19.3 Strengths of Acids and Bases Connecting to Your World Lemons and grapefruits have a sour taste because they contain citric acid. When you make lemonade, or cut up a grapefruit, you probably do not wear safety goggles or chemicalresistant clothing even though you are working with an acid. However, some acids require such precautions. For example, sulfuric acid is a widely used industrial chemical that can quickly cause severe burns if it comes into contact with skin. In this section, you will learn what makes some acids weak acids and other acids strong acids. Strong and Weak Acids and Bases Acids are classified as strong or weak depending on the degree to which they ionize in water. In general, strong acids are completely ionized in aqueous solution. Hydrochloric acid and sulfuric acid are strong acids. HCl(g) H 2 O(l) H 3 O (aq) Cl (aq) (100% ionized) Weak acids ionize only slightly in aqueous solution. The ionization of ethanoic acid (acetic acid), a typical weak acid, is not complete. CH H 3 O + 1aq 2 + CH 3 COO - 3 COOH 1aq 2 + H 2 O 1 l 2 1aq2 PJ E Ethanoic acid Water Hydronium ion Ethanoate ion Table 19.6 shows the relative strengths of some common acids and bases. Table 19.6 Relative Strengths of Common Acids and Bases Substance Formula Relative Strength Hydrochloric acid HCl Nitric acid HNO 3 s Strong Acid Sulfuric acid H 2 SO 4 Phosphoric acid H 3 PO 4 Ethanoic acid CH 3 COOH Carbonic acid H 2 CO 3 Hypochlorous acid HClO Neutral Solution Ammonia NH 3 Sodium silicate Na 2 SiO 3 Calcium hydroxide Ca(OH) 2 Sodium hydroxide NaOH Potassium hydroxide KOH Section Resources Print Guided Reading and Study Workbook, Section 19.3 Core Teaching Resources, Section 19.3 Review Transparencies, T223 T224 s Increasing strength of acid Neutral Solution Increasing strength of base Strong Base Guide for Reading Key Concepts How does the value of an acid dissociation constant relate to the strength of an acid? How can you calculate an acid dissociation constant (K a ) of a weak acid? Vocabulary strong acids weak acids acid dissociation constant (K a ) strong bases weak bases base dissociation constant (K b ) Reading Strategy Comparing and Contrasting Compare the concentrations of H and OH in solutions of strong acids and weak acids. Explain these differences. Do the same for strong bases and weak bases. Section 19.3 Strengths of Acids and Bases 605 Technology Interactive Textbook with ChemASAP, Problem-Solving 19.23, Assessment 19.3 Go Online, Section 19.3 19.3 1 FOCUS Objectives 19.3.1 Define strong acids and weak acids. 19.3.2 Describe how an acid s strength is related to the value of its acid dissociation constant. 19.3.3 Calculate an acid dissociation constant (K a ) from concentration and ph measurements. 19.3.4 Order acids by strength according to their acid dissociation constants (K a ). 19.3.5 Order bases by strength according to their base dissociation constants (K b ). Guide for Reading Build Vocabulary Graphic Organizer Students can make two columns labeled Acid and Base. Under each column, write the related vocabulary words and their definitions. Reading Strategy Preview Students can preview the information in this section by skimming the headings, visuals, and boldfaced material. 2 INSTRUCT Have students study the photograph and read the text that opens the section. Ask, What is an example of a weak acid? (lemon or grapefruit) What is an example of a strong acid? (sulfuric acid) Strong and Weak Acids and Bases Use Visuals Table 19.6 Have students study the table. Ask, Which is the weakest acid in the table? (hypochlorous acid) Which is the weakest base? (ammonia) Acids, Bases, and Salts 605
