Weak Acids and Bases

Most acids and bases are weak. They do not hand over all their protons or accept all available protons. Instead, they reach an equilibrium - and the position of that equilibrium is described by Ka or Kb.

Weak Acid Equilibrium

A weak acid HA partially dissociates in water:

HA + H₂O ⇌ H₃O⁺ + A⁻

The equilibrium constant for this reaction is Ka (the acid dissociation constant):

Common weak acids and their Ka values:

Weak Base Equilibrium

A weak base B accepts a proton from water:

B + H₂O ⇌ BH⁺ + OH⁻

The equilibrium constant for this reaction is Kb (the base dissociation constant):

The Relationship Between Ka, Kb, and Kw

For any conjugate acid-base pair, the product of Ka and Kb always equals Kw:

Example: Acetic acid has $K_a = 1.8 \times 10^{-5}$. What is $K_b$ for the acetate ion (CH₃COO⁻)?

$K_b = K_w / K_a = (1.0 \times 10^{-14}) / (1.8 \times 10^{-5}) = 5.6 \times 10^{-10}$

This confirms that acetate is a much weaker base than acetic acid is an acid.

pKa and pKb - The Log Scale

Just as pH = -log[H⁺], we define:

• pKa = -log(Ka) - a smaller pKa means a stronger acid
• pKb = -log(Kb) - a smaller pKb means a stronger base

The “p” operator simply converts to a more convenient scale. An acid with $K_a = 10^{-5}$ has $pK_a = 5$. An acid with $K_a = 10^{-10}$ has $pK_a = 10$. The smaller the $pK_a$, the stronger the acid.

Percent Dissociation

For weak acids, percent dissociation tells you what fraction of the acid molecules have donated their proton:

% dissociation = ([H⁺] at equilibrium / initial [HA]) x 100

Key facts about percent dissociation:

• Diluting a weak acid increases percent dissociation (Le Chatelier’s principle - adding water shifts equilibrium right)
• Ka does not change with dilution (it is a constant at a given temperature)
• A stronger weak acid (larger Ka) has a higher percent dissociation at the same concentration