Weak Acid and Base Equilibria

Learning Objective 8.3.A Explain the relationship among pH, pOH, and concentrations of all species in a solution of a monoprotic weak acid or weak base.

Quick Notes

Weak acids and bases do not completely dissociate in solution.

They exist in equilibrium with their conjugate forms.

K_a (acid dissociation constant) and K_b (base dissociation constant) are used to describe the extent of ionization and the “strength” of the weak acid or base.
Relationships:
- K_a = [H₃O⁺][A⁻] / [HA]
- pK_a = −log K_a
- K_b = [OH⁻][BH⁺] / [B]
- pK_b = −log K_b
- K_w = K_a × K_b
- pK_w = pK_a + pK_b (at 25 °C, pK_w = 14.0)

Full Notes

Weak Acids

A weak acid only partially ionizes in water. This means only a small fraction of the acid molecules react with water to form hydronium ions (H₃O⁺). As a result, the concentration of H₃O⁺ in solution is much lower than the initial concentration of the acid.

An equilibrium is established between:

Undissociated acid molecules (HA)
Conjugate base ions (A⁻)
Hydronium ions (H₃O⁺)

The equilibrium can be written:

AP Chemistry weak acid equilibrium showing HA reacting with water to form H3O+ and A−

Where

HA = weak acid
A⁻ = conjugate base ion
H₃O⁺ = hydronium ion

For exampleethanoic acid (CH₃COOH):

AP Chemistry diagram of ethanoic acid partially ionizing in water to produce H3O+ and CH3COO−

CH₃COOH ⇌ H₃O⁺ + CH₃COO⁻
where HA = CH₃COOH and A⁻ = CH₃COO⁻
Only a small proportion of CH₃COOH molecules ionize, so the solution contains a mixture of all three species.

Acid Dissociation Constant, K_a

Because weak acids form an equilibrium system, we use an equilibrium constant, K_a, to quantify the extent of ionization:

AP Chemistry formula tile showing Ka equals product of hydronium and conjugate base concentrations over undissociated acid concentration

AP Chemistry formula tile showing pKa equals negative log of Ka

AP Chemistry tile showing Ka equals 10 to the power of negative pKa

Smaller K_a = weaker acid
Larger pK_a = weaker acid

Percent ionization of a weak acid:
% ionization = ([H₃O⁺] at equilibrium / initial [HA]) × 100

Weak Bases

Weak bases react partially with water. They accept protons to form their conjugate acids and produce hydroxide ions (OH⁻). Unlike strong bases, which dissociate fully, weak bases establish an equilibrium in solution.

For a generic weak base, B:

AP Chemistry weak base equilibrium showing B plus H2O forming BH+ and OH−

Where

B is the weak base
BH⁺ is the conjugate acid formed when the base accepts a proton
OH⁻ is the hydroxide ion released into solution, increasing basicity

The position of this equilibrium depends on how effectively the base accepts protons from water (its base strength).

Base Dissociation Constant, K_b

As with weak acids, the strength of a weak base is described by an equilibrium constant:

AP Chemistry formula tile showing Kb equals product of BH+ and OH− concentrations over base concentration

AP Chemistry formula tile showing pKb equals negative log of Kb

AP Chemistry tile showing Kb equals 10 to the power of negative pKb

Smaller K_b = weaker base
Larger pK_b = weaker base
The majority of the base remains unreacted in solution.

Percent ionization of a weak base:
% ionization = ([OH⁻] at equilibrium / initial [B]) × 100

Relationship Between K_a and K_b

Acids and bases exist in conjugate pairs. If you know the strength of an acid, you can Acids and bases exist in conjugate pairs, and their strengths are linked. If you know the strength of a weak acid (K_a), you can determine the strength of its conjugate base (K_b), and vice versa.

Key Relationship:
K_a × K_b = K_w
pK_a + pK_b = pK_w
At 25 °C:
K_w = 1.0 × 10⁻¹⁴
pK_w = 14.00

This allows interconversion between K_a and K_b (or pK_a and pK_b) for any conjugate pair.

Deriving the Relationship

For a weak acid, HA:

AP Chemistry weak acid with water forming hydronium and conjugate base

AP Chemistry expression for Ka in terms of H+ A− and HA

And for its conjugate base, A⁻:

AP Chemistry conjugate base reacting with water to form HA and OH−

AP Chemistry expression for Kb of A− in terms of HA, OH−, and A−

Multiplying these together:

AP Chemistry derivation showing Ka times Kb equals Kw after cancelling A− and HA, resulting in [H+][OH−] = Kw

Matt’s exam tip

Don’t forget H⁺ and H₃O⁺ can be used interchangeably in these expressions — like on this page deliberately. Get comfortable seeing both used.

Summary

Weak acids and bases partially ionize, and their behavior is described by K_a and K_b.
Use equilibrium expressions and ICE tables to calculate pH, [H₃O⁺], or [OH⁻].
The percent ionization reflects how much acid or base reacts.
K_a and K_b are linked through K_w: K_a × K_b = K_w and pK_a + pK_b = 14 at 25 °C.