Brønsted–Lowry theory of acids and bases

1. Overview

In the Brønsted-Lowry theory, an acid gives away a proton (an H⁺ ion) and a base takes one in. This section covers the common acids and alkalis, strong and weak acids, the pH scale, neutralisation and salts, and how pH changes during a titration, which decides the indicator to use. It is the AS base for the pH and buffer calculations at A Level (topic 25.1).

Key Definitions

• Brønsted-Lowry acid: a species that donates a proton (an H⁺ ion) to another species.
• Brønsted-Lowry base: a species that accepts a proton (an H⁺ ion) from another species.
• Alkali: a base that dissolves in water to give hydroxide ions, OH⁻(aq); the common alkalis are sodium hydroxide, potassium hydroxide and ammonia.
• Strong acid: an acid that is fully dissociated into ions in aqueous solution, for example hydrochloric acid, HCl(aq) → H⁺(aq) + Cl⁻(aq).
• Weak acid: an acid that is only partially dissociated into ions in aqueous solution, so the solution holds an equilibrium mixture of acid molecules and ions, for example ethanoic acid.
• Weak base: a base that is only partially dissociated in aqueous solution; in aqueous ammonia only a small fraction of the NH₃ molecules react with water to form NH₄⁺ and OH⁻ ions, whereas a strong base such as sodium hydroxide is fully dissociated.
• Neutralisation: the reaction of an acid with an alkali, in which H⁺(aq) ions and OH⁻(aq) ions combine to form water, H₂O(l), and a salt is formed.
• Salt: an ionic compound formed when one or more of the H⁺ ions that an acid can donate are replaced by metal ions or ammonium ions, as happens in neutralisation.
• Equivalence point: the point in a titration at which the acid and the alkali have been mixed in exactly the amounts shown by the balanced equation, so neither is in excess.
• End point: the point in a titration at which the indicator changes colour; a suitable indicator gives an end point at the same volume as the equivalence point.

Content

The common acids and alkalis

Acid	Formula	Strong or weak	H⁺ ions donated per formula	Salts it forms
hydrochloric acid	HCl	strong	1	chlorides, e.g. NaCl
nitric acid	HNO₃	strong	1	nitrates, e.g. KNO₃
sulfuric acid	H₂SO₄	strong	2	sulfates, e.g. Na₂SO₄, and hydrogensulfates, e.g. NaHSO₄
ethanoic acid	CH₃COOH	weak	1	ethanoates, e.g. CH₃COONa

Ethanoic acid donates only the H of its -COOH group. The three H atoms of the CH₃ group are bonded to carbon and are not acidic.

Alkali	Formula	Strong or weak	Source of OH⁻(aq)
sodium hydroxide	NaOH	strong	fully dissociated into Na⁺(aq) and OH⁻(aq)
potassium hydroxide	KOH	strong	fully dissociated into K⁺(aq) and OH⁻(aq)
ammonia	NH₃	weak	a small fraction of the molecules react with water: NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

Aqueous ammonia is sometimes labelled "ammonium hydroxide", but write it as NH₃(aq).

The Brønsted-Lowry theory

Every acid-base reaction is a proton transfer: an acid is a proton donor and a base is a proton acceptor. To accept the proton, a base needs a lone pair of electrons, which forms a new dative covalent bond.

When hydrogen chloride dissolves, it donates a proton to water. HCl is the acid and H₂O the base:

HCl(g) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq)

H₃O⁺ is the oxonium ion (also called the hydroxonium ion); H⁺(aq) is shorthand for it, and you may write either. With ammonia, water plays the opposite part: it donates a proton, and NH₃ accepts it with its lone pair:

NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

So water can act as an acid or a base, depending on its partner. The theory does not need water at all: in NH₃(g) + HCl(g) → NH₄Cl(s), HCl donates a proton straight to NH₃, giving white smoke.

What an acid becomes. Once an acid has donated its proton, what is left could accept one back, so it is a base: HCl gives Cl⁻, and NH₄⁺ gives NH₃. To find it, remove one H and lower the charge by one: H₂SO₄ becomes HSO₄⁻, not HSO₄ or SO₄²⁻. Two species that differ by one H⁺ like this are called a conjugate acid-base pair; that name and its uses come at A Level (topic 25.1).

Worked example 1: spotting the acid and the base

Question: For each forward reaction, identify the Brønsted-Lowry acid and base.

