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A2 · Practice questions · Ka, pKa and the pH of weak acids

From Ka to pH.

Six original Cambridge-style questions on Kw, Ka, pKa and pH calculations.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Strong: [H+] = c. Weak: [H+] = √(Ka c).

01
Calculation
[2 marks]

Calculate the pH of 0.0500 mol dm−3 barium hydroxide, Ba(OH)2, at 298 K.

  • [OH−] = 2 × 0.0500 = 0.100 mol dm−3. ✓
  • [H+] = 1.00 × 10−14 ÷ 0.100 = 1.00 × 10−13 mol dm−3, so pH = 13.0. ✓
02
Calculation
[3 marks]

Methanoic acid has Ka = 1.78 × 10−4 mol dm−3. Calculate the pH of a 0.0500 mol dm−3 solution.

  • [H+]2 = Ka × c = 1.78 × 10−4 × 0.0500 = 8.90 × 10−6. ✓
  • [H+] = 2.98 × 10−3 mol dm−3. ✓
  • pH = −log(2.98 × 10−3) = 2.53. ✓
03
Calculation
[3 marks]

A 0.200 mol dm−3 solution of a weak acid HA has pH 2.72. Calculate Ka and pKa.

  • [H+] = 10−2.72 = 1.91 × 10−3 mol dm−3. ✓
  • Ka = (1.91 × 10−3)2 ÷ 0.200 = 1.81 × 10−5 mol dm−3. ✓
  • pKa = −log(1.81 × 10−5) = 4.74. ✓
04
Explain
[2 marks]

State the two assumptions made when the pH of a weak acid is calculated using [H+] = √(Ka × c).

  • [H+] = [A−]: all the H+ comes from the acid, and the ionisation of water is ignored. ✓
  • The acid is so slightly ionised that [HA] at equilibrium is equal to its initial concentration c. ✓
05
Calculation
[2 marks]

Calculate the pH of 0.00200 mol dm−3 potassium hydroxide at 298 K.

  • [H+] = 1.00 × 10−14 ÷ 0.00200 = 5.00 × 10−12 mol dm−3. ✓
  • pH = 11.3. ✓
06
Explain
[3 marks]

At 323 K, Kw = 5.48 × 10−14 mol2 dm−6. Calculate the pH of pure water at 323 K and explain whether it is acidic, neutral or alkaline.

  • In pure water [H+] = [OH−], so [H+] = √(5.48 × 10−14) = 2.34 × 10−7 mol dm−3. ✓
  • pH = 6.63. ✓
  • It is still neutral, because [H+] = [OH−]; Kw is larger because the ionisation of water is endothermic. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.