Weak acids do not fully dissociate in water, so their pH cannot usually be found by treating the acid concentration as the hydrogen ion concentration. Instead, the pH depends on the acid dissociation constant, Ka, and the equilibrium concentrations of the acid and its ions. This matters in biology, environmental chemistry, medicine, and food science, where many important acids are weak acids.
An ICE table gives a clear way to organize the starting amount, the change, and the final equilibrium amounts.
Key Facts
- For a weak acid HA: HA(aq) + H2O(l) ⇌ H3O+(aq) + A−(aq)
- Ka = [H3O+][A−]/[HA]
- pH = −log[H3O+]
- For initial acid concentration C and change x: Ka = x^2/(C − x)
- Small-x approximation: if x is much smaller than C, then Ka ≈ x^2/C and x ≈ sqrt(KaC)
- Percent ionization = ([H3O+]eq / initial [HA]) × 100%
Vocabulary
- Weak acid
- A weak acid is an acid that only partially donates protons to water at equilibrium.
- Ka
- Ka is the acid dissociation constant that measures how strongly a weak acid produces ions in water.
- ICE table
- An ICE table organizes the Initial, Change, and Equilibrium concentrations for a reaction.
- Small-x approximation
- The small-x approximation treats a very small concentration change as negligible compared with the initial concentration.
- Percent ionization
- Percent ionization is the percentage of the original weak acid molecules that form ions at equilibrium.
Common Mistakes to Avoid
- Using the initial weak acid concentration as [H3O+] is wrong because weak acids only partially ionize, so the equilibrium [H3O+] is usually much smaller.
- Forgetting to subtract x from [HA] in the ICE table is wrong because acid molecules are consumed as H3O+ and A− form.
- Using the small-x approximation without checking it is risky because it is only valid when percent ionization is small, often less than about 5%.
- Confusing Ka with pH is wrong because Ka measures equilibrium strength, while pH is calculated from the hydronium ion concentration.
Practice Questions
- 1 A 0.100 M solution of acetic acid has Ka = 1.8 × 10^-5. Use the small-x approximation to calculate [H3O+] and pH.
- 2 A 0.250 M solution of a weak acid HA has Ka = 6.4 × 10^-6. Calculate the approximate pH and percent ionization.
- 3 Two weak acids have the same initial concentration, but acid A has a larger Ka than acid B. Explain which solution has the lower pH and why.