Chapter 10 Acids and Bases

Many of us are familiar with the group of chemicals called acids. But do you know what it takes for a compound to be an acid? Actually, there are several different definitions of acid that chemistry uses, and each definition is appropriate under different circumstances. Less familiar---but just as important to chemistry and ultimately to us---is the group of chemicals known as bases. Both acids and bases are important enough that we devote an entire chapter to them---their properties and their reactions. Figure 10.1 "Prevalence of Acids and Bases" illustrates how common acids and bases are in everyday life.

10.1 Arrhenius Definition of Acids and Bases¶

One way to define a class of compounds is by describing the various characteristics its members have in common. In the case of the compounds known as acids, the common characteristics include a sour taste, the ability to change the color of the vegetable dye litmus to red, and the ability to dissolve certain metals and simultaneously produce hydrogen gas. For the compounds called bases, the common characteristics are a slippery texture, a bitter taste, and the ability to change the color of litmus to blue. Acids and bases also react with each other to form compounds generally known as salts.

Chemists prefer, however, to have definitions for acids and bases in chemical terms. The Swedish chemist Svante Arrhenius developed the first chemical definitions of acids and bases in the late 1800s. Arrhenius defined an acid^[1] as a compound that increases the concentration of hydrogen ion (H⁺) in aqueous solution. Many acids are simple compounds that release a hydrogen cation into solution when they dissolve. Similarly, Arrhenius defined a base^[2] as a compound that increases the concentration of hydroxide ion (OH⁻) in aqueous solution. Many bases are ionic compounds that have the hydroxide ion as their anion, which is released when the base dissolves in water.

Many bases and their aqueous solutions are named using the normal rules of ionic compounds that were presented in Chapter 3 "Ionic Bonding and Simple Ionic Compounds", Section 3.4 "Ionic Nomenclature"; that is, they are named as hydroxide compounds. For example, the base sodium hydroxide (NaOH) is both an ionic compound and an aqueous solution. However, aqueous solutions of acids have their own naming rules. The names of binary acids (compounds with hydrogen and one other element in their formula) are based on the root of the name of the other element preceded by the prefix hydro- and followed by the suffix -ic acid. Thus, an aqueous solution of HCl [designated “HCl(aq)”] is called hydrochloric acid, H₂S(aq) is called hydrosulfuric acid, and so forth. Acids composed of more than two elements (typically hydrogen and oxygen and some other element) have names based on the name of the other element, followed by the suffix -ic acid or -ous acid, depending on the number of oxygen atoms in the acid’s formula. Other prefixes, like per- and hypo-, also appear in the names for some acids. Unfortunately, there is no strict rule for the number of oxygen atoms that are associated with the -ic acid suffix; the names of these acids are best memorized. Table 10.1 "Formulas and Names for Some Acids and Bases" lists some acids and bases and their names. Note that acids have hydrogen written first, as if it were the cation, while most bases have the negative hydroxide ion, if it appears in the formula, written last.

Table 10.1 Formulas and Names for Some Acids and Bases

Example 1¶

Name each substance.

1. HF(aq)

2. Sr(OH)₂(aq)

Solution

1. This acid has only two elements in its formula, so its name includes the hydro- prefix. The stem of the other element’s name, fluorine, is fluor, and we must also include the -ic acid ending. Its name is hydrofluoric acid.

2. This base is named as an ionic compound between the strontium ion and the hydroxide ion: strontium hydroxide.

Skill-Building Exercise¶

Name each substance.

1. H₂Se(aq)

2. Ba(OH)₂(aq)

Notice that one base listed in Table 10.1 "Formulas and Names for Some Acids and Bases"---ammonia---does not have hydroxide as part of its formula. How does this compound increase the amount of hydroxide ion in aqueous solution? Instead of dissociating into hydroxide ions, ammonia molecules react with water molecules by taking a hydrogen ion from the water molecule to produce an ammonium ion and a hydroxide ion:

NH₃(aq) + H₂O(ℓ) → NH₄⁺(aq) + OH⁻(aq)

Because this reaction of ammonia with water causes an increase in the concentration of hydroxide ions in solution, ammonia satisfies the Arrhenius definition of a base. Many other nitrogen-containing compounds are bases because they too react with water to produce hydroxide ions in aqueous solution.

As we noted previously, acids and bases react chemically with each other to form salts. A salt is a general chemical term for any ionic compound formed from an acid and a base. In reactions where the acid is a hydrogen ion containing compound and the base is a hydroxide ion containing compound, water is also a product. The general reaction is as follows:

acid + base → water + salt

The reaction of acid and base to make water and a salt is called neutralization^[3]. Like any chemical equation, a neutralization chemical equation must be properly balanced. For example, the neutralization reaction between sodium hydroxide and hydrochloric acid is as follows:

NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(ℓ)

with coefficients all understood to be one. The neutralization reaction between sodium hydroxide and sulfuric acid is as follows:

2NaOH(aq) + H₂SO₄(aq) → Na₂SO₄(aq) + 2H₂O(ℓ)

Once a neutralization reaction is properly balanced, we can use it to perform stoichiometry calculations, such as the ones we practiced in Chapter 5 "Introduction to Chemical Reactions" and Chapter 6 "Quantities in Chemical Reactions".

Example 2¶

Nitric acid [HNO₃(aq)] can be neutralized by calcium hydroxide [Ca(OH)₂(aq)].

