Acids and Bases — AP Chemistry Study Guide

For: AP Chemistry candidates sitting AP Chemistry.

Covers: Brønsted-Lowry definitions, pH calculations, Ka/Kb equilibria for weak acids/bases, buffers (Henderson-Hasselbalch), titration curves, indicators, and polyprotic acids — AP Chemistry Unit 8.

You should already know: Equilibrium ICE tables (Unit 7), stoichiometry (Unit 4).

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Chemistry style for educational use. They are not reproductions of past College Board papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official College Board mark schemes for grading conventions.

1. Why Acids and Bases Matter

Unit 8 makes up about 11–15% of AP Chemistry — one of the heaviest single units. It's also a guaranteed FRQ topic, often combined with equilibrium (Unit 7) into a multi-part problem on a buffer or titration.

The unifying framework: an acid is a proton (${\text{H}}^{+}$) donor, a base is a proton acceptor. Every problem in this unit is fundamentally about who has the proton, in what concentration, and how the resulting equilibrium shifts.

2. The Brønsted-Lowry framework

Three vocabulary items you must distinguish:

• Acid (HA): donates H⁺.
• Conjugate base (A⁻): what's left after the acid donates. Stronger acid → weaker conjugate base, and vice versa.
• Conjugate acid (BH⁺): what a base becomes after accepting H⁺.

In water: $\text{HA}+{\text{H}}_2\text{O}\rightleftharpoons {\text{H}}_3{\text{O}}^{+}+{\text{A}}^{-}$. Water is amphoteric (acts as both acid and base in different reactions).

3. pH and the autoionisation of water

Water self-ionises slightly: ${\text{H}}_2\text{O}+{\text{H}}_2\text{O}\rightleftharpoons {\text{H}}_3{\text{O}}^{+}+{\text{OH}}^{-}$, with $K_w=[{\text{H}}_3{\text{O}}^{+}][{\text{OH}}^{-}]=1.0\times 10^{-14}$ at 25 °C.

$$\text{pH}=-\log [{\text{H}}_3{\text{O}}^{+}],\text{pOH}=-\log [{\text{OH}}^{-}],\text{pH}+\text{pOH}=14$$

A solution at pH 7 is neutral, < 7 acidic, > 7 basic. A change of 1 pH unit means a 10× change in [H₃O⁺].

4. Strong acids and bases

Strong acids fully ionise. Memorise the strong acids: HCl, HBr, HI, HNO₃, HClO₄, HClO₃, H₂SO₄ (only first proton). Their conjugate bases are negligibly weak.

Strong bases (group 1 hydroxides, plus Ca(OH)₂, Sr(OH)₂, Ba(OH)₂) fully dissociate.

For strong acid/base, [H⁺] (or [OH⁻]) equals the formal concentration: $$\text{pH of 0.010 M HCl}=-\log (0.010)=2.00$$ $$\text{pH of 0.010 M NaOH}:\text{pOH}=2.00,\text{ so pH}=12.00$$

5. Weak acids and bases — Ka, Kb

Weak acids only partially ionise: $$\text{HA}\rightleftharpoons {\text{H}}^{+}+{\text{A}}^{-},K_a=\frac{[{\text{H}}^{+}][{\text{A}}^{-}]}{[\text{HA}]}$$

Smaller $K_a$ → weaker acid. $\text{p}{K}_a=-\log K_a$.

For a weak acid HA at initial concentration $C$:

1. Set up an ICE table with $x=[{\text{H}}^{+}]$ at equilibrium.
2. $K_a=x^2/(C-x)$.
3. If $C/K_a>500$, approximation $x\ll C$ is valid: $x\approx \sqrt{K_a\cdot C}$.

For a weak base, swap to $K_b$ and solve for $[{\text{OH}}^{-}]$. $K_a\cdot K_b=K_w$ relates an acid and its conjugate base.

6. Buffers — Henderson-Hasselbalch

A buffer resists pH change on addition of small amounts of acid or base. It's a mixture of a weak acid and its conjugate base in similar concentrations.

The Henderson-Hasselbalch equation: $$\text{pH}=\text{p}{K}_a+\log \frac{[{\text{A}}^{-}]}{[\text{HA}]}$$

The buffer is most effective when $\text{pH}\approx \text{p}{K}_a$ (i.e. equal moles of acid and conjugate base). Buffer capacity is the amount of acid or base it can absorb before pH changes by 1 unit.

