Chapter 12 Acids and Bases

12.1 Arrhenius Acids and Bases

Historically, the first chemical definition of an acid and a base was put forward by Svante Arrhenius, a Swedish chemist, in 1884. An Arrhenius acidA compound that increases the hydrogen ion concentration in aqueous solution. is a compound that increases the H⁺ ion concentration in aqueous solution. The H⁺ ion is just a bare proton, and it is rather clear that bare protons are not floating around in an aqueous solution. Instead, chemistry has defined the hydronium ionThe actual chemical species that represents a hydrogen ion. (H₃O⁺) as the actual chemical species that represents an H⁺ ion. H⁺ ions and H₃O⁺ ions are often considered interchangeable when writing chemical equations (although a properly balanced chemical equation should also include the additional H₂O). Classic Arrhenius acids can be considered ionic compounds in which H⁺ is the cation. Table 12.1 "Some Arrhenius Acids" lists some Arrhenius acids and their names.

An Arrhenius baseA compound that increases the hydroxide ion concentration in aqueous solution. is a compound that increases the OH⁻ ion concentration in aqueous solution. Ionic compounds of the OH⁻ ion are classic Arrhenius bases.

Acids have some properties in common. They turn litmus, a plant extract, red. They react with some metals to give off H₂ gas. They react with carbonate and hydrogen carbonate salts to give off CO₂ gas. Acids that are ingested typically have a sour, sharp taste. (The name acid comes from the Latin word acidus, meaning “sour.”) Bases also have some properties in common. They are slippery to the touch, turn litmus blue, and have a bitter flavor if ingested.

Acids and bases have another property: they react with each other to make water and an ionic compound called a salt. A saltAny ionic compound that is formed from a reaction between an acid and a base., in chemistry, is any ionic compound made by combining an acid with a base. A reaction between an acid and a base is called a neutralization reactionThe reaction of an acid and a base to produce water and a salt. and can be represented as follows:

acid + base → H₂O + salt

The stoichiometry of the balanced chemical equation depends on the number of H⁺ ions in the acid and the number of OH⁻ ions in the base.

12.2 Brønsted-Lowry Acids and Bases

The Arrhenius definition of acid and base is limited to aqueous (that is, water) solutions. Although this is useful because water is a common solvent, it is limited to the relationship between the H⁺ ion and the OH⁻ ion. What would be useful is a more general definition that would be more applicable to other chemical reactions and, importantly, independent of H₂O.

In 1923, Danish chemist Johannes Brønsted and English chemist Thomas Lowry independently proposed new definitions for acids and bases, ones that focus on proton transfer. A Brønsted-Lowry acidAny species that can donate a proton to another molecule. is any species that can donate a proton (H⁺) to another molecule. A Brønsted-Lowry baseAny species that can accept a proton from another molecule. is any species that can accept a proton from another molecule. In short, a Brønsted-Lowry acid is a proton donor (PD), while a Brønsted-Lowry base is a proton acceptor (PA).

It is easy to see that the Brønsted-Lowry definition covers the Arrhenius definition of acids and bases. Consider the prototypical Arrhenius acid-base reaction:

$$\underset{\text{acid}}{{\text{H}}^{\text{+}}\text{(aq)}}+\underset{\text{base}}{{\text{OH}}^{-}\text{(aq)}}\to {\text{H}}_{\text{2}}\text{O(}\ell \text{)}$$

The acid species and base species are marked. The proton, however, is (by definition) a proton donor (labeled PD), while the OH⁻ ion is acting as the proton acceptor (labeled PA):

$$\underset{\text{PD}}{{\text{H}}^{\text{+}}\text{(aq)}}+\underset{\text{PA}}{{\text{OH}}^{-}\text{(aq)}}\to {\text{H}}_{\text{2}}\text{O(}\ell \text{)}$$

The proton donor is a Brønsted-Lowry acid, and the proton acceptor is the Brønsted-Lowry base:

$$\underset{\text{BL acid}}{{\text{H}}^{\text{+}}\text{(aq)}}+\underset{\text{BL base}}{{\text{OH}}^{-}\text{(aq)}}\to {\text{H}}_{\text{2}}\text{O(}\ell \text{)}$$

Thus H⁺ is an acid by both definitions, and OH⁻ is a base by both definitions.

