The concept of an acid–base reaction was first proposed in 1754 by Guillaume-François Rouelle, who introduced the word "base" into chemistry to mean a substance which reacts with an acid to give it solid form (as a salt).

In 1838, Justus von Liebig proposed that an acid is a hydrogen-containing compound whose hydrogen can be replaced by a metal.

[9][10] 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.

[note 1] Thus, in modern times, the symbol H+ is interpreted as a shorthand for H3O+, because it is now known that a bare proton does not exist as a free species in aqueous solution.

Under this definition, pure H2SO4 and HCl dissolved in toluene are not acidic, and molten NaOH and solutions of calcium amide in liquid ammonia are not alkaline.

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 H+, Cl−, Na+ and OH−.

Baking powder is used to cause the dough for breads and cakes to "rise" by creating millions of tiny carbon dioxide bubbles.

The bubbles are created because, when the baking powder is combined with water, the sodium bicarbonate and acid salts react to produce gaseous carbon dioxide.

For example, starting with sodium bicarbonate and monocalcium phosphate (Ca(H2PO4)2), the reaction produces carbon dioxide by the following stoichiometry:[17]

[11][20] In this approach, acids and bases are fundamentally different in behavior from salts, which are seen as electrolytes, subject to the theories of Debye, Onsager, and others.

The calculation of pH under the Arrhenius model depended on alkalis (bases) dissolving in water (aqueous solution).

The Brønsted–Lowry model expanded what could be pH tested using insoluble and soluble solutions (gas, liquid, solid).

The Brønsted–Lowry model explains this, showing the dissociation of water into low concentrations of hydronium and hydroxide ions:

This equation is demonstrated in the image below: Here, one molecule of water acts as an acid, donating an H+ and forming the conjugate base, OH−, and a second molecule of water acts as a base, accepting the H+ ion and forming the conjugate acid, H3O+.

Thus, some substances, which many chemists considered to be acids, such as SO3 or BCl3, are excluded from this classification due to lack of hydrogen.

Similarly, compounds of group 15 elements with a formula DY3, such as amines, NR3, and phosphines, PR3, can behave as Lewis bases.

Adducts between them have the formula X3A←DY3 with a dative covalent bond, shown symbolically as ←, between the atoms A (acceptor) and D (donor).

For instance, carbon monoxide acts as a Lewis base when it forms an adduct with boron trifluoride, of formula F3B←CO.

Edward Curtis Franklin studied the acid–base reactions in liquid ammonia in 1905 and pointed out the similarities to the water-based Arrhenius theory.

Germann, working with liquid phosgene, COCl2, formulated the solvent-based theory in 1925, thereby generalizing the Arrhenius definition to cover aprotic solvents.

[24] Germann pointed out that in many solutions, there are ions in equilibrium with the neutral solvent molecules: For example, water and ammonia undergo such dissociation into hydronium and hydroxide, and ammonium and amide, respectively:

Some aprotic systems also undergo such dissociation, such as dinitrogen tetroxide into nitrosonium and nitrate,[note 3] antimony trichloride into dichloroantimonium and tetrachloroantimonate, and phosgene into chlorocarboxonium and chloride:

The unique strength of this definition shows in describing the reactions in aprotic solvents; for example, in liquid N2O4:

Also, it has been thought that there is something intrinsically acidic about hydrogen compounds, a property not shared by non-hydrogenic solvonium salts.

This theory is also useful in the systematisation of the reactions of noble gas compounds, especially the xenon oxides, fluorides, and oxofluorides.

[4] Usanovich's theory can be summarized as defining an acid as anything that accepts negative species or donates positive ones, and a base as the reverse.

In 1963, Ralph Pearson proposed a qualitative concept known as the Hard and Soft Acids and Bases principle.

The E and C parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form.

The W term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric acid or base.

When these two equations are combined by eliminating the hydrogen ion concentration, an expression for the equilibrium constant, K is obtained.