Acid-Base Equilibrium (Ka and pH)

Calculating pH of weak acid and base solutions using ICE tables

Golden Rule: Use an ICE table. The change row has x in the products and −x in the reactants. Solve for x = [H⁺], then pH = −log(x).

• Step 1: Write the dissociation equation — For a weak acid HA: HA ⇌ H⁺ + A⁻. For a weak base B: B + H₂O ⇌ BH⁺ + OH⁻. Write the Ka or Kb expression from the equation.
• Step 2: Set up the ICE table — Initial: [HA]₀ = C, [H⁺] = 0, [A⁻] = 0. Change: −x, +x, +x. Equilibrium: (C − x), x, x. Substitute into Ka: Ka = x²/(C − x).
• Step 3: Solve for x — Try approximation first: x ≈ √(Ka · C). Check: if x/C > 5%, discard the approximation and solve x² + Ka·x − Ka·C = 0 using the quadratic formula.
• Step 4: Calculate pH — For acid: pH = −log(x). For base: pOH = −log(x), then pH = 14 − pOH (at 25°C). Check that pH < 7 for acids and pH > 7 for bases.