1. Write a balanced chemical equation for the reaction between these two compounds and identify the salt it produces.

2. For one reaction, 16.8 g of HNO₃ is present initially. How many grams of Ca(OH)₂ are needed to neutralize that much HNO₃?

3. In a second reaction, 805 mL of 0.672 M Ca(OH)₂ is present initially. What volume of 0.432 M HNO₃ solution is necessary to neutralize the Ca(OH)₂ solution?

Solution

1. Because there are two OH⁻ ions in the formula for Ca(OH)₂, we need two moles of HNO₃ to provide H⁺ ions. The balanced chemical equation is as follows:

   Ca(OH)₂(aq) + 2HNO₃(aq) → Ca(NO₃)₂(aq) + 2H₂O(ℓ)

   The salt formed is calcium nitrate.

2. This calculation is much like the calculations we did in Chapter 6 "Quantities in Chemical Reactions". First we convert the mass of HNO₃ to moles using its molar mass of 1.01 + 14.00 + 3(16.00) = 63.01 g/mol; then we use the balanced chemical equation to determine the related number of moles of Ca(OH)₂ needed to neutralize it; and then we convert that number of moles of Ca(OH)₂ to the mass of Ca(OH)₂ using its molar mass of 40.08 + 2(1.01) + 2(16.00) = 74.10 g/mol.

   $$16.8\text{~g}\cancel{\text{~HNO}_{\text{3}}}\, \times \,\frac{1\text{~mol}\cancel{\text{~HNO}_{\text{3}}}}{63.01\text{~g}\cancel{\text{~HNO}_{\text{3}}}}\, \times \,\frac{1\text{~mol}\cancel{\text{~Ca(OH)}_{\text{2}}}}{2\text{~mol}\cancel{\text{~HNO}_{\text{3}}}}\, \times \,\frac{74.10\text{~g~Ca(OH)}_{\text{2}}}{1\text{~mol}\cancel{\text{~Ca(OH)}_{\text{2}}}} = 9.88\text{~g~Ca(OH)}_{\text{2}}\text{~needed}$$

3. Having concentration information allows us to employ the skills we developed in Chapter 9 "Solutions". First, we use the concentration and volume data to determine the number of moles of Ca(OH)₂ present. Recognizing that 805 mL = 0.805 L,

   $$0.672\text{~M~Ca(OH)}_{\text{2}} = \frac{\text{mol~Ca(OH)}_{\text{2}}}{0.805\text{~L~soln}}$$

   (0.672 M CaOH)₂ × (0.805 L soln) = mol Ca(OH)₂ = 0.541 mol Ca(OH)₂

   We combine this information with the proper ratio from the balanced chemical equation to determine the number of moles of HNO₃ needed:

   $$0.541\cancel{\text{~mol~Ca(OH)}_{\text{2}}} \times \frac{2\text{~mol~HNO}_{\text{3}}}{1\cancel{\text{~mol~Ca(OH)}_{\text{2}}}} = 1.08\text{~mol~HNO}_{\text{3}}$$

   Now, using the definition of molarity one more time, we determine the volume of acid solution needed:

   $$0.432\text{~M~HNO}_{\text{3}} = \frac{1.08\text{~mol~HNO}_{\text{3}}}{\text{volume~of~HNO}_{\text{3}}}$$
   $$\text{volume~of~HNO}_{\text{3}} = \frac{1.08\text{~mol~HNO}_{\text{3}}}{0.432\text{~M~HNO}_{\text{3}}} = 2.50\text{~L} = \text{2}\text{.50} \times \text{10}^{\text{3}}\text{~mL~HNO}_{\text{3}}$$

Skill-Building Exercise¶

Hydrocyanic acid [HCN(aq)] can be neutralized by potassium hydroxide [KOH(aq)].

1. Write a balanced chemical equation for the reaction between these two compounds and identify the salt it produces.

2. For one reaction, 37.5 g of HCN is present initially. How many grams of KOH are needed to neutralize that much HCN?

3. In a second reaction, 43.0 mL of 0.0663 M KOH is present initially. What volume of 0.107 M HCN solution is necessary to neutralize the KOH solution?

Concept Review Exercises¶

1. Give the Arrhenius definitions of an acid and a base.

2. What is neutralization?

Answers¶

1. Arrhenius acid: a compound that increases the concentration of hydrogen ion (H⁺) in aqueous solution; Arrhenius base: a compound that increases the concentration of hydroxide ion (OH⁻) in aqueous solution.

2. the reaction of an acid and a base

Exercises¶

1. Give two examples of Arrhenius acids.

2. Give two examples of Arrhenius bases.

3. List the general properties of acids.

4. List the general properties of bases.

5. Name each compound.

   1. HBr(aq)

   2. Ca(OH)₂(aq)

   3. HNO₃(aq)

   4. Fe(OH)₃(aq)

6. Name each compound.

   1. HI(aq)

   2. Cu(OH)₂(aq)

   3. H₃PO₄(aq)

   4. CsOH(aq)

7. Propose a name for water (H₂O) using the rules for naming acids.

8. Propose a name for hydrogen peroxide (H₂O₂) using the rules for naming acids.

9. Write a balanced chemical equation for the neutralization of Ba(OH)₂(aq) with HNO₃(aq).

10. Write a balanced chemical equation for the neutralization of H₂SO₄(aq) with Cr(OH)₃(aq).

11. How many moles of sodium hydroxide (NaOH) are needed to neutralize 0.844 mol of acetic acid (HC₂H₃O₂)? (Hint: begin by writing a balanced chemical equation for the process.)

