Titrations Based on Acid–Base Reactions: Quantitative Applications

Quantitative Applications

Although many quantitative applications of acid–base titrimetry have been replaced by other analytical methods, there are several important applications that continue to be listed as standard methods. In this section we review the general application of acid–base titrimetry to the analysis of inorganic and organic compounds, with an emphasis on selected applications in environmental and clinical analysis. First, however, we discuss the selection and standardization of acidic and basic titrants.

Selecting and Standardizing a Titrant 

Most common acid–base titrants are not readily available as primary standards and must be standardized before they can be used in a quantitative analysis. Standardization is accomplished by titrating a known amount of an appropriate acidic or basic primary standard.

The majority of titrations involving basic analytes, whether conducted in aque- ous or nonaqueous solvents, use HCl, HClO₄, or H₂SO₄ as the titrant. Solutions of these titrants are usually prepared by diluting a commercially available concentrated stock solution and are stable for extended periods of time. Since the concentrations of concentrated acids are known only approximately,* the titrant’s concentration is determined by standardizing against one of the primary standard weak bases listed in Table 9.7.

The most common strong base for titrating acidic analytes in aqueous solutions is NaOH. Sodium hydroxide is available both as a solid and as an approximately 50% w/v solution. Solutions of NaOH may be standardized against any of the pri- mary weak acid standards listed in Table 9.7. The standardization of NaOH, how- ever, is complicated by potential contamination from the following reaction be- tween CO₂ and OH–.

CO2(g) + 2OH–(aq)  - > CO₃²â€“(aq) + H₂O(l)         …. 9.7

When CO₂ is present, the volume of NaOH used in the titration is greater than that needed to neutralize the primary standard because some OH– reacts with the CO₂

The calculated concentration of OH–, therefore, is too small. This is not a problem when titrations involving NaOH are restricted to an end point pH less than 6. Below this pH any CO₃2– produced in reaction 9.7 reacts with H₃O+ to form car- bonic acid.

CO₃2–(aq)+ 2H₃O+(aq) → H₂CO₃(aq)+ 2H O(l)

Combining reactions 9.7 and 9.8 gives an overall reaction of

CO₂(g)+ H₂O(l) → H₂CO₃(aq)

which does not include OH–. Under these conditions the presence of CO₂ does not affect the quantity of OH– used in the titration and, therefore, is not a source of de- terminate error.

For pHs between 6 and 10, however, the neutralization of CO₃2– requires only one proton

CO₃2–(aq)+H₃O+(aq) → HCO3–(aq)+H O(l)

and the net reaction between CO₂ and OH– is

CO₂(g)+ OH–(aq) → HCO₃–(aq)

Under these conditions some OH– is consumed in neutralizing CO₂. The result is a determinate error in the titrant’s concentration. If the titrant is used to analyze an analyte that has the same end point pH as the primary standard used during stan- dardization, the determinate errors in the standardization and the analysis cancel, and accurate results may still be obtained.

Solid NaOH is always contaminated with carbonate due to its contact with the atmosphere and cannot be used to prepare carbonate-free solutions of NaOH. So- lutions of carbonate-free NaOH can be prepared from 50% w/v NaOH since Na₂CO₃ is very insoluble in concentrated NaOH. When CO₂ is absorbed, Na₂CO₃ precipitates and settles to the bottom of the container, allowing access to the carbonate-free NaOH. Dilution must be done with water that is free from dissolved CO₂. Briefly boiling the water expels CO₂ and, after cooling, it may be used to pre- pare carbonate-free solutions of NaOH. Provided that contact with the atmosphere is minimized, solutions of carbonate-free NaOH are relatively stable when stored in polyethylene bottles. Standard solutions of sodium hydroxide should not be stored in glass bottles because NaOH reacts with glass to form silicate.

Inorganic Analysis 

Acid–base titrimetry is a standard method for the quantitative analysis of many inorganic acids and bases. Standard solutions of NaOH can be used in the analysis of inorganic acids such as H₃PO₄ or H₃AsO₄, whereas standard solutions of HCl can be used for the analysis of inorganic bases such as Na₂CO₃.

