M15Q2: Relative Strengths of Acids and Bases

Chem 103 Textbook Team; Chem 104 Textbook Team

M15Q2: Relative Strengths of Acids and Bases

Learning Objectives

Write balanced chemical equations for aqueous solutions of acids or bases.
Recognize common strong and weak acids and bases.
Predict relative acid or base strength using K_a and K_b values or other tabular data.
| Strengths of Acids and Bases |
Write equilibrium constant expressions for weak acids and bases (K_a, K_b)
Write chemical equations for acid-base reactions and predict whether the reaction will be product-favored or reactant-favored at equilibrium based on K_a or K_b values.

We can rank the strengths of acids by the extent to which they ionize in aqueous solution. A strong acid (HA) yields 100% (or very nearly so) of H₃O⁺ and A⁻ when the acid ionizes in water; Table 1 lists several strong acids. A weak acid gives small amounts of H₃O⁺ and A⁻. The same is true of bases: strong bases dissociate 100% (or very nearly so).

Table 1. Some of the common strong acids and bases.
6 Strong Acids	8 Strong Bases
HCl hydrochloric acid	LiOH lithum hydroxide
HBr hydrobromic acid	NaOH sodium hydroxide
HI hydroiodic acid	KOH potassium hydroxide
HNO₃ nitric acid	RbOH rubidium hydroxide
HClO₄ perchloric acid	CsOH cesium hydroxide
H₂SO₄ sulfuric acid	Ca(OH)₂ calcium hydroxide
	Sr(OH)₂ strontium hydroxide
	Ba(OH)₂ barium hydroxide

Strengths of Acids

The relative strengths of acids may be determined by measuring their equilibrium constants in aqueous solutions. In solutions of the same concentration, stronger acids ionize to a greater extent, and so yield higher concentrations of hydronium ions than do weaker acids. The equilibrium constant for an acid is called the acid-ionization constant, K_a. For the reaction of an acid HA:

HA(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + A^–(aq)

we write the equation for the ionization constant as:

K_a = $\dfrac{[\text{H}_{3}\text{O}^{+}][\text{A}^{-}]}{[\text{HA}]}$

where the concentrations are those at equilibrium. The larger the K_a of an acid, the larger the concentration of H₃O⁺ and A⁻ relative to the concentration of the nonionized acid, HA. Thus a stronger acid has a larger ionization constant than does a weaker acid. The ionization constants increase as the strengths of the acids increase. (A table of ionization constants of weak acids appears in Appendix I.)

The following data on acid-ionization constants indicate the order of acid strength:

CH₃COOH(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + CH₃COO^–(aq) K_a = 1.8 × 10^-5HNO₂(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + NO₂^–(aq) K_a = 7.4 × 10^-4HSO₄^–(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + SO₄^2-(aq) K_a = 1.1 × 10^-2

CH₃COOH < HNO₂ < HSO₄^–

Another measure of the strength of an acid is its percent ionization. The percent ionization of a weak acid is the ratio of the concentration of the hydronium ion at equilibrium to the initial acid concentration, times 100:

percent ionization = $\dfrac{[\text{H}_{3}\text{O}^{+}]_{eq}}{[\text{HA}]_{0}}$ × 100

Because the ratio includes the initial concentration, the percent ionization for a solution of a given weak acid varies depending on the original concentration of the acid, and actually decreases with increasing acid concentration. (Note that [H₃O⁺]_eq is calculated using an ICE table).

Strengths of Bases

We can rank the strengths of bases by their tendency to form hydroxide ions in aqueous solution. The reaction of a Brønsted-Lowry base with water is given by the following reactions:

B(aq) + H₂O(ℓ) ⇌ HB⁺(aq) + OH^–(aq)
A^–(aq) + H₂O(ℓ) ⇌ HA(aq) + OH^–(aq)

Water is the acid that reacts with the base, HB⁺ is the conjugate acid of the base B, and the hydroxide ion is the conjugate base of water. A strong base yields 100% (or very nearly so) of OH⁻ and HB⁺ when it reacts with water; Table 1 lists several strong bases. A weak base yields a small proportion of hydroxide ions. Soluble ionic hydroxides such as NaOH are considered strong bases because they dissociate completely when dissolved in water.

