E. Chemical Systems and Equilibrium · Acid-Base and Solubility EquilibriaConjugate Acid-Base Pairs and Relative Strength
E3.6 E3.7 E2.1About 70 minutes
Learning goals- I can identify conjugate acid-base pairs in a Brønsted-Lowry reaction.
- I can write the conjugate base of an acid and the conjugate acid of a base.
- I can explain why a stronger acid has a weaker conjugate base.
- I can use a table of relative strengths to predict whether reactants or products are favoured in a proton-transfer equilibrium.
Words to know
conjugate base
The particle left after an acid donates a proton. HF → F⁻.
conjugate acid
The particle formed when a base accepts a proton. NH₃ → NH₄⁺.
conjugate acid-base pair
Two particles whose formulas differ by exactly one proton (H⁺), such as CH₃COOH / CH₃COO⁻.
relative strength
How readily an acid donates protons (or a base accepts them) compared with other acids (or bases).
levelling effect
In water, every acid stronger than H₃O⁺ reacts completely to form H₃O⁺, so all strong acids appear equally strong. Likewise OH⁻ is the strongest base that can exist in water.
Every proton transfer runs both ways
In the last lesson, acetic acid gave a proton to water. But the products can react too: the acetate ion can take a proton back from a hydronium ion. Weak-acid reactions are reversible, and at equilibrium both reactions happen at the same rate (you studied dynamic equilibrium in the unit Chemical Equilibrium).
So in the reverse reaction there is also an acid and a base:
CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO⁻(aq) + H₃O⁺(aq)
- Forward: CH₃COOH donates a proton (acid); H₂O accepts it (base).
- Reverse: H₃O⁺ donates a proton (acid); CH₃COO⁻ accepts it (base).
Every Brønsted-Lowry equilibrium therefore has two acids and two bases, and they come in matched pairs.
Conjugate acid-base pairs
When an acid loses a proton, what is left is its conjugate base. When a base gains a proton, it becomes its conjugate acid. The two members of a conjugate pair differ by exactly one H⁺.
- CH₃COOH and CH₃COO⁻ are a conjugate pair (acid and its conjugate base).
- H₂O and H₃O⁺ are a conjugate pair (base and its conjugate acid).
A quick way to label any equation: write acid₁, base₂, base₁, acid₂ under the four species. Acid₁ and base₁ are one pair; base₂ and acid₂ are the other. One pair is always made of one reactant and one product; a pair is never two reactants.
Strong acid, weak conjugate base
Hydrochloric acid gives up its proton completely in water. That means its conjugate base, Cl⁻, has almost no tendency to take a proton back. Chloride is a negligibly weak base: putting NaCl in water does not make it basic.
Acetic acid gives up its proton only partly. That means acetate has a real tendency to take a proton back. Acetate is a weak base, and a solution of sodium acetate is slightly basic.
The general rule: the stronger an acid, the weaker its conjugate base, and the weaker an acid, the stronger its conjugate base. You will make this exact with numbers (Ka × Kb = Kw) in the lesson on weak bases. For now, use the ranking in the figure, which is based on measured equilibrium constants at 25 °C.
Which side does an equilibrium favour?
In a proton-transfer equilibrium, two bases compete for the proton. The stronger base wins most of the time, so the equilibrium favours the side with the weaker acid and the weaker base.
A reliable method:
- Label the acid on each side (the reactant acid and the product acid).
- Find both acids in the table.
- The equilibrium favours the side with the weaker acid. If the reactant acid is stronger, products are favoured (K > 1). If the product acid is stronger, reactants are favoured (K < 1).
The levelling effect
HCl, HBr, HI, HNO₃, HClO₄ and the first proton of H₂SO₄ all react completely with water. In water they all become H₃O⁺, so they look equally strong: water "levels" them. H₃O⁺ is the strongest acid that can exist in water, and in the same way OH⁻ is the strongest base that can exist in water. To tell strong acids apart, chemists use a less basic solvent such as pure acetic acid.
Worked exampleExample 1: Label the conjugate pairs
Identify the conjugate acid-base pairs in HF(aq) + NH₃(aq) ⇌ F⁻(aq) + NH₄⁺(aq).
- HF loses a proton and becomes F⁻: HF is acid₁ and F⁻ is base₁.
- NH₃ gains a proton and becomes NH₄⁺: NH₃ is base₂ and NH₄⁺ is acid₂.
