Diprotic Acid Species Fractions

Species fractions give the proportions of a diprotic acid present as H₂A, HA⁻ and A²⁻ at a specified pH. The relation is useful for Estimate pH-dependent speciation in titrations, buffers and acid–base equilibria.. For pKa₁=4, pKa₂=8 and pH=6, D=10⁻¹²+10⁻¹⁰+10⁻¹²=1.02×10⁻¹⁰. The fractions are α₀≈0.0098, α₁≈0.9804 and α₂≈0.0098. Check: they sum to 1. 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: α₀: fraction present as H₂A (dimensionless); α₁: fraction present as HA⁻ (dimensionless); α₂: fraction present as A²⁻ (dimensionless); K_a1: first acid dissociation constant (dimensionless); K_a2: second acid dissociation constant (dimensionless); [H+]: hydrogen-ion concentration (mol/L). Follow Species fractions and Ka values are dimensionless; use a consistent standard concentration for [H⁺]. 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 model assumes one diprotic acid in a single aqueous phase with defined stepwise dissociation constants. Concentration expressions approximate activities in dilute solutions. Complexation, additional protonation states or nonideal conditions require an expanded model. 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: For pKa₁=4, pKa₂=8 and pH=6, D=10⁻¹²+10⁻¹⁰+10⁻¹²=1.02×10⁻¹⁰. The fractions are α₀≈0.0098, α₁≈0.9804 and α₂≈0.0098. Check: they sum to 1. Check Species fractions and Ka values are dimensionless; use a consistent standard concentration for [H⁺] 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.

Diprotic Acid Species Fractions is related to Henderson-Hasselbalch-Gleichung, pH-Wert-Definition, Massenwirkungsgesetz (Gleichgewichtskonstante), Buffer Capacity of an Acid–Base Pair, Distribution Ratio in Liquid–Liquid Extraction, but answers a distinct question: Estimate pH-dependent speciation in titrations, buffers and acid–base equilibria.. 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.