Окисно-відновне титрування: Чому потенціал стрибає на рівновазі

Обмін протонами та електронами

Редокс-титровання є структурним відображенням титрування кислотою-лугом: замість переміщення протонів між слабкою кислотою та її кон’югатом, переміщуються електрони між окисленою та зведеною формами двох хімічних пар. Прогрес реакції відстежується не за допомогою pH-метра, а за допомогою інертного електрода (зазвичай платини), який вимірює потенціал розчину E, відрегульований відносно стандартного електрода.

The Nerst equation drives the curve

Every redox half-reaction has its own Nernst equation relating the measured potential to the concentration ratio of its oxidized and reduced forms:

E = E° - (RT / nF) · ln( [Red] / [Ox] ) E° standard potential of the couple n number of electrons transferred F Faraday's constant At any point during the titration both couples present in solution are, in principle, linked by the same electrode potential — but whichever couple has both its oxidized and reduced forms present in comparable, measurable amounts is the one whose Nernst equation effectively fixes E at that moment.

E = E° - (RT / nF) · ln( [Red] / [Ox] )

  E°  standard potential of the couple
  n   number of electrons transferred
  F   Faraday's constant

Redox Titration: Before, at, and after equivalence

Before equivalence, the analyte couple dominates the measurable concentration ratio, so the analyte's own Nernst equation sets the potential. After equivalence, essentially all analyte has been consumed and it is the titrant couple's ratio, of excess oxidized titrant to reduced titrant produced, that sets E instead. The handoff between the two regimes happens right around equivalence, and it is exactly there that E rises steeply, because both concentration ratios are changing rapidly through several orders of magnitude with each small addition of titrant.

The equivalence-point potential

Combining the two half-reaction Nernst equations with the stoichiometric condition that electrons lost by one couple equal electrons gained by the other at equivalence gives a closed-form expression for the equivalence-point potential: E_eq = (n1·E1° + n2·E2°) / (n1 + n2). When both couples transfer the same number of electrons this collapses to a simple average of the two standard potentials; when n1 ≠ n2 the couple with the larger n pulls the equivalence potential closer to its own standard potential.

What makes the jump sharp

The steepness of the potential jump near equivalence is set by how far apart the two couples' standard potentials sit. A large gap, roughly ΔE° > 0.2 V, gives a sharp, easily read jump — a titrant couple far more oxidizing than the analyte couple drives the reaction essentially to completion at every point, keeping the endpoint crisp. A small gap, ΔE° < 0.2 V, gives a shallow, gradual change that is much harder to pinpoint accurately, whether by eye with a redox indicator or by a potentiometric electrode.

Frequently asked questions

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