## 10.5 The Strengths of Acids and Bases

### Learning Objectives

1. Describe the difference between strong and weak acids and bases.
2. Describe how a chemical reaction reaches chemical equilibrium.
3. Define the pH scale and use it to describe acids and bases.
4. Determine the pH of acidic and basic solutions.

Acids and bases do not all demonstrate the same degree of chemical activity in solution. Different acids and bases have different strengths.

## Strong and Weak Acids

Let us consider the strengths of acids first. A small number of acids ionize completely in aqueous solution. For example, when HCl dissolves in water, every molecule of HCl separates into a hydronium ion and a chloride ion:

HCl(aq) is one example of a strong acidAn acid that is 100% ionized in aqueous solution., which is a compound that is essentially 100% ionized in aqueous solution. There are very few strong acids. The important ones are listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)".

Table 10.2 Strong Acids and Bases (All in Aqueous Solution)

Acids Bases
HCl LiOH
HBr NaOH
HI KOH
HNO3 Mg(OH)2
H2SO4 Ca(OH)2
HClO4

By analogy, a strong baseA base that is 100% ionized in aqueous solution. is a compound that is essentially 100% ionized in aqueous solution. As with acids, there are only a few strong bases, which are also listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)".

If an acid is not listed in Table 10.2 "Strong Acids and Bases (All in Aqueous Solution)", it is likely a weak acidAn acid that is less than 100% ionized in aqueous solution., which is a compound that is not 100% ionized in aqueous solution. Similarly, a weak baseA base that is less than 100% ionized in aqueous solution. is a compound that is not 100% ionized in aqueous solution. For example, acetic acid (HC2H3O2) is a weak acid. The ionization reaction for acetic acid is as follows:

HC2H3O2(aq) + H2O(ℓ) → H3O+(aq) + C2H3O2(aq)

Depending on the concentration of HC2H3O2, the ionization reaction may occur only for 1%–5% of the acetic acid molecules.

### Looking Closer: Household Acids and Bases

Many household products are acids or bases. For example, the owner of a swimming pool may use muriatic acid to clean the pool. Muriatic acid is another name for hydrochloric acid [HCl(aq)]. Vinegar has already been mentioned as a dilute solution of acetic acid [HC2H3O2(aq)]. In a medicine chest, one may find a bottle of vitamin C tablets; the chemical name of vitamin C is ascorbic acid (HC6H7O6).

One of the more familiar household bases is ammonia (NH3), which is found in numerous cleaning products. As we mentioned previously, ammonia is a base because it increases the hydroxide ion concentration by reacting with water:

NH3(aq) + H2O(ℓ) → NH4+(aq) + OH(aq)

Many soaps are also slightly basic because they contain compounds that act as Brønsted-Lowry bases, accepting protons from water and forming excess hydroxide ions. This is one reason that soap solutions are slippery.

Perhaps the most dangerous household chemical is the lye-based drain cleaner. Lye is a common name for sodium hydroxide, although it is also used as a synonym for potassium hydroxide. Lye is an extremely caustic chemical that can react with grease, hair, food particles, and other substances that may build up and form a clog in a pipe. Unfortunately, lye can also attack tissues and other substances in our bodies. Thus, when we use lye-based drain cleaners, we must be very careful not to touch any of the solid drain cleaner or spill the water it was poured into. Safer, nonlye drain cleaners use peroxide compounds to react on the materials in the clog and clear the drain.

Drain cleaners can be made from a reactive material that is less caustic than a base.

## Chemical Equilibrium

The behavior of weak acids and bases illustrates a key concept in chemistry. Does the chemical reaction describing the ionization of a weak acid or base just stop when the acid or base is done ionizing? Actually, no. Rather, the reverse process—the reformation of the molecular form of the acid or base—occurs, ultimately at the same rate as the ionization process. For example, the ionization of the weak acid HC2H3O2 (aq) is as follows:

HC2H3O2(aq) + H2O(ℓ) → H3O+(aq) + C2H3O2(aq)

The reverse process also begins to occur:

H3O+(aq) + C2H3O2(aq) → HC2H3O2(aq) + H2O(ℓ)

Eventually, there is a balance between the two opposing processes, and no additional change occurs. The chemical reaction is better represented at this point with a double arrow:

HC2H3O2(aq) + H2O(ℓ) ⇆ H3O+(aq) + C2H3O2(aq)

The ⇆ implies that both the forward and reverse reactions are occurring, and their effects cancel each other out. A process at this point is considered to be at chemical equilibrium (or equilibrium)The condition in which the extent of a chemical reaction does not change any further.. It is important to note that the processes do not stop. They balance out each other so that there is no further net change; that is, chemical equilibrium is a dynamic equilibrium.

### Example 9

Write the equilibrium chemical equation for the partial ionization of each weak acid or base.

