Ka and Kb: measuring acid and base strength
Learn what Ka and Kb measure, how to interconvert them with Kw = Ka·Kb, and why pKa is the convenient way to compare acid strengths.
Quick answer
Ka is the equilibrium constant for an acid's dissociation (HA ⇌ H⁺ + A⁻); Kb is the same for a base (B + H₂O ⇌ BH⁺ + OH⁻). Larger values mean stronger acids/bases, and for any conjugate pair Ka × Kb = Kw = 1.0 × 10⁻¹⁴.
Example: Acetic acid: Ka = 1.8 × 10⁻⁵ (pKa = 4.74). Its conjugate base acetate has Kb = 10⁻¹⁴/(1.8 × 10⁻⁵) = 5.6 × 10⁻¹⁰ — a weak base, as expected.
What you will learn
- Write Ka and Kb expressions from dissociation equations.
- Use Kw = Ka × Kb to convert between a pair's constants.
- Compare acid strengths using Ka and pKa.
- Explain why Ka applies to weak acids only.
Ka: quantifying weak acids
For the weak acid equilibrium
the acid dissociation constant is
Ka measures how far dissociation proceeds: Ka = 1.8 × 10⁻⁵ for acetic acid (weak), versus Ka ≈ 10⁷ for HCl (strong — so large it is never used). Because Ka values span orders of magnitude, chemists often use pKa = −log Ka: acetic acid's pKa is 4.74. Lower pKa always means a stronger acid.
Kb: the same idea for bases
Bases get the parallel treatment. For ammonia:
(Water is omitted as the pure-liquid solvent.) Kb = 1.8 × 10⁻⁵ makes ammonia a weak base — coincidentally the same number as acetic acid's Ka, but that is coincidence, not law. Larger Kb means a stronger base, and pKb = −log Kb works just like pKa.
The Kw bridge between Ka and Kb
Multiply the Ka expression of an acid by the Kb expression of its conjugate base and everything cancels except water's autoionization:
This single relationship ties each conjugate pair together. Acetate ion's Kb = Kw/Ka = 5.6 × 10⁻¹⁰: the conjugate base of a weak acid is a weak base, but a measurable one — which is why sodium acetate solutions are basic. In log form: pKa + pKb = 14.00.
Using Ka: pH and percent dissociation
Ka turns into predictions. For 0.10 M acetic acid: [H⁺] ≈ √(Ka·C) = √(1.8 × 10⁻⁶) = 1.3 × 10⁻³ M, so pH = 2.87. The percent dissociation is [H⁺]/C × 100% = 1.3% — confirming 'weak.'
Ka also ranks acids at a glance: HF (Ka = 6.8 × 10⁻⁴, pKa 3.17) is stronger than acetic acid (pKa 4.74), which is stronger than HCN (Ka = 4.9 × 10⁻¹⁰, pKa 9.31). One number orders them all.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Acid dissociation constant | M (often) | Acid dissociation constant for HA ⇌ H⁺ + A⁻ | |
| Base dissociation constant | M (often) | Base dissociation constant for B + H₂O ⇌ BH⁺ + OH⁻ |
Common mistakes
Strong acids dissociate essentially completely, so their Ka values are enormous and rarely tabulated — there is no equilibrium to describe. Ka is a tool for weak acids; for strong acids, [H⁺] simply equals the concentration.
Bigger Ka = stronger acid, always. Ka is the equilibrium constant for dissociation — a large Ka means the equilibrium lies far toward H⁺ and the conjugate base, which is exactly what 'strong' means.
For any conjugate pair, Ka × Kb = Kw = 1.0 × 10⁻¹⁴. Know one and you know the other. Acetate's Kb = Kw/Ka = 10⁻¹⁴/(1.8 × 10⁻⁵) = 5.6 × 10⁻¹⁰ — a weak base, as expected for the conjugate of a weak acid.
Real-world applications
Buffer design: Ka sets the pH a buffer can hold.
Drug chemistry: Ka values predict whether a drug is ionized at blood pH.
Environmental science: Ka of carbonic acid governs ocean pH.
Analytical chemistry: titration curve shapes follow from Ka values.
Frequently asked questions
How do I write the Ka expression?
Write the dissociation equation, then Ka = [H⁺][conjugate base]/[acid] — pure water omitted. For CH₃COOH ⇌ H⁺ + CH₃COO⁻: Ka = [H⁺][CH₃COO⁻]/[CH₃COOH]. Coefficients become exponents, as in any K expression.
What is pKa?
pKa = −log Ka, exactly like pH. Acetic acid: Ka = 1.8 × 10⁻⁵ → pKa = 4.74. Lower pKa = stronger acid, and the log scale makes comparisons easy: an acid with pKa 2 is 100× stronger than one with pKa 4.
Are Ka and Kb of 'similar' acids and bases related?
Kb for ammonia (NH₃ + H₂O ⇌ NH₄⁺ + OH⁻) is 1.8 × 10⁻⁵ — numerically equal to acetic acid's Ka by coincidence, not by rule. The real relationship is within a conjugate pair: Ka(NH₄⁺) × Kb(NH₃) = Kw.
Do polyprotic acids have multiple Ka values?
Yes — for polyprotic acids each step has its own Ka, always decreasing: H₃PO₄ has Ka₁ = 7.5 × 10⁻³, Ka₂ = 6.2 × 10⁻⁸, Ka₃ = 4.8 × 10⁻¹³. Each proton is harder to remove than the last because the ion grows more negative.