Unit 8 · Topic 8.3 Beta

Weak Acid and Base Equilibria

A weak acid or base reacts with water only partly, so its pH comes from an equilibrium.

Practice 5: Mathematical RoutinesPractice 6: Argumentation

Question set for this topic

Part 1 · Hook

Why this matters

Vinegar is about 0.8 M acetic acid, yet you can splash it on a salad. A hydrochloric acid solution of the same concentration would have a pH near 0. The difference is that most acetic acid molecules never give up their proton: the reaction reaches equilibrium with the acid mostly intact.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. For A ⇌ 2 B with K = 4.0 × 10⁻⁶ and [A]₀ = 0.10 M, what does the small-x approximation replace (0.10 − x) with?

  1. 0.10
  2. x
  3. 0.10 + x
  4. 2x
Show the answer

When K is small, x is tiny compared with 0.10, so 0.10 − x ≈ 0.10. You check afterwards that x is under 5% of 0.10.

  • Correct: 0.10:
  • x:
  • 0.10 + x:
  • 2x:

2. What is the pH of 0.010 M HCl?

  1. 2.00
  2. 12.00
  3. 0.010
  4. 1.00
Show the answer

HCl is strong: [H₃O⁺] = 0.010 M, pH = 2.00.

  • Correct: 2.00:
  • 12.00:
  • 0.010:
  • 1.00:

3. What is the conjugate base of HNO₂?

  1. NO₂⁻
  2. H₂NO₂⁺
  3. NO₂
  4. OH⁻
Show the answer

Remove one H⁺ from the acid: HNO₂ → NO₂⁻.

  • Correct: NO₂⁻:
  • H₂NO₂⁺:
  • NO₂:
  • OH⁻:

Part 4 · See it

See it first

Two boxes holding the same amount of acid. The strong acid has become six hydronium ions and six anions with no molecules left. The weak acid box has five whole HA molecules and only one hydronium ion and one A minus ion, so it has fewer hydronium ions and a higher pH.
The same amount of acid: the strong acid is all ions, the weak acid mostly whole molecules. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. A weak acid holds its proton fairly tightlyHA + H₂O ⇌ H₃O⁺ + A⁻ reaches equilibrium with most HA un-ionized (Ka ≪ 1)
  2. Only a small amount x ionizesan ICE table gives Ka = x²/(C − x) ≈ x²/C, so [H₃O⁺] ≈ √(Ka·C)
  3. Diluting lowers every concentrationQ falls below Ka, so a larger fraction ionizes: percent ionization rises
  4. An acid and its conjugate base are linked through waterKa × Kb = Kw, so the weaker the acid, the stronger its conjugate base

Part 6 · Key ideas

Key ideas

  • Weak acid: Ka ≪ 1, mostly un-ionized. Larger Ka (smaller pKa) = stronger acid.
  • Weak acid pH: [H₃O⁺] = x ≈ √(Ka × C). Check x < 5% of C; if not, solve the quadratic.
  • Weak base: same method with Kb to find [OH⁻], then pOH, then pH.
  • Ka × Kb = Kw for a conjugate pair; pKa + pKb = 14.00 at 25 °C. Kb is not 1/Ka.

Part 7 · Misconception

A common mistake

The wrong idea: A weak acid is one that is dilute.

What actually happens: Weak means it ionizes only partly (Ka ≪ 1); dilute means low concentration. Concentrated acetic acid is still weak, and 0.0010 M HCl is still strong.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data table

Ka values of four acids

Acid dissociation constants at 25 °C. Each acid gives up one proton: HA + H₂O ⇌ H₃O⁺ + A⁻.

Ka at 25 °C
AcidFormulaKa
Hypochlorous acidHOCl3.0 × 10⁻⁸
Acetic acidCH₃COOH1.8 × 10⁻⁵
Nitrous acidHNO₂4.0 × 10⁻⁴
Hydrofluoric acidHF6.8 × 10⁻⁴

1. What is the pH of 0.20 M acetic acid?

Type a number.

Show the answer

Ka = x² / (0.20 − x) = 1.8 × 10⁻⁵. Assume x ≪ 0.20: x = √(1.8 × 10⁻⁵ × 0.20) = 1.90 × 10⁻³ M = [H₃O⁺]. Check: 0.9% of 0.20, under 5%, so the assumption holds. pH = −log(1.9 × 10⁻³) = 2.72.

  • Answer: 2.72

2. For 0.10 M solutions of each acid, which has the highest pH?

  1. Hypochlorous acid
  2. Hydrofluoric acid
  3. Nitrous acid
  4. Acetic acid
Show the answer

At equal concentration, the acid with the smallest Ka ionizes least, makes the least H₃O⁺ and so has the highest pH. HOCl has Ka = 3.0 × 10⁻⁸.

  • Correct: Hypochlorous acid: Right: the smallest Ka, the least H₃O⁺.
  • Hydrofluoric acid: HF has the largest Ka here, so it gives the most H₃O⁺ and the lowest pH.
  • Nitrous acid: HNO₂ has the second-largest Ka, so its pH is low.
  • Acetic acid: Acetic acid ionizes more than HOCl (Ka 1.8 × 10⁻⁵ vs 3.0 × 10⁻⁸), so its pH is lower.

