# 16.E: Acid–Base Equilibria (Exercises)

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## 16.2: Brønsted–Lowry Acids and Bases

### Conceptual Problems

1. Identify the conjugate acid–base pairs in each equilibrium.
1. $$HSO^−_{4(aq)}+H_2O_{(l)} \rightleftharpoons SO^{2−}_{4(aq)}+H_3O^+_{(aq)}$$
2. $$C_3H_7NO_{2(aq)}+H_3O^+_{(aq)} \rightleftharpoons C_3H_8NO^+_{2(aq)}+H_2O_{(l)}$$
3. $$CH_3CO_2H_{(aq)}+NH_{3(aq)} \rightleftharpoons CH_3CO^−_{2(aq)}+NH^+_{4(aq)}$$
4. $$SbF_{5(aq)}+2HF_{(aq)} \rightleftharpoons H_2F^+_{(aq)}+SbF^−_{6(aq)}$$
2. Identify the conjugate acid–base pairs in each equilibrium.
1. $$HF(aq)+H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)}+F^−_{(aq)}$$
2. $$CH_3CH_2NH_{2(aq)}+H_2O_{(l)} \rightleftharpoons CH_3CH_2NH^+_{3(aq)}+OH^−_{(aq)}$$
3. $$C_3H_7NO_{2(aq)}+OH^−_{(aq)} \rightleftharpoons C_3H_6NO^−_{2(aq)}+H_2O_{(l)}$$
4. $$CH_3CO_2H_{(aq)}+2HF_{(aq)} \rightleftharpoons CH_3C(OH)_2+(aq)+HF^−_{2(aq)}$$
3. Salts such as NaH contain the hydride ion ($$H^−$$). When sodium hydride is added to water, it produces hydrogen gas in a highly vigorous reaction. Write a balanced chemical equation for this reaction and identify the conjugate acid–base pairs.
4. Write the expression for $$K_a$$ for each reaction.
1. $$HCO^−_{3(aq)}+H_2O_{(l)} \rightleftharpoons CO^{2−}_{3(aq)}+H_3O^+_{(aq)}$$
2. $$formic\; acid_{(aq)}+H_2O_{(l)} \rightleftharpoons formate_{(aq)}+H_3O^+_{(aq)}$$
3. $$H_3PO_{4(aq)}+H_2O_{(l)} \rightleftharpoons H_2PO^−_{4(aq)}+H_3O^+_{(aq)}$$
5. Write an expression for the ionization constant $$K_b$$ for each reaction.
1. $$OCH^−_{3(aq)}+H_2O_{(l)} \rightleftharpoons HOCH_{3(aq)}+OH−(aq)$$
2. $$NH^−_{2(aq)}+H_2O_{(l)} \rightleftharpoons NH_{3(aq)}+OH^−_{(aq)}$$
3. $$S^{2−}_{(aq)}+H_2O_{(l)} \rightleftharpoons HS^−_{(aq)}+OH^−_{(aq)}$$
6. Predict whether each equilibrium lies primarily to the left or to the right.
1. $$HBr_{(aq)}+H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)}+Br^−_{(aq)}$$
2. $$NaH_{(soln)}+NH_{3(l)} \rightleftharpoons H2(soln)+NaNH_{2(soln)}$$
3. $$OCH^−_{3(aq)}+NH_{3(aq)} \rightleftharpoons CH3OH(aq)+NH^−_{2(aq)}$$
4. $$NH_{3(aq)}+HCl_{(aq)} \rightleftharpoons NH^+_{4(aq)}+Cl^−_{(aq)}$$
7. Species that are strong bases in water, such as $$CH_3^−$$, $$NH_2^−$$, and $$S^{2−}$$, are leveled to the strength of $$OH^−$$, the conjugate base of $$H_2O$$. Because their relative base strengths are indistinguishable in water, suggest a method for identifying which is the strongest base. How would you distinguish between the strength of the acids $$HIO_3$$, $$H_2SO_4$$, and $$HClO_4$$?
8. Is it accurate to say that a 2.0 M solution of $$H_2SO_4$$, which contains two acidic protons per molecule, is 4.0 M in $$H^+$$? Explain your answer.
9. The alkalinity of soil is defined by the following equation: alkalinity = $$[HCO_3^−] + 2[CO_3^{2−}] + [OH^−] − [H^+]$$. The source of both $$HCO_3^−$$ and $$CO_3^{2−}$$ is $$H_2CO_3$$. Explain why the basicity of soil is defined in this way.
10. Why are aqueous solutions of salts such as $$CaCl_2$$ neutral? Why is an aqueous solution of $$NaNH_2$$ basic?
11. Predict whether aqueous solutions of the following are acidic, basic, or neutral.
1. $$Li_3N$$
2. $$NaH$$
3. $$KBr$$
4. $$C_2H_5NH_3^+Cl^−$$
12. When each compound is added to water, would you expect the $$pH$$ of the solution to increase, decrease, or remain the same?
1. $$LiCH_3$$
2. $$MgCl_2$$
3. $$K_2O$$
4. $$(CH_3)_2NH_2^+Br^−$$
13. Which complex ion would you expect to be more acidic: $$Pb(H_2O)_4^{2+}$$ or $$Sn(H_2O)_4^{2+}$$? Why?
14. Would you expect $$Sn(H_2O)_4^{2+}$$ or $$Sn(H_2O)_6^{4+}$$ to be more acidic in aqueous solutions? Why?
15. Is it possible to arrange the hydrides $$LiH$$, $$RbH$$, $$KH$$, $$CsH$$, and $$NaH$$ in order of increasing base strength in aqueous solution? Why or why not?