12. How many moles of perchloric acid (HClO₄) are needed to neutralize 0.052 mol of calcium hydroxide [Ca(OH)₂]? (Hint: begin by writing a balanced chemical equation for the process.)

13. Hydrazoic acid (HN₃) can be neutralized by a base.

    1. Write the balanced chemical equation for the reaction between hydrazoic acid and calcium hydroxide.

    2. How many milliliters of 0.0245 M Ca(OH)₂ are needed to neutralize 0.564 g of HN₃?

14. Citric acid (H₃C₆H₅O₇) has three hydrogen atoms that can form hydrogen ions in solution.

    1. Write the balanced chemical equation for the reaction between citric acid and sodium hydroxide.

    2. If an orange contains 0.0675 g of H₃C₆H₅O₇, how many milliliters of 0.00332 M NaOH solution are needed to neutralize the acid?

15. Magnesium hydroxide [Mg(OH)₂] is an ingredient in some antacids. How many grams of Mg(OH)₂ are needed to neutralize the acid in 158 mL of 0.106 M HCl(aq)? It might help to write the balanced chemical equation first.

16. Aluminum hydroxide [Al(OH)₃] is an ingredient in some antacids. How many grams of Al(OH)₃ are needed to neutralize the acid in 96.5 mL of 0.556 M H₂SO₄(aq)? It might help to write the balanced chemical equation first.

Answers¶

1. HCl and HNO₃ (answers will vary)

3. sour taste, react with metals, react with bases, and turn litmus red

5. 1. hydrobromic acid

   2. calcium hydroxide

   3. nitric acid

   4. iron(III) hydroxide

7. perhaps hydroxic acid

9. 2HNO₃(aq) + Ba(OH)₂(aq) → Ba(NO₃)₂(aq) + 2H₂O

11. 0.844 mol

13. 1. 2HN₃(aq) + Ca(OH)₂ → Ca(N₃)₂ + 2H₂O

    2. 268 mL

15. 0.488 g

10.2 Brønsted-Lowry Definition of Acids and Bases¶

Ammonia (NH₃) increases the hydroxide ion concentration in aqueous solution by reacting with water rather than releasing hydroxide ions directly. In fact, the Arrhenius definitions of an acid and a base focus on hydrogen ions and hydroxide ions. Are there more fundamental definitions for acids and bases?

In 1923, the Danish scientist Johannes Brønsted and the English scientist Thomas Lowry independently proposed new definitions for acids and bases. Rather than considering both hydrogen and hydroxide ions, they focused on the hydrogen ion only. A Brønsted-Lowry acid^[4] is a compound that supplies a hydrogen ion in a reaction. A Brønsted-Lowry base^[5], conversely, is a compound that accepts a hydrogen ion in a reaction. Thus, the Brønsted-Lowry definitions of an acid and a base focus on the movement of hydrogen ions in a reaction, rather than on the production of hydrogen ions and hydroxide ions in an aqueous solution.

Let us use the reaction of ammonia in water to demonstrate the Brønsted-Lowry definitions of an acid and a base. Ammonia and water molecules are reactants, while the ammonium ion and the hydroxide ion are products:

NH₃(aq) + H₂O(ℓ) → NH₄⁺(aq) + OH⁻(aq)

What has happened in this reaction is that the original water molecule has donated a hydrogen ion to the original ammonia molecule, which in turn has accepted the hydrogen ion. We can illustrate this as follows:

Because the water molecule donates a hydrogen ion to the ammonia, it is the Brønsted-Lowry acid, while the ammonia molecule---which accepts the hydrogen ion---is the Brønsted-Lowry base. Thus, ammonia acts as a base in both the Arrhenius sense and the Brønsted-Lowry sense.

Is an Arrhenius acid like hydrochloric acid still an acid in the Brønsted-Lowry sense? Yes, but it requires us to understand what really happens when HCl is dissolved in water. Recall that the hydrogen atom is a single proton surrounded by a single electron. To make the hydrogen ion, we remove the electron, leaving a bare proton. Do we really have bare protons floating around in aqueous solution? No, we do not. What really happens is that the H⁺ ion attaches itself to H₂O to make H₃O⁺, which is called the hydronium ion. For most purposes, H⁺ and H₃O⁺ represent the same species, but writing H₃O⁺ instead of H⁺ shows that we understand that there are no bare protons floating around in solution. Rather, these protons are actually attached to solvent molecules.

With this in mind, how do we define HCl as an acid in the Brønsted-Lowry sense? Consider what happens when HCl is dissolved in H₂O:

HCl + H₂O(ℓ) → H₃O⁺(aq) + Cl⁻(aq)

We can depict this process using Lewis electron dot diagrams:

Now we see that a hydrogen ion is transferred from the HCl molecule to the H₂O molecule to make chloride ions and hydronium ions. As the hydrogen ion donor, HCl acts as a Brønsted-Lowry acid; as a hydrogen ion acceptor, H₂O is a Brønsted-Lowry base. So HCl is an acid not just in the Arrhenius sense but also in the Brønsted-Lowry sense. Moreover, by the Brønsted-Lowry definitions, H₂O is a base in the formation of aqueous HCl. So the Brønsted-Lowry definitions of an acid and a base classify the dissolving of HCl in water as a reaction between an acid and a base---although the Arrhenius definition would not have labeled H₂O a base in this circumstance.