Section 19.3 (continued) Use Visuals Figure 19.16. Explain to students that the bar graphs compare the extent of ionization or dissociation of strong to weak acids. Ask, What is the primary difference between strong and weak acids? (Strong acids are nearly 100% dissociated, while weak acids are only partially dissociated.) Interpreting Graphs a. The strong acid dissociates completely, forming equal amounts of ions. b. The amount of acid that dissociates is equal to the amount of the two resulting ions. c. The bar graph for the first dissociation of oxalic acid should show low concentrations of H + and HOOCCOO. The bar graph for the second dissociation should show even lower concentrations of H + and OOCCOO 2. Perceptive students may note that [H + ] in the second bar graph actually should be much higher than [OOCCOO 2 ] because of the H + ions produced in the first dissociation. Enrichment Question L3 Relate the amount of dissociation with the properties of strong and weak acids. (With increasing amount of dissociation, the acid becomes stronger.) Figure 19.16 Dissociation of an acid () in water yields H 3 O and A. The bar graphs compare the extent of dissociation of strong, weak, and very weak acids. INTERPRETING GRAPHS a. Explain In the graph for the strong acid, why are the heights of the H 3 O and A bars the same as the height of bar? b. Inferring In the graph for the weak acid, why is the height of the H 3 O bar the same as the distance from the top of the second bar to the dotted line? c. Apply Concepts Draw a bar graph for the dissociation of the weak diprotic acid, oxalic acid. Be sure to include the first and second dissociation. 606 Chapter 19 Acid Dissociation Constant In an aqueous solution of ethanoic acid, fewer than 1% of ethanoic acid molecules are ionized at any instant. Therefore, ethanoic acid is considered a weak acid. Figure 19.16 compares the extent of dissociation of strong, weak, and very weak acids. A strong acid completely dissociates in water. As a result, [H 3 O ] is high. Hydrochloric acid and sulfuric acid are examples of strong acids. On the other hand, weak acids, such as boric acid and carbonic acid, remain largely undissociated. The [H 3 O ] of a weak acid is low. You can write the equilibrium-constant expression from the balanced chemical equation. The equilibrium-constant expression for ethanoic acid is shown below. 3H 3 O+ 4 COOH4 3H 2 O4 Relative number of moles Relative number of moles Relative number of moles Dissociation of a Strong Acid, Weak Acid, and Very Weak Acid H 3 O A Complete uuuuuy dissociation Strong Acid (aq) H 2 O(l) uy H 3 O (aq) A (aq) Moderate uuuuuy dissociation (aq) H 2 O(l) Very little uuuuuy dissociation Weak Acid H 3 O E H 3O (aq) A (aq) DJ Very Weak Acid H 3 O (aq) H 2 O(l) E H 3O (aq) A (aq) DJ A A 606 Chapter 19
Table 19.7 Dissociation Constants of Weak Acids Acid Ionization K a (25 C) Oxalic acid HOOCCOOH(aq) H (aq) HOOCCOO (aq) 5.6 10 2 HOOCCOO (aq) H (aq) OOCCOO 2 (aq) For dilute solutions, the concentration of water is a constant. It can be combined with to give an acid dissociation constant. An acid dissociation constant (K a ) is the ratio of the concentration of the dissociated (or ionized) form of an acid to the concentration of the undissociated (nonionized) form. The dissociated form includes both the H 3 O and the anion. 3H 2 O4 K a 3H 3 O+ 4 COOH4 The acid dissociation constant (K a ) reflects the fraction of an acid in the ionized form. For this reason, dissociation constants are sometimes called ionization constants. If the value of the dissociation constant is small, then the degree of dissociation or ionization of the acid in the solution is small. Weak acids have small K a values. The stronger an acid is, the larger is its K a value. A larger value of K a means the dissociation or ionization of the acid is more complete. For example, nitrous acid (HNO 2 ) has a K a of 4.4 10 4, whereas ethanoic acid (acetic acid) has a K a of 1.8 10 5. This means that nitrous acid is more ionized in solution than ethanoic acid. Nitrous acid is a stronger acid than ethanoic acid. Therefore, a strong acid has a higher [H 3 O ] and a large dissociation constant. Conversely, a weak acid has a low [H 3 O ] and a small dissociation constant. Diprotic and triprotic acids lose their hydrogens one at a time. Each ionization reaction has a separate dissociation constant. Thus, phosphoric acid (H 3 PO 4 ) has three dissociation constants to go with its three ionizable hydrogens. Table 19.7 shows the ionization reactions