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Lesson 3 · 25 min

Polyprotic acids and speciation

Phosphoric acid, carbonic acid, and amino acids take different forms at different pH. Speciation diagrams show exactly who is present in blood, seawater, and cells.

In this lesson

  • Write the stepwise ionization of a polyprotic acid with its pKa\mathrm{p}K_\mathrm{a} values
  • Describe the share of each species at any pH with distribution fractions α
  • Read the dominant species off a speciation diagram and explain “one pH unit, a tenfold ratio”
  • Apply speciation to blood, seawater, and amino acids

Carbon dioxide dissolved in seawater is not one thing: it is a mixture of COX2(aq)\ce{CO2(aq)}, HCOX3X−\ce{HCO3-}, and COX3X2−\ce{CO3^2-} whose proportions are set by pH. Shellfish and corals build calcium carbonate from COX3X2−\ce{CO3^2-} — so even a 0.1 drop in ocean pH shakes their supply of building material. To see why, you need a speciation diagram.

Predict first

In seawater at pH 8.1, which form holds most of the dissolved inorganic carbon?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

One proton at a time

Acids that can give up more than one proton are polyprotic. They always release protons one step at a time, and each step is harder than the last — pulling a positive proton off an already negative ion costs more:

HX3POX4⇌HX2POX4X−+HX+pKa1=2.15\ce{H3PO4 <=> H2PO4- + H+}\quad \mathrm{p}K_{\mathrm{a}1} = 2.15
HX2POX4X−⇌HPOX4X2−+HX+pKa2=7.20\ce{H2PO4- <=> HPO4^2- + H+}\quad \mathrm{p}K_{\mathrm{a}2} = 7.20
HPOX4X2−⇌POX4X3−+HX+pKa3=12.38\ce{HPO4^2- <=> PO4^3- + H+}\quad \mathrm{p}K_{\mathrm{a}3} = 12.38
αi=[H+]n−i K1K2⋯Ki∑j=0n[H+]n−j K1⋯Kj\alpha_i = \frac{[\mathrm{H^+}]^{n-i}\,K_1 K_2\cdots K_i}{\sum_{j=0}^{n}[\mathrm{H^+}]^{n-j}\,K_1\cdots K_j}
Distribution fractions depend only on pH, not on total concentration; they always sum to 1.
αi\alpha_i
fraction of the form that has lost ii protons
nn
number of ionizable protons (n=3n = 3 for phosphoric acid)
KiK_i
ii-th acid dissociation constant

Speciation diagrams obey two handy rules:

  • At pH = p$K_{\mathrm{a}i}$ the two neighbouring forms are 50 : 50.
  • Each pH unit away changes their ratio tenfold; two units, a hundredfold. So once the pH is more than 2 units from a pKa\mathrm{p}K_\mathrm{a}, you can often treat one form alone.
Alpha fractions and log c–pH diagrams

Speciation explorer

pKa = 2.148, 7.198, 12.375

blood 01234567891011121314pH00.20.40.60.81α
  • H₃PO₄
  • H₂PO₄⁻
  • HPO₄²⁻
  • PO₄³⁻

pH 7.40 Dominant species: HPOX4X2−\ce{HPO4^2-}

  • HX3POX4\ce{H3PO4} 0.000%
  • HX2POX4X−\ce{H2PO4-} 38.6%
  • HPOX4X2−\ce{HPO4^2-} 61.4%
  • POX4X3−\ce{PO4^3-} 0.001%

Drag the line to change pH

Alpha curves follow directly from the pKa values (25 °C, zero ionic strength): at each pKa two neighbouring forms are 50 : 50. The log view uses 0.1 M total and draws [H⁺] and [OH⁻]; their crossings with the species lines locate the pH of the pure solutions.
Switch to the log view: the dashed lines are [HX+][\ce{H+}] and [OHX−][\ce{OH-}]. Then look at glycine — around neutral pH it exists mostly as the zwitterion HX3NX+CHX2COOX−\ce{H3N+CH2COO-}.

Worked example

How much carbonate does ocean acidification remove?

Using pure-water constants (pK1=6.35\mathrm{p}K_1 = 6.35, pK2=10.33\mathrm{p}K_2 = 10.33), compare the fraction of COX3X2−\ce{CO3^2-} at pH 8.1 and pH 7.8.

Concept check

In blood plasma at pH 7.40, which phosphate form dominates?

Try the calculation

Citric acid has pKa\mathrm{p}K_\mathrm{a} values 3.13, 4.76, and 6.40. At pH 5.58, what is the ratio [HCitX2−]/[HX2CitX−][\ce{HCit^2-}]/[\ce{H2Cit-}]?

Key takeaways

  • Polyprotic acids ionize stepwise, with successively larger pKa\mathrm{p}K_\mathrm{a} values.
  • Distribution fractions depend only on pH; at pH = pKaiK_{\mathrm{a}i} neighbours are 50 : 50 and each unit changes their ratio tenfold.
  • Phosphate in blood is mostly HPOX4X2−\ce{HPO4^2-} and HX2POX4X−\ce{H2PO4-}; inorganic carbon in seawater is mostly HCOX3X−\ce{HCO3-}.
  • Ionic strength shifts effective constants; accurate seawater work needs seawater-specific constants.
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Data and references

  1. D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), Ch. 10 (polyprotic acid–base equilibria); Appendix G.
  2. F. J. Millero, “Thermodynamics of the carbon dioxide system in the oceans”, Geochim. Cosmochim. Acta 59, 661–677 (1995).
  3. R. E. Zeebe, D. Wolf-Gladrow, CO₂ in Seawater: Equilibrium, Kinetics, Isotopes, Elsevier (2001).
  4. T. J. Lueker, A. G. Dickson, C. D. Keeling, “Ocean pCO₂ calculated from dissolved inorganic carbon, alkalinity, and equations for K₁ and K₂”, Mar. Chem. 70, 105–119 (2000): pK₂* = 8.97 at 25 °C and salinity 35.