4.4: Acid-Base Reactions

Skills to Develop

• To know the characteristic properties of acids and bases.

• To predict acid-base neutralization reactions.

Acid–base reactions are essential in both biochemistry and industrial chemistry. Moreover, many of the substances we encounter in our homes, the supermarket, and the pharmacy are acids or bases. For example, aspirin is an acid (acetylsalicylic acid), and antacids are bases. In fact, every amateur chef who has prepared mayonnaise or squeezed a wedge of lemon to marinate a piece of fish has carried out an acid–base reaction. Before we discuss the characteristics of such reactions, let’s first describe some of the properties of acids and bases.

The Arrhenius Definition of Acids and Bases

Although the general properties of acids and bases have been known for more than a thousand years, the definitions of acid and base have changed dramatically as scientists have learned more about them. In ancient times, an acid was any substance that had a sour taste (e.g., vinegar or lemon juice), caused consistent color changes in dyes derived from plants (e.g., turning blue litmus paper red), reacted with certain metals to produce hydrogen gas and a solution of a salt containing a metal cation, and dissolved carbonate salts such as limestone (CaCO₃) with the evolution of carbon dioxide. In contrast, a base was any substance that had a bitter taste, felt slippery to the touch, and caused color changes in plant dyes that differed diametrically from the changes caused by acids (e.g., turning red litmus paper blue). Although these definitions were useful, they were entirely descriptive.

The first person to define acids and bases in detail was the Swedish chemist Svante Arrhenius (1859–1927; Nobel Prize in Chemistry, 1903). According to the Arrhenius definition, an acid is a substance like hydrochloric acid that dissolves in water to produce H⁺ ions (protons; Equation \(\ref{4.3.1}\)), and a base is a substance like sodium hydroxide that dissolves in water to produce hydroxide (OH⁻) ions (Equation \(\ref{4.3.2}\)):

\[ \underset{an\: Arrhenius\: acid}{HCl_{(g)}} \xrightarrow {H_2 O_{(l)}} H^+_{(aq)} + Cl^-_{(aq)} \label{4.3.1}\]

\[ \underset{an\: Arrhenius\: base}{NaOH_{(s)}} \xrightarrow {H_2O_{(l)}} Na^+_{(aq)} + OH^-_{(aq)} \label{4.3.2}\]

According to Arrhenius, the characteristic properties of acids and bases are due exclusively to the presence of H⁺ and OH⁻ ions, respectively, in solution. Although Arrhenius’s ideas were widely accepted, his definition of acids and bases had two major limitations:

1. First, because acids and bases were defined in terms of ions obtained from water, the Arrhenius concept applied only to substances in aqueous solution.
2. Second, and more important, the Arrhenius definition predicted that only substances that dissolve in water to produce \(H^+\) and \(OH^−\) ions should exhibit the properties of acids and bases, respectively. For example, according to the Arrhenius definition, the reaction of ammonia (a base) with gaseous HCl (an acid) to give ammonium chloride (Equation \(\ref{4.3.3}\)) is not an acid–base reaction because it does not involve \(H^+\) and \(OH^−\):

\[NH_{3\;(g)} + HCl_{(g)} \rightarrow NH_4Cl_{(s)} \label{4.3.3}\]

The Brønsted–Lowry Definition of Acids and Bases

Because of the limitations of the Arrhenius definition, a more general definition of acids and bases was needed. One was proposed independently in 1923 by the Danish chemist J. N. Brønsted (1879–1947) and the British chemist T. M. Lowry (1874–1936), who defined acid–base reactions in terms of the transfer of a proton (H⁺ ion) from one substance to another.

According to Brønsted and Lowry, an acid (a substance with at least one hydrogen atom that can dissociate to form an anion and an \(H^+\) ion (a proton) in aqueous solution, thereby forming an acidic solution) is any substance that can donate a proton, and a base (a substance that produces one or more hydroxide ions (\(OH^-\) and a cation when dissolved in aqueous solution, thereby forming a basic solution) is any substance that can accept a proton. The Brønsted–Lowry definition of an acid is essentially the same as the Arrhenius definition, except that it is not restricted to aqueous solutions. The Brønsted–Lowry definition of a base, however, is far more general because the hydroxide ion is just one of many substances that can accept a proton. Ammonia, for example, reacts with a proton to form \(NH_4^+\), so in Equation \(\ref{4.3.3}\), \(NH_3\) is a Brønsted–Lowry base and \(HCl\) is a Brønsted–Lowry acid. Because of its more general nature, the Brønsted–Lowry definition is used throughout this text unless otherwise specified.

