Acids are substances that can give away a hydrogen ion (H⁺), also called a proton. When an acid, represented by HA, is added to water (H₂O), it gives a proton to a water molecule, which then becomes a hydronium ion (H₃O⁺). This process also yields a conjugate base (A^–). However, not all acids fully dissociate in solution. Strong acids dissociate completely. Weak acids undergo partial dissociation, establishing a dynamic equilibrium between the undissociated acid and its dissociation products: ^[1-4]

 HA (aq) + H₂O (l) ⇆ H₃O⁺ (aq) + A^– (aq)

To quantify the extent of this dissociation, chemists use a parameter called the acid dissociation constant, denoted as K_a. The value of K_a is calculated using the equilibrium concentrations of the species involved in the above dissociation reaction:

K_a = [H₃O⁺][A^–] / [HA] 

Where:

[HA]: Concentration of the undissociated acid

[H₃O⁺]: Concentration of the hydronium ion

[A^–]: Concentration of the conjugate base

Significance

The acid dissociation constant is generally used to predict how acids will behave in chemical reactions, especially in buffer solutions. A higher K_a value means that the substance dissociates more in water, resulting in the production of a higher number of hydrogen ions. Thus, K_a is a direct measure of the acid strength in aqueous solutions. ^[1-8]

Alternative Measurement Scale

The values of the acid dissociation constant (K_a) can span several orders of magnitude, ranging from extremely large for strong acids to very small for weak acids. Because such wide variations make direct comparisons difficult, chemists often use a more convenient logarithmic scale known as pK_a.

Mathematically, pKa is defined as the negative base-10 logarithm of the Ka value:

pK_a = – log₁₀ (K_a)

Both K_a and pK_a are dimensionless, but pK_a provides a more intuitive way to express acid strength; the lower the pK_a, the stronger the acid, and vice versa.

Example Problem

Acetic acid (CH₃COOH) is a common weak acid with a K_a of 1.8 x 10^-5 at 25 °C. Calculate its pK_a.

Solution

Use the above formula to evaluate pK_a.

pK_a = – log₁₀ (1.8 x 10^-5) ≈ 4.74

Therefore, pK_a of acetic acid is 4.74.

Interpreting K_a and pK_a

From the dissociation equation, we can infer that:

• A higher K_a (or lower pK_a) indicates greater acid dissociation and higher hydrogen ion concentration. It means the acid is stronger.
• A lower Ka (or higher pKa) indicates less dissociation, meaning the acid is weaker.

For reference, the hydronium ion (H₃O⁺) is assigned a K_a of 1 and a pK_a of 0. It serves as a conceptual benchmark between weak and strong acids. Acids that are stronger than H₃O⁺ (pK_a < 0) are generally considered strong acids because they dissociate almost completely in water. Their K_a values are so large they are often treated as immeasurable or effectively infinite. ^[1-6]

Table of K_a and pK_a Values (at 25 °C)

The table below lists selected acids in order of decreasing K_a values, along with their conjugate bases: ^[1]

Relationship Between pK_a and pH

The strength of an acid, expressed through its pK_a, is closely tied to the acidity of the solution, represented by the pH scale. This relationship is described by the Henderson–Hasselbalch equation: ^[8]

pH = pKa + log ([A^–]/[HA])

This equation is particularly useful in understanding buffer solutions, where both the weak acid and its conjugate base coexist in equilibrium. It allows chemists to predict the pH of a solution or design buffers with a desired pH by adjusting the ratio of acid to conjugate base.