7. Titration curves

Pouring base into acid (or vice versa) gives a characteristic S-shape. Key points:

• Initial pH: pH of the analyte alone.
• Half-equivalence point: half the analyte has been neutralised. For a weak acid: $\text{pH}=\text{p}{K}_a$ at this point.
• Equivalence point: moles of titrant = moles of analyte. Strong-strong: pH = 7. Weak acid + strong base: pH > 7 (conjugate base hydrolyses). Strong acid + weak base: pH < 7.
• After equivalence: pH driven by excess titrant.

For a polyprotic acid (H₂SO₃, H₃PO₄), there are multiple equivalence points — one per ionisable proton.

8. Indicators

A pH indicator is itself a weak acid where HIn and In⁻ have different colours. Colour change occurs over $\text{pH}=\text{p}{K}_a\pm 1$. Choose an indicator whose $\text{p}{K}_a$ is close to the equivalence-point pH.

Common pairings: phenolphthalein ($\text{p}{K}_a\approx 9$, colourless → pink) for strong acid + weak base or weak acid + strong base; methyl orange ($\text{p}{K}_a\approx 3.5$) for strong acid + weak base.

9. Worked Example

A 0.100 M solution of acetic acid (CH₃COOH, $K_a=1.8\times 10^{-5}$) is mixed in equal volumes with 0.100 M sodium acetate (CH₃COONa). Calculate the pH. Then 0.005 mol of HCl is added to 1 L of this buffer — what is the new pH?

Solution. After mixing equal volumes, both [HA] and [A⁻] are 0.0500 M.

Initial pH (Henderson-Hasselbalch): $$\text{p}{K}_a=-\log (1.8\times 10^{-5})=4.74$$ $$\text{pH}=4.74+\log (0.0500/0.0500)=4.74+0=4.74$$

After adding 0.005 mol HCl: HCl reacts with A⁻ → HA + Cl⁻.

• Moles A⁻: $0.0500-0.005=0.0450$ mol.
• Moles HA: $0.0500+0.005=0.0550$ mol.
• New pH: $4.74+\log (0.0450/0.0550)=4.74+\log (0.818)=4.74+(-0.087)=4.65$.

Interpretation: pH dropped by only 0.09 units despite adding 0.005 mol of strong acid — that's the buffer working. Without the buffer, 0.005 mol HCl in 1 L would give pH ≈ 2.3.

10. Common Pitfalls

• Forgetting water's autoionisation: very dilute strong acid (e.g. $10^{-8}$ M HCl) can't have pH 8 — water's contribution to [H⁺] dominates. Solve the full $K_w$ equation.
• Mis-applying Henderson-Hasselbalch to non-buffer solutions: HH is valid only when both HA and A⁻ are present in significant amounts.
• Forgetting that [HA] = [A⁻] at half-equivalence: at this point pH = pKa, regardless of starting concentration.
• Mixing up Ka and Kb: write the equilibrium first to be sure which constant you need.
• Polyprotic confusion: Ka1 ≫ Ka2 ≫ Ka3 for stepwise deprotonation; treat each step separately.

11. Practice Questions (CED Style)

1. Calculate the pH of 0.025 M ammonia ($K_b=1.8\times 10^{-5}$).
2. A 25.0 mL sample of 0.150 M acetic acid is titrated with 0.100 M NaOH. Calculate the volume of NaOH needed to reach the half-equivalence point and predict the pH there.
3. Phosphoric acid ($K_{a1}=7.5\times 10^{-3}$, $K_{a2}=6.2\times 10^{-8}$, $K_{a3}=4.2\times 10^{-13}$) is titrated with NaOH. At what pH does the second equivalence point occur, approximately, and which indicator would you choose?

12. Quick Reference Cheatsheet

• Brønsted-Lowry: acid donates H⁺, base accepts H⁺; conjugate pairs swap an H⁺.
• pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14.
• Strong acids (memorise): HCl, HBr, HI, HNO₃, HClO₄, HClO₃, H₂SO₄ (1st only).
• Weak acid pH: ICE table, $K_a=x^2/(C-x)$, approximate when $C/K_a>500$.
• Buffer: $\text{pH}=\text{p}{K}_a+\log ([{\text{A}}^{-}]/[\text{HA}])$. Best when pH ≈ pKa.
• Half-equivalence: pH = pKa.
• Equivalence pH: =7 (strong+strong), >7 (weak acid + strong base), <7 (strong acid + weak base).
• $K_a\cdot K_b=K_w=1.0\times 10^{-14}$.

13. What's Next

Acids & Bases links forward to Unit 9 (Apps of Thermodynamics) which adds the redox/electrochemistry frame — common AP FRQs ask you to combine an acid/base buffer pH with $\Delta G$ from cell potentials. Use Ollie to walk through any specific buffer or titration: "Why does my titration curve have a flat part before the equivalence point?" or "Should I approximate or solve the quadratic for this weak acid problem?".