Example 3¶

Aniline (C₆H₅NH₂) is slightly soluble in water. It has a nitrogen atom that can accept a hydrogen ion from a water molecule just like the nitrogen atom in ammonia does. Write the chemical equation for this reaction and identify the Brønsted-Lowry acid and base.

Solution

C₆H₅NH₂ and H₂O are the reactants. When C₆H₅NH₂ accepts a proton from H₂O, it gains an extra H and a positive charge and leaves an OH⁻ ion behind. The reaction is as follows:

C₆H₅NH₂(aq) + H₂O(ℓ) → C₆H₅NH₃⁺(aq) + OH⁻(aq)

Because C₆H₅NH₂ accepts a proton, it is the Brønsted-Lowry base. The H₂O molecule, because it donates a proton, is the Brønsted-Lowry acid.

Skill-Building Exercise¶

1. Caffeine (C₈H₁₀N₄O₂) is a stimulant found in coffees and teas. When dissolved in water, it can accept a proton from a water molecule. Write the chemical equation for this process and identify the Brønsted-Lowry acid and base.

The Brønsted-Lowry definitions of an acid and a base can be applied to chemical reactions that occur in solvents other than water. The following example illustrates.

Example 4¶

Sodium amide (NaNH₂) dissolves in methanol (CH₃OH) and separates into sodium ions and amide ions (NH₂⁻). The amide ions react with methanol to make ammonia and the methoxide ion (CH₃O⁻). Write a balanced chemical equation for this process and identify the Brønsted-Lowry acid and base.

Solution

The equation for the reaction between NH₂⁻ and CH₃OH to make NH₃ and CH₃O⁻ is as follows:

NH₂⁻(solv) + CH₃OH(ℓ) → NH₃(solv) + CH₃O⁻(solv)

The label (solv) indicates that the species are dissolved in some solvent, in contrast to (aq), which specifies an aqueous (H₂O) solution. In this reaction, we see that the NH₂⁻ ion accepts a proton from a CH₃OH molecule to make an NH₃ molecule. Thus, as the proton acceptor, NH₂⁻ is the Brønsted-Lowry base. As the proton donor, CH₃OH is the Brønsted-Lowry acid.

Skill-Building Exercise¶

1. Pyridinium chloride (C₅H₅NHCl) dissolves in ethanol (C₂H₅OH) and separates into pyridinium ions (C₅H₅NH⁺) and chloride ions. The pyridinium ion can transfer a hydrogen ion to a solvent molecule. Write a balanced chemical equation for this process and identify the Brønsted-Lowry acid and base.

Concept Review Exercise¶

1. Give the definitions of a Brønsted-Lowry acid and a Brønsted-Lowry base.

Answer¶

1. A Brønsted-Lowry acid is a proton donor, while a Brønsted-Lowry base is a proton acceptor.

Exercises¶

1. Label each reactant as a Brønsted-Lowry acid or a Brønsted-Lowry base.

   HCl(aq) + NH₃(aq) → NH₄⁺(aq) + Cl⁻(aq)

2. Label each reactant as a Brønsted-Lowry acid or a Brønsted-Lowry base.

   H₂O(ℓ) + N₂H₄(aq) → N₂H₅⁺(aq) + OH⁻(aq)

3. Explain why a Brønsted-Lowry acid can be called a proton donor.

4. Explain why a Brønsted-Lowry base can be called a proton acceptor.

5. Write the chemical equation of the reaction of ammonia in water and label the Brønsted-Lowry acid and base.

6. Write the chemical equation of the reaction of methylamine (CH₃NH₂) in water and label the Brønsted-Lowry acid and base.

7. Demonstrate that the dissolution of HNO₃ in water is actually a Brønsted-Lowry acid-base reaction by describing it with a chemical equation and labeling the Brønsted-Lowry acid and base.

8. Identify the Brønsted-Lowry acid and base in the following chemical equation:

   C₃H₇NH₂(aq) + H₃O⁺(aq) → C₃H₇NH₃⁺(aq) + H₂O(ℓ)

9. Write the chemical equation for the reaction that occurs when cocaine hydrochloride (C₁₇H₂₂ClNO₄) dissolves in water and donates a proton to a water molecule. (When hydrochlorides dissolve in water, they separate into chloride ions and the appropriate cation.)

10. If codeine hydrobromide has the formula C₁₈H₂₂BrNO₃, what is the formula of the parent compound codeine?

Answers¶

1. HCl: Brønsted-Lowry acid; NH₃: Brønsted-Lowry base

3. A Brønsted-Lowry acid gives away an H⁺ ion---nominally, a proton---in an acid-base reaction.

5. NH₃ + H₂O → NH₄⁺ + OH⁻; NH₃: Brønsted-Lowry base; H₂O: Brønsted-Lowry acid

7. HNO₃ + H₂O → H₃O⁺ + NO₃⁻; HNO₃: Brønsted-Lowry acid; H₂O: Brønsted-Lowry base

9. C₁₇H₂₂NO₄₊ + H₂O → H₃O⁺ + C₁₇H₂₁NO₄

10.3 Water: Both an Acid and a Base¶

Water (H₂O) is an interesting compound in many respects. Here, we will consider its ability to behave as an acid or a base.

