Arrhenius Acids and Bases

In 1884 a 25-year-old Swedish student submitted a doctoral thesis that his examiners almost failed. Svante Arrhenius claimed that when salts, acids and bases dissolve in water, they split into electrically charged particles, even before any electric current is passed through them. Many chemists found this absurd. Nineteen years later the same idea won him the 1903 Nobel Prize in Chemistry.

His theory of electrolytic dissociation gave chemistry its first clear, modern definition of acids and bases. It is still the version most students meet first, and understanding it well makes the later definitions much easier.

The Arrhenius definitions

• An Arrhenius acid is a substance that increases the concentration of hydrogen ions (H⁺) when dissolved in water.
• An Arrhenius base is a substance that increases the concentration of hydroxide ions (OH⁻) when dissolved in water.

That’s it. Both definitions are tied to water and to two specific ions.

Arrhenius acids in action

Hydrogen chloride dissolves and dissociates:

HCl(aq) → H⁺(aq) + Cl⁻(aq)

Nitric acid does the same:

HNO₃(aq) → H⁺(aq) + NO₃⁻(aq)

Sulfuric acid can release two hydrogen ions per molecule, in two steps:

H₂SO₄(aq) → H⁺(aq) + HSO₄⁻(aq) HSO₄⁻(aq) ⇌ H⁺(aq) + SO₄²⁻(aq)

The first step is complete; the second only goes partly. Acids that can release more than one proton are called polyprotic.

Ethanoic acid, the acid in vinegar, is an Arrhenius acid too, but it only partly dissociates:

CH₃COOH(aq) ⇌ CH₃COO⁻(aq) + H⁺(aq)

Arrhenius bases in action

Sodium hydroxide dissolves and its ions separate:

NaOH(s) → Na⁺(aq) + OH⁻(aq)

Calcium hydroxide does the same, releasing two hydroxide ions per formula unit:

Ca(OH)₂(s) → Ca²⁺(aq) + 2OH⁻(aq)

In the Arrhenius picture, the typical base is a metal hydroxide.

Neutralisation in the Arrhenius model

If acids supply H⁺ and bases supply OH⁻, neutralisation is simply those two ions combining:

H⁺(aq) + OH⁻(aq) → H₂O(l)

The other ions (for example Na⁺ and Cl⁻ from sodium hydroxide and hydrochloric acid) are left in solution unchanged. They’re spectator ions, and if you evaporate the water they crystallise out together as a salt.

This explained a puzzling experimental fact. When chemists measured the heat released by neutralising different strong acids with different strong bases, they kept getting almost the same value, about 57 kJ per mole of water formed. Arrhenius’s theory explained why: whichever strong acid and strong base you use, the reaction that actually happens is always H⁺ + OH⁻ → H₂O.

Strong and weak electrolytes

Arrhenius’s work also explained why some acid solutions conduct electricity much better than others of the same concentration.

• Hydrochloric acid at 0.1 mol/dm³ conducts strongly because almost every HCl molecule has become ions.
• Ethanoic acid at 0.1 mol/dm³ conducts weakly because only about 1% of the molecules have dissociated.

This is the origin of the terms strong acid and weak acid. It was Arrhenius who first linked strength to the degree of dissociation. Our guide to strong vs weak acids builds on this.

The evidence that convinced chemists

Arrhenius didn’t just assert that ions exist in solution; he pointed to measurements that nobody else could explain. When you dissolve a substance in water, the freezing point drops by an amount that depends on the number of dissolved particles, not their identity. One mole of sugar lowers the freezing point of a kilogram of water by about 1.86 °C. One mole of sodium chloride lowers it by almost twice as much, and one mole of calcium chloride by almost three times as much.

If salts stayed as intact units, those numbers would make no sense. If sodium chloride splits into two ions and calcium chloride into three, they fit neatly. Jacobus van ’t Hoff had measured these “abnormal” results; Arrhenius supplied the reason. The same argument applied to acids: hydrochloric acid behaved as if it contained two particles per formula unit, while ethanoic acid behaved as if it were barely dissociated at all.

Worked examples: classify these substances

1. HBr dissolved in water. HBr → H⁺ + Br⁻. It increases [H⁺], so it’s an Arrhenius acid.

2. KOH dissolved in water. KOH → K⁺ + OH⁻. It increases [OH⁻], so it’s an Arrhenius base.

3. CH₄ (methane) bubbled into water. Methane barely dissolves and releases neither H⁺ nor OH⁻. Neither, even though it contains hydrogen.

4. NaCl dissolved in water. NaCl → Na⁺ + Cl⁻. No change in [H⁺] or [OH⁻]. Neither; it’s a neutral salt.

5. NH₃ dissolved in water. This is the awkward one. Ammonia contains no hydroxide, yet its solution is alkaline. Strictly, Arrhenius’s definition works only if you allow ammonia to react with water first: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. Early chemists invented a substance called “ammonium hydroxide”, NH₄OH, to force ammonia into the Arrhenius mould. No such molecule has ever been isolated. The problem is better solved by the Brønsted–Lowry definition.

Where the Arrhenius definition breaks down

The theory was a huge step forward, but it has three clear limits.

1. It only works in water. Hydrogen chloride and ammonia react in the gas phase to form a white smoke of ammonium chloride:

HCl(g) + NH₃(g) → NH₄Cl(s)

A proton has moved from HCl to NH₃, so this is obviously an acid–base reaction. But there’s no water, no H⁺(aq) and no OH⁻(aq), so the Arrhenius definition can’t describe it.

2. It can’t explain bases without hydroxide. Ammonia, amines, carbonate ions and ethanoate ions all make water alkaline without containing OH⁻.

3. It ignores the role of water. H⁺ doesn’t really float free in water; it’s attached to a water molecule as H₃O⁺. Water is an active participant, not just a backdrop.

The Brønsted–Lowry theory (1923) fixes all three problems by defining acids as proton donors and bases as proton acceptors, in any medium. The Lewis theory goes further still, dealing with electron pairs rather than protons. Compare all three in acid–base definitions.

Why we still teach Arrhenius

If the theory has limits, why start with it? Because for the huge majority of practical chemistry, which happens in water with common acids and hydroxides, it gives exactly the right answers with the simplest possible picture. It’s also the direct basis of pH: pH measures hydrogen ion concentration in water, which is an Arrhenius idea through and through.

Think of the three definitions like maps at different scales. The Arrhenius map covers the familiar neighbourhood of aqueous chemistry very clearly. You only need the bigger maps when you travel further.

Quick self-check

1. Write the dissociation equation for lithium hydroxide in water.
2. Why is the heat of neutralisation nearly the same for HCl + NaOH and HNO₃ + KOH?
3. Give one reaction that the Arrhenius definition cannot classify.

Answers: (1) LiOH → Li⁺ + OH⁻. (2) Both are really H⁺ + OH⁻ → H₂O; the other ions are spectators. (3) The gas-phase reaction HCl + NH₃ → NH₄Cl.

Key takeaways

• Arrhenius acids increase [H⁺] in water; Arrhenius bases increase [OH⁻] in water.
• Neutralisation is H⁺ + OH⁻ → H₂O, with the other ions forming a salt.
• The theory explained electrical conductivity, strong vs weak acids, and the constant heat of neutralisation.
• It fails for non-aqueous reactions and for bases like ammonia, which is why the Brønsted–Lowry definition was developed.
• See how H⁺ concentration becomes a pH value, or try the pH calculator.