and dissociation constants of some common weak acids, ranked by the value of the first dissociation constant of each acid. 5.1 10 5 Phosphoric acid H 3 PO 4 (aq) H (aq) H 2 PO 4 (aq) 7.5 10 3 H 2 PO 4 (aq) H (aq) HPO 4 2 (aq) HPO 4 2 (aq) H (aq) PO 4 3 (aq) 6.2 10 8 4.8 10 13 Methanoic acid HCOOH(aq) H (aq) HCOO (aq) 1.8 10 4 Benzoic acid C 6 H 5 COOH(aq) H (aq) C 6 H 5 COO (aq) 6.3 10 5 Ethanoic acid CH 3 COOH(aq) H (aq) CH 3 COO (aq) 1.8 10 5 Carbonic acid H 2 CO 3 (aq) H (aq) HCO 3 (aq) 4.3 10 7 HCO 3 (aq) H (aq) CO 3 2 (aq) 4.8 10 11 Figure 19.17 A solution of phosphoric acid is used to remove lime deposits from plumbing fixtures. Lime deposits are calcium carbonate. LIME- GONE Discuss Remind students that, in solution, the negative ion of an acid is a base. Explain that strong acids, such as nitric acid, dissociate almost completely because the negative ion is a very weak base. That is, its tendency to combine with a hydrogen ion is slight. In contrast, the dissociation of a weak acid, such as carbonic acid, is limited, because its negative ion is a relatively strong base. These ions combine with most of the available hydrogen ions to form the undissociated form of the acid again. The terms strong and weak, as applied to acids, are often confused with the concept of concentration. Stress that the dissociation of an acid or base into ions involves the establishment of equilibrium. The terms strong and weak refer to the position of the equilibrium. When a strong acid or base dissolves, the equilibrium favors the products. When a weak acid or base dissolves, the equilibrium favors the reactants. Show students that the extent to which products or reactants are favored can be determined from the values of K a or K b. Also, discuss how values of K a and K b can be used to compare the strengths of acids and bases. Checkpoint What distinguishes a strong acid from a weak acid? Section 19.3 Strengths of Acids and Bases 607 Facts and Figures Losing Ions Diprotic and triprotic acids lose their hydrogen ions one at a time. Each successive ion is more difficult to lose from the negative ion. Phosphoric acid (H 3 PO 4 ) loses one hydrogen ion relatively easily, leaving an H 2 PO 4 ion. This negatively charged ion loses fewer hydrogen ions than phosphoric acid, and even fewer hydrogen ions leave HPO 4 2. Although phosphoric acid contains three acidic hydrogens, it does not have a high degree of ionization and is, therefore, a relatively weak acid. Answers to... Checkpoint Stronger acids have larger K a values and ionize more completely to produce H 3 O + ions. Acids, Bases, and Salts 607
Section 19.3 (continued) CLASS Activity Shampoo Survey Purpose Students compare shampoos for normal, dry, or oily hair. Materials different brands and types of shampoo; 10-mL graduated cylinder; beakers; universal indicator paper Procedure Have groups of students conduct a survey of shampoo products. Each group should gather data on a different brand and type of shampoo. Decide as a class what information should be included in the survey and how the data will be reported. To assure uniform ph testing, have groups prepare 1% shampoo solutions and use universal indicator paper. Expected Outcome Shampoos labeled for use on normal, dry, or oily hair are formulated by controlling the strength and amount of the synthetic detergent. The quantity of the active ingredient controls the defatting action, which removes oil from the hair. Figure 19.18 Window cleaners use an ammonia solution to clean glass because it is a weak base. Being a weak base also makes ammonia relatively safe to use. Base Dissociation Constant Just as there are strong acids and weak acids, there are also strong bases and weak bases. Strong bases dissociate completely into metal ions and hydroxide ions in aqueous solution. Some strong bases, such as calcium hydroxide and magnesium hydroxide, are not very soluble in water. The small amounts of these bases that do dissolve dissociate completely. Weak bases react with water to form the hydroxide ion and the conjugate acid of the base. Ammonia is an example of a weak base. The equilibrium of this equation greatly favors the reverse reaction. Only about 1% of the ammonia is present as NH 4, the conjugate acid of NH 3. The concentrations of NH 4 and OH are low and equal. The equilibriumconstant expression for the reaction of ammonia with water is The concentration of water is constant in dilute solutions. It can be combined with to give a base dissociation constant (K b ). 