AP Chemistry: Acid-Base Equilibria and pH Calculations
Acid-base equilibrium problems show up across multiple AP Chem FRQs every year. The mistake students make is using the wrong method for the problem type. Here’s the decision tree.
Method by problem type
- Strong acid or strong base: dissociation is complete. [H+] or [OH-] equals the initial concentration. Then pH = −log[H+].
- Weak acid or weak base: ICE table with Ka or Kb. Often use small-x approximation if Ka or Kb < 10−4 and initial concentration is reasonable.
- Buffer: Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]). Works because the buffer resists pH changes from small acid/base additions.
- Titration: identify the region (before equivalence, at equivalence, after equivalence). Before: buffer (HH equation). At equivalence: weak acid/weak base of the conjugate. After: excess strong acid/base.
- Polyprotic acid: typically only the first dissociation matters significantly. Use Ka1 with ICE table.
Worked example — weak acid
Calculate pH of 0.10 M acetic acid (Ka = 1.8 × 10−5).
ICE table on HC2H3O2 ⇄ H+ + C2H3O2-:
| HC2H3O2 | H+ | C2H3O2- | |
|---|---|---|---|
| I | 0.10 | 0 | 0 |
| C | −x | +x | +x |
| E | 0.10−x | x | x |
Ka = x²/(0.10−x) = 1.8 × 10−5. Small-x approximation valid (Ka small relative to initial). x² / 0.10 = 1.8 × 10−5, so x = 1.34 × 10−3. pH = −log(1.34 × 10−3) = 2.87.
Worked example — buffer
Buffer of 0.20 M acetic acid and 0.10 M sodium acetate (Ka = 1.8 × 10−5). Find pH.
pKa = −log(1.8 × 10−5) = 4.74. By Henderson-Hasselbalch: pH = 4.74 + log(0.10/0.20) = 4.74 + log(0.5) = 4.74 − 0.30 = 4.44.
Common mistakes
- Treating a weak acid like a strong acid. The whole point of Ka is that only a small fraction dissociates.
- Forgetting that Ka · Kb = Kw for conjugate pairs. This relates the Ka of an acid to the Kb of its conjugate base.
- Wrong sign in pH conversions. pH = −log[H+], not log[H+]. Easy to drop the negative.
- Using Henderson-Hasselbalch when there's no buffer. HH only applies when significant amounts of both HA and A- are present.
Need a long-term AP Chemistry mentor, not just a one-off explanation? Learn about AP Chemistry mentorship at Palo Alto Mentor. Most of our students stay with the same mentor for 3–5 years.