14.3 Relative strengths of acids and bases  (Page 2/18)

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:

Water is the acid that reacts with the base, HB ⁺ is the conjugate acid of the base B, and the hydroxide ion is the conjugate base of water. A strong base yields 100% (or very nearly so) of OH ⁻ and HB ⁺ when it reacts with water; [link] lists several strong bases. A weak base yields a small proportion of hydroxide ions. Soluble ionic hydroxides such as NaOH are considered strong bases because they dissociate completely when dissolved in water.

As we did with acids, we can measure the relative strengths of bases by measuring their base-ionization constant ( K _b ) 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:

we write the equation for the ionization constant as:

where the concentrations are those at equilibrium. Again, we do not include [H ₂ O] in the equation because water is the solvent. The chemical reactions and ionization constants of the three bases shown are:

A table of ionization constants of weak bases appears in Appendix I (with a partial list in [link] ). As with acids, percent ionization can be measured for basic solutions, but will vary depending on the base ionization constant and the initial concentration of the solution.

Consider the ionization reactions for a conjugate acid-base pair, HA − A ⁻ :

Adding these two chemical equations yields the equation for the autoionization for water:

As shown in the previous chapter on equilibrium, the K expression for a chemical equation derived from adding two or more other equations is the mathematical product of the other equations’ K expressions. Multiplying the mass-action expressions together and cancelling common terms, we see that:

For example, the acid ionization constant of acetic acid (CH ₃ COOH) is 1.8 $\times$ 10 ⁻⁵ , and the base ionization constant of its conjugate base, acetate ion $({\text{CH}}_3{\text{COO}}^{\text{−}}),$ is 5.6 $\times$ 10 ⁻¹⁰ . The product of these two constants is indeed equal to K _w :

The extent to which an acid, HA, donates protons to water molecules depends on the strength of the conjugate base, A ⁻ , of the acid. If A ⁻ is a strong base, any protons that are donated to water molecules are recaptured by A ⁻ . Thus there is relatively little A ⁻ and ${\text{H}}_3{\text{O}}^{\text{+}}$ in solution, and the acid, HA, is weak. If A ⁻ is a weak base, water binds the protons more strongly, and the solution contains primarily A ⁻ and H ₃ O ⁺ —the acid is strong. Strong acids form very weak conjugate bases, and weak acids form stronger conjugate bases ( [link] ).