10.4 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.

Acids and bases do not all demonstrate the same degree of activity in solution. Different acids and bases have different strengths.  As with strong and weak electrolytes, the difference lies with how completely the acid or base ionizes or dissociates in water.  Strong acids and bases completely dissociate into component ions, represented in an equation by using a single-headed arrow →.  Weak acids and bases have some ionization, but at equilibrium, most of the acid or base remains in the form of molecules, represented in an equation using a double-headed arrow ↔.

Strong and Weak Acids

A small number of strong 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 + H2O(ℓ) →H3O+(aq) + Cl−(aq)

HCl(aq) is one example of a strong acid, 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)

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

By analogy, a strong base 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 acid that is far less than 100% ionized in aqueous solution. Similarly, a weak base 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, only for 1%–5% of the acetic acid molecules may be ionized.

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 is 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. 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.  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. When using lye-based drain cleaners, safe practice would be to wear gloves and protective safety glasses!. Safer, non-lye drain cleaners use peroxide compounds to react on the materials in the clog and clear the drain.

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 as well. 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, When there is no net change in concentrations, the reaction is considered to be at chemical equilibrium (or equilibrium). 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 6

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)

 

Furthermore, the autoionization of water is actually an equilibrium process, so it is 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, which is based on the concentration of the hydronium (or hydrogen) ion in aqueous solution. A neutral (neither acidic nor basic) solution, one that has the same concentration of hydrogen 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, including some biological fluids.

Table 10.3 The pH Values of Some Common Solutions
Solution pH [H3O+]
battery acid 0.3
stomach acid 1–2
lemon or lime juice 2.1
vinegar 2.8–3.0
Coca-Cola 3.0 1 x 10-3 M
wine 2.8–3.8
beer 4–5
coffee 5.0 1 x 10-5 M
milk 6.0 1 x 10-6 M
urine 6.0 1 x 10-6 M
pure H2O 7.000 1.00 x 10-7 M
(human) blood 7.3–7.5
sea water 8.0 1 x 10-8 M
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, given molarity of H3O+  [H3O+]

The molarity of H3O+ symbolized by [H3O+] can vary over 14 orders of magnitude, that is, from 0.00000000000001 M to 1 M.  Because of this wide range, the pH scale is defined on a logarithmic basis, where a difference of one pH unit reflects a 10-fold difference in [H3O+].  Mathematically, pH = -log [H3O+].  When [H3O+] is 1 x 10-x, the pH is x.  See entries for Coca-Cola®, coffee, milk, urine, pure water, and sea water in Table 10.3 above.  But if the coefficient is other than 1, it is necessary to use a calculator.  Different brands of calculators use different steps, and it is up to the student to determine the steps for their own calculator.  pH is a unitless value.

Example 7

Calculate the pH for a solution that has the given value for [H3O+].

  1. [H3O+]= 4.56 x 10-4 M
  2. [H3O+]= 8.2 x 10-9 M

Solution

  1. pH = -log [H3O+]= -log(4.56 x 10-4 ) = 3.341035 (calculator answer).  Logs have their own sig fig rules.  The only sig figs in the [H3O+] are the coefficient, not the power of ten.  The only sig figs in the pH are the digits after the decimal because the digits before the decimal point represent the power of ten.  So with 3 digits in the coefficient, the pH should be rounded to have 3 sig figs after the decimal point, 3.34.
  2. pH = -log [H3O+]= -log(8.2 x 10-9 ) = 8.086186 (calculator answer), properly rounded for sig figs, 8.09.

Calculating [H3O+], given pH

[H3O+] = 10-pH  This is the inverse of the equation to determine pH. If pH is a whole number x, then the [H3O+] value is 1 x 10-x M.  Again, see entries for Coca-Cola®, coffee, milk, urine, pure water, and sea water in Table 10.3 above.  Most pH meters report pHs with one or two decimal places though, so again it is necessary to use a calculator, and each student must know the steps for their own calculator. [H3O+]  values must be reported in standard scientific notation, not left as 10 to non-whole number value.

Example 8

Calculate the [H3O+], given the pH.

  1. pH is 7.00
  2. pH is 11.351

Solution

  1. [H3O+] = 10-pH = 10-7.00= 1.0 x 10-7 M.  pH had 2 zeros after the decimal point, indicating 2 sig figs, so the coefficient has 2 sig figs total.
  2. [H3O+] = 10-pH = 10-11.351= 4.47 x 10-12 M.  pH had 3 zeros after the decimal point, indicating 3 sig figs, so the coefficient has 3 sig figs total.

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.

Answers

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.

Exercises

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. Calculate the pH of a solution that has [H3O+] = 5.21 x 10-4 M.  Is the solution acidic, basic, or neutral?

    18. Calculate the pH of a solution that has [H3O+] = 1.25 x 10-10 M. Is the solution acidic, basic, or neutral?

    19. Calculate the [H3O+] of a solution that has a pH of 11.7.  Is the solution acidic, basic, or neutral?

    20. Calculate the [H3O+] of a solution that has a pH of 3.86.  Is the solution acidic, basic, or neutral?

     

     

Answers