The Hydronium Ion

Because isolated protons are very unstable and hence very reactive, an acid never simply “loses” an H⁺ ion. Instead, the proton is always transferred to another substance, which acts as a base in the Brønsted–Lowry definition. Thus in every acid–base reaction, one species acts as an acid and one species acts as a base. Occasionally, the same substance performs both roles, as you will see later. When a strong acid dissolves in water, the proton that is released is transferred to a water molecule that acts as a proton acceptor or base, as shown for the dissociation of sulfuric acid:

\[ \underset{acid\: (proton\: donor)}{H_2 SO_4 (l)} + \underset{base\: (proton\: acceptor)} {H_2 O(l)} \rightarrow \underset{acid}{H _3 O^+ (aq)} + \underset{base}{HSO_4^- (aq)} \label{4.3.11}\]

Technically, therefore, it is imprecise to describe the dissociation of a strong acid as producing \(H^+_{(aq)}\) ions, as we have been doing. The resulting \(H_3O^+\) ion, called the hydronium ion and is a more accurate representation of \(H^+_{(aq)}\). For the sake of brevity, however, in discussing acid dissociation reactions, we often show the product as \(H^+_{(aq)}\) (as in Equation \(\ref{4.3.7}\)) with the understanding that the product is actually the\(H_3O^+ _{(aq)}\) ion.

Conversely, bases that do not contain the hydroxide ion accept a proton from water, so small amounts of OH⁻ are produced, as in the following:

\[ \underset{base}{NH_3 (g)} + \underset{acid}{H_2 O(l)} \rightleftharpoons \underset{acid}{NH_4^+ (aq)} + \underset{base}{OH^- (aq)} \label{4.3.12}\]

In chemical equations such as these, a double arrow is used to indicate that both the forward and reverse reactions occur simultaneously, so the forward reaction does not go to completion. Instead, the solution contains significant amounts of both reactants and products. Over time, the reaction reaches a state in which the concentration of each species in solution remains constant. The reaction is then said to be in equilibrium (the point at which the rates of the forward and reverse reactions become the same, so that the net composition of the system no longer changes with time). In this reaction, water acts as an acid by donating a proton to ammonia, and ammonia acts as a base by accepting a proton from water. Thus water can act as either an acid or a base by donating a proton to a base or by accepting a proton from an acid. Substances that can behave as both an acid and a base are said to be amphoteric.

The products of an acid–base reaction are also an acid and a base. In Equation \(\ref{4.3.11}\), for example, the products of the reaction are the hydronium ion, here an acid, and the hydrogen sulfate ion, here a weak base. In Equation \(\ref{4.3.12}\), the products are NH₄⁺, an acid, and OH⁻, a base. The product NH₄⁺ is called the conjugate acid of the base NH₃, and the product OH⁻ is called the conjugate base of the acid H₂O. Thus all acid–base reactions actually involve two conjugate acid–base pairs: the Brønsted–Lowry acid and the base it forms after donating its proton, and the Brønsted–Lowry base and the acid it forms after accepting a proton. In Equation \(\ref{4.3.12}\), they are NH₄⁺/NH₃ and H₂O/OH⁻.

Strengths of Acids and Bases

We will not discuss the strengths of acids and bases quantitatively until next semester. Qualitatively, however, we can state that strong acids react essentially completely with water to give \(H^+\) and the corresponding anion. Similarly, strong bases dissociate essentially completely in water to give \(OH^−\) and the corresponding cation. Strong acids and strong bases are both strong electrolytes. In contrast, only a fraction of the molecules of weak acids and weak bases react with water to produce ions, so weak acids and weak bases are also weak electrolytes. Typically less than 5% of a weak electrolyte dissociates into ions in solution, whereas more than 95% is present in undissociated form.

