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pH and pOH of Strong Acids and Bases

Determine strong-acid/base ion populations after dilution under a justified concentration model.

AP Chemistry Topic 8.2 · CED printed p. 147 / PDF p. 154. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.

Before you start
  • Dissociation equations
  • Dilution
  • Kw

For a dissolved strong monoprotic acid at ordinary AP concentrations, ionization is essentially complete: HCl + H2O → H3O+ + Cl−. Thus hydronium is approximately the formal acid concentration after any dilution. HCl, HBr, HI, HClO4, and HNO3 are familiar strong acids. Sulfuric acid is strong for its first proton; its second proton comes from HSO4−, whose ionization is an equilibrium. Do not silently assume [H3O+] = 2C for every H2SO4 solution. Use an explicitly supplied completion assumption or relevant second-step equilibrium data.

A dissolved group 1 hydroxide releases one OH− per formula unit. A dissolved group 2 hydroxide M(OH)2 releases two: hydroxide concentration is 2C, not C. Strong dissociation and high solubility are different properties; not every group 2 hydroxide can make an arbitrarily concentrated solution. Use the amount that is actually dissolved. Determine pOH from the hydroxide concentration and use pH = pKw − pOH at the stated temperature. Track spectator ions too: they matter for charge balance even when they do not determine pH.

These short calculations rely on a sensible concentration range. At extremely low acid/base concentrations, water autoionization cannot be neglected; an alleged 10−8 M strong acid should not be called basic just because −log C = 8. At high ionic strength, activity differs from molarity. Most AP exercises use concentrations for which the ideal dilute model and negligible water contribution are appropriate. State that assumption, convert mL to L when finding moles, and use the final total volume after dilution. Strong versus weak concerns extent of proton transfer, while dilute versus concentrated concerns amount per volume.

Let's work through it

  1. A 10.0 mL sample of 0.0200 M HCl is diluted to 100.0 mL at 25 °C.
  2. Moles HCl = 0.0200 mol L−1 × 0.0100 L = 2.00 × 10−4 mol. Dilution changes volume, not these moles.
  3. Final [H3O+] ≈ 2.00 × 10−4/0.1000 = 0.00200 M. pH = 2.699; pOH = 11.301.
  4. The final solution contains nearly 0.00200 M Cl− and negligible molecular HCl. The approximation is appropriate because 0.00200 M greatly exceeds neutral-water hydronium.

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Question 1 of 20 self-assessed

Question 1

Is a 0.001 M HCl solution weak because it is dilute?

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Retrieval 1

Is a 0.001 M HCl solution weak because it is dilute?

Worked answer and reason

No. It is a dilute solution of a strong acid.

Acid strength concerns ionization, not how much acid was added.

Retrieval 2

Why double C for dissolved Ca(OH)2?

Worked answer and reason

Every formula unit releases two hydroxide ions.

The dissociation coefficient controls the concentration.

Catch the tempting mistake

All H atoms in an acid formula ionize completely.
Only ionizable protons and their step-specific equilibria count; molecular formula alone is insufficient.

Put it to work

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For the teacher
  • Ask for ionic populations, not only pH. If the student ignores 2OH−, use a particle balance before another numerical problem.

Unit planning and formative guidance →

Source objectives and scope

Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →

8.2.A
Calculate pH and pOH based on concentrations of all species in a solution of a strong acid or a strong base.
8.2.A.1
Molecules of a strong acid (e.g., HCl, HBr, HI, HClO4, H2SO4, and HNO3) will completely ionize in aqueous solution to produce hydronium ions and the conjugate base of the acid. As such, the concentration of H3O+ in a strong acid solution is equal to the initial concentration of the strong acid, and thus the pH of the strong acid solution is easily calculated.
8.2.A.2
When dissolved in solution, strong bases (e.g., group I and II hydroxides) completely dissociate to produce hydroxide ions. As such, the concentration of OH− in a strong base solution is equal to the initial concentration of a group I hydroxide and double the initial concentration of a group II hydroxide, and thus the pOH (and pH) of the strong base solution is easily calculated.
Science references for this teaching
Glossary and deeper reading · 6 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

  • Hydronium

    Hydronium is the H₃O⁺ ion used in the introductory model of proton behavior in water. Aqueous H⁺ notation is shorthand for a solvated proton rather than a bare proton moving independently in the liquid. For example, a Brønsted acid can transfer a proton to water and form hydronium.

    Read more: Introduction to Acids and Bases →

  • Dilution

    Dilution lowers solute concentration by adding solvent while conserving the solute amount when no reaction or loss occurs. Concentration calculations use the final solution volume rather than simply the volume of solvent added. For example, increasing a solution's volume from 100 to 200 milliliters halves its concentration if its solute amount is unchanged.

    Read more: Solutions and Mixtures →

  • Formula unit

    A formula unit specifies the simplest whole-number ratio of ions in an ionic compound. It is a counting unit for an extended solid rather than an isolated molecule. For example, one calcium chloride formula unit represents one calcium ion and two chloride ions.

    Read more: Moles and Molar Mass →

  • Solubility

    Solubility describes how much of a substance can dissolve in a specified solvent under stated conditions. It depends on the solute, solvent, temperature, and other relevant conditions and is distinct from how fast dissolution occurs. For example, two salts can have different equilibrium solubilities in water at the same temperature.

    Read more: Solubility →

  • Strong acid or base

    A strong acid transfers protons essentially completely to water in the applicable aqueous-solution model. A dissolved strong hydroxide base dissociates into its constituent ions and supplies hydroxide; it does not have to react with water to generate that hydroxide. Strength is distinct from concentration and, for a solid base, from how much can dissolve. For example, dissolved sodium hydroxide supplies sodium and hydroxide ions even when the prepared solution is dilute.

  • Ionic strength

    Ionic strength summarizes dissolved-ion concentrations with weighting by the square of each ion's charge number. It helps describe deviations between ionic activities and concentrations. For example, at equal concentration a divalent ion contributes more to ionic strength than a monovalent ion.

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