Unit 8: Acids and Bases

Unit 8 covers the pH scale, strong and weak acids and bases, equilibrium constants K_a and K_b, acid-base reactions and salt hydrolysis, titration curves, the molecular structures that make acids strong or weak, buffers and the Henderson-Hasselbalch equation, buffer capacity, and the effect of pH on solubility.

8.1 The pH Scale and Water

The hydronium ion, H₃O⁺, is the form hydrogen takes in water. You will see H⁺(aq) and H₃O⁺(aq) used interchangeably, but H₃O⁺ is preferred because a bare proton does not exist on its own in solution. The pH is defined as pH = −log[H₃O⁺], and pOH as pOH = −log[OH⁻]. A tenfold change in ion concentration moves the pH by exactly one unit.

Water reacts with itself in autoionization: 2H₂O ⇌ H₃O⁺ + OH⁻. The ion product of water is K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C. Taking the negative log of both sides gives pH + pOH = 14 at 25°C. A neutral solution is one where [H₃O⁺] = [OH⁻], which at 25°C means pH = pOH = 7.0.

8.2 Strong Acids and Strong Bases

A strong acid ionizes completely in water, so [H₃O⁺] equals the initial acid concentration. There are six to memorize: HCl, HBr, HI, HClO₄, HNO₃, and H₂SO₄ (first proton only). A strong base dissociates completely: the Group 1 hydroxides (NaOH, KOH) and the Group 2 hydroxides (Ca(OH)₂, Ba(OH)₂, Sr(OH)₂). For Group 1 bases [OH⁻] equals the initial concentration, but Group 2 hydroxides release two hydroxides each, so [OH⁻] is double.

Example: 0.010 M HCl gives [H₃O⁺] = 0.010 M, so pH = 2.00. For 0.020 M Ca(OH)₂, [OH⁻] = 0.040 M, pOH = 1.40, and pH = 12.60.

8.3 Weak Acids, Weak Bases, and Equilibrium Constants

A weak acid only partially ionizes, so [H₃O⁺] is much less than the initial concentration. Its strength is measured by the acid ionization constant K_a = [H₃O⁺][A⁻]/[HA], with pK_a = −log K_a. A weak base partially produces hydroxide, with base ionization constant K_b = [OH⁻][HB⁺]/[B] and pK_b = −log K_b. For any conjugate acid-base pair, K_a × K_b = K_w, or equivalently pK_a + pK_b = 14.

To find the pH of a weak acid solution, set up the equilibrium. For 0.10 M acetic acid (K_a = 1.8 × 10⁻⁵): x² / 0.10 ≈ 1.8 × 10⁻⁵, so x = [H₃O⁺] = 1.3 × 10⁻³ M and pH = 2.87. The percent ionization is x divided by the initial concentration, here about 1.3 percent. Percent ionization rises as the acid gets more dilute, which is why K_a is the reliable measure of strength, not the percent.

8.4 Acid-Base Reactions and Salt Hydrolysis

When a strong acid and strong base mix, H₃O⁺ + OH⁻ → 2H₂O goes quantitatively, and the pH is set by whichever reactant is in excess. Equal moles give pH 7.

Mixing a weak acid with a strong base also goes quantitatively: HA + OH⁻ → A⁻ + H₂O. With excess weak acid remaining, you have a buffer. With equimolar amounts, only the conjugate base A⁻ remains, and it reacts with water (A⁻ + H₂O ⇌ HA + OH⁻), so the solution is slightly basic. The mirror image holds for weak base plus strong acid: B + H₃O⁺ → HB⁺ + H₂O, and equimolar amounts leave the conjugate acid HB⁺, giving a slightly acidic solution. This reaction of a conjugate with water is called salt hydrolysis, and it is the reason these mixtures are not neutral. A weak acid plus weak base mixture is different: HA + B ⇌ A⁻ + HB⁺ reaches equilibrium rather than reacting quantitatively.

8.5 Acid-Base Titrations

A titration curve plots pH against the volume of titrant added. The equivalence point is where moles of titrant equal moles of analyte originally present. Its pH is set by whatever species dominates there: pH 7 for strong acid with strong base, above 7 for a weak acid titrated with strong base (conjugate base hydrolyzes), and below 7 for a weak base titrated with strong acid (conjugate acid hydrolyzes).