3H 2 O4 K b 3NH 4 + 4 3OH - 4 3NH 3 4 In general, the base dissociation constant (K b ) is the ratio of the concentration of the conjugate acid times the concentration of the hydroxide ion to the concentration of the conjugate base. The general form of this equation is as follows. The magnitude of K b indicates the ability of a weak base to compete with the very strong base OH for hydrogen ions. Because bases such as ammonia are weak relative to the hydroxide ion, K b for such bases is usually small. The K b for ammonia is 1.8 10 5. The smaller the value of K b, the weaker is the base. Checkpoint NH NH 4+ 1aq2 + OH - 3 1aq2 + H 2 O 1l 2 1aq2 PJ E Ammonia Water Ammonium Hydroxide ion ion 3NH 4 + 4 3OH - 4 3NH 3 4 3H 2 O4 K b 3conjugate acid4 3OH- 4 3conjugate base4 Which is larger, the K a of a weak acid or the K a of a strong acid? 608 Chapter 19 608 Chapter 19
Table 19.8 Concentration of Some Common Laboratory Acids and Bases Concentration Acid or base Moles/liter (molarity) Grams/liter Concentrated hydrochloric acid 12 438 Dilute hydrochloric acid 6 219 Concentrated sulfuric acid 18 1764 Dilute sulfuric acid 6 588 Concentrated phosphoric acid 15 1470 Concentrated nitric acid 16 1008 Dilute nitric acid 6 378 Ethanoic acid, glacial 17 1020 Ethanoic acid, dilute 6 360 Dilute sodium hydroxide 6 240 Concentrated aqueous ammonia 15 255 Dilute aqueous ammonia 6 102 Concentration and Strength The words concentrated and dilute indicate how much of an acid or base is dissolved in solution. These terms refer to the number of moles of the acid or base in a given volume. The words strong and weak refer to the extent of ionization or dissociation of an acid or base. They indicate how many of the particles ionize or dissociate into ions. Hydrochloric acid (HCl)(aq) is a strong acid; it is completely dissociated into ions. Gastric juice in the stomach is a dilute solution of hydrochloric acid. A relatively small number of HCl molecules are present in a given volume of gastric juice, but they are all dissociated into ions. A sample of hydrochloric acid added to a large volume of water becomes more dilute, but it is still a strong acid. Vinegar is a dilute solution of a weak acid, ethanoic acid. Pure ethanoic acid (glacial acetic acid) is still a weak acid, even though it is highly concentrated. Solutions of ammonia can be dilute or concentrated, depending on the amount of ammonia dissolved in a given volume of water. In any solution of ammonia, however, whether concentrated or dilute, ammonia will be a weak base because the amount of ionization will be small. Table 19.8 lists the concentrations of acids and bases commonly found in the laboratory. Calculating Dissociation Constants Discuss Explain how the dissociation constant of an acid or base can be determined experimentally from the concentration of the solution and its ph. The calculation is based on the assumption that the acid molecule forms an equal number of hydrogen ions and negative ions when it dissociates. This is true only if there is no additional source of either hydrogen ions or the negative ions. Point out that calculating K a is much more complicated in the case of a polyprotic acid. The dissociation of H 3 PO 4, for example, involves three separate ionizations, each with its own K a. Calculating Dissociation Constants You can calculate the acid dissociation constant (K a ) of a weak acid or the base dissociation constant (K b ) of a weak base from experimental data. To find the K a of a weak acid or the K b of a weak base, substitute the measured concentrations of all the substances present at equilibrium into the expression for K a or K b. For a weak acid, you can determine these concentrations experimentally if you know the initial molar concentration of the acid and the ph (or [H 3 O ]) of the solution at equilibrium. Section 19.3 Strengths of Acids and Bases 609 Answers to... Checkpoint The K a of a strong acid is larger. Acids, Bases, and Salts 609