Ammonia (NH₃) is a base even though it does not contain OH⁻ ions in its formula. Instead, it generates OH⁻ ions as the product of a proton-transfer reaction with H₂O molecules; NH₃ acts like a Brønsted-Lowry base, and H₂O acts like a Brønsted-Lowry acid:

A reaction with water is called hydrolysisA reaction with water.; we say that NH₃ hydrolyzes to make NH₄⁺ ions and OH⁻ ions.

Even the dissolving of an Arrhenius acid in water can be considered a Brønsted-Lowry acid-base reaction. Consider the process of dissolving HCl(g) in water to make an aqueous solution of hydrochloric acid. The process can be written as follows:

HCl(g) + H₂O(ℓ) → H₃O⁺(aq) + Cl⁻(aq)

HCl(g) is the proton donor and therefore a Brønsted-Lowry acid, while H₂O is the proton acceptor and a Brønsted-Lowry base. These two examples show that H₂O can act as both a proton donor and a proton acceptor, depending on what other substance is in the chemical reaction. A substance that can act as a proton donor or a proton acceptor is called amphiproticA substance that can act as a proton donor or a proton acceptor.. Water is probably the most common amphiprotic substance we will encounter, but other substances are also amphiprotic.

In the reaction between NH₃ and H₂O,

the chemical reaction does not go to completion; rather, the reverse process occurs as well, and eventually the two processes cancel out any additional change. At this point, we say the chemical reaction is at equilibrium. Both processes still occur, but any net change by one process is countered by the same net change by the other process; it is a dynamic, rather than a static, equilibrium. Because both reactions are occurring, it makes sense to use a double arrow instead of a single arrow:

What do you notice about the reverse reaction? The NH₄⁺ ion is donating a proton to the OH⁻ ion, which is accepting it. This means that the NH₄⁺ ion is acting as the proton donor, or Brønsted-Lowry acid, while OH⁻ ion, the proton acceptor, is acting as a Brønsted-Lowry base. The reverse reaction is also a Brønsted-Lowry acid base reaction:

This means that both reactions are acid-base reactions by the Brønsted-Lowry definition. If you consider the species in this chemical reaction, two sets of similar species exist on both sides. Within each set, the two species differ by a proton in their formulas, and one member of the set is a Brønsted-Lowry acid, while the other member is a Brønsted-Lowry base. These sets are marked here:

The two sets—NH₃/NH₄⁺ and H₂O/OH⁻—are called conjugate acid-base pairsTwo species whose formulas differ by only a hydrogen ion.. We say that NH₄⁺ is the conjugate acid of NH₃, OH⁻ is the conjugate base of H₂O, and so forth. Every Brønsted-Lowry acid-base reaction can be labeled with two conjugate acid-base pairs.

12.3 Acid-Base Titrations

The reaction of an acid with a base to make a salt and water is a common reaction in the laboratory, partly because so many compounds can act as acids or bases. Another reason that acid-base reactions are so prevalent is because they are often used to determine quantitative amounts of one or the other. Performing chemical reactions quantitatively to determine the exact amount of a reagent is called a titrationA chemical reaction performed quantitatively to determine the exact amount of a reagent.. A titration can be performed with almost any chemical reaction for which the balanced chemical equation is known. Here, we will consider titrations that involve acid-base reactions.

In a titration, one reagent has a known concentration or amount, while the other reagent has an unknown concentration or amount. Typically, the known reagent (the titrantThe reagent of known concentration.) is added to the unknown quantity and is dissolved in solution. The unknown amount of substance (the analyteThe reagent of unknown concentration.) may or may not be dissolved in solution (but usually is). The titrant is added to the analyte using a precisely calibrated volumetric delivery tube called a burette (also spelled buret; see Figure 12.1 "Equipment for Titrations"). The burette has markings to determine how much volume of solution has been added to the analyte. When the reaction is complete, it is said to be at the equivalence pointThe point of the reaction when all the analyte has been reacted with the titrant.; the number of moles of titrant can be calculated from the concentration and the volume, and the balanced chemical equation can be used to determine the number of moles (and then concentration or mass) of the unknown reactant.

For example, suppose 25.66 mL (or 0.02566 L) of 0.1078 M HCl was used to titrate an unknown sample of NaOH. What mass of NaOH was in the sample? We can calculate the number of moles of HCl reacted:

# mol HCl = (0.02566 L)(0.1078 M) = 0.002766 mol HCl

We also have the balanced chemical reaction between HCl and NaOH:

HCl + NaOH → NaCl + H₂O

So we can construct a conversion factor to convert to number of moles of NaOH reacted:

$$\text{0}\text{.002766}\cancel{\text{ mol HCl}}\times \frac{\text{1 mol NaOH}}{1\cancel{\text{ mol HCl}}}=\text{0}\text{.002766 mol NaOH}$$

Then we convert this amount to mass, using the molar mass of NaOH (40.00 g/mol):

$$\text{0}\text{.002766}\cancel{\text{ mol NaOH}}\times \frac{40.00\text{ g NaOH}}{\text{1}\cancel{\text{ mol NaOH}}}=0.1106\text{ g NaOH}$$

This is type of calculation is performed as part of a titration.