For a weak acid or weak base titration, the half-equivalence point is the landmark worth memorizing. Halfway to equivalence, [HA] = [A⁻], and the Henderson-Hasselbalch equation reduces to pH = pK_a. Reading the pH at the half-equivalence point off a titration curve is the standard way to determine an unknown acid's pK_a. The buffer region around it is the flattest part of the curve. Polyprotic acid titration curves show one equivalence point per acidic proton, so H₃PO₄ gives three, and each step has its own half-equivalence pH equal to that proton's pK_a.

8.6 Molecular Structure and Acid/Base Strength

Acid strength can be predicted from structure. The pattern to learn is that anything stabilizing the conjugate base makes the acid stronger, because a stable A⁻ means HA gives up its proton more willingly.

• Binary acids (H–X). Down a group, bond strength dominates: HI > HBr > HCl > HF, because the H–I bond is weakest and breaks most easily. Across a period, electronegativity dominates: HF > H₂O > NH₃ > CH₄.
• Oxyacids. More oxygens mean a stronger acid: HClO < HClO₂ < HClO₃ < HClO₄. The electronegative oxygens pull electron density away through inductive effects, stabilizing the anion.
• Resonance. Carboxylic acids (–COOH) are weak acids partly because the carboxylate anion is resonance-stabilized, with the negative charge spread over two oxygens.
• Conjugates. Strong acids have very weak conjugate bases (Cl⁻, NO₃⁻), and strong bases have very weak conjugate acids. Common weak bases are ammonia and other nitrogenous bases, plus carboxylate ions, the conjugates of carboxylic acids.

8.7 pH, pK_a, and Indicators

The relationship between pH and pK_a tells you which form of an acid predominates. When the solution pH is below the acid's pK_a, the protonated form HA predominates. When pH is above pK_a, the deprotonated form A⁻ predominates. At pH = pK_a they are equal. This is the logic behind both buffers and titrations: moving the pH past a pK_a converts one form into the other.

An acid-base indicator is itself a weak acid whose protonated and deprotonated forms have different colors. It changes color over a range of about pK_a ± 1. Choose an indicator whose pK_a sits near the titration's equivalence-point pH: phenolphthalein (around pH 8–10) for weak acid–strong base titrations, methyl orange (around pH 3–4) for strong acid–weak base titrations.

8.8 Buffers

A buffer solution contains large concentrations of both members of a conjugate acid-base pair, such as CH₃COOH and CH₃COO⁻. Added base is consumed by the conjugate acid (HA + OH⁻ → A⁻ + H₂O) and added acid is consumed by the conjugate base (A⁻ + H₃O⁺ → HA + H₂O), so the pH barely moves. A buffer needs both members present in appreciable amounts: a solution of HA alone, or A⁻ alone, is not a buffer.

8.9 The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation gives a buffer's pH directly: pH = pK_a + log([A⁻]/[HA]). It comes from taking the negative log of the K_a expression and rearranging. When [A⁻] = [HA], the log term is zero and pH = pK_a, which is why equal-concentration buffers sit exactly at the acid's pK_a.

Example: a buffer with 0.20 M acetate and 0.10 M acetic acid (pK_a = 4.74) has pH = 4.74 + log(0.20/0.10) = 4.74 + 0.30 = 5.04. A buffer resists pH change best near its pK_a, within about one pH unit either way. To prepare a buffer at a target pH, pick an acid whose pK_a is close to the target, then set the ratio to fine-tune.

8.10 Buffer Capacity

Buffer capacity is how much added acid or base a buffer can absorb before its pH shifts significantly. Raising the concentrations of both components while keeping the ratio fixed leaves the pH unchanged but increases capacity, because there are more moles of each member to do the neutralizing. A buffer with extra conjugate acid resists added base better, and one with extra conjugate base resists added acid better. Diluting a buffer does not change its pH (the ratio is unchanged) but it does lower its capacity.

8.11 pH and Solubility

A salt's solubility depends on pH when one of its ions comes from a weak acid, a weak base, or hydroxide. The reasoning is Le Châtelier's principle: lowering the pH protonates a basic anion and removes it from solution, pulling more solid into solution. Calcium carbonate dissolves better in acid because CO₃²⁻ + 2H⁺ → CO₂ + H₂O consumes the carbonate. Salts of strong-acid anions, like AgCl, show no pH effect because Cl⁻ is too weak a base to be protonated.

Confusions That Cost Points

Practice Questions

Original questions written for this guide in the style of the AP exam. Answers and explanations are on the next page, so complete the questions before checking them.

Answer Key

1. B. HNO₃ is a strong acid, so it ionizes completely: [H₃O⁺] = 0.010 M and pH = −log(0.010) = 2.00. A confuses pH with pOH arithmetic. C would be the pH of a 0.0010 M solution. D is the pH of 0.010 M NaOH, the strong base with the same concentration.

2. B. A buffer works best within about one pH unit of the acid's pK_a, so match pK_a to the target pH. Acetic acid's pK_a of 4.74 is exactly the target. A buffers near pH 9.26, far from the target. C buffers near 6.37, outside the useful range. D is not a buffer at all: Cl⁻ is the conjugate of a strong acid and does not hydrolyze.

3. C. At equivalence all the acetic acid has become acetate, CH₃COO⁻, which hydrolyzes water to produce OH⁻. The solution is basic, so pH is greater than 7. A assumes every neutralization lands at pH 7, which is true only for strong acid with strong base. B describes a weak base titrated with strong acid. D is the pH at the half-equivalence point, where [HA] = [A⁻].

4. C. CaCO₃ has the basic anion CO₃²⁻, which is protonated in acid (CO₃²⁻ + 2H⁺ → CO₂ + H₂O), pulling more solid into solution by Le Châtelier's principle. A and D have anions from strong acids (Cl⁻) that are not protonated. B responds only slightly because HSO₄⁻ is a relatively strong acid.

One-Page Recall Check

• Write the definitions of pH and pOH, and derive pH + pOH = 14 from K_w.
• Explain why pH 7 is neutral only at 25°C.
• List the six strong acids and the strong bases, and state the [OH⁻] for 0.020 M Ba(OH)₂.
• Write the K_a expression for a generic weak acid and calculate the pH of 0.10 M acetic acid (K_a = 1.8 × 10⁻⁵).
• State the K_a × K_b = K_w relationship and use it to find K_b for acetate.
• Predict whether the equivalence point is acidic, basic, or neutral for each of the four acid-base mixture types.
• Explain salt hydrolysis and why a solution of NaCH₃COO is basic.
• Sketch the three titration curve shapes and label the equivalence point, half-equivalence point, and buffer region on each.
• State what the pH equals at the half-equivalence point of a weak acid titration and why.
• Rank HF, HCl, HBr, HI by acid strength and justify the order.
• Explain why adding oxygens strengthens an oxyacid.
• State the Henderson-Hasselbalch equation and use it to find the pH of a 0.20 M / 0.10 M acetate buffer.
• Explain the difference between buffer pH and buffer capacity.
• Predict which salts become more soluble in acid and explain why with Le Châtelier's principle.

Key terms for this unit

pH, pOH, Hydronium ion (H₃O⁺), Autoionization of water, Ion product of water (K_w), Neutral solution, Strong acid, Strong base, Weak acid, Acid ionization constant (K_a), Weak base, Base ionization constant (K_b), Percent ionization, K_a × K_b = K_w, Strong acid–strong base neutralization, Weak acid + strong base mixtures, Weak base + strong acid mixtures, Weak acid + weak base mixtures, Salt hydrolysis, Titration curve, Equivalence point (acid-base titration), Half-equivalence point, Polyprotic acid titrations, Structural factors in acid/base strength, Carboxylic acids, Nitrogenous bases and carboxylate ions, Weak conjugates of strong acids and bases, pH vs. pK_a (predominant form), Acid-base indicator, Buffer solution, Henderson-Hasselbalch equation, Buffer capacity, pH effect on solubility.

About this guide. Written for Rycal and aligned to the College Board AP Chemistry course framework, Unit 8. All questions and explanations are original Rycal writing. Rycal is independent and is not affiliated with or endorsed by the College Board.