The first modern definition of acids and bases in molecular terms was devised by Svante Arrhenius. A hydrogen theory of acids, it followed from his 1884 work with Friedrich Wilhelm Ostwald in establishing the presence of ions in aqueous solution and led to Arrhenius receiving the Nobel Prize in Chemistry in 1903.
As defined by Arrhenius:
* An Arrhenius acid is a substance that ionises in water to form hydrogen ions (); that is, an acid increases the concentration of H ions in an aqueous solution.
This causes the protonation of water, or the creation of the hydronium () ion. Thus, in modern times, the symbol  is interpreted as a shorthand for , because it is now known that a bare proton does not exist as a free species in aqueous solution. This is the species which is measured by pH indicators to measure the acidity or basicity of a solution. 
* An Arrhenius base is a substance that dissociates in water to form hydroxide () ions; that is, a base increases the concentration of  ions in an aqueous solution. 
The Arrhenius definitions of acidity and alkalinity are restricted to aqueous solutions and are not valid for most non-aqueous solutions, and refer to the concentration of the solvent ions. Under this definition, pure  and HCl dissolved in toluene are not acidic, and molten NaOH and solutions of calcium amide in liquid ammonia are not alkaline. This led to the development of the Brønsted–Lowry theory and subsequent Lewis theory to account for these non-aqueous exceptions.
The reaction of an acid with a base is called a neutralization reaction. The products of this reaction are a salt and water.
In this traditional representation an acid–base neutralization reaction is formulated as a double-replacement reaction. For example, the reaction of hydrochloric acid (HCl) with sodium hydroxide (NaOH) solutions produces a solution of sodium chloride (NaCl) and some additional water molecules.
The modifier (aq) in this equation was implied by Arrhenius, rather than included explicitly. It indicates that the substances are dissolved in water. Though all three substances, HCl, NaOH and NaCl are capable of existing as pure compounds, in aqueous solutions they are fully dissociated into the aquated ions  and .