Polyprotic Acid pH Calculator
Calculate pH and the species distribution of a polyprotic acid, and simulate its titration with a strong base.
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What it does
The polyprotic acid pH calculator handles acids that can lose more than one proton — phosphoric, citric, carbonic, oxalic, sulfuric, and the amino acids. Because the successive dissociations overlap, the pH of these acids is not given by the first pKa alone, and the fraction of each protonation state varies continuously with pH. The calculator returns the equilibrium pH together with the distribution of every species, and a titration mode that plots pH against added strong base and marks each equivalence volume. It is written for anyone who needs the speciation, not just a single number: buffer designers, analytical chemists, and students meeting polyprotic equilibria for the first time.
How it works
Each successive dissociation has its own acidity constant, and the cumulative constant for losing i protons is the product of the first i of them. Dividing that by the hydrogen ion concentration to the power i, then normalising across all species, gives the fraction of the acid in each state at a given pH. Summing i times each fraction gives the average charge on the acid, and the solution must satisfy charge balance: the protons plus any added base cation must equal the hydroxide plus the acid negative charge, with the ion product of water fixing the last term. The equation is monotonic in the hydrogen ion concentration, so the calculator solves it by bisection rather than by extracting a root of a high-degree polynomial. The titration mode evaluates the same equation at each added volume, with both the acid and the base diluted by the growing total volume.
Worked example
For 0.1 M phosphoric acid (pKa 2.15, 7.2, 12.35) the approximate first protonation gives around pH 1.58, and the full calculation returns pH 1.63; at that pH roughly 97 percent of the acid is H₃PO₄ and the rest is H₂PO₄⁻, with the doubly charged form below 0.1 percent. For 0.1 M glycine, an amino acid with pKa 2.35 and 9.78, the charge balance puts the zwitterion at pH about 6.06, close to the familiar average of the two pKa values. Titrating 25 mL of 0.1 M acetic acid with 0.1 M sodium hydroxide gives an equivalence volume of 25 mL and a pH of about 8.7 at that point, because the acetate formed is itself a weak base.
When to use it
Use it to find the ionic form of a drug or buffer ingredient at a working pH, to see how much of a triprotic acid is fully deprotonated when preparing a salt, or to estimate the equivalence volumes before a titration. Two limits matter. The constants are for 25 °C and zero ionic strength; temperature and added salt shift pKa, so calibrate against a measurement when the exact value matters. And the model uses concentrations rather than activities, which understates the correction as the ionic strength rises above about 0.1 mol/L.
FAQ
- What is a polyprotic acid?
- It is an acid that can release more than one proton, each with its own pKa. Phosphoric acid loses three, citric acid three, carbonic acid two, and sulfuric acid two, the first of them effectively completely. Because the dissociations overlap, the pH depends on all of the constants together, not on the first one alone.
- How is the species distribution calculated?
- For each protonation state the tool forms the cumulative constant, the product of the pKa values up to that state, divides it by the hydrogen ion concentration to the power of the number of protons lost, and normalises across all states. The result is the fraction of the acid in each form at the computed pH, and the fractions always sum to one.
- Why is the pH not just half of (pKa₁ − log c)?
- That shortcut assumes only the first proton dissociates and ignores the rest. For phosphoric acid it gives about 1.58, while the full charge balance gives 1.63, and for EDTA or citric acid the difference is larger because several pKa values lie close together. The calculator solves the charge balance directly, so the later dissociations are included.
- How does the titration mode work?
- At each added volume of strong base the tool dilutes both the acid and the base by the growing total volume, then solves the same charge balance for the new pH. It marks every equivalence volume, the volume that neutralises each successive proton, which for a diprotic acid appears at one and again at two equivalents of base.