1.

1. $$\overset{\text{acid 1}}{HSO^−_{4(aq)}} + \underset{\text{base 2}}{H_2O_{(l)}} \rightleftharpoons \overset{\text{base 1}}{SO^{2−}_{4(aq)}} + \underset{\text{acid 2}}{H_3O^+_{(aq)}}$$
2. $$\underset{\text{base 2}}{C_3H_7NO_{2(aq)}} + \overset{\text{acid 1}}{H_3O^+_{(aq)}} \rightleftharpoons \underset{\text{acid 2}}{C_3H_8NO^+_{2(aq)}} + \overset{\text{base 1}}{H_2O_{(l)}}$$
3. $$\overset{\text{acid 1}}{HOAc_{(aq)}} + \underset{\text{base 2}}{NH_{3(aq)}} \rightleftharpoons \overset{\text{base 1}}{CH_3CO^−_{2(aq)}} + \underset{\text{acid 2}}{NH^+_{4(aq)}}$$
4. $$\overset{\text{acid 1}}{SbF_{5(aq)}} + \underset{\text{base 2}}{2HF_{(aq)}} \rightleftharpoons \underset{\text{acid 2}}{H_2F^+_{(aq)}} + \overset{\text{base 1}}{SbF_6^−(aq)}$$

### Numerical Problems

1. Arrange these acids in order of increasing strength.\
• acid A: $$pK_a = 1.52$$
• acid B: $$pK_a = 6.93$$
• acid C: $$pK_a = 3.86$$

Given solutions with the same initial concentration of each acid, which would have the highest percent ionization?

1. Arrange these bases in order of increasing strength:
• base A: $$pK_b = 13.10$$
• base B: $$pK_b = 8.74$$
• base C: $$pK_b = 11.87$$

Given solutions with the same initial concentration of each base, which would have the highest percent ionization?

1. Calculate the $$K_a$$ and the $$pK_a$$ of the conjugate acid of a base with each $$pK_b$$ value.
1. 3.80
2. 7.90
3. 13.70
4. 1.40
5. −2.50
2. Benzoic acid is a food preservative with a $$pK_a$$ of 4.20. Determine the $$K_b$$ and the $$pK_b$$ for the benzoate ion.
3. Determine $$K_a$$ and $$pK_a$$ of boric acid $$[B(OH)_3]$$, solutions of which are occasionally used as an eyewash; the $$pK_b$$ of its conjugate base is 4.80.