How does one know if a reaction is at its equivalence point? Usually, the person performing the titration adds a small amount of an indicatorA substance whose color change indicates the equivalence point of a titration., a substance that changes color depending on the acidity or basicity of the solution. Because different indicators change colors at different levels of acidity, choosing the correct one is important in performing an accurate titration.

12.4 Strong and Weak Acids and Bases and Their Salts

Except for their names and formulas, so far we have treated all acids as equals, especially in a chemical reaction. However, acids can be very different in a very important way. Consider HCl(aq). When HCl is dissolved in H₂O, it completely dissociates into H⁺(aq) and Cl⁻(aq) ions; all the HCl molecules become ions:

$$\text{HCl }\stackrel{\text{100\%}}{\to }{\text{H}}^{+}{\text{(aq) + Cl}}^{-}\text{(aq)}$$

Any acid that dissociates 100% into ions is called a strong acidAny acid that is 100% dissociated into ions in aqueous solution.. If it does not dissociate 100%, it is a weak acidAny acid that is less than 100% dissociated into ions in aqueous solution.. HC₂H₃O₂ is an example of a weak acid:

$${\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\stackrel{~5\%}{\to }{\text{H}}^{\text{+}}{\text{(aq) + C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}^{-}\text{(aq)}$$

Because this reaction does not go 100% to completion, it is more appropriate to write it as an equilibrium:

$${\text{HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\rightleftarrows {\text{H}}^{\text{+}}{\text{(aq) + C}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}^{-}\text{(aq)}$$

As it turns out, there are very few strong acids, which are given in Table 12.2 "Strong Acids and Bases". If an acid is not listed here, it is a weak acid. It may be 1% ionized or 99% ionized, but it is still classified as a weak acid.

The issue is similar with bases: a strong baseAny base that is 100% dissociated into ions in aqueous solution. is a base that is 100% ionized in solution. If it is less than 100% ionized in solution, it is a weak baseAny base that is less than 100% dissociated into ions in aqueous solution.. There are very few strong bases (see Table 12.2 "Strong Acids and Bases"); any base not listed is a weak base. All strong bases are OH^– compounds. So a base based on some other mechanism, such as NH₃ (which does not contain OH⁻ ions as part of its formula), will be a weak base.

Certain salts will also affect the acidity or basicity of aqueous solutions because some of the ions will undergo hydrolysis, just like NH₃ does to make a basic solution. The general rule is that salts with ions that are part of strong acids or bases will not hydrolyze, while salts with ions that are part of weak acids or bases will hydrolyze.

Consider NaCl. When it dissolves in an aqueous solution, it separates into Na⁺ ions and Cl⁻ ions:

NaCl → Na⁺(aq) + Cl⁻(aq)

Will the Na⁺(aq) ion hydrolyze? If it does, it will interact with the OH⁻ ion to make NaOH:

Na⁺(aq) + H₂O → NaOH + H⁺(aq)

However, NaOH is a strong base, which means that it is 100% ionized in solution:

NaOH → Na⁺(aq) + OH⁻(aq)

The free OH⁻(aq) ion reacts with the H⁺(aq) ion to remake a water molecule:

H⁺(aq) + OH⁻(aq) → H₂O

The net result? There is no change, so there is no effect on the acidity or basicity of the solution from the Na⁺(aq) ion. What about the Cl⁻ ion? Will it hydrolyze? If it does, it will take an H⁺ ion from a water molecule:

Cl⁻(aq) + H₂O → HCl + OH⁻

However, HCl is a strong acid, which means that it is 100% ionized in solution:

HCl → H⁺(aq) + Cl⁻(aq)

The free H⁺(aq) ion reacts with the OH⁻(aq) ion to remake a water molecule:

H⁺(aq) + OH⁻(aq) → H₂O

The net result? There is no change, so there is no effect on the acidity or basicity of the solution from the Cl⁻(aq) ion. Because neither ion in NaCl affects the acidity or basicity of the solution, NaCl is an example of a neutral saltAn ionic compound that does not affect the acidity of its aqueous solution..

