A-Level Chemistry May/June 2025 Q3(b)(i): The value of the acid dissociation constant, Ka, of butanoic acid, CH3CH2CH2COOH, is 1.…

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  For a weak acid like butanoic acid (HA), the dissociation is: $HA \rightleftharpoons H^+ + A^-$

  The expression for the acid dissociation constant, $K_a$, is: $K_a = \frac{[H^+][A^-]}{[HA]}$

  We assume that $[H^+] = [A^-]$ and that the equilibrium concentration of the acid, $[HA]_{eqm}$, is approximately equal to its initial concentration, $[HA]_{initial}$, because dissociation is slight.

  $K_a \approx \frac{[H^+]^2}{[HA]_{initial}}$

  Rearranging to solve for $[H^+]$: $[H^+] = \sqrt{K_a \times [HA]_{initial}}$ $[H^+] = \sqrt{(1.51 \times 10^{-5}) \times 0.100}$ $[H^+] = \sqrt{1.51 \times 10^{-6}}$ $[H^+] = 1.2288... \times 10^{-3} \text{ mol dm}^{-3}$ $[H^+] = 1.23 \times 10^{-3} \text{ mol dm}^{-3}$ (to 3 s.f.)

  Now, calculate the pH: $pH = -\log_{10}[H^+]$ $pH = -\log_{10}(1.2288... \times 10^{-3})$ $pH = 2.9099...$ $pH = 2.91$ (to 2 d.p.)

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  How the marks are awarded

  • M1 — Correctly calculating the hydrogen ion concentration, [H+], to be 1.23 × 10-3 mol dm-3 by using the weak acid approximation formula and taking the square root of Ka multiplied by the acid concentration.
  • M2 — Correctly calculating the pH from the [H+] value using the formula pH = -log10[H+], and giving the final answer to two decimal places as 2.91.

  Common mistakes

  • Forgetting to take the square root when calculating [H+], instead just multiplying Ka by the concentration.
  • Rounding the intermediate [H+] value too early, which can lead to an inaccurate final pH (e.g., 2.90).
  • Incorrectly applying the logarithm, for example by omitting the negative sign in the pH = -log10[H+] formula.
  • Giving the final pH answer to an incorrect number of decimal places, such as 2.9 or 2.910, instead of the standard two.

  Examiner tip: Master the weak acid approximation (Ka ≈ [H+]² / [HA]) as it is the fundamental and quickest method for calculating the pH of weak acid solutions.

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