View the simulation of strong and weak acids and bases at the molecular level.

As we did with acids, we can measure the relative strengths of bases by measuring their base-ionization constant (K_b) in aqueous solutions. In solutions of the same concentration, stronger bases ionize to a greater extent, and so yield higher hydroxide ion concentrations than do weaker bases. A stronger base has a larger ionization constant than does a weaker base. For the reaction of a base, B or A^–:

B(aq) + H₂O(ℓ) ⇌ HB⁺(aq) + OH^–(aq)
A^–(aq) + H₂O(ℓ) ⇌ HA(aq) + OH^–(aq)

we write the equation for the ionization constant as:

K_b = $\dfrac{[\text{HB}^{+}][\text{OH}^{-}]}{[\text{B}]}$ or K_b = $\dfrac{[\text{HA}][\text{OH}^{-}]}{[\text{A}^{-}]}$

where the concentrations are those at equilibrium. Again, we do not include [H₂O] in the equilibrium expression because water is the solvent. The chemical reactions and ionization constants of the three bases shown are:

CH₃COO^–(aq) + H₂O(ℓ) ⇌ CH₃COOH(aq) + OH^–(aq) K_b = 5.6 × 10^-10NO₂^–(aq) + H₂O(ℓ) ⇌ HNO₂(aq) + OH^–(aq) K_b = 1.4 × 10^-11NH₃(aq) + H₂O(ℓ) ⇌ NH₄⁺(aq) + OH^–(aq) K_b = 1.8 × 10^-5

NO₂^– < CH₃COO^– < NH₃

A table of ionization constants of weak bases appears in Appendix I. As with acids, percent ionization can be measured for basic solutions, but will vary depending on the base ionization constant and the initial concentration of the solution.

Relative Strengths of Acids and Bases

The extent to which an acid, HA, donates protons to water molecules depends on the strength of the conjugate base, A⁻, of the acid. If A^– is a weak base, then the protons will not bind as strongly, relative to water, and the solution will contain more A^– and H₃O⁺ (stronger conjugate acid). If A⁻ is a strong base, any protons that are donated to water molecules are recaptured by A⁻, and the solution will contain more HA and OH^–. Thus there is relatively little A⁻ and H₃O⁺ in solution, and the acid, HA, is weak. If A⁻ is a weak base, water binds the protons more strongly, and the solution contains primarily A⁻ and H₃O⁺—the acid is strong. Strong acids form very weak conjugate bases, and weak acids form stronger conjugate bases (Figure 1).

The diagram shows two horizontal bars. The first, labeled, “Relative acid strength,” at the top is red on the left and gradually changes to purple on the right. The red end at the left is labeled, “Stronger acids.” The purple end at the right is labeled, “Weaker acids.” Just outside the bar to the lower left is the label, “K subscript a.” The bar is marked off in increments with a specific acid listed above each increment. The first mark is at 1.0 with H subscript 3 O superscript positive sign. The second is ten raised to the negative two with H C l O subscript 2. The third is ten raised to the negative 4 with H F. The fourth is ten raised to the negative 6 with H subscript 2 C O subscript 3. The fifth is ten raised to a negative 8 with C H subscript 3 C O O H. The sixth is ten raised to the negative ten with N H subscript 4 superscript positive sign. The seventh is ten raised to a negative 12 with H P O subscript 4 superscript 2 negative sign. The eighth is ten raised to the negative 14 with H subscript 2 O. Similarly the second bar, which is labeled “Relative conjugate base strength,” is purple at the left end and gradually becomes blue at the right end. Outside the bar to the left is the label, “Weaker bases.” Outside the bar to the right is the label, “Stronger bases.” Below and to the left of the bar is the label, “K subscript b.” The bar is similarly marked at increments with bases listed above each increment. The first is at ten raised to the negative 14 with H subscript 2 O above it. The second is ten raised to the negative 12 C l O subscript 2 superscript negative sign. The third is ten raised to the negative ten with F superscript negative sign. The fourth is ten raised to a negative eight with H C O subscript 3 superscript negative sign. The fifth is ten raised to the negative 6 with C H subscript 3 C O O superscript negative sign. The sixth is ten raised to the negative 4 with N H subscript 3. The seventh is ten raised to the negative 2 with P O subscript 4 superscript three negative sign. The eighth is 1.0 with O H superscript negative sign. — **Figure 1.** This diagram shows the relative strengths of conjugate acid-base pairs, as indicated by their ionization constants in aqueous solution.

