Overview
This lecture covers solving pH problems using weak acid and weak base equilibria, the use of the ICE table, the KA and KB equilibrium constants, percent dissociation, and the 5% approximation rule to simplify calculations.
Weak Acid Equilibrium & pH Calculation
- The acid dissociation constant (KA) represents the equilibrium between weak acid (HA) and its ions in water.
- Always use equilibrium concentrations (brackets denote molarity at equilibrium).
- Initial concentrations of hydronium (H₃O⁺) and hydroxide (OH⁻) from water are negligible compared to acid/base ionization.
- For weak acids, the change in acid concentration due to ionization is often negligible.
- Set up an ICE table: initial, change, and equilibrium concentrations for all species.
- If x (amount ionized) is much less than the initial acid concentration, approximate [HA] at equilibrium as initial [HA].
- Solve for x (which equals [H⁺]) using the simplified equation: KA ≈ x² / [HA]_initial.
- The 5% rule: approximation is valid if x is less than 5% of initial [HA].
- If approximation is not valid, solve the full quadratic equation.
Determining KA from pH
- Given pH and initial concentration, find [H⁺] using [H⁺] = 10^(–pH).
- Set up the KA expression: KA = x² / ([HA]_initial – x).
- If x is small, use approximation; otherwise, solve exactly.
- Express answers with correct significant figures for pH and KA.
Percent Dissociation
- Percent dissociation = ([H⁺]_equilibrium / [HA]_initial) × 100%.
- As acid concentration decreases, percent dissociation increases.
- Percent dissociation is proportional to √(KA / [HA]_initial).
- Larger KA increases percent dissociation.
Polyprotic Acids
- Polyprotic acids can release more than one proton, with multiple dissociation steps.
- Each dissociation step (KA₁, KA₂, KA₃) has a progressively smaller KA value.
- Later dissociation steps are harder due to greater electrostatic attraction.
Weak Base Equilibrium & pH Calculation
- Weak bases (with lone pairs) react with water to form conjugate acid and OH⁻.
- KB is the base dissociation constant; larger KB means a stronger base.
- Set up ICE table similarly to acids.
- Use 5% rule for approximation: KB ≈ x² / [B]_initial.
- Solve for [OH⁻]; then use [H⁺] = KW / [OH⁻] or pOH = –log[OH⁻]; pH = 14 – pOH.
Key Terms & Definitions
- KA — Acid dissociation constant; measures strength of a weak acid.
- KB — Base dissociation constant; measures strength of a weak base.
- ICE Table — Table for Initial, Change, Equilibrium concentrations.
- 5% Rule — Approximation is valid if x < 5% of initial concentration.
- Percent Dissociation — Fraction of acid/base molecules ionized, as a percentage.
- Polyprotic Acid — Acid that can donate more than one proton per molecule.
Action Items / Next Steps
- Practice setting up and solving ICE tables for weak acids and bases.
- Apply the 5% rule and justify approximations.
- Calculate KA or KB given either pH or concentration.
- Calculate percent dissociation for various solutions.
- Review polyprotic acid equilibria examples.