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II-10: pH, pOH and weak-acid equilibrium

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Module II-10 · Recommended before: Before acid-base calculations

pH, pOH and weak-acid equilibrium

Acid-base equilibria require logarithms and careful concentration balances. For weak acids, the small-x approximation is valid only if checked.

Learn the method

pH = −log₁₀[H₃O⁺]; at 25 °C, pH + pOH = 14.00

  1. Identify [H₃O⁺] or [OH⁻].
  2. Use pH = −log₁₀[H₃O⁺] or pOH = −log₁₀[OH⁻].
  3. At 25 °C, pH+pOH = 14.00 under dilute aqueous conditions.
  4. If using K_a or K_b, solve the equilibrium expression.
  5. Check reasonableness.

Common mistake: pH+pOH = 14.00 is a 25 °C relationship and should not be assumed universally.

Worked example

Problem: At 25 °C, an aqueous solution has [OH⁻] = 1.0×10⁻⁴ M. Calculate pH.

Step-by-step solution: pOH = 4.00; pH = 14.00−4.00 = 10.00.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Weak-acid estimate

For a weak HA with Ka = 1.0×10⁻⁵ and initial concentration 0.100 M, x≈√(KaC)=1.0×10⁻³ M, giving pH≈3.00; x/C≈1%, so the approximation is reasonable.

Temperature dependence

At 25 °C, pH+pOH=14.00 is useful for dilute aqueous systems. For other temperatures, calculate pKw from Kw at that temperature.

Polyprotic acid steps

For a diprotic acid, Ka₁ and Ka₂ describe separate ionizations. When Ka₁≫Ka₂, the first dissociation often dominates [H₃O⁺], but the second step may matter for speciation.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. At 25 °C, [OH⁻] = 1.0 × 10^-6 M. Find pH.
Hint for question 1

Determine pOH first, then use the 25 °C relation.

Question 2. At 25 °C, [OH⁻] = 1.0 × 10^-7 M. Find pH.
Hint for question 2

Determine pOH first, then use the 25 °C relation.

Question 3. At 25 °C, [OH⁻] = 1.0 × 10^-8 M. Find pH.
Hint for question 3

Determine pOH first, then use the 25 °C relation.

Question 4. At 25 °C, [OH⁻] = 1.0 × 10^-9 M. Find pH.
Hint for question 4

Determine pOH first, then use the 25 °C relation.

Question 5. At 25 °C, [OH⁻] = 1.0 × 10^-10 M. Find pH.
Hint for question 5

Determine pOH first, then use the 25 °C relation.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

W3C WCAG 2.2 accessibility guidance.

Applied practice: Weak-acid approximations and pH

These ungraded questions extend the scored five-question check. Work each problem before opening its solution; progress records are not changed.

  1. Challenge 1. A monoprotic weak acid has initial concentration 0.100 M and Kₐ = 1.8 × 10⁻⁵. Estimate pH and check the small-x assumption.

    Show worked solution for challenge 1

    Approximate [H₃O⁺] = √(KₐC) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M. pH ≈ 2.87. Ionization is 1.34% of 0.100 M, below the common 5% guideline.

  2. Challenge 2. Find pH when [H₃O⁺] = 2.00 × 10⁻³ M.

    Show worked solution for challenge 2

    pH = −log₁₀(2.00 × 10⁻³) = 2.699 (three decimal places for three significant figures in concentration).

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.