Section 19.3 (continued) Sample Problem 19.5 Answers 22. K a = (4.2 10-3 )(4.2 10-3 )/(9.58 10-2 ) = 1.8 10-4 23. K a = (9.86 10-4 )(9.86 10-4 )/(2.0 10-1 ) = 4.86 10-6 Practice Problems Plus A solution of a weak acid, exactly 0.500M, has a [H + ] = 5.77 10-6 M a. What is the ph of this solution? (5.239) b. What is the value of K a for this acid? (6.66 10-11 ) Math Handbook For a math refresher and practice, direct students to scientific notation, page R56. Stone Conservator Have students do research about the sources and causes of acid rain. (Acid rain is thought to be due principally to the release of sulfur oxides and nitrogen oxides into the atmosphere. ) Ask, How do weather patterns affect the distribution of environmental damage due to acid rain? (Prevailing winds generally carry pollutants from west to east.) What types of vegetation, if any, are most resistant to acid rain, or tend to thrive in acidic soils? (Students may wish to speak to staff at nurseries for help answering this question.) What types of conservation efforts are used to adjust the ph of lakes and rivers that become too acidic? (A special slurry of CaCO 3, or limestone, is sometimes added to lakes and rivers to control ph.) Math Handbook For help with scientific notation, go to page R56. Problem-Solving 19.23 Solve Problem 23 with the help of an interactive guided tutorial. withchemasap 610 Chapter 19 In general, for an acid in water you can find K a by substituting the concentrations of the acid, [], the negative ion from the dissociation of the acid, [A ], and the hydrogen ion, [H ], into the equation below. SAMPLE PROBLEM 19.5 K a 3H+ 43A - 4 34 Calculating a Dissociation Constant A 0.1000M solution of ethanoic acid is only partially ionized. From measurements of the ph of the solution, [H ] is determined to be 1.34 10 3 M. What is the acid dissociation constant (K a ) of ethanoic acid? Analyze List the knowns and the unknown. Knowns [ethanoic acid] 0.1000M [H ] 1.34 10 3 M CH 3 COOH(aq) H 2 O(l) H 3 O (aq) CH 3 COO (aq) K a 3H+ 4 COOH4 Unknown K a? Calculate Solve for the unknown. Each molecule of CH 3 COOH that ionizes gives an H and a CH 3 COO ion. Therefore, at equilibrium [H ] [CH 3 COO ] 1.34 10 3 M. The equilibrium concentration of CH 3 COOH is the initial concentration minus the concentration of the ionized acid or (0.1000 0.00134)M 0.0987M. Concentration [CH 3 COOH] [H ] [CH 3 COO ] Initial 0.1000 0 0 Change 1.34 10 3 1.34 10 3 1.34 10 3 Equilibrium 0.0987 1.34 10 3 1.34 10 3 Practice Problems Substitute the equilibrium values into the expression for K a. K a 3H+ 4 COOH4 1.82 10-5 Evaluate Does the result make sense? The value of K a is consistent with that of a weak acid. Practice Problems 22. In an exactly 0.1M solution of methanoic acid, [H ] 4.2 10 3 M. Calculate the K a of methanoic acid. 11.34 10-3 2 11.34 10-3 2 0.0987 23. In an exactly 0.2M solution of a monoprotic weak acid, [H ] 9.86 10 4 M. What is the K a for this acid? Have students research chemistryrelated careers in the library or on the Internet. Students can then construct a table that describes the nature of the work, educational and training requirements, employment outlook, working conditions, and other necessary information. 610 Chapter 19