(a) HSO₄⁻(aq) + H₂O(l) ⇌ SO₄²⁻(aq) + H₃O⁺(aq)

(b) CO₃²⁻(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + OH⁻(aq)

(c) NH₄⁺(aq) + H₂O(l) ⇌ NH₃(aq) + H₃O⁺(aq)

Step 1: track the proton. The species that loses one H⁺ is the acid; the one that gains it is the base.

• (a) HSO₄⁻ loses H⁺ (to SO₄²⁻); H₂O gains it (to H₃O⁺).
• (b) H₂O loses H⁺ (to OH⁻); CO₃²⁻ gains it (to HCO₃⁻).
• (c) NH₄⁺ loses H⁺ (to NH₃); H₂O gains it (to H₃O⁺).

Step 2: check the charges. (a) −1 + 0 = −2 + 1; (b) −2 + 0 = −1 + (−1); (c) +1 + 0 = 0 + 1.

Answer: acids: (a) HSO₄⁻, (b) H₂O, (c) NH₄⁺; bases: (a) H₂O, (b) CO₃²⁻, (c) H₂O. Water is a base in (a) and (c) but an acid in (b). Reaction (c) shows that the ammonium ion is a weak acid, which matters for titration curves.

Strong and weak acids and bases

Strength is how far an acid or base dissociates into ions in aqueous solution.

A strong acid is fully dissociated, so write a single arrow:

HCl(aq) → H⁺(aq) + Cl⁻(aq) HNO₃(aq) → H⁺(aq) + NO₃⁻(aq)

A weak acid is partially dissociated. The equilibrium lies well to the left, so write ⇌. In 0.1 mol dm⁻³ ethanoic acid, only about 1% of the molecules are dissociated at any moment:

CH₃COOH(aq) ⇌ CH₃COO⁻(aq) + H⁺(aq)

Sulfuric acid donates its first proton completely, H₂SO₄(aq) → H⁺(aq) + HSO₄⁻(aq). The second, from HSO₄⁻, is only partly donated in water, but an alkali removes both, so 1 mol of H₂SO₄ neutralises 2 mol of NaOH.

NaOH and KOH are strong bases, fully dissociated in solution. Ammonia is a weak base: in 0.1 mol dm⁻³ NH₃(aq), only about 1% of the molecules have reacted with water at any moment.

Strong is not concentrated. Concentration is how much acid is dissolved per dm³. A concentrated weak acid can have a higher concentration of H⁺(aq) than a dilute strong acid: 1 mol dm⁻³ ethanoic acid has a lower pH than 0.001 mol dm⁻³ hydrochloric acid.

Dissociated is not dissolved. Ethanoic acid mixes with water in all proportions; only its splitting into ions is partial.

The pH scale

pH shows how acidic or alkaline a solution is: the higher the concentration of H⁺(aq), the lower the pH.

• Pure water has pH 7 at 298 K. It dissociates very slightly, H₂O(l) ⇌ H⁺(aq) + OH⁻(aq), giving equal, tiny concentrations of the two ions, so it is neutral.
• Acidic solutions have pH below 7: more H⁺(aq) than OH⁻(aq).
• Alkaline solutions have pH above 7: more OH⁻(aq) than H⁺(aq).

Each fall of one pH unit means ten times the concentration of H⁺(aq). Calculating pH comes at A Level; at AS you compare values. Pure water is neutral at any temperature, but its pH is exactly 7 only at 298 K.

How strong and weak acids behave differently

Compare solutions of the same concentration, for example 0.10 mol dm⁻³ HCl and 0.10 mol dm⁻³ CH₃COOH. Square brackets mean concentration in mol dm⁻³, so [H⁺(aq)] is the concentration of H⁺(aq). The weak acid is only partially dissociated, so its [H⁺(aq)] is much lower, and every difference below follows from that.

Test	Strong acid (HCl)	Weak acid (CH₃COOH)	Why
pH meter	about 1	about 3	lower [H⁺(aq)] gives a higher pH
universal indicator	red	orange	the same reason, shown roughly
conductivity	high	much lower	fewer ions to carry the current
magnesium ribbon	rapid effervescence	slow effervescence	fewer H⁺(aq) ions, so fewer collisions per second with the metal
total H₂ from equal volumes, excess Mg	the same	the same	see below

The universal indicator colours are those of a typical colour chart. Shades vary between brands, so always match the colour to the chart supplied.

Both acids react with magnesium as Mg(s) + 2H⁺(aq) → Mg²⁺(aq) + H₂(g); with ethanoic acid the salt is magnesium ethanoate, (CH₃COO)₂Mg.