1. HNO2(aq)
2. C5H5N(aq)

Solution

1. HNO2(aq) + H2O(ℓ) ⇆ NO2(aq) + H3O+(aq)
2. C5H5N(aq) + H2O(ℓ) ⇆ C5H5NH+(aq) + OH(aq)

### Skill-Building Exercise

Write the equilibrium chemical equation for the partial ionization of each weak acid or base.

1. HF(aq)

2. AgOH(aq)

### Note

Hydrofluoric acid [HF(aq)] is one chemical that reacts directly with glass. (Very few chemicals react with glass.) Hydrofluoric acid is used in glass etching.

Finally, you may realize that the autoionization of water is actually an equilibrium process, so it is more properly written with the double arrow:

H2O(ℓ) + H2O(ℓ) ⇆ H3O+(aq) + OH(aq)

## The pH Scale

One qualitative measure of the strength of an acid or a base solution is the pH scale. It is a logarithmic scale that relates the concentration of the hydronium ion in solution. A neutral (neither acidic nor basic) solution, one that has the same concentration of hydronium and hydroxide ions, has a pH of 7. A pH below 7 means that a solution is acidic, with lower values of pH corresponding to increasingly acidic solutions. A pH greater than 7 indicates a basic solution, with higher values of pH corresponding to increasingly basic solutions. Thus, given the pH of several solutions, you can state which ones are acidic, which ones are basic, and which are more acidic or basic than others. Table 10.3 "The pH Values of Some Common Solutions" lists the pH of several common solutions. Notice that some biological fluids are nowhere near neutral.

Table 10.3 The pH Values of Some Common Solutions

Solution pH
battery acid 0.3
stomach acid 1–2
lemon or lime juice 2.1
vinegar 2.8–3.0
Coca-Cola 3
wine 2.8–3.8
beer 4–5
coffee 5
milk 6
urine 6
pure H2O 7
(human) blood 7.3–7.5
sea water 8
antacid (milk of magnesia) 10.5
NH3 (1 M) 11.6
bleach 12.6
NaOH (1 M) 14.0

Weak acids and bases are relatively common. You may notice from Table 10.3 "The pH Values of Some Common Solutions" that many food products are slightly acidic. They are acidic because they contain solutions of weak acids. If the acid components of these foods were strong acids, the food would likely be inedible.

## Calculating pH

As we have seen, [H3O+] 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 [H3O+]:

pH = −log[H3O+]

pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on [H3O+], we can summarize as follows:

• If pH < 7, then the solution is acidic, and [H3O+] > 10-7
• If pH = 7, then the solution is neutral, and [H3O+] = 10-7
• If pH > 7, then the solution is basic, and [H3O+] < 10-7

pH is a logarithmic scale. A solution that has a pH of 1.0 has 10 times the [H3O+] as a solution with a pH of 2.0, which in turn has 10 times the [H3O+] as a solution with a pH of 3.0 and so forth.

Using the definition of pH, it is also possible to calculate [H3O+] from pH and vice versa. The general formula for determining [H3O+] from pH is as follows:

[H3O+] = 10−pH

You need to determine how to evaluate the above expression on your calculator. Ask your instructor if you have any questions.

### Example 10

What is the pH of each solution below?

1. [H3O+] = $1.00×{10}^{-5}$ M
2. [H3O+] = $7.50×{10}^{-8}$ M

Solution

1. $\mathrm{p}\mathrm{H}\mathrm{=}\mathrm{-}\mathrm{log}\mathrm{\left[}{\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}\mathrm{\right]}\mathrm{=}\mathrm{-}\mathrm{log}\mathrm{\left(}\phantom{\rule{.1667em}{0ex}}\mathrm{1.00}×{\mathrm{10}}^{\mathrm{-}\mathrm{5}}\phantom{\rule{.1667em}{0ex}}\mathrm{\right)}\mathrm{=}\mathrm{-}\mathrm{\left(}\mathrm{-}\mathrm{5.00}\mathrm{\right)}\mathrm{=}\mathrm{5.00}$
2. $\mathrm{p}\mathrm{H}\mathrm{=}\mathrm{-}\mathrm{log}\mathrm{\left[}{\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}\mathrm{\right]}\mathrm{=}\mathrm{-}\mathrm{log}\mathrm{\left(}\phantom{\rule{.1667em}{0ex}}\mathrm{7.50}×{\mathrm{10}}^{\mathrm{-}\mathrm{8}}\phantom{\rule{.1667em}{0ex}}\mathrm{\right)}\mathrm{=}\mathrm{-}\mathrm{\left(}\mathrm{-}\mathrm{7.12}\mathrm{\right)}\mathrm{=}\mathrm{7.12}$

Test Yourself

What is the pH of a solution that has a hydronium ion concentration of $1.11×{10}^{-9}$ M?

pH = 8.95

### Example 11

What are [H3O+] and [OH] for an aqueous solution whose pH is 4.88?

