Buffer Capacity of an Acid–Base Pair

Buffer capacity measures how much strong acid or base a solution can absorb per unit volume and pH change. The relation is useful for Size a buffer so expected acid or base additions cause a suitably small pH change.. At CT=0.10 mol/L and pH=pKa, β=2.303·CT/4=0.0576 mol·L⁻¹ per pH unit. Check: the ideal buffer capacity is maximal at pH=pKa. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: β: buffer capacity per volume and pH unit (mol·L⁻¹·pH⁻¹); C_T: total analytical concentration HA plus A− (mol/L); K_a: acid dissociation constant (dimensionless); [H+]: hydrogen-ion concentration (mol/L). Follow β in mol·L⁻¹ per pH unit · CT, Ka and [H⁺] in mol/L. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

This ideal monoprotic-buffer expression neglects water contributions and activity corrections. It is a local differential capacity at fixed temperature, not a fixed pH range. Polyprotic systems need contributions from each relevant dissociation step. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: At CT=0.10 mol/L and pH=pKa, β=2.303·CT/4=0.0576 mol·L⁻¹ per pH unit. Check: the ideal buffer capacity is maximal at pH=pKa. Check β in mol·L⁻¹ per pH unit · CT, Ka and [H⁺] in mol/L and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Buffer Capacity of an Acid–Base Pair is related to Henderson-Hasselbalch-Gleichung, Diprotic Acid Species Fractions, pH-Wert-Definition, but answers a distinct question: Size a buffer so expected acid or base additions cause a suitably small pH change.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.