In some circumstances, a water molecule will accept a proton and thus act as a Brønsted-Lowry base. We saw an example in the dissolving of HCl in H₂O:

HCl + H₂O(ℓ) → H₃O⁺(aq) + Cl⁻(aq)

In other circumstances, a water molecule can donate a proton and thus act as a Brønsted-Lowry acid. For example, in the presence of the amide ion (see Example 4 in Section 10.2 "Brønsted-Lowry Definition of Acids and Bases"), a water molecule donates a proton, making ammonia as a product:

H₂O(ℓ) + NH₂⁻(aq) → OH⁻(aq) + NH₃(aq)

In this case, NH₂⁻ is a Brønsted-Lowry base (the proton acceptor).

So, depending on the circumstances, H₂O can act as either a Brønsted-Lowry acid or a Brønsted-Lowry base. Water is not the only substance that can react as an acid in some cases or a base in others, but it is certainly the most common example---and the most important one. A substance that can either donate or accept a proton, depending on the circumstances, is called an amphiprotic^[6] compound.

A water molecule can act as an acid or a base even in a sample of pure water. About 6 in every 100 million (6 in 10⁸) water molecules undergo the following reaction:

H₂O(ℓ) + H₂O(ℓ) → H₃O⁺(aq) + OH⁻(aq)

This process is called the autoionization of water^[7] (Figure 10.2 "Autoionization") and occurs in every sample of water, whether it is pure or part of a solution. Autoionization occurs to some extent in any amphiprotic liquid. (For comparison, liquid ammonia undergoes autoionization as well, but only about 1 molecule in a million billion (1 in 10¹⁵) reacts with another ammonia molecule.)

Example 5¶

Identify water as either a Brønsted-Lowry acid or a Brønsted-Lowry base.

1. H₂O(ℓ) + NO₂⁻(aq) → HNO₂(aq) + OH⁻(aq)

2. HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)

Solution

1. In this reaction, the water molecule donates a proton to the NO₂⁻ ion, making OH⁻(aq). As the proton donor, H₂O acts as a Brønsted-Lowry acid.

2. In this reaction, the water molecule accepts a proton from HC₂H₃O₂, becoming H₃O⁺(aq). As the proton acceptor, H₂O is a Brønsted-Lowry base.

Skill-Building Exercise¶

Identify water as either a Brønsted-Lowry acid or a Brønsted-Lowry base.

1. HCOOH(aq) + H₂O(ℓ) → H₃O⁺(aq) + HCOO⁻(aq)

2. H₂O(ℓ) + PO₄³⁻(aq) → OH⁻(aq) + HPO₄²⁻(aq)

Concept Review Exercises¶

1. Explain how water can act as an acid.

2. Explain how water can act as a base.

Answers¶

1. Under the right conditions, H₂O can donate a proton, making it a Brønsted-Lowry acid.

2. Under the right conditions, H₂O can accept a proton, making it a Brønsted-Lowry base.

Exercises¶

1. Is H₂O(ℓ) acting as an acid or a base?

   H₂O(ℓ) + NH₄⁺(aq) → H₃O⁺(aq) + NH₃(aq)

2. Is H₂O(ℓ) acting as an acid or a base?

   CH₃⁻(aq) + H₂O(ℓ) → CH₄(aq) + OH⁻(aq)

3. In the aqueous solutions of some salts, one of the ions from the salt can react with water molecules. In some C₂H₃O₂⁻ solutions, the following reaction can occur:

   C₂H₃O₂⁻(aq) + H₂O(ℓ) → HC₂H₃O₂(aq) + OH⁻(aq)

   Is H₂O acting as an acid or a base in this reaction?

4. In the aqueous solutions of some salts, one of the ions from the salt can react with water molecules. In some NH₄⁺ solutions, the following reaction can occur:

   NH₄⁺(aq) + H₂O → NH₃(aq) + H₃O⁺(aq)

   Is H₂O acting as an acid or a base in this reaction?

5. Aluminum hydroxide [Al(OH)₃] is amphoteric; it reacts with both acids and bases. Propose the chemical equations for the reactions of Al(OH)₃ with H⁺ and with OH⁻.

6. Based on the information in this section, does ammonia (NH₃) autoionize more or less than water? Write the chemical equation for the autoionization of ammonia.

Answers¶

1. base

3. acid

5. Al(OH)₃ + H⁺ → HAl(OH)₃⁺; Al(OH)₃ + OH⁻ → Al(OH)₄⁻

10.4 The Strengths of Acids and Bases¶

Acids and bases do not all demonstrate the same degree of chemical activity in solution. Different acids and bases have different strengths.

Strong and Weak Acids¶

Let us consider the strengths of acids first. A small number of acids ionize completely in aqueous solution. For example, when HCl dissolves in water, every molecule of HCl separates into a hydronium ion and a chloride ion:

HCl(aq) is one example of a strong acid^[8], which is a compound that is essentially 100% ionized in aqueous solution. There are very few strong acids. The important ones are listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)".

Table 10.2 Strong Acids and Bases (All in Aqueous Solution)

By analogy, a strong base^[9] is a compound that is essentially 100% ionized in aqueous solution. As with acids, there are only a few strong bases, which are also listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)".

