BIOCHEMISTRY - L. Stryer - 1984

VOLUME 1

PART I. CONFORMATION AND DYNAMICS

APPENDIX. CONCEPTS OF ACIDITY AND BASICITY

Ionization of water

Water dissociates into a hydronium ion (H₃O⁺) and a hydroxyl ion (OH^-). For simplicity, the hydronium ion is denoted as a hydrogen ion (H⁺), and then the water dissociation process at equilibrium takes the form H₂O ⇄ H⁺ (OH^-.

The Equilibrium Constant K_p of this process is

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where the quantities in square brackets are expressed in molar concentrations. Since the concentration of water (55.5 M) changes very little during ionization, equation (1) can be simplified:

K_H2O = [H ⁺] [OH^-], (2)

where K_H2O is the ion product of water. At 25°C

K_H2O = 1.0 • 10^-14.

It is important to note the inversely proportional relationship between the concentrations of H⁺ and OH^- ions. If the H⁺ concentration increases, the OH^- concentration decreases, and vice versa. For example, if [H⁺] = 10^-2 M, then [OH^-] = 10^-12 M.

Definition of acids and bases

An acid acts as a proton donor, and a base acts as a proton acceptor.

The ionization of an acid produces its corresponding (conjugate) base, and conversely, the protonation of a base produces the corresponding acid. Thus, acetic acid and the acetate ion form a conjugate acid-base pair.

Definition of pH and pK values

The pH of a solution is a measure of its hydrogen ion concentration. The pH value is defined by the relation

Let us represent the ionization process of a weak acid at equilibrium:

HA ⇄ H⁺ + A^-.

The apparent equilibrium constant K of the ionization process is expressed by the equation

From this, the pK of an acid can be defined as

It follows from equation (4) that the pK of an acid is the pH at which the acid is half-dissociated.

The Henderson-Hasselbalch Equation

What is the relationship between the pH value and The ratio of acid to base in a solution? The desired formula can be derived from equation (4). Let us perform the following transformation:

Taking the logarithm of this expression, we get:

Substituting pH for lg 1/[H⁺] and pK for lg 1/K respectively, we obtain

This final expression is widely known as the Henderson-Hasselbalch equation.

Equation (8) can be used to calculate the pH of a solution if the molecular ratios of A^- and HA, as well as the pK of the acid, are known.

Suppose we have a 0.1 M solution of acetic acid containing 0.2 M acetate ions. The pK of acetic acid is 4.8. Consequently, the pH of the solution will be

Similarly, the pK of an acid can be calculated if the ratio of the molar concentrations of A-!!! and HA and the pH of the solution are known.

Buffer Capacity

A conjugate acid-base pair (such as the acetic acid-acetate ion pair discussed above) possesses an important property: it resists Changes in the pH of a solution. In other words, it acts as a buffer. Let us imagine that OH^- is added to a solution of acetic acid (HA):

The plot of the solution's pH against The amount of added OH^- ions is called The titration curve (Fig. 2.49). Note that the curve has an inflection point at pH 4.8, which corresponds to the pK of acetic acid. Near this pH value, relatively large amounts of added OH^- ions cause only a negligible change in pH. In general, weak acids exhibit their best buffering properties in the vicinity of their pK values.

Table 2.3. pK values of Some Amino Acids

Fig. 2.49. Titration curve of acetic acid

pK Values of Amino Acids

In amino acids like Glycine, two groups can ionize: the a!!!-carboxyl group and the protonated a-amino group. They can be titrated by adding a base (Fig. 2.50). The pK of the α-COOH group is 2.3, and the pK of the α-NH₃ group is 9.6. Other Amino Acids have approximately similar pK values for these groups. In some amino acids, notably aspartic acid, the side chain can also ionize. The pK values of ionizable amino acid side chains range from 3.9 (aspartic acid) to 12.5 (Arginine).

Fig. 2.50. Titration of ionizable groups of an amino acid