Things change, however, when we consider a salt like NaC₂H₃O₂. We already know that the Na⁺ ion won’t affect the acidity of the solution. What about the acetate ion? If it hydrolyzes, it will take an H⁺ from a water molecule:

C₂H₃O₂⁻(aq) + H₂O → HC₂H₃O₂ + OH⁻(aq)

Does this happen? Yes, it does. Why? Because HC₂H₃O₂ is a weak acid. Any chance a weak acid has to form, it will (the same with a weak base). As some C₂H₃O₂⁻ ions hydrolyze with H₂O to make the molecular weak acid, OH⁻ ions are produced. OH⁻ ions make solutions basic. Thus NaC₂H₃O₂ solutions are slightly basic, so such a salt is called a basic saltAn ionic compound whose aqueous solution is slightly basic..

There are also salts whose aqueous solutions are slightly acidic. NH₄Cl is an example. When NH₄Cl is dissolved in H₂O, it separates into NH₄⁺ ions and Cl⁻ ions. We have already seen that the Cl⁻ ion does not hydrolyze. However, the NH₄⁺ ion will:

NH₄⁺(aq) + H₂O → NH₃(aq) + H₃O⁺(aq)

Recall from Section 12.1 "Arrhenius Acids and Bases" that H₃O⁺ ion is the hydronium ion, the more chemically proper way to represent the H⁺ ion. This is the classic acid species in solution, so a solution of NH₄⁺(aq) ions is slightly acidic. NH₄Cl is an example of an acid saltAn ionic compound whose aqueous solution is slightly acidic.. The molecule NH₃ is a weak base, and it will form when it can, just like a weak acid will form when it can.

So there are two general rules: (1) If an ion derives from a strong acid or base, it will not affect the acidity of the solution. (2) If an ion derives from a weak acid, it will make the solution basic; if an ion derives from a weak base, it will make the solution acidic.

Some salts are composed of ions that come from both weak acids and weak bases. The overall effect on an aqueous solution depends on which ion exerts more influence on the overall acidity. We will not consider such salts here.

12.5 Autoionization of Water

We have already seen that H₂O can act as an acid or a base:

NH₃ + H₂O → NH₄⁺ + OH⁻ (H₂O acts as an acid) HCl + H₂O → H₃O⁺ + Cl⁻ (H₂O acts as a base)

It may not surprise you to learn, then, that within any given sample of water, some H₂O molecules are acting as acids, and other H₂O molecules are acting as bases. The chemical equation is as follows:

H₂O + H₂O → H₃O⁺ + OH⁻

This occurs only to a very small degree: only about 6 in 10⁸ H₂O molecules are participating in this process, which is called the autoionization of waterWater molecules act as acids (proton donors) and bases (proton acceptors) with each other to a tiny extent in all aqueous solutions.. At this level, the concentration of both H⁺(aq) and OH⁻(aq) in a sample of pure H₂O is about 1.0 × 10⁻⁷ M. If we use square brackets—[ ]—around a dissolved species to imply the molar concentration of that species, we have

[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M

for any sample of pure water because H₂O can act as both an acid and a base. The product of these two concentrations is 1.0 × 10⁻¹⁴:

[H⁺] × [OH⁻] = (1.0 × 10⁻⁷)(1.0 × 10⁻⁷) = 1.0 × 10⁻¹⁴

In acids, the concentration of H⁺(aq)—[H⁺]—is greater than 1.0 × 10⁻⁷ M, while for bases the concentration of OH⁻(aq)—[OH⁻]—is greater than 1.0 × 10⁻⁷ M. However, the product of the two concentrations—[H⁺][OH⁻]—is always equal to 1.0 × 10⁻¹⁴, no matter whether the aqueous solution is an acid, a base, or neutral:

[H⁺][OH⁻] = 1.0 × 10⁻¹⁴

This value of the product of concentrations is so important for aqueous solutions that it is called the autoionization constant of waterThe product of the hydrogen ion and hydroxide ion concentrations. and is denoted K_w:

K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴

This means that if you know [H⁺] for a solution, you can calculate what [OH⁻] has to be for the product to equal 1.0 × 10⁻¹⁴, or if you know [OH⁻], you can calculate [H⁺]. This also implies that as one concentration goes up, the other must go down to compensate so that their product always equals the value of K_w.