Why the total is the same. As H⁺(aq) is used up, the equilibrium CH₃COOH ⇌ CH₃COO⁻ + H⁺ shifts to the right (topic 7.1), so more acid dissociates until every proton has reacted. A weak acid reacts more slowly, but just as completely. Carbonates show the same pattern: slower effervescence, same total CO₂.

In a practical, record effervescence (fizzing), not "gas given off", and test the gas: hydrogen gives a squeaky pop with a lighted splint.

Worked example 2: magnesium with a strong and a weak acid

Question: One flask holds 50.0 cm³ of 0.200 mol dm⁻³ hydrochloric acid and another 50.0 cm³ of 0.200 mol dm⁻³ ethanoic acid. Excess magnesium ribbon is added to each. (a) Compare the initial rates of effervescence. (b) Calculate the total volume of hydrogen from each flask at room conditions ($V_{\text{m}}$ = 24.0 dm³ mol⁻¹). (c) Predict the volume from 50.0 cm³ of 0.200 mol dm⁻³ sulfuric acid.

(a) HCl is fully dissociated, so [H⁺(aq)] = 0.200 mol dm⁻³. Ethanoic acid is partially dissociated, so its [H⁺(aq)] is far lower, fewer H⁺ ions hit the magnesium each second, and it fizzes much more slowly.

(b) Step 1: amount of each acid. $$n = cV = 0.200 \times \frac{50.0}{1000} = 0.0100\ \text{mol}$$

Step 2: use the equation. 2 mol of H⁺ give 1 mol of H₂, and 1 mol of either acid supplies 1 mol of H⁺: $$n(\text{H}_2) = \frac{0.0100}{2} = 0.00500\ \text{mol}$$

Step 3: convert to a volume. $$V = n \times V_{\text{m}} = 0.00500 \times 24.0 = 0.120\ \text{dm}^3 = 120\ \text{cm}^3$$

Answer: 120 cm³ from each flask (3 s.f.); the ethanoic acid just takes longer.

(c) 1 mol of H₂SO₄ supplies 2 mol of H⁺, so $n(\text{H}^+) = 0.0200$ mol and $n(\text{H}_2) = 0.0100$ mol.

Answer: $V = 0.0100 \times 24.0 = 0.240$ dm³ = 240 cm³ (3 s.f.).

Neutralisation and salts

When an acid reacts with an alkali, H⁺(aq) from the acid and OH⁻(aq) from the alkali form water:

H⁺(aq) + OH⁻(aq) → H₂O(l)

This is neutralisation. The other ions, such as K⁺(aq) and NO₃⁻(aq), are spectator ions: they take no part, and together they make up the salt.

• KOH(aq) + HNO₃(aq) → KNO₃(aq) + H₂O(l)
• H₂SO₄(aq) + 2NaOH(aq) → Na₂SO₄(aq) + 2H₂O(l)
• H₂SO₄(aq) + NaOH(aq) → NaHSO₄(aq) + H₂O(l), with half as much alkali: the salt is sodium hydrogensulfate.

With a weak acid the ionic equation is still H⁺(aq) + OH⁻(aq) → H₂O(l): as OH⁻ removes H⁺, more acid dissociates, just as with magnesium, until all of it has reacted. CH₃COOH(aq) + OH⁻(aq) → CH₃COO⁻(aq) + H₂O(l) is also correct; it shows that the acid starts mostly as molecules. With ammonia the salt is an ammonium salt, NH₃(aq) + HCl(aq) → NH₄Cl(aq); overall, NH₃(aq) + H⁺(aq) → NH₄⁺(aq). Neutralisation is exothermic; its enthalpy change is in topic 5.1.

pH titration curves

A pH meter records the pH as alkali is added from a burette to a fixed volume of acid. A plot of pH against volume added is a pH titration curve. Every sketch needs four features:

1. Starting pH: about 1 for a 0.1 mol dm⁻³ strong acid, about 3 for 0.1 mol dm⁻³ ethanoic acid.
2. A gradual rise. With a weak acid, the pH rises quickly at first, then flattens into a gentle slope, because the mixture of weak acid and its salt resists change (a buffer, topic 25.1).
3. A steep, almost vertical section centred on the equivalence volume (none for weak acid with weak alkali).
4. Levelling off once the alkali is in excess, always below the pH of the alkali itself: about 12 to 13 with 0.1 mol dm⁻³ NaOH, only about 9 with 0.1 mol dm⁻³ ammonia.