Figure 2 lists a series of acids and bases in order of the decreasing strengths of the acids and the corresponding increasing strengths of the bases. The acid and base in a given row are conjugate to each other.

This figure includes a table separated into a left half which is labeled “Acids” and a right half labeled “Bases.” A red arrow points up the left side, which is labeled “Increasing acid strength.” Similarly, a blue arrow points downward along the right side, which is labeled “Increasing base strength.” Names of acids and bases are listed next to each arrow toward the center of the table, followed by chemical formulas. Acids listed top to bottom are sulfuric acid, H subscript 2 S O subscript 4, hydrogen iodide, H I, hydrogen bromide, H B r, hydrogen chloride, H C l, nitric acid, H N O subscript 3, hydronium ion ( in pink text) H subscript 3 O superscript plus, hydrogen sulfate ion, H S O subscript 4 superscript negative, phosphoric acid, H subscript 3 P O subscript 4, hydrogen fluoride, H F, nitrous acid, H N O subscript 2, acetic acid, C H subscript 3 C O subscript 2 H, carbonic acid H subscript 2 C O subscript 3, hydrogen sulfide, H subscript 2 S, ammonium ion, N H subscript 4 superscript +, hydrogen cyanide, H C N, hydrogen carbonate ion, H C O subscript 3 superscript negative, water (shaded in beige) H subscript 2 O, hydrogen sulfide ion, H S superscript negative, ethanol, C subscript 2 H subscript 5 O H, ammonia, N H subscript 3, hydrogen, H subscript 2, methane, and C H subscript 4. The acids at the top of the listing from sulfuric acid through nitric acid are grouped with a bracket to the right labeled “Undergo complete acid ionization in water.” Similarly, the acids at the bottom from hydrogen sulfide ion through methane are grouped with a bracket and labeled, “Do not undergo acid ionization in water.” The right half of the figure lists bases and formulas. From top to bottom the bases listed are hydrogen sulfate ion, H S O subscript 4 superscript negative, iodide ion, I superscript negative, bromide ion, B r superscript negative, chloride ion, C l superscript negative, nitrate ion, N O subscript 3 superscript negative, water (shaded in beige), H subscript 2 O, sulfate ion, S O subscript 4 superscript 2 negative, dihydrogen phosphate ion, H subscript 2 P O subscript 4 superscript negative, fluoride ion, F superscript negative, nitrite ion, N O subscript 2 superscript negative, acetate ion, C H subscript 3 C O subscript 2 superscript negative, hydrogen carbonate ion, H C O subscript 3 superscript negative, hydrogen sulfide ion, H S superscript negative, ammonia, N H subscript 3, cyanide ion, C N superscript negative, carbonate ion, C O subscript 3 superscript 2 negative, hydroxide ion (in blue), O H superscript negative, sulfide ion, S superscript 2 negative, ethoxide ion, C subscript 2 H subscript 5 O superscript negative, amide ion N H subscript 2 superscript negative, hydride ion, H superscript negative, and methide ion C H subscript 3 superscript negative. The bases at the top, from perchlorate ion through nitrate ion are group with a bracket which is labeled “Do not undergo base ionization in water.” Similarly, the lower 5 in the listing, from sulfide ion through methide ion are grouped and labeled “Undergo complete base ionization in water." — **Figure 2.** The chart shows the relative strengths of conjugate acid-base pairs.

The first six acids in Figure 2 are the most common strong acids. These acids are completely dissociated in aqueous solution. The conjugate bases of these acids are weaker bases than water. When one of these acids dissolves in water, their protons are completely transferred to water, the stronger base.