In practice, only a few strong acids are commonly encountered: HCl, HBr, HI, HNO₃, HClO₄, and H₂SO₄ (H₃PO₄ is only moderately strong). The most common strong bases are ionic compounds that contain the hydroxide ion as the anion; three examples are NaOH, KOH, and Ca(OH)₂. Common weak acids include HCN, H₂S, HF, oxoacids such as HNO₂ and HClO, and carboxylic acids such as acetic acid. The ionization reaction of acetic acid is as follows:

\[ CH_3 CO_2 H(l) \overset{H_2 O(l)}{\rightleftharpoons} H^+ (aq) + CH_3 CO_2^- (aq) \label{4.3.7}\]

Although acetic acid is very soluble in water, almost all of the acetic acid in solution exists in the form of neutral molecules (less than 1% dissociates).

The most common weak base is ammonia, which reacts with water to form small amounts of hydroxide ion:

\[ NH_3 (g) + H_2 O(l) \rightleftharpoons NH_4^+ (aq) + OH^- (aq) \label{4.3.10}\]

Most of the ammonia (>99%) is present in the form of NH₃(g). Amines, which are organic analogues of ammonia, are also weak bases, as are ionic compounds that contain anions derived from weak acids (such as S²⁻).

Table \(\PageIndex{1}\) lists some common strong acids and bases. Acids other than the six common strong acids are almost invariably weak acids. The only common strong bases are the hydroxides of the alkali metals and the heavier alkaline earths (Ca, Sr, and Ba); any other bases you encounter are most likely weak. Remember that there is no correlation between solubility and whether a substance is a strong or a weak electrolyte! Many weak acids and bases are extremely soluble in water. Also note that the strength of an acid or base refers only to its extent of dissociation in solution, not how dangerous it may be! For example, while hydrofluoric acid, HF, is classified as a weak acid based on its dissociation, it is still extremely caustic and even more dangerous than stronger acids such as HCl.

The strength of an acid or base indicates the extent of dissociation, not how hazardous it is.

Table \(\PageIndex{1}\): Common Strong Acids and Bases

Strong Acids		Strong Bases
Hydrogen Halides	Oxoacids	Group 1 Hydroxides	Hydroxides of Heavy Group 2 Elements
HCl	HNO3	LiOH	Ca(OH)2
HBr	H2SO4	NaOH	Sr(OH)2
HI	HClO4	KOH	Ba(OH)2
		RbOH
		CsOH

Example \(\PageIndex{1}\): Acid Strength

Classify each compound as a strong acid, a weak acid, a strong base, a weak base, or none of these.

1. CH₃CH₂CO₂H
2. CH₃OH
3. Sr(OH)₂
4. CH₃CH₂NH₂
5. HBrO₄

Given: compound

Asked for: acid or base strength

Strategy:

A Determine whether the compound is organic or inorganic.

B If inorganic, determine whether the compound is acidic or basic by the presence of dissociable H⁺ or OH⁻ ions, respectively. If organic, identify the compound as a weak base or a weak acid by the presence of an amine or a carboxylic acid group, respectively. Recall that all polyprotic acids except H₂SO₄ are weak acids.

Solution:

1. A This compound is propionic acid, which is organic. B It contains a carboxylic acid group analogous to that in acetic acid, so it must be a weak acid.
2. A CH₃OH is methanol, an organic compound that contains the −OH group. B As a covalent compound, it does not dissociate to form the OH⁻ ion. Because it does not contain a carboxylic acid (−CO₂H) group, methanol also cannot dissociate to form H⁺(aq) ions. Thus we predict that in aqueous solution methanol is neither an acid nor a base.
3. A Sr(OH)₂ is an inorganic compound that contains one Sr²⁺ and two OH⁻ ions per formula unit. B We therefore expect it to be a strong base, similar to Ca(OH)₂.
4. A CH₃CH₂NH₂ is an amine (ethylamine), an organic compound in which one hydrogen of ammonia has been replaced by an R group. B Consequently, we expect it to behave similarly to ammonia (Equation \(\ref{4.3.7}\)), reacting with water to produce small amounts of the OH⁻ ion. Ethylamine is therefore a weak base.
5. A HBrO₄ is perbromic acid, an inorganic compound. B It is not listed in Table \(\PageIndex{1}\) as one of the common strong acids, but that does not necessarily mean that it is a weak acid. If you examine the periodic table, you can see that Br lies directly below Cl in group 17. We might therefore expect that HBrO₄ is chemically similar to HClO₄, a strong acid—and, in fact, it is.