The curves below are for 20.0 cm³ of 0.100 mol dm⁻³ acid with 0.100 mol dm⁻³ alkali, so the equivalence point is at 20.0 cm³.

Acid + alkali	Starting pH	Steep section	pH at equivalence	Final pH
strong + strong (HCl + NaOH)	about 1	about 3 to 11	7	about 12 to 13
strong + weak (HCl + NH₃)	about 1	about 3 to 7	below 7 (about 5)	about 9
weak + strong (CH₃COOH + NaOH)	about 3	about 7 to 11	above 7 (about 9)	about 12 to 13
weak + weak (CH₃COOH + NH₃)	about 3	none	about 7	about 9

For strong + strong, one drop (about 0.05 cm³) either side of the equivalence point takes the pH from about 4 to about 10. More dilute solutions give a shorter steep section. If the acid is added to the alkali instead, the curve is flipped: it starts high and falls.

Why the equivalence point is not always at pH 7. At that point the flask holds just the salt in water:

• Strong + strong: in NaCl(aq), neither Na⁺ nor Cl⁻ reacts with water, so the pH is 7.
• Weak acid + strong alkali: the ethanoate ion is a base, CH₃COO⁻(aq) + H₂O(l) ⇌ CH₃COOH(aq) + OH⁻(aq), so the pH is above 7.
• Strong acid + weak alkali: the ammonium ion is a weak acid (Worked example 1(c)), so the pH is below 7.
• Weak + weak: both ions react slightly with water; for ammonium ethanoate the effects almost cancel.

Why weak + weak has no steep section. Just before the equivalence point the pH has already risen to about 6, because the acid is weak. Just after it, the weak alkali adds mostly NH₃ molecules and few OH⁻ ions, so the pH reaches only about 8. There is no big gap to jump across.

Choosing an indicator

An indicator is a weak acid whose two forms have different colours, and it changes colour over a narrow pH range. A question gives you the ranges, for example:

Indicator	pH range of colour change
methyl orange (red in acid, yellow in alkali)	2.9 to 4.6
bromophenol blue	3.0 to 4.5
thymol blue	8.0 to 9.6
thymolphthalein (colourless in acid, blue in alkali)	9.3 to 10.5

The rule: choose an indicator whose colour-change range lies inside the steep section. Then one drop at the equivalence point carries the pH right through the range, and the colour changes sharply at the correct volume.

Titration	Steep section	Suitable from this table
strong acid + strong alkali	about 3 to 11	any of the four
strong acid + weak alkali	about 3 to 7	methyl orange or bromophenol blue
weak acid + strong alkali	about 7 to 11	thymol blue or thymolphthalein
weak acid + weak alkali	none	none: follow the pH with a pH meter instead

Universal indicator is not suitable for titrations: it changes colour gradually across the whole pH scale, so it has no sharp end point.

Worked example 3: sketching a curve and choosing an indicator

Question: 20.0 cm³ of 0.105 mol dm⁻³ ethanoic acid is titrated with 0.140 mol dm⁻³ potassium hydroxide. (a) Calculate the volume of KOH(aq) at the equivalence point. (b) Describe the curve you would sketch. (c) Using the table above, choose an indicator and explain why methyl orange is unsuitable. (d) Explain why no indicator would work with 0.140 mol dm⁻³ aqueous ammonia instead of the KOH.

(a) Step 1: equation. CH₃COOH(aq) + KOH(aq) → CH₃COOK(aq) + H₂O(l), a 1 : 1 ratio.

Step 2: amount of acid. $$n = cV = 0.105 \times \frac{20.0}{1000} = 2.10 \times 10^{-3}\ \text{mol}$$

Step 3: volume of alkali. $$V = \frac{n}{c} = \frac{2.10 \times 10^{-3}}{0.140} = 0.0150\ \text{dm}^3 = 15.0\ \text{cm}^3$$

Answer: 15.0 cm³ (3 s.f.).

(b) Label the axes pH and volume of KOH added / cm³. Start at about pH 3 (weak acid), rise quickly a little, then slope gently. Draw the steep section at 15.0 cm³ from about pH 7 to about 11, with the equivalence point above 7 because the ethanoate ion is a base. Level off between pH 12 and 13.

(c) Thymolphthalein (9.3 to 10.5) or thymol blue (8.0 to 9.6): each range lies inside the steep section. Methyl orange (2.9 to 4.6) changes colour on the gentle slope, before even half of the 15.0 cm³ has been added, so its end point would come far too early.

Answer: thymolphthalein or thymol blue.