1. acid B < acid C < acid A (strongest)

3.

1. $$K_a = 6.3 \times 10^{−11}$$; $$pK_a = 10.20$$
2. $$K_a = 7.9 \times 10^{−7}$$; $$pK_a = 6.10$$
3. $$K_a = 0.50$$; $$pK_a = 0.30$$
4. $$K_a = 2.5 \times 10^{−13}$$; $$pK_a = 12.60$$
5. $$K_a = 3.2 \times 10^{−17}$$; $$pK_a = 16.50$$

5. $$K_a = 6.3 \times 10^{−10}$$; $$pK_a = 9.20$$

## 16.3: The Autoionization of Water

### Conceptual Problems

1. What is the relationship between the value of the equilibrium constant for the autoionization of liquid water and the tabulated value of the ion-product constant of liquid water ($$K_w$$)?
2. The density of liquid water decreases as the temperature increases from 25°C to 50°C. Will this effect cause $$K_w$$ to increase or decrease? Why?
3. Show that water is amphiprotic by writing balanced chemical equations for the reactions of water with $$HNO_3$$ and $$NH_3$$. In which reaction does water act as the acid? In which does it act as the base?
4. Write a chemical equation for each of the following.
1. Nitric acid is added to water.
2. Potassium hydroxide is added to water.
3. Calcium hydroxide is added to water.
4. Sulfuric acid is added to water.
5. Show that $$K$$ for the sum of the following reactions is equal to $$K_w$$.

$HMnO_{4(aq)} \rightleftharpoons H^+_{(aq)} + MnO^−_{4(aq)}$

$MnO^−_{4(aq)}+H_2O_{(l)} \rightarrow HMnO_{4(aq)} + OH^−_{(aq)}$

1.

$K_{auto} = \dfrac{[H_3O^+][OH^−]}{[H_2O]^2}$

$K_w = [H_3O^+][OH^−] = K_{auto}[H_2O]^2$

3.
water is the base: $H_2O_{(l)} + HNO_{3(g)} \rightarrow H_3O^+_{(aq)} + NO^−_{3(aq)}$
water is the acid: $H_2O_{(l)} + NH_{3(g)} \rightarrow OH^−_{(aq)} + NH^−_{4(aq)}$

### Numerical Problems

1. The autoionization of sulfuric acid can be described by the following chemical equation: $H_2SO_{4(l)}+H_2SO_{4(l)} \rightleftharpoons H_3SO^+_{4(soln)}+H_SO^−_{4(soln)}$ At 25°C, K = 3 × 10−4. Write an equilibrium constant expression for $$KH_2SO_4$$ that is analogous to $$K_w$$. The density of $$H_2SO_4$$ is 1.8 g/cm3 at 25°C. What is the concentration of H3SO4+? What fraction of $$H_2SO_4$$ is ionized?
2. An aqueous solution of a substance is found to have $$[H_3O]^+ = 2.48 \times 10^{−8}\; M$$. Is the solution acidic, neutral, or basic?
3. The pH of a solution is 5.63. What is its pOH? What is the [OH−]? Is the solution acidic or basic?
4. State whether each solution is acidic, neutral, or basic.
1. $$[H_3O^+] = 8.6 \times 10^{−3}\; M$$
2. $$[H_3O^+] = 3.7 \times 10^{−9}\; M$$
3. $$[H_3O^+] = 2.1 \times 10^{−7}\; M$$
4. $$[H_3O^+] = 1.4 \times 10^{−6}\; M$$
5. Calculate the pH and the pOH of each solution.
1. 0.15 M HBr
2. 0.03 M KOH
3. $$2.3 \times 10^{−3}\; M\; HNO_3$$
4. $$9.78 \times 10^{−2} \;M\; NaOH$$
5. 0.00017 M HCl
6. 5.78 M HI
6. Calculate the pH and the pOH of each solution.
1. 25.0 mL of $$2.3 \times 10^{−2}\; M\; HCl$$, diluted to 100 mL
2. 5.0 mL of 1.87 M NaOH, diluted to 125 mL
3. 5.0 mL of 5.98 M HCl added to 100 mL of water
4. 25.0 mL of 3.7 M $$HNO_3$$ added to 250 mL of water
5. 35.0 mL of 0.046 M HI added to 500 mL of water
6. 15.0 mL of 0.0087 M KOH added to 250 mL of water.
7. The pH of stomach acid is approximately 1.5. What is the $$[H^+]$$?
8. Given the pH values in parentheses, what is the $$[H^+]$$ of each solution?
1. household bleach (11.4)
2. milk (6.5)
3. orange juice (3.5)
4. seawater (8.5)
5. tomato juice (4.2)
9. A reaction requires the addition of 250.0 mL of a solution with a pH of 3.50. What mass of HCl (in milligrams) must be dissolved in 250 mL of water to produce a solution with this pH?
10. If you require 333 mL of a pH 12.50 solution, how would you prepare it using a 0.500 M sodium hydroxide stock solution?

