Brønsted–Lowry Theory and Conjugate Acid-Base Pairs

In the Brønsted-Lowry theory, an acid is a proton (H⁺) donor and a base is a proton acceptor, and every acid-base reaction involves two conjugate pairs: an acid and its conjugate base (formed when the acid loses a proton), and a base and its conjugate acid (formed when the base gains a proton). In brief: in NH₃ + H₂O ⇌ NH₄⁺ + OH⁻, water donates a proton (acid) and ammonia accepts it (base); the conjugate pairs are NH₄⁺/NH₃ and H₂O/OH⁻, and the stronger an acid is, the weaker its conjugate base.

The Brønsted-Lowry definition is wider than the Arrhenius definition. It does not need water as a solvent, and it explains why ammonia and carbonate are bases, why water can act as an acid or a base and which direction a reaction will go. This article explains the definitions, how to identify conjugate pairs, the idea of amphiprotic species, the relation between the strengths of conjugate acids and bases, a table of common conjugate pairs, worked examples that predict the direction of reactions and a short history.

What are the Brønsted-Lowry definitions?

Brønsted-Lowry acid: a molecule or ion that donates a proton (H⁺) to another species.
Brønsted-Lowry base: a molecule or ion that accepts a proton. To accept a proton, the base must have a lone pair of electrons that can form a bond to H⁺.

An acid-base reaction is a transfer of a proton from the acid to the base. For example, in water, HCl + H₂O → H₃O⁺ + Cl⁻: HCl is the acid (donor), and water is the base (acceptor). The reaction CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO⁻ shows a weak acid, so the reaction does not go to completion, as shown by the double arrow.

What are conjugate acid-base pairs?

A conjugate pair differs by one proton: the acid has one more H⁺ than its conjugate base. In HA + B ⇌ A⁻ + HB⁺, the pairs are HA/A⁻ and HB⁺/B. To find the conjugate base of an acid, remove one H⁺ (the charge decreases by 1). To find the conjugate acid of a base, add one H⁺ (the charge increases by 1).

What are amphiprotic substances?

An amphiprotic (or amphoteric) species can act as an acid or a base, depending on the other reactant. Water is the best-known case: with HCl it accepts a proton (base), and with NH₃ it donates one (acid). The anions of polyprotic acids with a hydrogen still attached, such as HCO₃⁻, HSO₄⁻, H₂PO₄⁻ and HPO₄²⁻, are also amphiprotic. For HCO₃⁻: as an acid, HCO₃⁻ + H₂O ⇌ CO₃²⁻ + H₃O⁺, and as a base, HCO₃⁻ + H₂O ⇌ H₂CO₃ + OH⁻.

How are the strengths of conjugate pairs related?

The stronger an acid, the weaker its conjugate base, and vice versa. A strong acid, such as HCl, has a conjugate base (Cl⁻) that has almost no tendency to accept a proton. A weak acid, such as HCN, has a conjugate base (CN⁻) that is a fairly strong base. For a conjugate pair in water, K_a × K_b = K_w = 1.0 × 10⁻¹⁴ at 25 °C, or pK_a + pK_b = 14.00. A proton transfer reaction favors the formation of the weaker acid and the weaker base. This is the rule used to predict the direction of the reaction.

Common conjugate pairs

Conjugate acid-base pairs, from strong acids to weak acids
Acid	Conjugate base	pK_a of the acid	Strength of the acid
HCl	Cl⁻	about −6	Strong
H₃O⁺	H₂O	−1.74	Strongest acid in water
HF	F⁻	3.17	Weak
CH₃COOH	CH₃COO⁻	4.76	Weak
H₂CO₃	HCO₃⁻	6.35	Weak
NH₄⁺	NH₃	9.25	Very weak
HCN	CN⁻	9.21	Very weak
HCO₃⁻	CO₃²⁻	10.33	Very weak
H₂O	OH⁻	15.74	Extremely weak

Worked examples

Identify the conjugate pairs. HSO₄⁻ + CO₃²⁻ ⇌ SO₄²⁻ + HCO₃⁻. HSO₄⁻ donates a proton, so it is the acid, and SO₄²⁻ is its conjugate base. CO₃²⁻ accepts a proton, so it is the base, and HCO₃⁻ is its conjugate acid.
Conjugate base of an acid. The conjugate base of H₂PO₄⁻ is HPO₄²⁻. The conjugate base of H₂O is OH⁻. The conjugate base of NH₃ (acting as an acid) is NH₂⁻.
Conjugate acid of a base. The conjugate acid of NH₃ is NH₄⁺. The conjugate acid of CO₃²⁻ is HCO₃⁻. The conjugate acid of H₂O (as a base) is H₃O⁺.
Predict the direction. HF + CN⁻ ⇌ F⁻ + HCN. HF (pK_a 3.17) is a stronger acid than HCN (pK_a 9.21), and CN⁻ is a stronger base than F⁻. The equilibrium favors the products. K = 10^{(9.21 − 3.17)} = 10^6.04 = 1.1 × 10⁶.
The reverse case. HCN + F⁻ ⇌ CN⁻ + HF has K = 10^−6.04 = 9 × 10⁻⁷, so it hardly proceeds.
Find K_b of a conjugate base. For acetic acid, K_a = 1.8 × 10⁻⁵, so the acetate ion has K_b = K_w ÷ K_a = 1.0 × 10⁻¹⁴ ÷ 1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰.
Amphiprotic water. In 2H₂O ⇌ H₃O⁺ + OH⁻, one water molecule acts as the acid (conjugate base OH⁻) and the other as the base (conjugate acid H₃O⁺).

How does Brønsted-Lowry compare with Arrhenius?

Arrhenius and Brønsted-Lowry definitions compared
Feature	Arrhenius	Brønsted-Lowry
Acid	Produces H⁺ in water	Proton donor
Base	Produces OH⁻ in water	Proton acceptor
Solvent	Water only	Any solvent or gas phase
NH₃ as a base	Needs NH₄OH	Accepts H⁺ directly
Conjugate pairs	Not defined	Central idea
Amphoteric behavior	Limited	Explains water and HCO₃⁻

Who developed the theory?

The Danish chemist Johannes Nicolaus Brønsted and the English chemist Thomas Martin Lowry proposed the definition independently in 1923, within a few weeks of each other. Brønsted’s work was in the context of the catalysis of reactions by acids and bases, and he emphasized the idea of conjugate pairs. The theory was particularly useful in explaining reactions in solvents other than water and gave a better quantitative basis for acid and base strengths. Gilbert N. Lewis proposed his wider definition in the same year.

Which mistakes are common?

Mistake 1: Changing the charge by the wrong amount

A conjugate pair differs by one proton: the acid has a charge one unit more positive than its conjugate base.

Mistake 2: Treating water as only a solvent

Water takes part: it accepts or donates a proton in many reactions.

Mistake 3: Writing a conjugate base by removing an atom other than H⁺

Remove just one proton. The conjugate base of H₂SO₄ is HSO₄⁻, not SO₄²⁻.

Mistake 4: Expecting the strong acid to have a strong conjugate base

The conjugate base of a strong acid is a very weak base, and the conjugate acid of a strong base is a very weak acid.