§ C-7 Acid–Base Titration, pH Curve & Visual Indicators (Grade 8–11 · Chemistry)
Neutralization curve HCl + NaOH → NaCl + H₂O, equivalence point & steep pH jump. Near the equivalence point, adding a single drop of base changes the hydrogen ion concentration [H⁺] ten-thousandfold, producing a sharp pH jump and indicator color transition.
Theory Summary & Scientific Mechanism
The acidity or basicity of an aqueous solution is quantified by its pH value: pH = -log ₁₀[H₃O⁺]. Due to water autoionization (2H₂O ⇄ H₃O⁺ + OH⁻), the ion-product constant of water at 25 ^°C is K_w = [H⁺][OH⁻] = 10⁻¹⁴ M², giving pH + pOH = 14. Solutions with pH 7 basic (alkaline).
In an acid-base titration of a strong monoprotic acid (HCl) with a strong base (NaOH), hydronium and hydroxide ions neutralize via H⁺ + OH⁻ → H₂O (Δ H = -57.3 kJ/mol). The equivalence point occurs at titrant volume Vₑq = (Cₐ Vₐ)/(C_b), where n(H⁺) = n(OH⁻). Because pH is logarithmic, adding a single drop of base (± 0.05 mL) at Vₑq produces a steep vertical titration jump spanning pH ≈ 4 to 10.
Acid-base indicators are weak organic acids or bases whose conjugate forms HInd and Ind⁻ exhibit distinct colors. Phenolphthalein is colorless in acidic and neutral media (pH < 8.2) and transitions sharply to a vivid magenta-pink within pH ∈ [8.2, 10.0], falling right inside the steep equivalence jump.
Everyday Analogy
Titration is chemical detective work accurate to a single drop! As long as free acid HCl remains in the flask, the solution stays crystal clear, but the moment the last H⁺ ion is neutralized at the equivalence point, a single extra drop of NaOH turns the entire flask vivid magenta!
Interactive Question & Derivation
How is the equivalence-point volume V_NaOH determined when titrating strong monoprotic acid HCl, and why does phenolphthalein turn magenta right on the steep titration jump?
- A: At equivalence, moles of acid and base are equal (C_HClV_HCl = C_NaOHV_NaOH); near this point pH jumps sharply from sim 4 to sim 10, sweeping across phenolphthalein’s transition range (pH 8.2–10.0)
- B: The equivalence point always occurs at pH = 1.0 regardless of added base volume
- C: Indicators change color only when the solution is boiled
Study Hint: At the equivalence point, moles of added base equal initial moles of acid: C_b Vₑq = Cₐ Vₐ. What is the exact pH of a neutral NaCl solution at 25 ^°C?
Proof & Explanation: During strong-acid / strong-base titration, before equivalence (V 9.
Key Equations & 3D Simulation Parameters
Vₑq = (C_HCl V_HCl)/(C_NaOH), pH = 14 + lg ≤ft((C_NaOHV - C_HClV₀)/(V₀ + V) ) (V > Vₑq)
- Added titrant volume V(NaOH) from burette: 0 … 40 mL (default: 18 mL)
- Initial acid concentration C(HCl) (V₀ = 25 mL): 0.05 … 0.15 mol/L (default: 0.1 mol/L)
- Titrant base concentration C(NaOH): 0.05 … 0.15 mol/L (default: 0.1 mol/L)
- Indicator (1=Phenolphthalein, 2=Bromothymol, 3=Methyl orange): 1 … 3 (default: 1)