Polyprotic Buffer Regions

Introduction

A polyprotic acid is not one buffer but several. Phosphoric acid, with three removable protons, offers three separate regions of strong buffering, each centred on a different stepwise pKa. Choosing the right region is the first design decision for any polyprotic buffer: pick the conjugate pair whose pKa is closest to the target pH and treat the other equilibria as minor. This page shows how to make that choice and when it needs refinement.

Core explanation

One region per pKa. A polyprotic acid HₙA has n stepwise dissociations, each with its own Ka. Near each pKa, two adjacent species dominate and form a buffer pair:

Acid pKa₁ pKa₂ pKa₃ --- --- --- --- Phosphoric acid 2.15 7.20 12.35 Carbonic acid (apparent) 6.35 10.33 — Citric acid 3.13 4.76 6.40

For phosphoric acid the regions are H₃PO₄/H₂PO₄⁻ near pH 2, H₂PO₄⁻/HPO₄²⁻ near pH 7 and HPO₄²⁻/PO₄³⁻ near pH 12.

Choosing the pair. For a target pH, find the pKa closest to it. The two species that differ by the proton described by that pKa form the relevant pair. Their ratio is then set by:

pH = pKaᵢ + log([base form]/[acid form])

where the base form carries one fewer proton than the acid form.

Why the other species can be ignored. If neighbouring pKa values are well separated, about three units or more as in phosphoric acid, then at a pH near one pKa the other equilibria are far from their own midpoints. At pH 7.2, for example, [H₃PO₄]/[H₂PO₄⁻] = 10^(2.15 − 7.2) ≈ 10⁻⁵, and [PO₄³⁻]/[HPO₄²⁻] ≈ 10⁻⁵. These minor species contain a negligible share of the phosphate.

When pKa values overlap. Citric acid has pKa values only 1.6 to 1.7 units apart. At pH 4.76 all of H₃Cit, H₂Cit⁻ and HCit²⁻ are present in significant amounts, and the single-pair equation gives only an approximate ratio. The distribution fractions for all species must be used for accurate work. The upside is that citrate buffers smoothly over a broad range, from about pH 2.5 to 7.5.

Useful range. Each region is effective roughly within pKa ± 1, where the base-to-acid ratio lies between 1:10 and 10:1. Outside this window, the minority component is too scarce to resist additions in one direction.

Step-by-step reasoning

1. List the stepwise pKa values of the polyprotic acid. 2. Locate the pKa nearest the target pH. 3. Name the two species linked by that dissociation. 4. Check that neighbouring pKa values are at least about two to three units away. 5. Calculate the required ratio from the Henderson–Hasselbalch equation. 6. If pKa values overlap, use full distribution fractions instead.

Visual explanation

On a titration curve of phosphoric acid with sodium hydroxide, three flat regions appear, centred at pH 2.15, 7.20 and 12.35 (the last is poorly defined in water). Each flat plateau is a buffer region; the steep rises between them mark the amphiprotic intermediate points.

Real-world analogy

A polyprotic acid is like a staircase with several landings. Each landing is a stable resting place, a buffer region, and you choose the landing nearest the floor you wish to reach rather than trying to stand halfway up a flight.

Real-world example

Molecular-biology buffers exploit the middle phosphate region because it sits close to neutral pH. Citrate–phosphate mixtures, often called McIlvaine buffers, combine the overlapping citric acid steps with phosphate to span roughly pH 2.2 to 8.0 using just two stock solutions.

Why?

Why is the best buffering at the pKa? There the ratio of the pair is 1:1, so equal reserves exist to consume added acid and added base, and the logarithmic curve of pH against ratio is at its flattest.

Common misconception

"Phosphate buffers work at any pH from 2 to 12." Phosphate has three separate regions with poor buffering between them, near pH 4.7 and 9.8, where the amphiprotic ions dominate and the solution changes pH quickly with added acid or base.

Worked example

Question: Choose a phosphate pair for a buffer at pH 2.50 and find the required ratio.

Reasoning: The pKa values are 2.15, 7.20 and 12.35; the closest is pKa₁ = 2.15, so the pair is H₃PO₄/H₂PO₄⁻. Then log([H₂PO₄⁻]/[H₃PO₄]) = 2.50 − 2.15 = 0.35, so the ratio is 10^0.35 = 2.2. The next pKa, 7.20, is almost five units away, so HPO₄²⁻ is negligible.

Answer: Use H₂PO₄⁻ and H₃PO₄ in a ratio of about 2.2 : 1. At pH 2.50, [H₃O⁺] = 3.2 × 10⁻³ mol dm⁻³, so the buffer should be reasonably concentrated to keep the approximation valid.

Quick check

1. Which phosphate conjugate pair should be used for a buffer at pH 11.8, and why? Answer: HPO₄²⁻/PO₄³⁻, because pKa₃ = 12.35 is the pKa closest to 11.8.

Exam focus

Always justify the choice of pair by quoting the nearest pKa, and write the pair in the correct order (acid form, then base form). A common mark-scheme point is recognising that the "acid" of the middle pair, H₂PO₄⁻, is itself an anion.

Advanced insight

At high pH the HPO₄²⁻/PO₄³⁻ pair is hampered because [OH⁻] near pH 12 is about 0.01 mol dm⁻³, comparable to buffer concentrations, and because activity effects on a triply charged ion are severe. The third phosphate region is therefore rarely used for precise work.

Summary

Each stepwise pKa of a polyprotic acid defines a buffer region of about ± 1 pH unit. To design a buffer, choose the pKa nearest the target pH and use the two adjacent species it links. When pKa values are widely separated, other species are negligible; when they overlap, as in citric acid, all species must be considered.

Practice questions

1. List the three buffer pairs available from phosphoric acid with their pKa values. Answer: H₃PO₄/H₂PO₄⁻ (2.15), H₂PO₄⁻/HPO₄²⁻ (7.20) and HPO₄²⁻/PO₄³⁻ (12.35). 2. Choose a carbonate pair for pH 10.0 and calculate the required ratio. Answer: HCO₃⁻/CO₃²⁻ (pKa 10.33); [CO₃²⁻]/[HCO₃⁻] = 10^(10.0 − 10.33) = 0.47. 3. Why is a single Henderson–Hasselbalch ratio only approximate for citrate buffers? Answer: Citric acid's pKa values are less than two units apart, so three species coexist in significant amounts and the pairs overlap. 4. At pH 7.20, estimate the ratio [H₃PO₄]/[H₂PO₄⁻]. Answer: 10^(2.15 − 7.20) ≈ 9 × 10⁻⁶, so H₃PO₄ is negligible.