Exercise \(\PageIndex{1}\): Acid Strength

Classify each compound as a strong acid, a weak acid, a strong base, a weak base, or none of these.

1. Ba(OH)₂
2. HIO₄
3. CH₃CH₂CH₂CO₂H
4. (CH₃)₂NH
5. CH₂O

Answer a

strong base

Answer b

strong acid

Answer c

weak acid

Answer d

weak base

Answer e

none of these; formaldehyde is a neutral molecule that does not dissociate in water

Polyprotic Acids

In addition to their strength, acids differ in the number of protons they can donate. For example, monoprotic acids (a compound that is capable of donating one proton per molecule) are compounds that are capable of donating a single proton per molecule. Monoprotic acids include HF, HCl, HBr, HI, HNO₃, and HNO₂. All carboxylic acids that contain a single −CO₂H group, such as acetic acid (CH₃CO₂H), are monoprotic acids, dissociating to form RCO₂⁻ and H⁺. A compound that can donate more than one proton per molecule is known as a polyprotic acid. For example, H₂SO₄ can donate two H⁺ ions in separate steps, so it is a diprotic acid (a compound that can donate two protons per molecule in separate steps). Sulfuric acid is unusual in that it is a strong acid when it donates its first proton (Equation \(\ref{4.3.8}\)) but a weak acid when it donates its second proton (Equation \(\ref{4.3.9}\)) as indicated by the single and double arrows, respectively:

\[ \underset{strong\: acid}{H_2 SO_4 (l)} \xrightarrow {H_2 O(l)} H ^+ (aq) + HSO_4 ^- (aq) \label{4.3.8}\]

\[ \underset{weak\: acid}{HSO_4^- (aq)} \rightleftharpoons H^+ (aq) + SO_4^{2-} (aq) \label{4.3.9}\]

Consequently, an aqueous solution of sulfuric acid contains \(H^+_{(aq)}\) ions and a mixture of \(HSO^-_{4\;(aq)}\) and \(SO^{2−}_{4\;(aq)}\) ions, but no \(H_2SO_4\) molecules.

All other polyprotic acids, such as H₃PO₄, are weak acids. H₃PO₄, which is capable of donating three protons in successive steps, is a triprotic acid (a compound that can donate three protons per molecule in separate steps), (Equation \(\ref{4.3.4}\), Equation \(\ref{4.3.5}\), and Equation \(\ref{4.3.6}\)):

\[ H_3 PO_4 (l) \overset{H_2 O(l)}{\rightleftharpoons} H ^+ ( a q ) + H_2 PO_4 ^- (aq) \label{4.3.4}\]

\[ H_2 PO_4 ^- (aq) \rightleftharpoons H ^+ (aq) + HPO_4^{2-} (aq) \label{4.3.5}\]

\[ HPO_4^{2-} (aq) \rightleftharpoons H^+ (aq) + PO_4^{3-} (aq) \label{4.3.6}\]

Again, because H₃PO₄, H₂PO₄⁻, and HPO₄²⁻ are all weak acids, the double arrow indicates that the reaction does not go to completion but rather reaches a state of equilibrium.

Neutralization Reactions

A neutralization reaction is one in which an acid and a base react in equivalent amounts to produce water and a salt (the general term for any ionic substance that does not have OH⁻ as the anion or H⁺ as the cation). If the base is a metal hydroxide, then the general formula for the reaction of an acid with a base is described as follows: Acid plus base yields water plus salt. For example, the reaction of equimolar amounts of HBr and NaOH to give water and a salt (NaBr) is a neutralization reaction:

\[ \underset{acid}{HBr(aq)} + \underset{base}{NaOH(aq)} \rightarrow \underset{water}{H_2 O(l)} + \underset{salt}{NaBr(aq)} \label{4.3.13}\]

Acid plus base yields water plus salt.