Inorganic acids and bases too weak to be analyzed by an aqueous acid–base titration can be analyzed by adjusting the solvent or by an indirect analysis. For ex- ample, the accuracy in titrating boric acid, H₃BO₃, with NaOH is limited by boric acid’s small acid dissociation constant of 5.8 x 10–10. The acid strength of boric acid, however, increases when mannitol is added to the solution because it forms a complex with the borate ion. The increase in K_a to approximately 1.5 x 10–4 results in a sharper end point and a more accurate titration. Similarly, the analysis of ammo- nium salts is limited by the small acid dissociation constant of 5.7 x 10–10 for NH₄+.

In this case, NH₄+ can be converted to NH by neutralizing with strong base. The NH₃, for which K_b is 1.8 x 10–5, is then removed by distillation and titrated with a standard strong acid titrant.

3NO₃–(aq) + 8Al(s) + 5OH–(aq)+ 2H₂O(l) → 8AlO₂–(aq) + 3NH₃ (aq)Inorganic analytes that are neutral in aqueous solutions may still be analyzed if they can be converted to an acid or base. For example, NO₃– can be quantitatively analyzed by reducing it to NH₃ in a strongly alkaline solution using Devarda’s alloy, a mixture of 50% w/w Cu, 45% w/w Al, and 5% w/w Zn.

Acid–base titrimetry continues to be listed as the standard method for the de- termination of alkalinity, acidity, and free CO₂ in water and wastewater analysis. Al- kalinity is a measure of the acid-neutralizing capacity of a water sample and is as- sumed to arise principally from OH–, HCO₃–, and CO₃2–, although other weak bases, such as phosphate, may contribute to the overall alkalinity. Total alkalinity is determined by titrating with a standard solution of HCl or H₂SO₄ to a fixed end point at a pH of 4.5, or to the bromocresol green end point. Alkalinity is reported as milligrams CaCO₃ per liter.The NH₃ is removed by distillation and titrated with HCl. Alternatively, NO₃– can be titrated as a weak base in an acidic nonaqueous solvent such as anhydrous acetic acid, using HClO₄ as a titrant.

When the sources of alkalinity are limited to OH–, HCO₃–, and CO₃2–, titra- tions to both a pH of 4.5 (bromocresol green end point) and a pH of 8.3 (phe- nolphthalein or metacresol purple end point) can be used to determine which species are present, as well as their respective concentrations. Titration curves for OH–, HCO₃–, and CO₃2– are shown in Figure 9.18. For a solution containing only OH– alkalinity, the volumes of strong acid needed to reach the two end points are identical. If a solution contains only HCO₃– alkalinity, the volume of strong acid needed to reach the end point at a pH of 8.3 is zero, whereas that for the pH 4.5 end point is greater than zero. When the only source of alkalinity is CO₃2–, the volume of strong acid needed to reach the end point at a pH of 4.5 is exactly twice that needed to reach the end point at a pH of 8.3.

Mixtures of OH– and CO₃2–, or HCO₃– and CO₃2– alkalinities also are possible. Consider, for example, a mixture of OH– and CO₃2–. The volume of strong acid needed to titrate OH– will be the same whether we titrate to the pH 8.3 or pH 4.5 end point. Titrating CO₃2– to the end point at a pH of 4.5, however, requires twice as much strong acid as when titrating to the pH 8.3 end point. Consequently, when titrating a mixture of these two ions, the volume of strong acid needed to reach the pH 4.5 end point is less than twice that needed to reach the end point at a pH of 8.3. For a mixture of HCO₃– and CO₃2–, similar reasoning shows that the volume of strong acid needed to reach the end point at a pH of 4.5 is more than twice that need to reach the pH 8.3 end point. Solutions containing OH– and HCO3– alkalini- ties are unstable with respect to the formation of CO₃2– and do not exist. Table 9.8 summarizes the relationship between the sources of alkalinity and the volume of titrant needed to reach the two end points.

Acidity is a measure of a water sample’s capacity for neutralizing base and is conveniently divided into strong acid and weak acid acidity. Strong acid acidity is due to the presence of inorganic acids, such as HCl, HNO₃, and H₂SO₄, and is com- monly found in industrial effluents and acid mine drainage. Weak acid acidity is usually dominated by the formation of H₂CO₃ from dissolved CO₂, but also includes contributions from hydrolyzable metal ions such as Fe3+, Al3+, and Mn2+. In addition, weak acid acidity may include a contribution from organic acids.

