pH and strong-acid calculations
Use a logarithmic scale and state the chemical assumptions behind a result.
Before you begin
- Moles per volume
- Base-10 logarithms
Interpret the logarithmic pH scale
For introductory dilute aqueous solutions, pH is approximated by −log₁₀[H⁺] when concentration is expressed in mol/dm³. More precisely, pH uses hydrogen-ion activity. A decrease of one pH unit corresponds to a tenfold increase in the value represented by the hydrogen-ion term, not a one-unit concentration increase.
Use complete dissociation only where justified
A dilute strong monoprotic acid such as HCl is treated as fully dissociated, giving approximately one mole of hydrogen ions per mole of acid. A weak acid is only partially dissociated and requires equilibrium information. For extremely dilute acid, water's contribution can no longer be ignored. Keep calculations within the assumptions stated in the question.
Worked example
Estimate the pH of 0.001 mol/dm³ HCl, assuming complete dissociation and negligible contribution from water.
Show the worked solution
- HCl supplies one hydrogen ion per acid molecule in the model.
- Use [H⁺] = 10⁻³ mol/dm³.
- Calculate −log₁₀(10⁻³) = 3.
pH ≈ 3.
Try it yourself
How does hydrogen-ion concentration at pH 2 compare with pH 4 in the dilute approximation?
Common mistakes
- Acid strength and acid concentration describe different properties.
What can you explain now?
A 0.01 mol/dm³ strong monoprotic acid is diluted tenfold. Estimate the new pH under the same assumptions.
Compare with the explanation
pH ≈ 3.
The concentration falls from 10⁻² to 10⁻³ mol/dm³. The logarithmic pH therefore rises from 2 to 3.
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