When you have a solution of a particular acid or base, you need to look at the formula of the acid or base to determine the number of H⁺ or OH⁻ ions in the formula unit because [H⁺] or [OH⁻] may not be the same as the concentration of the acid or base itself.

For strong acids and bases, [H⁺] and [OH⁻] can be determined directly from the concentration of the acid or base itself because these ions are 100% ionized by definition. However, for weak acids and bases, this is not so. The degree, or percentage, of ionization would need to be known before we can determine [H⁺] and [OH⁻].

12.6 The pH Scale

As we have seen, [H⁺] and [OH⁻] values can be markedly different from one aqueous solution to another. So chemists defined a new scale that succinctly indicates the concentrations of either of these two ions.

pHThe negative logarithm of the hydrogen ion concentration. is a logarithmic function of [H⁺]:

pH = −log[H⁺]

pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on [H⁺], we can summarize as follows:

• If pH < 7, then the solution is acidic.
• If pH = 7, then the solution is neutral.
• If pH > 7, then the solution is basic.

This is known as the pH scaleThe range of values from 0 to 14 that describes the acidity or basicity of a solution.. You can use pH to make a quick determination whether a given aqueous solution is acidic, basic, or neutral.

Table 12.3 "Typical pH Values of Various Substances*" gives the typical pH values of some common substances. Note that several food items are on the list, and most of them are acidic.

pH is a logarithmic scale. A solution that has a pH of 1.0 has 10 times the [H⁺] as a solution with a pH of 2.0, which in turn has 10 times the [H⁺] as a solution with a pH of 3.0 and so forth.

Using the definition of pH, it is also possible to calculate [H⁺] (and [OH⁻]) from pH and vice versa. The general formula for determining [H⁺] from pH is as follows:

[H⁺] = 10^−pH

You need to determine how to evaluate the above expression on your calculator. Ask your instructor if you have any questions. The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits after the decimal point is what determines the number of significant figures in the final answer:

There is an easier way to relate [H⁺] and [OH⁻]. We can also define pOHThe negative logarithm of the hydroxide ion concentration. similar to pH:

pOH = −log[OH⁻]

(In fact, p“anything” is defined as the negative logarithm of that anything.) This also implies that

[OH⁻] = 10^−pOH

A simple and useful relationship is that for any aqueous solution,

pH + pOH = 14

This relationship makes it simple to determine pH from pOH or pOH from pH and then calculate the resulting ion concentration.

12.7 Buffers

As indicated in Section 12.4 "Strong and Weak Acids and Bases and Their Salts", weak acids are relatively common, even in the foods we eat. But we occasionally encounter a strong acid or base, such as stomach acid, which has a strongly acidic pH of 1.7. By definition, strong acids and bases can produce a relatively large amount of H⁺ or OH⁻ ions and consequently have marked chemical activities. 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 [approximated as 0.1 M HCl(aq)] were added to the bloodstream and no correcting mechanism were present, the pH of the blood would decrease from about 7.4 to about 4.7—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 bufferA solution that resists dramatic changes in pH., 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 HC₂H₃O₂ (a weak acid) and NaC₂H₃O₂ (the salt derived from that weak acid). Another example of a buffer is a solution containing NH₃ (a weak base) and NH₄Cl (a salt derived from that weak base).

Let us use an HC₂H₃O₂/NaC₂H₃O₂ buffer to demonstrate how buffers work. If a strong base—a source of OH⁻(aq) ions—is added to the buffer solution, those OH⁻ ions will react with the HC₂H₃O₂ 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 OH⁻ ions react to make H₂O, so 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 H⁺ ions and C₂H₃O₂⁻ ions are present in the same solution, they will come together to make HC₂H₃O₂:

H⁺(aq) + C₂H₃O₂⁻(aq) → HC₂H₃O₂(aq)

Rather than changing the pH dramatically and making the solution acidic, the added H⁺ ions react to make molecules of a weak acid. Figure 12.2 "The Actions 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, NH₃ molecules can react with any excess H⁺ ions introduced by strong acids:

NH₃(aq) + H⁺(aq) → NH₄⁺(aq)

while the NH₄⁺(aq) ion can react with any OH⁻ ions introduced by strong bases:

NH₄⁺(aq) + OH⁻(aq) → NH₃(aq) + H₂O(ℓ)

Buffers work well only for limited amounts of added strong acid or base. Once either solute is completely reacted, the solution is no longer a buffer, and rapid changes in pH may occur. We say that a buffer has a certain capacityThe amount of strong acid or base a buffer can counteract.. 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 [the second compound 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.