Arrhenius Definition of Acids and Bases

According to the Arrhenius definition, an acid is a substance that increases the concentration of hydrogen ions (H⁺) in aqueous solution, and a base is a substance that increases the concentration of hydroxide ions (OH⁻). In brief: HCl is an Arrhenius acid because it ionizes in water, HCl → H⁺ + Cl⁻, and NaOH is an Arrhenius base because it dissociates, NaOH → Na⁺ + OH⁻; neutralization is the reaction H⁺ + OH⁻ → H₂O.

The Arrhenius theory was the first successful definition of acids and bases in terms of ions, and it is still the basis for general chemistry. It is limited to aqueous solutions, and later theories extended it. This article explains the definitions, gives examples of acids and bases with their dissociation equations, explains the meaning of H⁺ and H₃O⁺, describes neutralization as seen by Arrhenius, works through pH calculations for strong acids and bases, lists the limitations and tells the story of Arrhenius and his theory.

What are the Arrhenius definitions?

• Arrhenius acid: a compound that contains hydrogen and ionizes in water to produce hydrogen ions, H⁺(aq). Example: HNO₃ → H⁺ + NO₃⁻.
• Arrhenius base: a compound that contains the hydroxide group and dissociates in water to produce hydroxide ions, OH⁻(aq). Example: KOH → K⁺ + OH⁻.

The strength of an acid or a base is determined by how completely it ionizes. Strong acids and bases ionize completely, and weak ones only partially. The theory explained why solutions of acids and bases conduct electricity (because of ions) and why the properties of all acids are similar (because of the common H⁺ ion).

What is the hydronium ion?

A free proton does not exist in water. It attaches to a water molecule through a coordinate bond to form the hydronium ion: H⁺ + H₂O → H₃O⁺. In practice, the hydronium ion is surrounded by several more water molecules, as in H₉O₄⁺. The symbols H⁺(aq) and H₃O⁺(aq) are used interchangeably, and the concentration of hydrogen ions is the concentration of hydronium ions.

Examples of Arrhenius acids and bases

How does neutralization work in the Arrhenius theory?

When an Arrhenius acid reacts with an Arrhenius base, the H⁺ and OH⁻ ions combine to form water: H⁺(aq) + OH⁻(aq) → H₂O(l). The other ions form a salt. Arrhenius pointed out that the enthalpy of neutralization of any strong acid with any strong base is almost constant, about −57 kJ per mole of water formed, because the net reaction is the same in all cases, which supported his theory. For the reaction HCl + NaOH → NaCl + H₂O, the ionic equation is H⁺ + Cl⁻ + Na⁺ + OH⁻ → Na⁺ + Cl⁻ + H₂O, and the net ionic equation is H⁺ + OH⁻ → H₂O.

Worked examples

1. Identify the acid. Which of NaCl, HBr, CH₃OH, KOH and H₃PO₄ are Arrhenius acids? HBr (gives H⁺ in water) and H₃PO₄ are acids. KOH is a base. NaCl is a salt. CH₃OH (methanol) contains OH but does not give OH⁻, so it is neither an acid nor a base in water.
2. pH of a strong acid. 0.0500 mol/L HNO₃ ionizes completely, so [H⁺] = 0.0500 mol/L and pH = −log(0.0500) = 1.30.
3. pH of a strong base. 0.020 mol/L Ba(OH)₂ gives [OH⁻] = 2 × 0.020 = 0.040 mol/L. pOH = −log(0.040) = 1.40, and pH = 14.00 − 1.40 = 12.60.
4. Amount of H⁺ in a sample. 25.0 mL of 0.100 mol/L H₂SO₄ contains 2.50 × 10⁻³ mol of H₂SO₄, which can release up to 5.00 × 10⁻³ mol of H⁺ in total (both protons).
5. Neutralization energy. The reaction of 50.0 mL of 1.00 mol/L HCl with 50.0 mL of 1.00 mol/L NaOH forms 0.0500 mol of water and releases 0.0500 × 57.1 = 2.86 kJ. The solution is 100.0 g, and with c = 4.18 J/(g·°C) the temperature rises by 2,860 ÷ (100.0 × 4.18) = 6.8 °C.
6. A weak acid. In 0.100 mol/L acetic acid, about 1.3% of the molecules ionize. [H⁺] = 1.3 × 10⁻³ mol/L and pH = 2.89, compared with pH 1.00 for 0.100 mol/L HCl.

What are the limitations?

• The theory applies only to aqueous solutions. Acid-base reactions occur in other solvents, such as liquid ammonia, and in the gas phase, for example NH₃(g) + HCl(g) → NH₄Cl(s).
• It requires the presence of H and OH. Ammonia, NH₃, is a base in practice but contains no hydroxide. Arrhenius explained it by the formation of NH₄OH, which does not exist as a distinct compound.
• It does not explain why salts such as sodium carbonate and sodium acetate make basic solutions or why ammonium chloride is acidic.
• It does not account for the role of the solvent, as the H⁺ ion is always bonded to water.

These limitations led to the Brønsted-Lowry theory (1923), based on proton transfer, and the Lewis theory (1923), based on electron pairs.

How did Arrhenius develop his theory?

Svante Arrhenius, a Swedish chemist, studied the electrical conductivity of solutions for his doctoral thesis, which he defended in 1884 at the University of Uppsala. He proposed that salts, acids and bases dissociate into charged particles in water, even without an electric current. His examiners gave the thesis a low grade, since the idea of ions in solution seemed odd, but Wilhelm Ostwald and Jacobus van ‘t Hoff supported it. The theory of electrolytic dissociation explained freezing-point depression data and the properties of acids, and Arrhenius received the Nobel Prize in Chemistry in 1903. He also proposed in 1896 that carbon dioxide in the atmosphere can warm the Earth, an early prediction of the greenhouse effect.

Which mistakes are common?

Mistake 1: Calling every compound with OH a base

Alcohols, such as ethanol (CH₃CH₂OH), do not release OH⁻ in water.

Mistake 2: Saying that all hydrogen atoms in an acid are acidic

In acetic acid, only the hydrogen in the carboxyl group (COOH) ionizes. The three hydrogens on the methyl group do not.

Mistake 3: Forgetting that the theory works only in water

For other solvents or the gas phase, use the Brønsted-Lowry or Lewis definitions.

Mistake 4: Confusing strong with concentrated

Strength relates to the degree of ionization, and concentration to the amount per volume.