Those acids that lie between the hydronium ion and water in Figure 2 form conjugate bases that can compete with water for possession of a proton. Both hydronium ions and nonionized acid molecules are present in equilibrium in a solution of one of these acids. Compounds that are weaker acids than water (those found below water in the column of acids) in Figure 2 exhibit no observable acidic behavior when dissolved in water. Their conjugate bases are stronger than the hydroxide ion, and if any conjugate base were formed, it would react with water to re-form the acid.

The extent to which a base forms hydroxide ion in aqueous solution depends on the strength of the base relative to that of the hydroxide ion, as shown in the last column in Figure 2. A strong base, such as one of those lying below hydroxide ion, accepts protons from water to yield 100% of the conjugate acid and hydroxide ion. Those bases lying between water and hydroxide ion accept protons from water, but a mixture of the hydroxide ion and the base results. Bases that are weaker than water (those that lie above water in the column of bases) show no observable basic behavior in aqueous solution.

Demonstration: Fizzing Races

Set up. The same amount of NaHCO₃(s) is added to two flasks, one which contains HCl(aq) and the other HOAc(aq) (or CH₃COOH). Both flasks contain the same volume and molarity of acid.

Prediction. Write the balanced reaction that occurs in each flask. Predict what will happen to the balloons both initially and at the end of each reaction.

Explanation: The reactions within the flasks are:

HCl(aq) + NaHCO₃(s) → CO₂(g) + H₂O(ℓ) + NaCl(aq)

CH₃COOH(aq) + NaHCO₃(s) → CO₂(g) + H₂O(ℓ) + NaCH₃COO(aq)

The reaction in the flask that contains HCl reacts very quickly, almost immediately inflating the balloon. The flask that contains CH₃COOH reacts much more slowly, but ultimately inflates the balloon to the same volume.

HCl is a strong acid and is fully dissociated in solution. So all of the acidic protons (H⁺) are free to react immediately. CH₃COOH is a weak acid and only partially dissociated in solution, which results in fewer H⁺ ions initially available to react. As CO₂ is produced, the reaction continually shifts towards products and the CH₃COOH ultimately fully reacts, but more slowly as the H⁺ ions are created gradually.

Key Concepts and Summary

Not all acids and bases donate and accept protons to the same extent. We find that 6 acids react to nearly 100% completion and classify these as strong acids. Likewise, 8 bases react to nearly 100% completion and we classify these as strong bases. For the simplicity of this course, all other acids and bases do not react 100% and reactants are always present at the end of the reaction. These molecules are classified as weak acids or bases and the K_a for the equilibrium reaction of the acid or base with water gives us insight into how much the acid or base reacts with water. The greater the K_a value, the stronger the acid. The greater the K_b value, the stronger the base.

Key Equations

acid: HA(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + A^–(aq) | K_a = $\dfrac{[\text{H}_{3}\text{O}^{+}][\text{A}^{-}]}{[\text{HA}]}$
base: B(aq) + H₂O(ℓ) ⇌ HB⁺(aq) + OH^–(aq) | K_b = $\dfrac{[\text{HB}^{+}][\text{OH}^{-}]}{[\text{B}]}$
base: A^–(aq) + H₂O(ℓ) ⇌ HA(aq) + OH^–(aq) | K_b = $\dfrac{[\text{HA}][\text{OH}^{-}]}{[\text{A}^{-}]}$
percent ionization = $\dfrac{[\text{H}_{3}\text{O}^{+}]_{eq}}{[\text{HA}]_{0}}$ × 100

Glossary

acid-ionization constant, K_a: the equilibrium constant when an acid reacts with water to produce the conjugate base and hydronium ion

base-ionization constant, K_b: the equilibrium constant when a base reacts with water to produce the conjugate acid and hydroxide ion