Stone Conservator As more is learned about the damaging effects of airborne pollutants, such as acid rain, there is a growing concern to preserve historic buildings and pieces of sculpture from damage. Stone conservators work to prevent and repair the damage to stone used in buildings and sculptures. Stone conservators must clean statues properly to remove pollution deposits. One method they use is to apply a thin, clay mudpack to the stone s surface to pull out the deposits. Lasers are also used to remove pollution from stone. When making repairs, stone conservators sometimes use surgical microscopes to examine the surfaces of statues. If the stone 19.3 Section Assessment 24. Key Concept Compare a strong acid and a weak acid in terms of the acid dissociation constant. 25. Key Concept How do you determine the K a of a weak acid or the K b of a weak base? 26. Which acid in Table 19.6 would you expect to have the lowest ionization constant? 27. Acid HX has a very small value of K a. How do the relative amounts of H and HX compare at equilibrium? 28. Write the equations for the ionization or dissociation of the following acids and bases in water. a. nitric acid b. ethanoic acid c. ammonia d. magnesium hydroxide 29. Compare the terms strong/weak and concentrated/dilute as they pertain to acids and bases. was originally painted, the original paint is chemically analyzed to determine its composition. In addition, conservators research and apply methods to preserve the stone once it has been repaired. One preservation technique is to seal the stone to prevent water, which carries dissolved gases and salts, from seeping into the pores of the stone. Cause and Effect Paragraph The chief cause of tooth decay is the weak acid called lactic acid (C 3 H 6 O 3 ). Lactic acid is formed in the mouth by the action of specific bacteria, such as Streptococcus mutans, on sugars present in sticky plaque on tooth surfaces. Research current efforts to thwart tooth decay. Write a report summarizing your findings. Assessment 19.3 Test yourself on the concepts in Section 19.3. withchemasap Stone conservators often work for museums, universities, or private companies that specialize in the cleaning and restoration of stone objects. They must have knowledge of both chemistry and art because they often work closely with both chemists and museum personnel. A stone conservator s level of education may range from a bachelor s degree to a doctorate. For: Careers in Chemistry Visit: PHSchool.com Web Code: cdb-1193 3 ASSESS Evaluate Understanding Ask, List the two conditions needed to calculate the dissociation constant of a weak acid. (You must know the initial molar concentration of the acid and the ph or [H + ] of the solution at equilibrium.) Reteach Table 19.7, may pose difficulties for some students. Use an example to explain the information in the table. Point out that the K a for each acid is equal to the product of the concentrations of the ions on the right of the equation, divided by the concentration of the non-ionized acid. Also explain that the K a value is a quantitative indication of acid strength. A lower K a value means the reactants are favored in the equilibrium; thus, the acid is weaker. As a class activity, have students prepare a numbered list of steps for calculating dissociation constants. Give them a different example than those in Sample Problem 19.5, and have them use the numbered procedure to work through the problem. To thwart tooth decay, reduce sugar intake; brush and floss regularly; use a fluoride toothpaste or rinse; and have regular dental check-ups to catch minor decay early. 24. A strong acid is completely ionized in aqueous solution and has a large K a. A weak acid is ionized only slightly in aqueous solution and has a small K a. 25. Substitute the measured concentrations of all the substances present at equilibrium into the expressions for K a or K b. 26. hypochlorous acid 27. The [HX] is much greater than the [H + ]. 28. a. HNO 3 + H 2 O H 3 O + + NO 3 b. CH 3 COOH + H 2 O CH 3 COO + H 3 O + Section 19.3 Assessment Section 19.3 Strengths of Acids and Bases 611 c. NH 3 + H 2 O NH + 4 + OH d. Mg(OH) 2 Mg 2+ + 2OH 29. Strong acids and bases are completely ionized in aqueous solution. Weak acids and bases ionize only slightly in aqueous solution. Concentrated acid or base solutions contain large amounts (high concentrations) of acid or base. Dilute acid or base solutions contain small amounts (low concentrations) of acid or base. If your class subscribes to the Interactive Textbook, use it to review key concepts in Section 19.3. with ChemASAP Acids, Bases, and Salts 611