If an acid is not listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)", it is likely a weak acid^[10], which is a compound that is not 100% ionized in aqueous solution. Similarly, a weak base^[11] is a compound that is not 100% ionized in aqueous solution. For example, acetic acid (HC₂H₃O₂) is a weak acid. The ionization reaction for acetic acid is as follows:

HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)

Depending on the concentration of HC₂H₃O₂, the ionization reaction may occur only for 1%--5% of the acetic acid molecules.

Chemical Equilibrium¶

The behavior of weak acids and bases illustrates a key concept in chemistry. Does the chemical reaction describing the ionization of a weak acid or base just stop when the acid or base is done ionizing? Actually, no. Rather, the reverse process---the reformation of the molecular form of the acid or base---occurs, ultimately at the same rate as the ionization process. For example, the ionization of the weak acid HC₂H₃O₂ (aq) is as follows:

HC₂H₃O₂(aq) + H₂O(ℓ) → H₃O⁺(aq) + C₂H₃O₂⁻(aq)

The reverse process also begins to occur:

H₃O⁺(aq) + C₂H₃O₂⁻(aq) → HC₂H₃O₂(aq) + H₂O(ℓ)

Eventually, there is a balance between the two opposing processes, and no additional change occurs. The chemical reaction is better represented at this point with a double arrow:

HC₂H₃O₂(aq) + H₂O(ℓ) ⇆ H₃O⁺(aq) + C₂H₃O₂⁻(aq)

The ⇆ implies that both the forward and reverse reactions are occurring, and their effects cancel each other out. A process at this point is considered to be at chemical equilibrium (or equilibrium)^[12]. It is important to note that the processes do not stop. They balance out each other so that there is no further net change; that is, chemical equilibrium is a dynamic equilibrium.

Example 6¶

Write the equilibrium chemical equation for the partial ionization of each weak acid or base.

1. HNO₂(aq)

2. C₅H₅N(aq)

Solution

1. HNO₂(aq) + H₂O(ℓ) ⇆ NO₂⁻(aq) + H₃O⁺(aq)

2. C₅H₅N(aq) + H₂O(ℓ) ⇆ C₅H₅NH⁺(aq) + OH⁻(aq)

Skill-Building Exercise¶

Write the equilibrium chemical equation for the partial ionization of each weak acid or base.

1. HF(aq)

2. AgOH(aq)

Finally, you may realize that the autoionization of water is actually an equilibrium process, so it is more properly written with the double arrow:

H₂O(ℓ) + H₂O(ℓ) ⇆ H₃O⁺(aq) + OH⁻(aq)

The pH Scale¶

One qualitative measure of the strength of an acid or a base solution is the pH scale^[13], which is based on the concentration of the hydronium (or hydrogen) ion in aqueous solution. A neutral (neither acidic nor basic) solution, one that has the same concentration of hydrogen and hydroxide ions, has a pH of 7. A pH below 7 means that a solution is acidic, with lower values of pH corresponding to increasingly acidic solutions. A pH greater than 7 indicates a basic solution, with higher values of pH corresponding to increasingly basic solutions. Thus, given the pH of several solutions, you can state which ones are acidic, which ones are basic, and which are more acidic or basic than others. Table 10.3 "The pH Values of Some Common Solutions" lists the pH of several common solutions. Notice that some biological fluids are nowhere near neutral.

Table 10.3 The pH Values of Some Common Solutions

Weak acids and bases are relatively common. You may notice from Table 10.3 "The pH Values of Some Common Solutions" that many food products are slightly acidic. They are acidic because they contain solutions of weak acids. If the acid components of these foods were strong acids, the food would likely be inedible.

Concept Review Exercises¶

1. Explain the difference between a strong acid or base and a weak acid or base.

2. Explain what is occurring when a chemical reaction reaches equilibrium.

3. Define pH.

Answers¶

1. A strong acid or base is 100% ionized in aqueous solution; a weak acid or base is less than 100% ionized.

2. The overall reaction progress stops because the reverse process balances out the forward process.

3. pH is a measure of the hydrogen ion concentration.

Exercises¶

1. Name a strong acid and a weak acid.

2. Name a strong base and a weak base.

3. Is each compound a strong acid or a weak acid? Assume all are in aqueous solution.

   1. HF

   2. HC₂H₃O₂

   3. HCl

   4. HClO₄

4. Is each compound a strong acid or a weak acid? Assume all are in aqueous solution.

   1. H₂SO₄

   2. HSO₄⁻

   3. HPO₄²⁻

   4. HNO₃

5. Is each compound a strong base or a weak base? Assume all are in aqueous solution.

   1. NH₃

   2. NaOH

   3. Mg(OH)₂

   4. Cu(OH)₂

6. Is each compound a strong base or a weak base? Assume all are in aqueous solution.

   1. KOH

   2. H₂O

   3. Fe(OH)₂

   4. Fe(OH)₃

7. Write the chemical equation for the equilibrium process for each weak acid in Exercise 3.

8. Write the chemical equation for the equilibrium process for each weak acid in Exercise 4.

9. Write the chemical equation for the equilibrium process for each weak base in Exercise 5.

10. Write the chemical equation for the equilibrium process for each weak base in Exercise 6.

11. Which is the stronger acid---HCl(aq) or HF(aq)?

12. Which is the stronger base---KOH(aq) or Ni(OH)₂(aq)?

13. Consider the two acids in Exercise 11. For solutions that have the same concentration, which one would you expect to have a lower pH?

14. Consider the two bases in Exercise 12. For solutions that have the same concentration, which one would you expect to have a higher pH?

