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pH of strong acids and bases

For a strong acid or base, the hard part is done before any math: it dissociates completely, so its ion concentration is handed to you. Take a log and you have the pH.

§1

From concentration to pH.

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pH = −log[H⁺] measures acidity, and pOH = −log[OH⁻] measures basicity. At 25 °C they are linked by pH + pOH = 14. A lower pH means a higher [H⁺] (more acidic).

A strong acid or base dissociates completely, so you know the ion concentration directly: a 0.010 M strong acid gives [H⁺] = 0.010 M (unless it provides more than one H⁺).

Count carefully: a diprotic strong acid gives two H⁺ per formula unit, and a base like Ca(OH)₂ gives two OH⁻. Get the ion concentration, then take the log.

UNIT 8 TOPIC 8.2 • pH AND pOH OF STRONG ACIDS AND BASES THE pH SCALE Strong acids and bases dissociate completely, so concentration maps directly to pH or pOH. READING THE SCALE · 0 = MOST ACIDIC · 7 = NEUTRAL · 14 = MOST BASIC acidic neutral basic 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.010 M HCl pH = 2 pure water pH = 7 0.0010 M NaOH pH = 11 CORE RELATIONSHIPS pH = −log[H₃O⁺] pOH = −log[OH⁻] pH + pOH = 14 (at 25 °C) Strong acids fully dissociate: 0.010 M HCl → [H₃O⁺] = 0.010 so pH = 2 A LOGARITHMIC SCALE Each 1 pH unit = a 10× change in [H⁺] pH 2 10× more H⁺ pH 3 baseline pH 4 10× less H⁺ pH 2 has 10× more H⁺ than pH 3. STRONG BASE → pH A base gives [OH⁻], so find pOH first, then convert: pOH = −log[OH⁻] pH = 14 − pOH (25 °C) 0.0010 M NaOH → [OH⁻] = 0.0010 pOH = 3 → pH = 11 CED ANCHOR Kw = [H₃O⁺][OH⁻] = 1.0×10⁻¹⁴ at 25 °C — this ties the two scales together: pH + pOH = 14. AP Chemistry · Unit 8 · Acids and Bases
Fig. 8.2.1 pH = −log[H⁺] and pOH = −log[OH⁻], with pH + pOH = 14 at 25 °C. A strong acid or base dissociates completely, so its ion concentration equals its concentration (times the number of H⁺ or OH⁻ provided), and the pH follows.
§2

Computing pH for a strong acid/base.

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Count the ions, then take the log.

  1. Note complete dissociation. A strong acid or base fully ionizes in solution.
  2. Count ions per formula unit. One H⁺ for HCl, two for H₂SO₄; two OH⁻ for Ca(OH)₂.
  3. Find the ion concentration. Multiply the concentration by the number of ions provided.
  4. Take the log. pH = −log[H⁺], or find pOH and use pH = 14 − pOH.
§3

The pieces you'll meet.

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Logs and complete dissociation.

pH
pH
−log[H⁺]; lower means more acidic.
pOH
pOH
−log[OH⁻]; lower means more basic.
sum
pH + pOH
= 14 at 25 °C.
strong
Strong acid/base
Dissociates completely.
count
Ion count
Number of H⁺ or OH⁻ per formula unit.
scale
pH scale
Roughly 0–14; lower is more acidic, higher more basic.
§4

Worked example: pH of a strong acid and base.

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Strong acid. For 0.010 M HCl, complete dissociation gives [H⁺] = 0.010 M. pH = −log(0.010) = 2.

Diprotic acid. For 0.010 M H₂SO₄ (treating both protons as strong), [H⁺] ≈ 0.020 M, so pH = −log(0.020) ≈ 1.7 — lower, because it provides two H⁺.

Strong base. For 0.010 M NaOH, [OH⁻] = 0.010 M, so pOH = 2 and pH = 14 − 2 = 12.

Key point. Count the ions each formula unit provides before taking the log; a lower pH corresponds to a higher [H⁺].

§5

Mistakes that cost real points.

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Pitfall · 01

"A higher pH means a more acidic solution."

It is the reverse: a lower pH means more acidic (higher [H⁺]), and a higher pH means more basic. The pH scale runs opposite to acidity because of the negative sign in the logarithm.

Fix. Read a lower pH as more acidic and a higher pH as more basic; the scale runs opposite to [H⁺].

Pitfall · 02

"A strong acid only partially dissociates, so you need Ka."

Strong acids (and bases) dissociate completely, so there is no equilibrium and no Ka needed — the ion concentration equals the acid concentration (times the ions per formula unit). Partial dissociation is a weak-acid concept.

Fix. Treat strong acids/bases as fully dissociated; use the concentration directly, no Ka.

Pitfall · 03

"A diprotic acid gives the same [H⁺] as a monoprotic acid of the same concentration."

A diprotic strong acid provides two H⁺ per formula unit, so its [H⁺] is about double that of a monoprotic acid at the same concentration, giving a lower pH. Miscounting the protons gives the wrong pH.

Fix. Multiply the concentration by the number of H⁺ (or OH⁻) each formula unit releases before taking the log.

§6

Skill Check.

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