Weak Acids/Bases: Ka, Kb & pH

You’ll be able to

Distinguish strong from weak acids and bases by degree of ionization
Relate Ka, Kb, and pKa to acid strength
Calculate the pH of a weak acid solution using an ICE table

Strong means complete; weak means partial

A strong acid (HCl, HNO₃, H₂SO₄) ionizes essentially 100% in water — write it with a single arrow (→). A weak acid (like acetic acid) only partially ionizes, reaching an equilibrium (⇌) where most molecules stay intact. Same story for bases: strong bases (NaOH, KOH) dissociate fully, while weak bases like NH₃ only partly react. At equal concentration, a strong acid gives a much higher [H⁺] — and thus a lower pH — than a weak one.

Ka, Kb, and pKa measure strength

For a weak acid HA ⇌ H⁺ + A⁻, the acid ionization constant is Ka = [H⁺][A⁻] ÷ [HA]. A larger Ka means more ionization, so a stronger acid. Because Ka values span many orders of magnitude, we compress them: pKa = −log(Ka). A smaller pKa means a stronger acid. Weak bases get the analogous Kb, and for a conjugate pair Ka × Kb = Kw.

Acid ionization constant

Ka = [H⁺][A⁻] / [HA] pKa = −log(Ka)

Larger Ka ↔ smaller pKa ↔ stronger acid. For a conjugate pair, Ka × Kb = Kw = 1.0 × 10⁻¹⁴.

The ICE table for a weak acid

To find the pH of a weak acid you must solve its equilibrium. Set up an ICE table (Initial, Change, Equilibrium). Starting with concentration C and letting x be the amount that ionizes, equilibrium concentrations are [HA] = C − x and [H⁺] = [A⁻] = x. Substituting into Ka gives x² ÷ (C − x) = Ka. When ionization is small, the approximation C − x ≈ C makes this easy: x ≈ √(Ka·C).

Worked example

Find the pH of 0.10 M acetic acid, CH₃COOH (Ka = 1.8 × 10⁻⁵).

1.Reaction: CH₃COOH ⇌ H⁺ + CH₃COO⁻. Let x = [H⁺] at equilibrium.
2.ICE gives Ka = x² / (0.10 − x). Since Ka is small, approximate 0.10 − x ≈ 0.10.
3.x² = Ka · C = (1.8 × 10⁻⁵)(0.10) = 1.8 × 10⁻⁶.
4.x = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M = [H⁺].
5.pH = −log(1.34 × 10⁻³) = 2.87.
6.Validity check: x/C = 1.34 × 10⁻³ / 0.10 = 1.3%, well under 5%, so the approximation holds.

Answer: pH = 2.87

Tip

The "5% rule": the shortcut C − x ≈ C is safe when x is less than 5% of C. If x comes out larger (a fairly strong weak acid or a dilute solution), drop the approximation and solve the full quadratic.

Checkpoint

An acid has Ka = 1.8 × 10⁻⁵. What is its pKa?

Checkpoint

Estimate the pH of 0.10 M solution of a weak acid with Ka = 1.0 × 10⁻⁴.

On the exam

Do not confuse concentration with strength. A concentrated weak acid can still have a modest pH, and a dilute strong acid can be nearly neutral. Ka/pKa describes how completely an acid ionizes; molarity describes how much acid is present.

Answer the 2 checkpoints as you read.