Composition of Polyprotic Acid Solutions as a Function of pH

During titration of polyprotic acids like maleic acid with sodium hydroxide, three species coexist: H2M (fully protonated), HM− (singly deprotonated), and M2− (fully deprotonated). Their relative concentrations change as pH increases, with each species dominating at different stages of the titration curve.

Alpha values (α0, α1, α2) represent the fraction of each species as a decimal. Initially, α0 = 0.7 means 70% H2M and α1 = 0.3 means 30% HM−. As base is added, these fractions shift, with each alpha approaching unity at its corresponding equivalence point, tracking solution composition during acid base titrations.

Polyprotic acids have two ionizable protons, so they release protons in two distinct steps. Each deprotonation event produces an equivalence point on the titration curve. At the first equivalence point, H2M converts to HM−; at the second, HM− converts to M2−.

At the first equivalence point, alpha-one (α1), representing the fraction of HM−, reaches its maximum and approaches unity (approximately 1.0). Simultaneously, alpha-knot (α0) decreases to nearly zero, indicating complete conversion of H2M to the intermediate HM− species during the titration process.

The fraction of each species depends exclusively on pH and is independent of total acid concentration. As pH increases during titration, alpha values shift predictably: H2M dominates at low pH, HM− at intermediate pH, and M2− at high pH, following the acid's ionization constants.

Between the first and second equivalence points, alpha-two (α2), representing M2− fraction, increases progressively. At the second equivalence point, α2 approaches unity while α1 decreases to near zero, indicating nearly complete conversion of HM− to the fully deprotonated M2− form.

Plotting alpha values against base volume creates a visual map of species distribution throughout titration of polyprotic acids with a strong base. The curves show how each species rises and falls, with crossover points indicating where species concentrations are equal and equivalence points marking maximum conversion.