17.7 Relative Strengths of Acids and Bases
Learning Objectives
- Assess the relative strengths of acids and bases according to their ionization constants
- Rationalize trends in acid–base strength in relation to molecular structure
- Carry out equilibrium calculations for weak acid–base systems
We can rank the strengths of acids by the extent to which they ionize in aqueous solution. The reaction of an acid with water is given by the general expression:
Water is the base that reacts with the acid HA, A− is the conjugate base of the acid HA, and the hydronium ion is the conjugate acid of water. A strong acid yields 100% (or very nearly so) of H3O+ and A− when the acid ionizes in water; Figure 17.7a lists several strong 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, Ka. For the reaction of an acid HA:
we write the equation for the ionization constant as:
where the concentrations are those at equilibrium. Although water is a reactant in the reaction, it is the solvent as well, so we do not include [H2O] in the equation. The larger the Ka 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.
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 ionized acid to the initial acid concentration, times 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.
Example 17.7a
Calculation of Percent Ionization from pH
Calculate the percent ionization of a 0.125-M solution of nitrous acid (a weak acid), with a pH of 2.09.
Solution
The percent ionization for an acid is:
The chemical equation for the dissociation of the nitrous acid is: [latex]\text{HNO}_2(aq)\;+\;\text{H}_2\text{O}(l)\;{\rightleftharpoons}\;\text{NO}_2^{\;\;-}(aq)\;+\;\text{H}_3\text{O}^{+}(aq)[/latex].
Since [latex]10^{-\text{pH}} = [\text{H}_3\text{O}^{+}][/latex], we find that 10−2.09 = 8.1 × 10−3M, so that percent ionization is:
Remember, the logarithm 2.09 indicates a hydronium ion concentration with only two significant figures.
Exercise 17.7a
Calculate the percent ionization of a 0.10-M solution of acetic acid with a pH of 2.89..
Check Your Answer[1]
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: