Buffer solutions

A buffer minimises the change in pH when small amounts of acid or alkali are added; its pH changes slightly, not at all. No buffer is unlimited: once one reservoir (the weak acid or its conjugate base) is used up, the pH changes sharply, so 'whatever amount' is wrong. Buffers can work at any pH, for example about 4.8 for ethanoic acid and ethanoate or about 9 for ammonia and ammonium, so they are not defined by pH 7. A buffer holds the pH near its own value; it does not bring the solution to pH 7.

NH₃ is a weak base and NH₄⁺ is its conjugate acid: added H⁺ is removed by NH₃ + H⁺ → NH₄⁺, and added OH⁻ by NH₄⁺ + OH⁻ → NH₃ + H₂O, giving an alkaline buffer (about pH 9). HCl is a strong acid and Cl⁻ is too weak a base to take up added H⁺, so HCl and NaCl cannot buffer. NaOH is a strong base with no partner that can remove added OH⁻. Sodium chloride in water contains no weak acid or weak base at all.

The conjugate base HCO₃⁻ takes up the added H⁺, forming H₂CO₃, so [H⁺] and the pH (about 7.4) barely change. H₂CO₃ + OH⁻ is how the buffer removes added alkali, not acid. H₂CO₃ → H⁺ + HCO₃⁻ releases H⁺, which would lower the pH rather than resist the change. Dissolving CO₂ to form H₂CO₃ is how carbonic acid forms in blood, but it does not remove added H⁺.

With [HA] = [A⁻], [H⁺] = K_a = 1.74 × 10⁻⁵ mol dm⁻³, so pH = pK_a = 4.76. 2.88 is the pH of 0.100 mol dm⁻³ ethanoic acid alone; the ethanoate ions suppress its ionisation and raise the pH. 7.00 assumes the acid and its salt neutralise each other, but they do not react. 9.24 is 14 − 4.76, which mixes up pK_a with pOH.

The equivalence point is at 25.0 cm³ and about pH 8.7, and the steep section runs from roughly pH 7 to 11. Range B (8.3 to 10.0, phenolphthalein) lies inside it, so the colour change happens at the equivalence volume. Range A (3.1 to 4.4) lies in the gentle buffer region near the start, so methyl orange would change colour gradually and far too early. Only strong acid and strong base titrations have an equivalence point near pH 7; a weak acid and strong base give an alkaline equivalence point because the ethanoate ion is basic. Weak acids titrate perfectly well against strong bases; it is weak acid against weak base that has no sharp end point. Note also that at 12.5 cm³, half-neutralisation, pH = pK_a = 4.76.

[H⁺] = 1.74 × 10⁻⁵ × 0.200 ÷ 0.100 = 3.48 × 10⁻⁵ mol dm⁻³, so pH = 4.46. More acid than salt makes the buffer more acidic than pK_a. 5.06 inverts the ratio, using [A⁻] ÷ [HA]. 4.76 is the pH only when the two concentrations are equal. 2.73 ignores the salt and treats 0.200 mol dm⁻³ ethanoic acid on its own with √(K_a c).

n(acid) = 0.0100 mol and n(NaOH) = 0.00250 mol. The reaction CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O leaves 0.00750 mol acid and forms 0.00250 mol ethanoate in the same volume, a 3 : 1 ratio. [H⁺] = 1.74 × 10⁻⁵ × 3 = 5.22 × 10⁻⁵ mol dm⁻³, pH 4.28. 4.46 takes the 0.200 : 0.100 ratio of the two starting concentrations and forgets that the NaOH uses up acid. 4.76 assumes half-neutralisation, but only a quarter of the acid has reacted. 5.24 inverts the 3 : 1 ratio.

The ethanoate removes the acid: CH₃COO⁻ + H⁺ → CH₃COOH. Now n(CH₃COOH) = 0.0110 mol and n(CH₃COO⁻) = 0.00900 mol, so [H⁺] = 1.74 × 10⁻⁵ × 0.0110 ÷ 0.00900 = 2.13 × 10⁻⁵ mol dm⁻³, pH 4.67: a fall of only 0.09. 3.00 is what the same HCl would give in 1.00 dm³ of pure water, ignoring the buffer. 4.76 claims the pH does not change at all; a buffer reduces the change but does not remove it. 4.85 shifts the ratio the wrong way, as if alkali had been added.