If we write the complete ionic equation for the reaction in Equation \(\ref{4.3.13}\), we see that \(Na^+_{(aq)}\) and \(Br^−_{(aq)}\) are spectator ions and are not involved in the reaction:

\[ H^+ (aq) + \cancel{Br^- (aq)} + \cancel{Na^+ (aq)} + OH^- (aq) \rightarrow H_2 O(l) + \cancel{Na^+ (aq)} + \cancel{Br^- (aq)} \label{4.3.14}\]

The overall reaction is therefore simply the combination of H⁺(aq) and OH⁻(aq) to produce H₂O, as shown in the net ionic equation:

\[H^+(aq) + OH^-(aq) \rightarrow H_2O(l)\label{4.3.15}\]

The net ionic equation for the reaction of any strong acid with any strong base is identical to Equation \(\ref{4.3.15}\).

The strengths of the acid and the base generally determine whether the reaction goes to completion. The reaction of any strong acid with any strong base goes essentially to completion, as does the reaction of a strong acid with a weak base, and a weak acid with a strong base. Examples of the last two are as follows:

\[ \underset{strong\: acid}{HCl(aq)} + \underset{weak\: base}{NH_3 (aq)} \rightarrow \underset{salt}{NH_4 Cl(aq)} \label{4.3.16}\]

\[ \underset{weak\: acid} {CH_3 CO _2 H(aq)} + \underset{strong\: base}{NaOH(aq)} \rightarrow \underset{salt}{CH _3 CO _2 Na(aq)} + H_2 O(l) \label{4.3.17}\]

Sodium acetate is written with the organic component first followed by the cation, as is usual for organic salts. Most reactions of a weak acid with a weak base also go essentially to completion. One example is the reaction of acetic acid with ammonia:

\[ \underset{weak\: acid}{CH _3 CO _2 H(aq)} + \underset{weak\: base}{NH_3 (aq)} \rightarrow \underset{salt}{CH_3 CO_2 NH_4 (aq)} \label{4.3.18}\]

An example of an acid–base reaction that does not go to completion is the reaction of a weak acid or a weak base with water, which is both an extremely weak acid and an extremely weak base.

Except for the reaction of a weak acid or a weak base with water, acid–base reactions essentially go to completion.

In some cases, the reaction of an acid with an anion derived from a weak acid (such as HS⁻) produces a gas (in this case, H₂S). Because the gaseous product escapes from solution in the form of bubbles, the reverse reaction cannot occur. Therefore, these reactions tend to be forced, or driven, to completion. Examples include reactions in which an acid is added to ionic compounds that contain the HCO₃⁻, SO₃²⁻, CN⁻, or S²⁻ anions, all of which are driven to completion:

\[ HCO_3^- (aq) + H^+ (aq) \rightarrow H_2 CO_3 (aq) \rightarrow CO_2 (g) + H_2 O(l) \label{4.3.19}\]

\[ 2H^+ (aq) + SO_3^{2-} (aq) \rightarrow SO_2 (g) + H_2 O(l) \]

\[ CN^- (aq) + H^+ (aq) \rightarrow HCN(g) \label{4.3.20}\]

\[ S ^{2-} (aq) + H^+ (aq) \rightarrow HS^- (aq) \label{4.3.21}\]

\[ HS^- (aq) + H^+ (aq) \rightarrow H_2 S(g) \]

The reactions in Equations \(\ref{4.3.19}\)-\(\ref{4.3.21}\) are responsible for the rotten egg smell that is produced when metal sulfides come in contact with acids.

Example \(\PageIndex{2}\): Neutralizing Propionic Acid

Calcium propionate is used to inhibit the growth of molds in foods, tobacco, and some medicines. Write a balanced chemical equation for the reaction of aqueous propionic acid (CH₃CH₂CO₂H) with aqueous calcium hydroxide [Ca(OH)₂] to give calcium propionate. Do you expect this reaction to go to completion, making it a feasible method for the preparation of calcium propionate?