Chemistry End of Section Exercises

What compounds and ions are found in a solution of aqueous CH₃COOH? Of aqueous HCl?
Write a chemical equation to describe the proton transfer reaction that occurs when the following acids are added to water:
1. HNO₃
2. PH₄⁺
3. H₂S
4. CH₃CH₂COOH
5. CH₃COOH
6. H₂PO₄^–
7. HS^–
Write a chemical equation to describe the proton transfer reaction that occurs when the following bases are added to water:
1. C₅H₅N
2. (CH₃)₃N
3. HS^–
4. H₂PO₃^–
5. CH₃COO^–
6. NO₂^–
7. NH₃
Which of the compounds below is a weak base?
1. CH₃CH₂OH
4. CH₃CH₂NH₂
From the equilibrium concentrations given, calculate K_a for each of the weak acids and K_b for each of the weak bases.
1. CH₃COOH:
  [H₃O⁺] = 1.34 × 10^-3 M; [CH₃COO^–] = 1.34 × 10^-3 M; [CH₃COOH] = 9.855 × 10^-2 M
2. ClO^–:
  [OH^–] = 4.0 × 10^-4 M; [HClO] = 2.38 × 10^-5 M; [ClO^–] = 0.273 M
3. C₆H₅NH₃⁺:
  [H₃O⁺] = 2.3 × 10^-3 M; [C₆H₅NH₃⁺] = 0.233 M; [C₆H₅NH₂] = 2.3 × 10^-3 M
Both HF and HCN ionize in water to a limited extent. Which of the conjugate bases, F⁻ or CN⁻, is the stronger base? (See Figure 2).
Write a chemical equation for the acid base reaction between F^– and H₂S. Will the reaction be reactant or product favored? (See Figure 2).
Which of the following solutions will have the lowest percentage ionization in water?
1. 0.10 M HNO₃(aq)
2. 0.20 M HNO₃(aq)
3. 0.10 M HCOOH, K_a = 1.8 × 10^-4
4. 0.10 M HClO, K_a = 3.0 × 10^-8
5. 1.0 M HClO, K_a = 3.0 × 10^-8
In which of the following solutions will 0.050 moles of bromous acid, HBrO₃, have the highest percent ionization?
1. 1 L of 1 M HNO₃
2. 1 L of pure water
3. 10 L of 1 M HNO₃
4. 10 L of pure water
5. 10 L of 1 M sodium bromite, NaBrO₃
Which of the following solutions would you expect to have the largest number of ions?
1. 0.02 M ammonia
2. 0.02 M HCl
3. 0.02 M NaCl
4. 0.20 M acetic acid
5. 0.20 M NaOH

Answers to Chemistry End of Section Exercises

CH₃COOH: H₂O, CH₃COOH, H₃O⁺, OH^–, and CH₃COO^–;
HCl: H₂O, H₃O⁺, Cl^–, and OH^–
(a) HNO₃(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + NO₃^–(aq)
(b) PH₄⁺(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + PH₃(aq)
(c) H₂S(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + HS^–(aq)
(d) CH₃CH₂COOH(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + CH₃CH₂COO^–(aq)
(e) CH₃COOH(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + CH₃COO^–(aq)
(f) H₂PO₄^–(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + HPO₄^2-(aq)
(g) HS-(aq)+ H₂O(ℓ) ⇌ H₃O⁺(aq) + S^2-(aq)
(a) C₅H₅N(aq) + H₂O(ℓ) ⇌ OH^–(aq) + C₅H₅NH⁺(aq)
(b) (CH₃)₃N(aq) + H₂O(ℓ) ⇌ OH^–(aq) + (CH₃)₃NH⁺(aq)
(c) HS^–(aq) + H₂O(ℓ) ⇌ OH^–(aq) + H₂S(aq)
(d) H₂PO₃^–(aq) + H₂O(ℓ) ⇌ OH^–(aq) + H₃PO₄(aq)
(e) CH₃COO^–(aq) + H₂O(ℓ) ⇌ OH^–(aq) + CH₃COOH(aq)
(f) NO₂^–(aq) + H₂O(ℓ) ⇌ OH^–(aq) + HNO₂(aq)
(g) NH₃(aq) + H₂O(ℓ) ⇌ OH^–(aq) + NH₄⁺(aq)
D
(a) K_a = 1.82 × 10^-5
(b) K_b = 3.5 × 10^-8
(c) K_a = 2.3 × 10^-5
CN^–
F^–(aq) + H₂S(aq) ⇌ HF(aq) + HS^–(aq); reactant favored
E
D
E

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