pH calculations
Summary
pH calculations use pH = −log[H⁺] to turn an acid or base concentration into a pH. A strong acid gives [H⁺] equal to its concentration; a weak acid needs Ka, often with the approximation [H⁺] ≈ √(Ka·C). Each pH unit is a tenfold change in [H⁺].
Detail
Meaning: pH calculations convert between [H⁺] and pH. A strong acid dissociates essentially completely, so [H⁺] equals its concentration. For a weak acid, Ka = x²/(C − x); if x is small compared with C, [H⁺] = x ≈ √(Ka·C). For a base, find [OH⁻] the same way with Kb, then use pOH.
Equation: pH = −log[H⁺]; pH + pOH = 14 at 25 °C; pH = pKa + log([A⁻]/[HA]). [H⁺] is in mol/L (the SI unit is mol/m³, but the exam uses M). [A⁻] and [HA] are the conjugate base and weak acid concentrations in mol/L. pH, pOH and pKa have no units.
On the MCAT: Calculators are not allowed, so you estimate. Write [H⁺] as a × 10⁻ⁿ. The pH lies between n − 1 and n, and is about n − 0.5 when a is near 3. Expect weak acid pH from Ka, buffer ratios, half-equivalence points (pH = pKa), and dilution: diluting a strong acid tenfold raises its pH by 1.
Common confusion: Students report pH 8 for 10⁻⁸ M HCl. At that dilution, water's own autoionization (10⁻⁷ M H⁺) matters, so the pH is just below 7. Also remember that a one-unit pH change is a tenfold change in [H⁺], not a change of one unit of concentration.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- Chemistry: The Molecular Nature of Matter and Change
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.