The relative strengths of acids may be quantified 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:
$$HA(aq)+H_2O(l)⇌H_3O^+(aq)+A^-(aq),$$
the acid ionization constant is written
$$K_a=\frac{[H_3O^+][A^-]}{[HA]}$$
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 $H_3O^+$ and A− relative to the concentration of the nonionized acid, HA, in an equilibrium mixture, and the stronger the acid. An acid is classified as “strong” when it undergoes complete ionization, in which case the concentration of HA is zero and the acid ionization constant is immeasurably large (Ka ≈ ∞). Acids that are partially ionized are called “weak,” and their acid ionization constants may be experimentally measured. A table of ionization constants for weak acids is provided in this appendix, and the complimentary one for bases is here.
To illustrate this idea, three acid ionization equations and Ka values are shown below. The ionization constants increase from first to last of the listed equations, indicating the relative acid strength increases in the order $CH_3 CO_2 H< HNO_2 < HSO_4^-$:
$$CH_3CO_2H(aq)+H_2O(l)⇌H_3O^+(aq)+CH_3CO_2^-(aq)\qquad K_a=1.8×10^{-5}$$
$$HNO_2(aq)+H_2O(l)⇌H_3O^+(aq)+NO_2^-(aq)\qquad K_a=4.6×10^{-4}$$
$$HSO_4^-(aq)+H_2O(l)⇌H_3O^+(aq)+SO_4^{2-}(aq)\qquad K_a=1.2×10^{-2}$$
Another measure of the strength of an acid is its percent ionization. The percent ionization of a weak acid is defined in terms of the composition of an equilibrium mixture:
$$\text{% ionization}=\frac{[H_3O^+]_{eq}}{[HA]_0}\times 100$$
where the numerator is equivalent to the concentration of the acid’s conjugate base (per stoichiometry, [A−] = [H3O+]). Unlike the Ka value, the percent ionization of a weak acid varies with the initial concentration of acid, typically decreasing as concentration increases. Equilibrium calculations of the sort described later in this chapter can be used to confirm this behavior.
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:
Converting the provided pH to hydronium ion molarity yields
$$[H_3O^+]=10^{-2.09}=0.0081\;M$$Substituting this value and the provided initial acid concentration into the percent ionization equation gives
$$\frac{8.1×10^{-3}}{0.125}\times 100=6.5\text{%}$$(Recall the provided pH value of 2.09 is logarithmic, and so it contains just two significant digits, limiting the certainty of the computed percent ionization.)
Check Your Learning
Calculate the percent ionization of a 0.10-M solution of acetic acid with a pH of 2.89.
Answer:
1.3% ionized
View the simulation of strong and weak acids and bases at the molecular level:
Just as for acids, the relative strength of a base is reflected in the magnitude of its base-ionization constant (Kb) 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:
$$B(aq)+H_2O(l)⇌HB^+(aq)+OH^-(aq),$$
the ionization constant is written as
$$K_b=\frac{[HB^+][OH^-]}{[B]}$$
Inspection of the data for three weak bases presented below shows the base strength increases in the order $NO_2^- < CH_2CO_2^- < NH_3$.
$$NO_2^-(aq)+H_2O(l)⇌HNO_2(aq)+OH^-(aq)\qquad K_b=2.17×10^{-11}$$
$$CH_3CO_2^-(aq)+H_2O(l)⇌CH_3CO_2H(aq)+OH^-(aq)\qquad K_b=5.6×10^{-10}$$
$$NH_3(aq)+H_2O(l)⇌NH_4^+(aq)+OH^-(aq)\qquad K_b=1.8×10^{-5}$$
A table of ionization constants for weak bases appears is here. As for acids, the relative strength of a base is also reflected in its percent ionization, computed as
$$\text{% ionization}=\frac{[OH^-]_{eq}}{[B]_0}\times 100\text{%}$$
but will vary depending on the base ionization constant and the initial concentration of the solution.