# 14.3 Relative strengths of acids and bases  (Page 3/18)

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[link] 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.

The first six acids in [link] 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 [link] 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 [link] 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 [link] . 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.

## The product Ka$×$Kb = Kw

Use the K b for the nitrite ion, ${\text{NO}}_{2}{}^{\text{−}},$ to calculate the K a for its conjugate acid.

## Solution

K b for ${\text{NO}}_{2}{}^{\text{−}}$ is given in this section as 2.17 $×$ 10 −11 . The conjugate acid of ${\text{NO}}_{2}{}^{\text{−}}$ is HNO 2 ; K a for HNO 2 can be calculated using the relationship:

${K}_{\text{a}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{K}_{\text{b}}=1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-14}={K}_{\text{w}}$

Solving for K a , we get:

${K}_{\text{a}}=\phantom{\rule{0.2em}{0ex}}\frac{{K}_{\text{w}}}{{K}_{\text{b}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-14}}{2.17\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}}\phantom{\rule{0.2em}{0ex}}=4.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}$

This answer can be verified by finding the K a for HNO 2 in Appendix H .

We can determine the relative acid strengths of ${\text{NH}}_{4}{}^{\text{+}}$ and HCN by comparing their ionization constants. The ionization constant of HCN is given in Appendix H as 4.9 $×$ 10 −10 . The ionization constant of ${\text{NH}}_{4}{}^{\text{+}}$ is not listed, but the ionization constant of its conjugate base, NH 3 , is listed as 1.8 $×$ 10 −5 . Determine the ionization constant of ${\text{NH}}_{4}{}^{\text{+}},$ and decide which is the stronger acid, HCN or ${\text{NH}}_{4}{}^{\text{+}}.$

${\text{NH}}_{4}{}^{\text{+}}$ is the slightly stronger acid ( K a for ${\text{NH}}_{4}{}^{\text{+}}$ = 5.6 $×$ 10 −10 ).

## The ionization of weak acids and weak bases

Many acids and bases are weak; that is, they do not ionize fully in aqueous solution. A solution of a weak acid in water is a mixture of the nonionized acid, hydronium ion, and the conjugate base of the acid, with the nonionized acid present in the greatest concentration. Thus, a weak acid increases the hydronium ion concentration in an aqueous solution (but not as much as the same amount of a strong acid).

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