15. Consider the list of substances in Table 10.3 "The pH Values of Some Common Solutions". What is the most acidic substance on the list that you have encountered recently?

16. Consider the list of substances in Table 10.3 "The pH Values of Some Common Solutions". What is the most basic substance on the list that you have encountered recently?

Answers¶

1. strong acid: HCl; weak acid: HC₂H₃O₂ (answers will vary)

3. 1. weak

   2. weak

   3. strong

   4. strong

5. 1. weak

   2. strong

   3. strong

   4. weak

7. 3a: HF(aq) ⇆ H⁺(aq) + F⁻(aq); 3b: HC₂H₃O₂(aq) ⇆ H⁺(aq) + C₂H₃O₂⁻(aq)

9. 5a: NH₃(aq) + H₂O ⇆ NH₄⁺(aq) + OH⁻(aq); 5d: Cu(OH)₂(aq) ⇆ Cu²⁺(aq) + 2OH⁻(aq)

11. HCl(aq)

13. HCl(aq)

15. (answers will vary)

10.5 Buffers¶

As indicated in Section 10.4 "The Strengths of Acids and Bases", weak acids are relatively common, even in the foods we eat. But we occasionally come across a strong acid or base, such as stomach acid, that has a strongly acidic pH of 1--2. By definition, strong acids and bases can produce a relatively large amount of hydrogen or hydroxide ions and, as a consequence, have a marked chemical activity. In addition, very small amounts of strong acids and bases can change the pH of a solution very quickly. If 1 mL of stomach acid [which we will approximate as 0.05 M HCl(aq)] is added to the bloodstream, and if no correcting mechanism is present, the pH of the blood would go from about 7.4 to about 4.9---a pH that is not conducive to continued living. Fortunately, the body has a mechanism for minimizing such dramatic pH changes.

The mechanism involves a buffer^[14], a solution that resists dramatic changes in pH. Buffers do so by being composed of certain pairs of solutes: either a weak acid plus a salt derived from that weak acid or a weak base plus a salt of that weak base. For example, a buffer can be composed of dissolved acetic acid (HC₂H₃O₂, a weak acid) and sodium acetate (NaC₂H₃O₂, a salt derived from that acid). Another example of a buffer is a solution containing ammonia (NH₃, a weak base) and ammonium chloride (NH₄Cl, a salt derived from that base).

Let us use an acetic acid--sodium acetate buffer to demonstrate how buffers work. If a strong base---a source of OH⁻(aq) ions---is added to the buffer solution, those hydroxide ions will react with the acetic acid in an acid-base reaction:

HC₂H₃O₂(aq) + OH⁻(aq) → H₂O(ℓ) + C₂H₃O₂⁻(aq)

Rather than changing the pH dramatically by making the solution basic, the added hydroxide ions react to make water, and the pH does not change much.

If a strong acid---a source of H⁺ ions---is added to the buffer solution, the H⁺ ions will react with the anion from the salt. Because HC₂H₃O₂ is a weak acid, it is not ionized much. This means that if lots of hydrogen ions and acetate ions (from sodium acetate) are present in the same solution, they will come together to make acetic acid:

H⁺(aq) + C₂H₃O₂⁻(aq) → HC₂H₃O₂(aq)

Rather than changing the pH dramatically and making the solution acidic, the added hydrogen ions react to make molecules of a weak acid. Figure 10.3 "The Action of Buffers" illustrates both actions of a buffer.

Buffers made from weak bases and salts of weak bases act similarly. For example, in a buffer containing NH₃ and NH₄Cl, ammonia molecules can react with any excess hydrogen ions introduced by strong acids:

NH₃(aq) + H⁺(aq) → NH₄⁺(aq)

while the ammonium ion [NH₄⁺(aq)] can react with any hydroxide ions introduced by strong bases:

NH₄⁺(aq) + OH⁻(aq) → NH₃(aq) + H₂O(ℓ)

Example 7¶

Which solute combinations can make a buffer solution? Assume all are aqueous solutions.

1. HCHO₂ and NaCHO₂

2. HCl and NaCl

3. CH₃NH₂ and CH₃NH₃Cl

4. NH₃ and NaOH

Solution

1. Formic acid (HCHO₂) is a weak acid, while NaCHO₂ is the salt made from the anion of the weak acid---the formate ion (CHO₂⁻). The combination of these two solutes would make a buffer solution.

2. Hydrochloric acid (HCl) is a strong acid, not a weak acid, so the combination of these two solutes would not make a buffer solution.

3. Methylamine (CH₃NH₂) is like ammonia with one of its hydrogen atoms substituted with a CH₃ (methyl) group. Because it is not on our list of strong bases, we can assume that it is a weak base. The compound CH₃NH₃Cl is a salt made from that weak base, so the combination of these two solutes would make a buffer solution.

4. Ammonia (NH₃) is a weak base, but NaOH is a strong base. The combination of these two solutes would not make a buffer solution.

Skill-Building Exercise¶

Which solute combinations can make a buffer solution? Assume all are aqueous solutions.

1. NaHCO₃ and NaCl

2. H₃PO₄ and NaH₂PO₄

3. NH₃ and (NH₄)₃PO₄

4. NaOH and NaCl

Buffers work well only for limited amounts of added strong acid or base. Once either solute is all reacted, the solution is no longer a buffer, and rapid changes in pH may occur. We say that a buffer has a certain capacity^[15]. Buffers that have more solute dissolved in them to start with have larger capacities, as might be expected.