1.

$K_{H_2SO_4}=[H_3SO_4^+][HSO_4^−]=K[H_2SO_4]_2$

$[H_3SO_4^+] = 0.3 M$

So the fraction ionized is 0.02.

3. $$pOH = 8.37$$; $$[OH^−] = 4.3 \times 10^{−9}\; M$$; acidic

5.

1. pH = 0.82; pOH = 13.18
2. pH = 12.5; pOH = 1.5
3. pH = 2.64; pOH = 11.36
4. pH = 12.990; pOH = 1.010
5. pH = 3.77; pOH = 10.23
6. pH = −0.762; pOH = 14.762

9. 2.9 mg HCl

## 16.10: Acid-Base Behavior and Chemical Structure

### Conceptual Problems

1. Several factors affect the relative strengths of acids and bases. For each pair, identify the most important factor in determining which is the stronger acid or base in aqueous solution.
1. $$CH_3CCl_2CH_2CO_2H$$ versus $$CH_3CH_2CH_2CO_2H$$
2. $$CH_3CO_2H$$ versus $$CH_3CH_2OH$$
3. $$HClO$$ versus $$HBrO$$
4. $$\ce{CH_3C(=O)NH_2}$$ versus $$CH_3CH_2NH_2$$
5. $$H_3AsO_4$$ versus $$H_3AsO_3$$
2. The stability of the conjugate base is an important factor in determining the strength of an acid. Which would you expect to be the stronger acid in aqueous solution—$$C_6H_5NH_3^+$$ or $$NH_4^+$$? Justify your reasoning.
3. Explain why $$H_2Se$$ is a weaker acid than $$HBr$$.
4. Arrange the following in order of decreasing acid strength in aqueous solution: $$H_3PO_4$$, $$CH_3PO_3H_2$$, and $$HClO_3$$.
5. Arrange the following in order of increasing base strength in aqueous solution: $$\ce{CH_3S−}$$, $$OH^−$$, and $$CF_3S^−$$.
6. Arrange the following in order of increasing acid strength in aqueous solution: $$HClO_2$$, $$HNO_2$$, and $$HNO_3$$.
7. Do you expect $$H_2SO_3$$ or $$H_2SeO_3$$ to be the stronger acid? Why?
8. Give a plausible explanation for why $$CF_3OH$$ is a stronger acid than $$CH_3OH$$ in aqueous solution. Do you expect $$CHCl_2CH_2OH$$ to be a stronger or a weaker acid than $$CH_3OH$$? Why?
9. Do you expect $$Cl_2NH$$ or $$NH_3$$ to be the stronger base in aqueous solution? Why?

$$CF_3S^− < CH_3S^− < OH^−$$ (strongest base)

$$NH_3$$; $$Cl$$ atoms withdraw electron density from $$N$$ in $$Cl_2NH$$.

