Phosphoric Acid as a Triprotic Example

Introduction

Phosphoric acid is the textbook triprotic acid, and for good reason. Its three pKa values are spread so widely that its behaviour is almost like three separate monoprotic acids stacked one above another. Phosphate is also everywhere: in fertilisers, in soft drinks, in detergents, in bone mineral and in DNA and ATP. Knowing which phosphate species is present at a given pH is essential in biochemistry, food science and environmental chemistry.

Core explanation

The family. Phosphoric acid loses its three protons in turn:

H₃PO₄ ⇌ H⁺ + H₂PO₄⁻ Ka1 = 7.5 × 10⁻³, pKa1 = 2.15

H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻ Ka2 = 6.2 × 10⁻⁸, pKa2 = 7.20

HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ Ka3 = 4.8 × 10⁻¹³, pKa3 = 12.32

The names follow the number of hydrogens: phosphoric acid, dihydrogenphosphate, hydrogenphosphate and phosphate (orthophosphate).

Dominance ranges. Because successive pKa values differ by about five units:

pH range Dominant species --- --- below 2.15 H₃PO₄ 2.15 to 7.20 H₂PO₄⁻ 7.20 to 12.32 HPO₄²⁻ above 12.32 PO₄³⁻

At most two species matter. At any pH, only the two species either side of the nearest pKa are significant. For example, at pH 7, nearly five pH units above pKa1, H₃PO₄ is less than 0.01% of the total, and PO₄³⁻ is even smaller. This allows phosphate problems to be reduced to a single conjugate pair almost every time.

Nearly pure intermediates. Midway between pKa values, at pH ½(2.15 + 7.20) = 4.68 and pH ½(7.20 + 12.32) = 9.76, the intermediate ions H₂PO₄⁻ and HPO₄²⁻ reach about 99.4% of the total. These are the approximate pH values of solutions of NaH₂PO₄ and Na₂HPO₄, and they correspond to the two clearly visible end points when phosphoric acid is titrated with sodium hydroxide. The third end point is not seen in water because PO₄³⁻ is a strong enough base to react extensively with water itself.

Charge and function. The average charge of phosphate at pH 7.4 is close to −1.6, a mix of H₂PO₄⁻ and HPO₄²⁻. In biochemistry, the phosphate groups of ATP and DNA are similarly ionised at physiological pH, which gives nucleic acids their strongly negative backbone.

Step-by-step reasoning

1. Locate the pH relative to the three pKa values. 2. Identify the nearest pKa: its conjugate pair holds almost all the phosphate. 3. Calculate the ratio [base]/[acid] = 10^(pH − pKa). 4. Convert to fractions: base fraction = ratio/(1 + ratio). 5. Treat the other two species as negligible unless pH is close to halfway between pKa values.

Visual explanation

On a pH line from 0 to 14, mark 2.15, 7.20 and 12.32. Write H₃PO₄, H₂PO₄⁻, HPO₄²⁻ and PO₄³⁻ in the four regions. The distribution diagram shows four almost separate crossing points, each looking like a monoprotic acid curve.

Real-world analogy

Phosphate behaves like a three-storey building with widely separated floors. At any given height you are either on one floor or on the stairs between two neighbouring floors — never on three floors at once.

Real-world example

Farmers apply phosphate fertilisers such as ammonium dihydrogenphosphate. In acidic soils the phosphate stays as H₂PO₄⁻, the form roots absorb most readily; in alkaline soils the more highly charged forms tend to bind calcium and precipitate, making phosphorus less available to crops.

Why?

Why are phosphoric acid's pKa values so widely spaced? All three protons sit on oxygen atoms of the same small PO₄ unit. Each proton removed leaves extra negative charge concentrated close to the remaining protons, so the electrostatic cost rises sharply at each step.

Common misconception

"Phosphoric acid is a strong acid because it is used to remove rust." Its first dissociation is only moderately strong (Ka1 = 7.5 × 10⁻³), and the later steps are weak. It is corrosive when concentrated, but it is classified as a weak acid.

Worked example

Question: What fraction of phosphate is HPO₄²⁻ in a solution at pH 7.40?

Reasoning: The nearest pKa is pKa2 = 7.20. Ratio [HPO₄²⁻]/[H₂PO₄⁻] = 10^(7.40 − 7.20) = 10^0.20 = 1.58. Fraction = 1.58 / (1 + 1.58) = 0.61.

Answer: About 61% HPO₄²⁻ and 39% H₂PO₄⁻, with H₃PO₄ and PO₄³⁻ both negligible.

Quick check

1. Which phosphate species dominates in a solution at pH 10? Answer: HPO₄²⁻, because pH 10 lies between pKa2 = 7.20 and pKa3 = 12.32.

Exam focus

Learn the three pKa values approximately (about 2, 7 and 12) and the names of the four species. Examiners frequently ask which species predominate at a given pH, or which conjugate pair would make a buffer for a chosen pH.

Advanced insight

Phosphoric acid condenses when heated to form diphosphate and longer polyphosphates, linked by P–O–P bonds. The same kind of linkage in ATP stores chemical energy: hydrolysis of the terminal phosphate bond releases free energy used by cells, and the ionisation state of the products at pH 7 contributes to how favourable the reaction is.

Summary

Phosphoric acid has pKa values of 2.15, 7.20 and 12.32, giving four species with clear dominance ranges. At any pH only one conjugate pair is significant, so a single ratio 10^(pH − pKa) usually describes the system. H₂PO₄⁻ and HPO₄²⁻ are nearly pure at pH 4.68 and 9.76, and the H₂PO₄⁻/HPO₄²⁻ pair governs phosphate near neutral pH.

Practice questions

1. Calculate [PO₄³⁻]/[HPO₄²⁻] at pH 12.00. Answer: 10^(12.00 − 12.32) = 10^(−0.32) = 0.48. 2. Which two phosphate species are significant at pH 3.0, and which is larger? Answer: H₃PO₄ and H₂PO₄⁻; H₂PO₄⁻ is larger, by a factor of 10^(0.85) ≈ 7. 3. Explain why only two end points are seen when phosphoric acid is titrated with sodium hydroxide. Answer: PO₄³⁻ is a strong enough base to react extensively with water, so the third proton is not removed sharply and no clear third end point appears. 4. State the approximate pH of a solution of Na₂HPO₄ and explain it. Answer: The ideal midpoint estimate is about 9.8, halfway between pKa2 and pKa3, where HPO₄²⁻ dominates; measured values are somewhat lower because of ionic-strength effects and water's contribution.