Solution

We need to evaluate the expression

[H3O+] = 10−4.88

Depending on the calculator you use, the method for solving this problem will vary. In some cases, the “−4.88” is entered and a “10x” key is pressed; for other calculators, the sequence of keystrokes is reversed. In any case, the correct numerical answer is as follows:

[H3O+] = 1.3 × 10−5 M

Next, we use the ion-product of water relationship, $\left[{\mathrm{H}}_{\mathrm{3}}{\mathrm{O}}^{\mathrm{+}}\mathrm{\right]}\mathrm{\left[}\mathrm{O}{\mathrm{H}}^{\mathrm{-}}\mathrm{\right]}\mathrm{=}{\mathit{K}}_{\mathrm{w}}$. From this, [OH] can be determined:

$[OH−]=1×10−141.3×10−5=7.7×10−10 M$

Test Yourself

What are [H3O+] and [OH] for an aqueous solution whose pH is 10.36?

[H3O+] = 4.4 × 10−11 M; [OH] = 2.3 × 10−4 M

### Concept Review Exercises

1. Explain the difference between a strong acid or base and a weak acid or base.

2. Explain what is occurring when a chemical reaction reaches equilibrium.

3. Define pH.

1. A strong acid or base is 100% ionized in aqueous solution; a weak acid or base is less than 100% ionized.

2. The overall reaction progress stops because the reverse process balances out the forward process.

3. pH is a measure of the hydronium-ion concentration.

### Key Takeaways

• Acids and bases can be strong or weak depending on the extent of ionization in solution.
• Most chemical reactions reach equilibrium at which point there is no net change.
• The pH scale is used to succinctly communicate the acidity or basicity of a solution.
• pH is a logarithmic function of [H3O+].
• [H3O+] can be calculated directly from pH.

### Exercises

1. Name a strong acid and a weak acid.

2. Name a strong base and a weak base.

3. Is each compound a strong acid or a weak acid? Assume all are in aqueous solution.

1. HF
2. HC2H3O2
3. HCl
4. HClO4
4. Is each compound a strong acid or a weak acid? Assume all are in aqueous solution.

1. H2SO4
2. HSO4
3. HPO42−
4. HNO3
5. Is each compound a strong base or a weak base? Assume all are in aqueous solution.

1. NH3
2. NaOH
3. Mg(OH)2
4. Cu(OH)2
6. Is each compound a strong base or a weak base? Assume all are in aqueous solution.

1. KOH
2. H2O
3. Fe(OH)2
4. Fe(OH)3
7. Write the chemical equation for the equilibrium process for each weak acid in Exercise 3.

8. Write the chemical equation for the equilibrium process for each weak acid in Exercise 4.

9. Write the chemical equation for the equilibrium process for each weak base in Exercise 5.

10. Write the chemical equation for the equilibrium process for each weak base in Exercise 6.

11. Which is the stronger acid—HCl(aq) or HF(aq)?

12. Which is the stronger base—KOH(aq) or Ni(OH)2(aq)?

13. Consider the two acids in Exercise 11. For solutions that have the same concentration, which one would you expect to have a lower pH?

14. Consider the two bases in Exercise 12. For solutions that have the same concentration, which one would you expect to have a higher pH?

15. Consider the list of substances in Table 10.3 "The pH Values of Some Common Solutions". What is the most acidic substance on the list that you have encountered recently?

16. Consider the list of substances in Table 10.3 "The pH Values of Some Common Solutions". What is the most basic substance on the list that you have encountered recently?

17. What is the pH of a solution when [H3O+] is 3.44 × 10−4 M?

18. What is the pH of a solution when [H3O+] is 5.32 × 10−11 M?

19. What is the pH of a solution when [OH-] is 3.44 × 10−4 M?

20. What is the pH of a solution when [OH-] is 5.32 × 10−11 M?

21. If a solution has a pH of 0.77, what is its [H3O+] and [OH]?

22. If a solution has a pH of 13.09, what is its [H3O+] and [OH]?

1. strong acid: HCl; weak acid: HC2H3O2 (answers will vary)

1. weak
2. weak
3. strong
4. strong
1. weak
2. strong
3. strong
4. weak
2. 3a: HF(aq) ⇆ H+(aq) + F(aq); 3b: HC2H3O2(aq) ⇆ H+(aq) + C2H3O2(aq)

3. 5a: NH3(aq) + H2O ⇆ NH4+(aq) + OH(aq); 5d: Cu(OH)2(aq) ⇆ Cu2+(aq) + 2OH(aq)

4. HCl(aq)

5. HCl(aq)