthalein was first synthesized by Bayer in 1871 and used as a visual indicator for acid-base titrations in 1877. Other indicators, such as methyl orange, soon followed. Despite the increasing availability of indicators, the absence of a theory of acid-base reactivity made selecting a proper indicator difficult. 

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. 

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... 

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. 

Many pharmaceutical compounds are weak acids or bases that can be analyzed by an aqueous or nonaqueous acid-base titration examples include salicylic acid, phenobarbital, caffeine, and sulfanilamide. Amino acids and proteins can be analyzed in glacial acetic acid, using HCIO4 as the titrant. For example, a procedure for determining the amount of nutritionally available protein has been developed that is based on an acid-base titration of lysine residues. ... 

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... 

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. 

Sensitivity For an acid-base titration we can write the following general analytical equation... 

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. 

Time, Cost, and Equipment Acid-base titrations require less time than most gravimetric procedures, but more time than many instrumental methods of analysis, particularly when analyzing many samples. With the availability of instruments for... 

Now that we know something about EDTA s chemical properties, we are ready to evaluate its utility as a titrant for the analysis of metal ions. To do so we need to know the shape of a complexometric EDTA titration curve. In Section 9B we saw that an acid-base titration curve shows the change in pH following the addition of titrant. The analogous result for a titration with EDTA shows the change in pM, where M is the metal ion, as a function of the volume of EDTA. In this section we learn how to calculate the titration curve. We then show how to quickly sketch the titration curve using a minimum number of calculations. 

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