## 16.11: Lewis Acids and Bases

### Problems

Identify the nature of each of the following as either a Lewis Acid or a Lewis Base:

1. $$NH_3$$
2. $$Ag^+$$
3. $$Ni^{2+}$$
4. $$Pt^{4+}$$
5. $$H_2O$$
6. $$SO_2$$

Explain why $$SiF_4$$ can act as a Lewis Acid.

Identify the nature of each of the following as either a Lewis Acid or a Lewis Base:

1. $$[Fe(CN)_6]^{3-}$$
2. $$[Ni(NH_3)_6]^{2+}$$
3. $$CdBr_4^{2-}$$

What is the product of the reaction of $$CO_2 + OH^- \rightarrow$$ ?

In the reactions below, which is the Lewis Acid and/or which is the Lewis Base?

1. $$NH_3 + H^+ \rightarrow NH_4^+$$
2. $$H_2O + H^+ \rightarrow H_3O^+$$

In the complex ion, $$[PtCl_6]^{2-}$$ which is the Lewis Acid and which is the Lewis base?

The reaction of $$AgCl$$ + $$NH_3$$ produces what complex ion?

### Solutions

Remember, a Lewis acid has an unfilled octet and thus is able to accept a pair of electrons. A Lewis base has a lone pair of electrons to "donate"

1. Lewis base: Nitrogen has a lone pair
2. Lewis acid: $$Ag^+$$ is a cation.
3. Lewis acid: $$Ni^{2+}$$ is a cation.
4. Lewis acid: $$Pt^{4+}$$ is a cation.
5. Lewis base: Oxygen has lone pairs
6. Lewis acid: Sulfur can accept the lone pair electrons from another atom.

$$SiF_4$$ has a central Silicon Atom which can expand its octet to 12 (compared to the typical 8) so that it forms $$[SiF_6]^{2-}$$.

Remember, a Lewis acid has an unfilled octet and thus is able to accept a pair of electrons. A Lewis base has a lone pair of electrons to "donate"

1. Lewis Acid: $$Fe^{3+}$$, Lewis Base: $$CN^-$$
2. Lewis Acid: $$Ni^{2+}$$, Lewis Base: $$NH_3$$
3. Lewis Acid: $$Cd^{2+}$$, Lewis Base: $$Br^-$$

This reaction forms a Bicarbonate ion. $$CO_2 + OH^- \rightarrow O--COH=O$$.

This problem is similar to number 3 & 4 above.

Lewis Acid: $$H^+$$, Lewis Base: $$NH_3$$

Lewis Acid: $$H^+$$, Lewis Base: $$H_2O$$

$$Pt^{4+}$$ is the Lewis acid and $$Cl^-$$ is the Lewis base.

$AgCl + 2NH_3 \rightarrow [Ag(NH_3)_2]^+ + Cl^-$

### Conceptual Problems

1. Construct a table comparing how OH, NH3, H2O, and BCl3 are classified according to the Arrhenius, the Brønsted–Lowry, and the Lewis definitions of acids and bases.

2. Describe how the proton (H+) can simultaneously behave as an Arrhenius acid, a Brønsted–Lowry acid, and a Lewis acid.

3. Would you expect aluminum to form compounds with covalent bonds or coordinate covalent bonds? Explain your answer.

4. Classify each compound as a Lewis acid or a Lewis base and justify your choice.

1. AlCl3
2. (CH3)3N
3. IO3
5. Explain how a carboxylate ion (RCO2) can act as both a Brønsted–Lowry base and a Lewis base.

### Numerical Problems

1. In each reaction, identify the Lewis acid and the Lewis base and complete the reaction by writing the products(s).

1. (CH3)2O + AlCl3
2. SnCl4 + 2 Cl
2. Use Lewis dot symbols to depict the reaction of BCl3 with dimethyl ether [(CH3)2O]. How is this reaction similar to that in which a proton is added to ammonia?