How to Calculate pH from Ka and Kb: Worked Weak Acid/Base Examples

Use Ka or Kb when the acid or base is weak and does not fully dissociate. Strong acids and bases usually allow direct concentration-to-pH conversion, but weak species require an equilibrium approach. The safest pattern is: write the reaction, build an ICE table, solve for x, then convert to pH or pOH.

For a weak acid HA in water: HA + H2O ⇌ H3O+ + A−. Start with initial concentration C for HA and 0 for products. Let the change be -x, +x, +x. Then Ka = x²/(C - x). If Ka is much smaller than C, try the small-x approximation so Ka ≈ x²/C, solve x, then check x/C × 100%. If that value is above 5%, solve the full expression instead.

For a weak base B in water: B + H2O ⇌ BH+ + OH−. Build the same ICE structure and solve using Kb. The solution gives [OH−], so compute pOH = -log[OH−], then convert with pH = 14.00 - pOH (at 25°C). Keep this two-step conversion explicit to avoid sign mistakes.

For a conjugate pair, Ka × Kb = Kw. This relation helps when one value is missing. If you know Ka for an acid, you can find Kb for its conjugate base with Kb = Kw/Ka. This is especially useful in buffer and hydrolysis problems where the conjugate species controls pH.

Common misses are using pH when the setup gave [OH−], skipping the 5% check, or mixing strong-acid logic into weak-acid problems. A fast reasonableness check: weak acids at moderate concentration should usually give mildly acidic pH, not values near 0; weak bases should give mildly basic pH, not values near 14. ChemistryIQ can analyze your handwritten ICE setup from a photo and flag algebra or conversion errors before submission. For educational purposes, always verify with your instructor and course materials.