Given: reactants and product

Asked for: balanced chemical equation and whether the reaction will go to completion

Strategy:

Write the balanced chemical equation for the reaction of propionic acid with calcium hydroxide. Based on their acid and base strengths, predict whether the reaction will go to completion.

Solution:

Propionic acid is an organic compound that is a weak acid, and calcium hydroxide is an inorganic compound that is a strong base. The balanced chemical equation is as follows:

\(2CH_3CH_2CO_2H(aq) + Ca(OH)_2(aq) \rightarrow (CH_3CH_2CO_2)_2Ca(aq) + 2H_2O(l)\)

The reaction of a weak acid and a strong base will go to completion, so it is reasonable to prepare calcium propionate by mixing solutions of propionic acid and calcium hydroxide in a 2:1 mole ratio.

Exercise \(\PageIndex{2}\)

Write a balanced chemical equation for the reaction of solid sodium acetate with dilute sulfuric acid to give sodium sulfate.

Answer

\[2CH_3CO_2Na(s) + H_2SO_4(aq) \rightarrow Na_2SO_4(aq) + 2CH_3CO_2H(aq) \nonumber\]

One of the most familiar and most heavily advertised applications of acid–base chemistry is antacids, which are bases that neutralize stomach acid. The human stomach contains an approximately 0.1 M solution of hydrochloric acid that helps digest foods. If the protective lining of the stomach breaks down, this acid can attack the stomach tissue, resulting in the formation of an ulcer. Because one factor that is believed to contribute to the formation of stomach ulcers is the production of excess acid in the stomach, many individuals routinely consume large quantities of antacids. The active ingredients in antacids include sodium bicarbonate and potassium bicarbonate (NaHCO₃ and KHCO₃; Alka-Seltzer); a mixture of magnesium hydroxide and aluminum hydroxide (Mg(OH)₂ and Al(OH)₃; Maalox, Mylanta); calcium carbonate (CaCO₃; Tums); and a complex salt, dihydroxyaluminum sodium carbonate (NaAl(OH)₂CO₃; original Rolaids). Each has certain advantages and disadvantages. For example, Mg(OH)₂ is a powerful laxative (it is the active ingredient in milk of magnesia), whereas Al(OH)₃ causes constipation. When mixed, each tends to counteract the unwanted effects of the other. Although all antacids contain both an anionic base (OH⁻, CO₃²⁻, or HCO₃⁻) and an appropriate cation, they differ substantially in the amount of active ingredient in a given mass of product.

Stomach acid. An antacid tablet reacts with 0.1 M HCl (the approximate concentration found in the human stomach).

Summary

An acidic solution and a basic solution react together in a neutralization reaction that also forms a salt. Acid–base reactions require both an acid and a base. In Brønsted–Lowry terms, an acid is a substance that can donate a proton (H⁺), and a base is a substance that can accept a proton. All acid–base reactions contain two acid–base pairs: the reactants and the products. Acids can donate one proton (monoprotic acids), two protons (diprotic acids), or three protons (triprotic acids). Compounds that are capable of donating more than one proton are generally called polyprotic acids. Acids also differ in their tendency to donate a proton, a measure of their acid strength. Strong acids react completely with water to produce H₃O⁺(aq) (the hydronium ion), whereas weak acids dissociate only partially in water. Conversely, strong bases react completely with water to produce the hydroxide ion, whereas weak bases react only partially with water to form hydroxide ions. The reaction of a strong acid with a strong base is a neutralization reaction, which produces water plus a salt. The acidity or basicity of an aqueous solution is described quantitatively using the pH scale. The pH of a solution is the negative logarithm of the H⁺ ion concentration and typically ranges from 0 for strongly acidic solutions to 14 for strongly basic ones. Because of the autoionization reaction of water, which produces small amounts of hydronium ions and hydroxide ions, a neutral solution of water contains 1 × 10⁻⁷ M H⁺ ions and has a pH of 7.0. An indicator is an intensely colored organic substance whose color is pH dependent; it is used to determine the pH of a solution.

Contributors

• Modified by Joshua Halpern (Howard University)

• Anna Christianson (Bellarmine University)