- Check that each pair differs by exactly one H⁺: HF/F⁻ ✓; NH₄⁺/NH₃ ✓.
Pairs: HF / F⁻ and NH₄⁺ / NH₃.
Worked exampleExample 2: Which side is favoured?
Predict whether reactants or products are favoured: HSO₄⁻(aq) + CO₃²⁻(aq) ⇌ SO₄²⁻(aq) + HCO₃⁻(aq).
- Reactant acid: HSO₄⁻. Product acid: HCO₃⁻ (it can give the proton back to SO₄²⁻).
- In the table, HSO₄⁻ is much higher (stronger) than HCO₃⁻.
- The equilibrium favours the side with the weaker acid, which is the product side.
- Check with the bases: CO₃²⁻ (reactant base) is a stronger base than SO₄²⁻ (product base), so the proton ends up on carbonate. Same answer.
Products are favoured (K > 1).
Worked exampleExample 3: A reaction that hardly goes
Predict whether reactants or products are favoured: CH₃COOH(aq) + F⁻(aq) ⇌ CH₃COO⁻(aq) + HF(aq).
- Reactant acid: CH₃COOH. Product acid: HF.
- In the table, HF is above CH₃COOH, so HF is the stronger acid.
- The weaker acid, CH₃COOH, is on the reactant side, so reactants are favoured.
Reactants are favoured (K < 1). Fluoride is too weak a base to pull many protons off acetic acid.
Just for funAn acid and its conjugate base walk into a café. The barista says, "You two look almost identical." They answer, "We are. There's just one proton between us."
Hands-on activityProton tug-of-war cards
You need: 18 small pieces of paper or index cards, a pen, and the strength ladder in this lesson.
- Write each of the 9 acids from the ladder on its own card, and each of the 9 conjugate bases on its own card. (Water and HCO₃⁻ each appear once in each pile, because both are amphiprotic. That is fine.)
- Shuffle each pile separately. Draw one acid card and one base card.
- Write the proton-transfer equation: the acid gives one H⁺ to the base. For example, HF + CO₃²⁻ ⇌ F⁻ + HCO₃⁻.
- Label acid₁, base₁, base₂, acid₂, and join the conjugate pairs.
- Predict which side is favoured using the ladder. Record the prediction.
- Repeat for 8 draws. If you draw an acid with its own conjugate base (for example HF with F⁻), the "reaction" just swaps them; note that nothing changes.
- Find the pattern: when is the reactant acid above the reactant base's conjugate acid on the ladder?
What to look for: products are favoured whenever the acid card sits higher on the ladder than the conjugate acid of the base card. For HF + CO₃²⁻: HF is above HCO₃⁻, so products are favoured. A partner can check each equation's charges, which must balance.
Your turn
1Write the conjugate base of (a) HNO₂ (b) H₂PO₄⁻ (c) NH₄⁺ (d) H₂O.
Remove one H⁺: (a) NO₂⁻ (b) HPO₄²⁻ (c) NH₃ (d) OH⁻.
2Write the conjugate acid of (a) HCOO⁻ (b) HPO₄²⁻ (c) CH₃NH₂ (d) H₂O.
Add one H⁺: (a) HCOOH (b) H₂PO₄⁻ (c) CH₃NH₃⁺ (d) H₃O⁺.
3Identify both conjugate pairs: H₂CO₃(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + H₃O⁺(aq).
H₂CO₃ / HCO₃⁻ and H₃O⁺ / H₂O.
4Identify both conjugate pairs: NH₄⁺(aq) + OH⁻(aq) ⇌ NH₃(aq) + H₂O(l).
NH₄⁺ / NH₃ and H₂O / OH⁻.
5Is Cl⁻ a stronger or weaker base than F⁻? Explain using their conjugate acids.
Weaker. HCl is a strong acid and HF is a weak acid. The stronger the acid, the weaker its conjugate base, so Cl⁻ is the weaker base.
6Predict which side is favoured: NH₄⁺(aq) + CO₃²⁻(aq) ⇌ NH₃(aq) + HCO₃⁻(aq).
Reactant acid NH₄⁺, product acid HCO₃⁻. On the ladder NH₄⁺ is above (stronger than) HCO₃⁻, so the weaker acid is on the product side: products are favoured.
More practice: warm-up
1How many protons separate the two members of a conjugate pair?
2What is the conjugate base of HCl?
3What is the conjugate acid of NH₃?