Human blood has a buffering system to minimize extreme changes in pH. One buffer in blood is based on the presence of HCO₃⁻ and H₂CO₃ [H₂CO₃ is another way to write CO₂(aq)]. With this buffer present, even if some stomach acid were to find its way directly into the bloodstream, the change in the pH of blood would be minimal. Inside many of the body’s cells, there is a buffering system based on phosphate ions.

Concept Review Exercise¶

1. Explain how a buffer prevents large changes in pH.

Answer¶

1. A buffer has components that react with both strong acids and strong bases to resist sudden changes in pH.

Exercises¶

1. Describe a buffer. What two related chemical components are required to make a buffer?

2. Can a buffer be made by combining a strong acid with a strong base? Why or why not?

3. Which solute combinations can make a buffer? Assume all are aqueous solutions.

   1. HCl and NaCl

   2. HNO₂ and NaNO₂

   3. NH₄NO₃ and HNO₃

   4. NH₄NO₃ and NH₃

4. Which solute combinations can make a buffer? Assume all are aqueous solutions.

   1. H₃PO₄ and Na₃PO₄

   2. NaHCO₃ and Na₂CO₃

   3. NaNO₃ and Ca(NO₃)₂

   4. HN₃ and NH₃

5. For each combination in Exercise 3 that is a buffer, write the chemical equations for the reactions of the buffer components when a strong acid and a strong base are added.

6. For each combination in Exercise 4 that is a buffer, write the chemical equations for the reaction of the buffer components when a strong acid and a strong base are added.

7. The complete phosphate buffer system is based on four substances: H₃PO₄, H₂PO₄⁻, HPO₄²⁻, and PO₄³⁻. What different buffer solutions can be made from these substances?

8. Explain why NaBr cannot be a component in either an acidic or a basic buffer.

9. Two solutions are made containing the same concentrations of solutes. One solution is composed of phosphoric acid and sodium phosphate, while the other is composed of hydrocyanic acid and sodium cyanide. Which solution should have the larger capacity as a buffer?

10. Two solutions are made containing the same concentrations of solutes. One solution is composed of ammonia and ammonium nitrate, while the other is composed of sulfuric acid and sodium sulfate. Which solution should have the larger capacity as a buffer?

Answers¶

1. A buffer resists sudden changes in pH. It has a weak acid or base and a salt of that weak acid or base.

3. 1. not a buffer

   2. buffer

   3. not a buffer

   4. buffer

5. 3b: strong acid: H⁺ + NO₂⁻ → HNO₂; strong base: OH⁻ + HNO₂ → H₂O + NO₂⁻; 3d: strong acid: H⁺ + NH₃ → NH₄⁺; strong base: OH⁻ + NH₄⁺ → H₂O + NH₃

7. Buffers can be made by combining H₃PO₄ and H₂PO₄⁻, H₂PO₄⁻ and HPO₄²⁻, and HPO₄²⁻ and PO₄³⁻.

9. the phosphoric acid--phosphate buffer

10.6 End-of-Chapter Material¶

Additional Exercises¶

1. The properties of a 1.0 M HCl solution and a 1.0 M HC₂H₃O₂ solution are compared. Measurements show that the hydrochloric acid solution has a higher osmotic pressure than the acetic acid solution. Explain why.

2. Of a 0.50 M HNO₃ solution and a 0.50 M HC₂H₃O₂ solution, which should have the higher boiling point? Explain why.

3. The reaction of sulfuric acid [H₂SO₄(aq)] with sodium hydroxide [NaOH(aq)] can be represented by two separate steps, with only one hydrogen ion reacting in each step. Write the chemical equation for each step.

4. The reaction of aluminum hydroxide [Al(OH)₃(aq)] with hydrochloric acid [HCl(aq)] can be represented by three separate steps, with only one hydroxide ion reacting in each step. Write the chemical equation for each step.

5. A friend brings you a small sample of an unknown chemical. Assuming that the chemical is soluble in water, how would you determine if the chemical is an acid or a base?

6. A neutral solution has a hydrogen ion concentration of about 1 × 10⁻⁷ M. What is the concentration of the hydroxide ion in a neutral solution?

7. The Lewis definitions of an acid and a base are based on electron pairs, not protons. A Lewis acid is an electron pair acceptor, while a Lewis base is an electron pair donor. Use Lewis diagrams to show that

   H⁺(aq) + OH⁻(aq) → H₂O(ℓ)

   is an acid-base reaction in the Lewis sense as well as in the Arrhenius and Brønsted-Lowry senses.

8. Given the chemical reaction

   NH₃(g) + BF₃(g) → NH₃---BF₃(s)

   show that the reaction illustrated by this equation is an acid-base reaction if we use the Lewis definitions of an acid and a base (see Exercise 7). The product contains a bond between the N and B atoms.

Answers¶

1. HCl is a strong acid and yields more ions in solution.

3. H₂SO₄ + NaOH → NaHSO₄ + H₂O; NaHSO₄ + NaOH → Na₂SO₄ + H₂O

5. One way is to add it to NaHCO₃; if it bubbles, it is an acid. Alternatively, add the sample to litmus and look for a characteristic color change (red for acid, blue for base).

7. 

   The O atom is donating an electron pair to the H⁺ ion, making the base an electron pair donor and the acid an electron pair acceptor.