U8.5 · Acid-Base TitrationsPractice · 酸碱滴定与滴定曲线

At equivalence n(acid) = n(OH⁻) = 31.25 × 0.0800 = 2.500 mmol, so c = 2.500 ÷ 25.00 = 0.1000 M. It doesn’t matter whether the acid is strong or weak: the equivalence point depends only on moles.

Equivalence takes 20.0 mL of NaOH and forms 2.00 mmol of NO₂⁻ in 40.0 mL, so [NO₂⁻] = 0.0500 M. K_b = 1.0 × 10⁻¹⁴ ÷ 4.6 × 10⁻⁴ = 2.2 × 10⁻¹¹, [OH⁻] = √(2.2 × 10⁻¹¹ × 0.0500) = 1.0 × 10⁻⁶ M, pOH = 5.98, pH = 8.02. Remember the volume has doubled, halving the concentration.

A strong acid exactly neutralized by a strong base leaves only K⁺ and NO₃⁻, neither of which affects pH, so pH = 7.00. A weak acid titrated by a strong base leaves a weak base (HCOO⁻, CN⁻) at equivalence, so pH > 7; a weak base titrated by a strong acid leaves the weak acid NH₄⁺, so pH < 7.

Adding half the OH⁻ turns exactly half the HA into A⁻, so they are equal. By the Henderson–Hasselbalch equation, pH = pKa + log 1 = pKa. That is how the pKa can be read off a titration curve at the half-equivalence point.

HCl is 2.000 mmol and NaOH 2.500 mmol, so we are past equivalence (20.00 mL) with 0.500 mmol of excess OH⁻ in 45.00 mL: [OH⁻] = 0.0111 M, pOH = 1.95, pH = 12.05.

The equivalence point is in the middle of the steep rise, about 25.0 mL, so the half-equivalence point is 12.5 mL. There [HA] = [A⁻], and Ka = [H⁺][A⁻]/[HA] gives [H⁺] = Ka, so pH = pKa. Reading the curve at 12.5 mL gives about 4.2. 2.6 is the pH before any base is added, 8.5 is the equivalence-point pH (the solution holds basic A⁻), and 7.0 applies only to a strong acid–strong base equivalence point.

Both equivalence points are at 25.0 mL (same moles of acid); the shapes differ. Q starts higher (about pH 2.9, since acetic acid only partly ionizes), has a gentle buffer region, a shorter steep rise, and an equivalence point near pH 8.7. P starts near pH 1.0 and has its equivalence point at pH 7. At acetic acid’s equivalence point the solution is sodium acetate, and CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ makes it basic. At the equivalence point acid and base have reacted exactly, so there is no excess NaOH.

Read the equivalence point (25.0 mL, the middle of the steep drop): about pH 5.3, acidic because NH₄⁺ in the solution is a weak acid. The indicator’s range should sit within the steep part and include the equivalence pH: methyl red, 4.4–6.2, fits. Phenolphthalein changes above pH 8, long before the equivalence point; bromothymol blue’s range lies above the equivalence pH; and methyl orange changes only near the end of the steep drop.