4What is the strongest acid that can exist in water?
5True or false: a pair of conjugates can be two reactants.
False. One member of each pair is a reactant and the other is a product.
More practice: on your own
1Label acid₁, base₂, base₁, acid₂: HCN(aq) + CH₃COO⁻(aq) ⇌ CN⁻(aq) + CH₃COOH(aq).
Acid₁ HCN, base₂ CH₃COO⁻, base₁ CN⁻, acid₂ CH₃COOH. Pairs HCN/CN⁻ and CH₃COOH/CH₃COO⁻.
2HCN is a weaker acid than CH₃COOH. Which side does the equilibrium in the previous question favour? Explain.
The equilibrium favours the side with the weaker acid. HCN (reactant) is weaker than CH₃COOH (product), so reactants are favoured.
3Use the ladder to predict the favoured side: HF(aq) + OH⁻(aq) ⇌ F⁻(aq) + H₂O(l).
Reactant acid HF; product acid H₂O. HF is far stronger than H₂O, so products are favoured (in fact, almost completely: this is a neutralization).
4Explain the levelling effect in your own words, using HCl and HNO₃ as examples.
Both HCl and HNO₃ donate their protons to water completely, so each solution really contains H₃O⁺. Whatever their "true" strengths, in water both behave as H₃O⁺ and seem equally strong. Water levels them to the strength of H₃O⁺.
5Rank these bases from strongest to weakest using the ladder: F⁻, OH⁻, CH₃COO⁻, Cl⁻.
Conjugate acids from weakest to strongest are H₂O, CH₃COOH, HF, HCl, so the bases rank OH⁻ > CH₃COO⁻ > F⁻ > Cl⁻.
Challenge
1HCO₃⁻ appears on both sides of the ladder. Write one equation where it acts as an acid toward OH⁻ and one where it acts as a base toward CH₃COOH, and predict the favoured side of each.
Acid: HCO₃⁻ + OH⁻ ⇌ CO₃²⁻ + H₂O. Reactant acid HCO₃⁻ is stronger than product acid H₂O: products favoured. Base: CH₃COOH + HCO₃⁻ ⇌ CH₃COO⁻ + H₂CO₃. Reactant acid CH₃COOH is stronger than product acid H₂CO₃: products favoured (and H₂CO₃ then breaks down to CO₂ and water, which is why vinegar fizzes with baking soda).
2Two acids HA and HB have conjugate bases A⁻ and B⁻. The equilibrium HA + B⁻ ⇌ A⁻ + HB has K = 2.5 × 10⁴. Which acid is stronger, and which conjugate base is stronger? Explain.
K ≫ 1 means products are favoured, so the product side holds the weaker acid and weaker base. HA is the stronger acid (HB is weaker), and therefore B⁻ is the stronger base (A⁻ is weaker).
3Why can't you rank HCl and HBr in water, but you can rank them in pure (glacial) acetic acid as the solvent?
Water is a strong enough base to take the proton completely from both, so both appear 100% ionized (levelled). Acetic acid is a much weaker base than water, so neither acid ionizes completely in it; the one that ionizes to a greater extent (HBr) is shown to be stronger.
Quiz
1. What is the conjugate base of H₂PO₄⁻?
2. In NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq), which is a conjugate acid-base pair?
4. A proton-transfer equilibrium favours the side that has
5. Using the strength ladder, which side is favoured in CH₃COOH(aq) + CO₃²⁻(aq) ⇌ CH₃COO⁻(aq) + HCO₃⁻(aq)?
6. Why do HCl and HNO₃ appear equally strong in water?
Big idea (E3.6, E3.7): every Brønsted-Lowry reaction contains two conjugate pairs that differ by one proton. The stronger an acid, the weaker its conjugate base, and an equilibrium favours the side with the weaker acid and weaker base.
How to help: Ask your teen to say each conjugate pair out loud as "___ loses a proton to become ___". Use the card activity: draw two cards and ask which way the reaction goes and why. They should point to the ladder and compare the two acids.
Common difficulties:
- Pairing two reactants (such as acid₁ with base₂). A pair is always one reactant and one product.
- Changing the formula but forgetting the charge, or changing by two protons instead of one.
- Comparing the wrong two species: compare the acid on the left with the acid on the right.
- Thinking "weak conjugate base" means "slightly basic". The conjugate bases of strong acids (Cl⁻, NO₃⁻) are so weak they have no effect on pH.