(d) With a weak acid and a weak alkali there is no steep section, so any indicator would change colour gradually over many cm³, with no sharp end point.

Key Equations

Brønsted-Lowry reaction (HA = acid, the proton donor; B = base, the proton acceptor): HA + B → A⁻ + BH⁺

Strong acid (full dissociation, single arrow): HCl(aq) → H⁺(aq) + Cl⁻(aq)

Weak acid (partial dissociation, equilibrium arrow): CH₃COOH(aq) ⇌ CH₃COO⁻(aq) + H⁺(aq)

Weak base: NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)

Neutralisation: H⁺(aq) + OH⁻(aq) → H₂O(l)

Acid with a reactive metal: Mg(s) + 2H⁺(aq) → Mg²⁺(aq) + H₂(g)

Amount in solution ($n$ in mol; $c$ in mol dm⁻³; $V$ in dm³, so divide cm³ by 1000): $$n = cV$$

Equivalence point ($c_{\text{a}}$, $V_{\text{a}}$ for the acid and $c_{\text{b}}$, $V_{\text{b}}$ for the alkali, volumes in the same unit; $x$ = H⁺ ions donated per acid formula, 1 for HCl, HNO₃ and CH₃COOH, 2 for H₂SO₄; NaOH, KOH and NH₃ each take one H⁺): $$x\,c_{\text{a}}V_{\text{a}} = c_{\text{b}}V_{\text{b}}$$

Gas volume at room conditions ($V_{\text{m}}$ = 24.0 dm³ mol⁻¹): $$V = n \times V_{\text{m}}$$

Common Mistakes to Avoid

• Mistake: saying an acid "releases" H⁺, or that a weak acid "gives few H⁺ ions". Fix: an acid is a proton donor, and a weak acid is partially dissociated; few H⁺ ions is the result, not the definition. Write: "ethanoic acid donates protons but is only partially dissociated in aqueous solution".
• Mistake: writing "partially dissolved" for "partially dissociated". Fix: ethanoic acid mixes with water in all proportions; only its splitting into CH₃COO⁻(aq) and H⁺(aq) is partial.
• Mistake: treating strong as concentrated. Fix: strength is the extent of dissociation. 1 mol dm⁻³ ethanoic acid is weak, but it is 1000 times more concentrated than 0.001 mol dm⁻³ hydrochloric acid, and its pH is lower.
• Mistake: saying a weak acid makes less hydrogen with magnesium. Fix: with excess metal, equal amounts of the two acids give the same total (120 cm³ each in Worked example 2); only the rate differs.
• Mistake: getting the formula wrong when an acid loses its proton. Fix: remove one H and lower the charge by one: H₃O⁺ becomes H₂O, NH₄⁺ becomes NH₃ and H₂SO₄ becomes HSO₄⁻.
• Mistake: putting every equivalence point at pH 7. Fix: only strong + strong is at 7; weak acid + strong alkali is above 7 (about 9), strong acid + weak alkali below 7 (about 5).
• Mistake: a sketch with no clear starting pH, the steep section at the wrong volume, or no levelling off. Fix: calculate the equivalence volume first (15.0 cm³ in Worked example 3), centre the vertical section on it, start near 1 for a strong acid or 3 for a weak acid, and level off below the pH of the alkali (about 12 to 13 for NaOH or KOH, about 9 for ammonia).
• Mistake: choosing an indicator because its range "includes 7", or naming universal indicator. Fix: the range must sit inside the steep section. For ethanoic acid with potassium hydroxide, thymolphthalein (9.3 to 10.5) works, but methyl orange (2.9 to 4.6) changes long before the equivalence point.

Exam Tips

• State what a strong or weak Brønsted-Lowry acid is in two parts: "acid" means proton donor, and "strong" or "weak" means fully or partially dissociated in aqueous solution. Give both parts.
• Explain a strong and weak acid difference as a chain: extent of dissociation, then [H⁺(aq)] at the same concentration, then the observation (pH, conductivity or rate of effervescence).
• Identify the acid and base in an equation by tracking which species loses one H⁺ and which gains it; check that the charges balance.
• Sketch a titration curve with labelled axes (pH; volume added / cm³), the right starting pH, a vertical section at the calculated equivalence volume, and a sensible final pH. These features matter, not exact values.
• Select an indicator by naming it and comparing its range with the steep section, for example "thymolphthalein, because 9.3 to 10.5 lies within the steep section, about pH 7 to 11".
• Write equations with state symbols, using → for strong acids and ⇌ for weak acids and ammonia.