§ C-15 Buffer Solutions, Henderson–Hasselbalch Equation & Buffer Capacity (Grade 10–11 · Buffer Solutions)
Comparing pH stability of an acetate buffer (CH₃COOH + CH₃COONa) against unbuffered water upon addition of strong acid HCl or base NaOH. A conjugate acid–base pair HA / A⁻ scavenges both added protons H⁺ and hydroxide ions OH⁻, locking solution pH within a narrow physiological window.
Theory Summary & Scientific Mechanism
Buffer solutions resist changes in pH upon addition of small amounts of strong acid or base. An acidic buffer pairs a weak acid HA (such as acetic acid CH₃COOH) with its conjugate base salt A⁻ (sodium acetate CH₃COONa).
Rearranging the acid dissociation equilibrium Kₐ = ([H⁺][A⁻])/([HA]) yields the Henderson–Hasselbalch equation: pH = pKₐ + lg ([A⁻])/([HA]). Added strong acid (H⁺) is scavenged by conjugate base ions (A⁻ + H⁺ → HA), whereas added strong base (OH⁻) is neutralized by weak acid molecules (HA + OH⁻ → A⁻ + H₂O), preventing drastic pH swings.
Buffer capacity β = 2.303 ([HA][A⁻])/([HA] + [A⁻]) is maximized when [HA] = [A⁻] (pH = pKₐ). In human physiology, the bicarbonate buffer (H₂CO₃ / HCO₃⁻) stabilizes arterial blood pH strictly between 7.35 and 7.45.
Everyday Analogy
A buffer acts like a shock absorber: one drop of strong acid plunges pure water from pH 7 to 2, whereas the conjugate pair HA / A⁻ absorbs added H⁺ or OH⁻ and keeps pH rock-steady (just as blood maintains pH 7.40)!
Interactive Question & Derivation
At what concentration ratio of weak acid [HA] to conjugate base salt [A⁻] does a buffer solution exhibit maximum buffer capacity βₘax, and what is its pH at that point?
- A: At equal molar concentrations [HA] = [A⁻]; here lg ([A⁻]/[HA]) = lg (1) = 0, so pH = pKₐ
- B: When only pure weak acid is present with zero salt ([A⁻] = 0)
- C: When salt concentration exceeds acid concentration by 1000× and pH = 14
Study Hint: By the Henderson–Hasselbalch equation pH = pKₐ + lg ([A⁻]/[HA]), maximum buffer capacity occurs when [HA] = [A⁻], where lg (1) = 0 and pH = pKₐ.
Proof & Explanation: By the Henderson–Hasselbalch equation pH = pKₐ + lg ([A⁻]/[HA]), when [HA] = [A⁻] the buffer neutralizes added H⁺ (A⁻ + H⁺ → HA) and added OH⁻ (HA + OH⁻ → A⁻ + H₂O) equally well, reaching peak buffer capacity βₘax = 0.576 Cₜot at pH = pKₐ.
Key Equations & 3D Simulation Parameters
pH = pKₐ + lg ≤ft(([A⁻]₀ + Δ C)/([HA]₀ - Δ C) )
- Weak acid concentration [HA] (CH₃COOH): 0.05 … 0.5 mol/L (default: 0.2 mol/L)
- Conjugate base salt concentration [A⁻] (CH₃COONa): 0.05 … 0.5 mol/L (default: 0.2 mol/L)
- Added strong acid HCl (−) or base NaOH (+): -0.15 … 0.15 mol/L (default: 0 mol/L)
- Acid dissociation exponent pKₐ: 3 … 9 (default: 4.76)