Acidity is determined by titrating with a standard solution of NaOH to fixed end points at pH 3.7 and pH 8.3. These end points are located potentiometrically, using a pH meter, or by using an appropriate indicator (bromophenol blue for pH 3.7, and metacresol purple or phenolphthalein for pH 8.3). Titrating to a pH of 3.7 provides a measure of strong acid acidity,* and titrating to a pH of 8.3 provides a measure of total acidity. Weak acid acidity is given indirectly as the difference be- tween the total and strong acid acidities. Results are expressed as the milligrams of CaCO₃ per liter that could be neutralized by the water sample’s acidity. An alterna- tive approach for determining strong and weak acidity is to obtain a potentiometric titration curve and use Gran plot methodology to determine the two equivalence points. This approach has been used, for example, in determining the forms of acid- ity in atmospheric aerosols.

Water in contact with either the atmosphere or carbonate-bearing sediments contains dissolved or free CO₂ that exists in equilibrium with gaseous CO₂ and the aqueous carbonate species H₂CO₃, HCO₃–, and CO₃2–. The concentration of free CO₂ is determined by titrating with a standard solution of NaOH to the phenol- phthalein end point, or to a pH of 8.3, with results reported as milligrams CO₂ per liter. This analysis is essentially the same as that for the determination of total acid- ity, and can only be applied to water samples that do not contain any strong acid acidity.

Organic Analysis 

The use of acid–base titrimetry for the analysis of organic com- pounds continues to play an important role in pharmaceutical, biochemical, agri- cultural, and environmental laboratories. Perhaps the most widely employed acid–base titration is the Kjeldahl analysis for organic nitrogen, described earlier in Method 9.1. This method continues to be used in the analysis of caffeine and sac- charin in pharmaceutical products, as well as for the analysis of proteins, fertilizers, sludges, and sediments. Any nitrogen present in the –3 oxidation state is quantita- tively oxidized to NH₄+. Some aromatic heterocyclic compounds, such as pyridine, are difficult to oxidize. A catalyst, such as HgO, is used to ensure that oxidation is complete. Nitrogen in an oxidation state other than –3, such as nitro- and azo- nitrogens, is often oxidized to N₂, resulting in a negative determinate error. Adding a reducing agent, such as salicylic acid, reduces the nitrogen to a –3 oxidation state, eliminating this source of error. Other examples of elemental analyses based on the conversion of the element to an acid or base are outlined in Table 9.9.

Several organic functional groups have weak acid or weak base properties that allow their direct determination by an acid–base titration. Carboxylic (—COOH), sulfonic (—SO₃H), and phenolic (—C₆H₅OH) functional groups are weak acids that can be successfully titrated in either aqueous or nonaqueous solvents. Sodium hydroxide is the titrant of choice for aqueous solutions. Nonaqueous titrations are often carried out in a basic solvent, such as ethylenediamine, using tetrabutylam- monium hydroxide, (C₄H₉)₄NOH, as the titrant. Aliphatic and aromatic amines are weak bases that can be titrated using HCl in aqueous solution or HClO₄ in glacial acetic acid. Other functional groups can be analyzed indirectly by use of a func- tional group reaction that produces or consumes an acid or base. Examples are shown in Table 9.10.

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 ana- lyzed in glacial acetic acid, using HClO₄ 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.

Quantitative Calculations 

In acid–base titrimetry the quantitative relationship be- tween the analyte and the titrant is determined by the stoichiometry of the relevant reactions. As outlined, stoichiometric calculations may be simplified by focusing on appropriate conservation principles. In an acid–base reaction the number of protons transferred between the acid and base is conserved; thus

The following example demonstrates the application of this approach in the direct analysis of a single analyte.

In an indirect analysis the analyte participates in one or more preliminary reac- tions that produce or consume acid or base. Despite the additional complexity, the stoichiometry between the analyte and the amount of acid or base produced or con- sumed may be established by applying the conservation principles outlined in Sec- tion 2C. Example 9.3 illustrates the application of an indirect analysis in which an acid is produced.

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.