In general, an acid is any molecule, ion, or chemical group that tends to release a hydrogen ion (H⁺), such as the carboxyl group (–COOH), which tends to dissociate to form the negatively charged carboxylate ion (–COO^–); or hydrochloric acid (HCl). Conversely, a base is any molecule, ion, or chemical group that readily combines with an H⁺, such as the hydroxyl ion (OH^–); ammonia (NH₃), which forms an ammonium ion (NH₄⁺); or the amino group (–NH₂).

When an acid is added to an aqueous solution, the [H⁺] increases, and the pH goes down. Conversely, when a base is added to a solution, the [H⁺] decreases, and the pH goes up. Because [H⁺][OH^–] = 10^–14 M², any increase in [H⁺] is coupled with a commensurate decrease in [OH^–], and vice versa.

Many biological molecules contain both acidic and basic groups. For example, in neutral solutions (pH = 7.0), many amino acids exist predominantly in the doubly ionized form, in which the carboxyl group has lost a proton and the amino group has accepted one:

where R represents the uncharged side chain. Such a molecule, containing an equal number of positive and negative ions, is called a zwitterion. Zwitterions, having no net charge, are neutral. At extreme pH values, only one of these two ionizable groups of an amino acid is charged: the –NH₂⁺ at low pH and the –COO^– at high pH.

The dissociation reaction for an acid (or acid group in a larger molecule) HA can be written as HA ⇌ H⁺ + A^–. The equilibrium constant for this reaction, denoted K_a (the subscript a stands for “acid”), is defined as K_a = [H⁺][A^–]/[HA]. Taking the logarithm of both sides and rearranging the result yields a very useful relation between the equilibrium constant and pH:

where pK_a equals –log K_a.

From this expression, commonly known as the Henderson-Hasselbalch equation, it can be seen that the pK_a of any acid is equal to the pH at which half the molecules are dissociated and half are neutral (undissociated). This is because when [A^–] = [HA], then log ([A^–]/[HA]) = 0, and thus pK_a = pH. The Henderson-Hasselbalch equation allows us to calculate the degree of dissociation of an acid—that is, the ratio of dissociated and undissociated forms—if both the pH of the solution and the pK_a of the acid are known. Experimentally, by measuring the [A^–] and [HA] as a function of the solution’s pH, one can calculate the pK_a of the acid and thus the equilibrium constant K_a for the dissociation reaction (Figure 2-26). Knowing the pK_a of a molecule not only provides an important description of its properties, but also allows us to exploit these properties to manipulate the acidity of an aqueous solution and to understand how biological systems control this critical characteristic of their aqueous fluids.