3. What is Kb for the fluoride ion, F⁻? Give your answer in scientific notation.

Type a number.

Show the answer

F⁻ is the conjugate base of HF. Ka × Kb = Kw, so Kb = (1.0 × 10⁻¹⁴) / (6.8 × 10⁻⁴) = 1.5 × 10⁻¹¹.

  • Answer: 1.5 × 10-11

Particle view

Three acid solutions of equal volume

Box 1HAHAHAHAHAHAHAHAHAHAHAHAH₃O⁺H₃O⁺A⁻A⁻Box 2H₃O⁺H₃O⁺H₃O⁺H₃O⁺H₃O⁺H₃O⁺H₃O⁺A⁻A⁻A⁻A⁻A⁻A⁻A⁻Box 3HAHAHAH₃O⁺A⁻

Key: HA a whole acid molecule; H₃O⁺ hydronium; A⁻ the anion left when HA loses a proton. Water is not drawn. Each box holds one kind of acid.

4. Which box represents a strong acid?

  1. Box 2
  2. Box 1
  3. Box 3
  4. A pH reading of each box is needed to tell
Show the answer

A strong acid ionizes fully, so no HA molecules remain. Only Box 2 has none.

  • Correct: Box 2: Right: only ions, no whole molecules.
  • Box 1: Box 1 is mostly whole HA molecules: a weak acid.
  • Box 3: Box 3 still has whole HA molecules: a weak acid.
  • A pH reading of each box is needed to tell: The particle view is enough: a strong acid leaves no whole HA molecules, and only Box 2 has none.

5. Boxes 1 and 3 contain the same acid at the same temperature. Which statement is best supported?

  1. Box 3 is the more dilute solution, and a larger fraction of its acid is ionized
  2. Box 3 has the larger Ka, because a larger fraction of its acid is ionized
  3. Box 3 has the lower pH, because a larger fraction of its acid is ionized
  4. Both boxes have the same percent ionization, because they hold the same acid
Show the answer

Box 1: 2 of 14 acid particles ionized (14%); Box 3: 1 of 4 (25%), with fewer acid particles in the same volume, so it is more dilute. Both boxes give the same Ka (2 × 2/12 = 1 × 1/3 in particle units), as one acid at one temperature must. Diluting a weak acid raises its percent ionization: Q = [H₃O⁺][A⁻]/[HA] falls below Ka on dilution, so more HA ionizes.

  • Correct: Box 3 is the more dilute solution, and a larger fraction of its acid is ionized: Right: fewer particles per volume, a larger fraction ionized.
  • Box 3 has the larger Ka, because a larger fraction of its acid is ionized: Ka is fixed for an acid at a given temperature; it does not change with concentration.
  • Box 3 has the lower pH, because a larger fraction of its acid is ionized: Box 3 has 1 H₃O⁺ against 2 in Box 1 in the same volume, so its pH is higher. A larger fraction ionized does not mean more H₃O⁺ when the solution is more dilute.
  • Both boxes have the same percent ionization, because they hold the same acid: Percent ionization depends on concentration as well as on the acid.

Experimental setup

A household ammonia solution

A cleaning solution is 0.15 M aqueous ammonia, NH₃, at 25 °C. For NH₃, Kb = 1.8 × 10⁻⁵.

NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

6. What is the pH of the ammonia cleaning solution?

Type a number.

Show the answer

pOH = −log(1.64 × 10⁻³) = 2.784; pH = 14.00 − 2.784 = 11.216, which is 11.22 (two significant figures in 0.15 M, two decimal places). Solving the quadratic gives 11.21; both are accepted.

  • Answer: 11.22

7. Solution 1 is 0.10 M HCl and Solution 2 is 0.10 M HF. Each is diluted tenfold. How do their pH values change?

  1. HCl rises by 1.0 unit; HF rises by less than 1.0 unit
  2. Both rise by exactly 1.0 unit
  3. HCl rises by 1.0 unit; HF rises by more than 1.0 unit
  4. Neither changes, because Ka and Kw do not change
Show the answer

HCl ionizes fully, so [H₃O⁺] falls tenfold and pH rises by 1.0. For HF, dilution makes Q < Ka, so more HF ionizes and partly offsets the dilution: [H₃O⁺] falls only by about √10, and pH rises by about 0.5.

  • Correct: HCl rises by 1.0 unit; HF rises by less than 1.0 unit: Right: dilution raises the percent ionization of the weak acid.
  • Both rise by exactly 1.0 unit: Only the strong acid follows the one-unit rule; the weak acid ionizes more when diluted.
  • HCl rises by 1.0 unit; HF rises by more than 1.0 unit: The extra ionization of HF on dilution makes its pH rise less, not more.
  • Neither changes, because Ka and Kw do not change: K values stay the same, but concentrations change, so pH changes.

Part 9 · Summary

Summary

A weak acid or base reacts with water only partly, so its pH comes from an equilibrium. With Ka (or Kb) and the concentration, an ICE table and the small-x approximation give [H₃O⁺] ≈ √(Ka·C). Percent ionization rises on dilution, and a conjugate pair obeys Ka × Kb = Kw.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections