Chemistry 30 · Acids and bases
Acid-base equilibrium
Acids and bases are equilibrium in disguise. Strength is how far the ionization goes, pH is a way of writing a concentration that spans fourteen powers of ten, and a titration is just careful arithmetic with moles.
Three definitions, one idea
The idea: each definition is broader than the last, and Chemistry 30 mostly runs on Bronsted-Lowry: acids donate protons, bases accept them.
| Definition | An acid | A base |
|---|---|---|
| Arrhenius | Produces H⁺ in water | Produces OH⁻ in water |
| Bronsted-Lowry | Donates a proton (H⁺) | Accepts a proton |
| Lewis | Accepts an electron pair | Donates an electron pair |
Bronsted-Lowry earns its keep because it explains bases with no OH in them. Ammonia is basic because NH₃ + H₂O ⇌ NH₄⁺ + OH⁻ — it takes a proton from water, and the hydroxide comes from the water, not the ammonia.
Conjugate pairs
Every proton transfer creates a pair on each side, differing by exactly one H⁺:
HF + H₂O ⇌ F⁻ + H₃O⁺
- HF and F⁻ are a conjugate acid-base pair — the acid and what is left after it donates.
- H₂O and H₃O⁺ are the other pair — the base and what it becomes after accepting.
- Water is amphiprotic: it donates to bases and accepts from acids, which is why it appears on both sides of this course.
Rule of thumb: the stronger the acid, the weaker its conjugate base. Chloride is a hopeless base precisely because HCl is such a good acid.
Strong and weak
The idea: strength is about how completely a substance ionizes; concentration is about how much of it is dissolved. They are independent.
| Strong | Weak | |
|---|---|---|
| Ionization | Essentially complete — a one-way arrow | Partial — an equilibrium arrow |
| In solution | Almost entirely ions | Mostly intact molecules |
| Ka | Very large; not usually quoted | Small — the smaller, the weaker |
| Examples | HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄; NaOH, KOH | CH₃COOH, HF, H₂CO₃, NH₃ |
A 0.10 mol/L solution of hydrochloric acid has [H₃O⁺] = 0.10 mol/L, because all of it ionized. A 0.10 mol/L solution of acetic acid has [H₃O⁺] of about 0.0013 mol/L — same concentration, a hundredth of the acidity, because only about 1% of it ionized.
Watch out: dilute is not the same as weak, and concentrated is not the same as strong. Concentrated acetic acid is a concentrated weak acid, and it is still vinegar.
pH, pOH and Ka
The idea: pH is a logarithm, so every whole number is a factor of ten. It exists because writing 0.000 000 001 mol/L gets old quickly.
| To find | Use |
|---|---|
| pH from [H₃O⁺] | pH = −log[H₃O⁺] |
| [H₃O⁺] from pH | [H₃O⁺] = 10⁻ᵖᴴ |
| pOH from [OH⁻] | pOH = −log[OH⁻] |
| The other one | pH + pOH = 14.00 at 25 °C |
| Ka from concentrations | Ka = [H₃O⁺][A⁻] ÷ [HA] |
Worked: pH from a hydroxide concentration
[OH⁻] = 1.0 × 10⁻⁵ mol/L
pOH = −log(1.0 × 10⁻⁵) = 5.00, so pH = 14.00 − 5.00 = 9.00 — basic, as a hydroxide concentration that high should be.
Worked: Ka from a measured pH
A 0.100 mol/L solution of a weak acid has pH 2.88.
- [H₃O⁺] = 10⁻²·⁸⁸ = 1.3 × 10⁻³ mol/L.
- Each ionization gives one H₃O⁺ and one A⁻, so [A⁻] is the same 1.3 × 10⁻³ mol/L.
- Almost none of the acid ionized, so [HA] ≈ 0.100 mol/L.
- Ka = (1.3 × 10⁻³)² ÷ 0.100 ≈ 1.8 × 10⁻⁵
That value identifies it as acetic acid. The approximation in step 3 is standard whenever the ionization is less than about 5% of the original concentration.
Significant figures: in a pH, only the decimal places count. A pH of 2.88 carries two significant figures, which is why the Ka above is quoted to two.
Titration and indicators
The idea: add a solution of known concentration until the reaction is exactly complete, then use the mole ratio to find the unknown.
Worked: finding a concentration
25.0 mL of hydrochloric acid is neutralized by 18.4 mL of 0.100 mol/L NaOH.
- Moles of base: (0.0184 L)(0.100 mol/L) = 1.84 × 10⁻³ mol.
- Mole ratio: HCl + NaOH → NaCl + H₂O is 1:1, so the acid also had 1.84 × 10⁻³ mol.
- Concentration: 1.84 × 10⁻³ mol ÷ 0.0250 L = 0.0736 mol/L.
With a diprotic acid such as H₂SO₄ the ratio is 1:2, and forgetting that halves the answer.
| Term | Means |
|---|---|
| Equivalence point | Where the moles added exactly match, by the equation's ratio |
| Endpoint | Where the indicator changes colour — chosen to be as close to equivalence as possible |
| Indicator | A weak acid whose conjugate base is a different colour; it changes over about two pH units |
The pH at equivalence is not always 7. It depends on what salt is left behind:
| Titration | pH at equivalence | Because |
|---|---|---|
| Strong acid + strong base | 7 | The salt does not react with water |
| Weak acid + strong base | Above 7 | The conjugate base left behind takes protons from water |
| Strong acid + weak base | Below 7 | The conjugate acid left behind donates protons to water |
Choose an indicator whose colour change falls inside the steep part of the curve: phenolphthalein, changing around pH 8–10, suits a weak acid titrated with a strong base; methyl orange, around pH 3–4, suits the reverse.