Arrhenius postulated that acids produce hydrogen ions and bases produce hydroxide ions when dissolving in water. This concept only applies to aqueous solutions.

Brønsted and Lowry suggested independently a more general definition of acids and bases. An acid is a proton donor (H+) and a base is a proton acceptor.

Pure water does not conduct an electrical current: no ions present. Neither does pure acetic acid (ijsazijn): no ions present.
A mixture of both liquids does conduct an electrical current: ions have been formed.

The reaction that occurs when an acid (like acetic acid for instance) is dissolved in water can be written as:

HA(aq)	+	H2O(l)		H3O+(aq)	+	A-(aq)
Acid		Base		Conjugate acid		Conjugate base

or in a more simple way:

HA(aq) H⁺(aq) + A^-(aq)

The equilibrium constant of this protolysis reaction of the acid is called the acid dissociation constant K_a:

The reaction that occurs when a base is dissolved in water can be written as:

B(aq)	+	H2O(l)		BH+(aq)	+	OH-(aq)
Base		Acid		Conjugate acid		Conjugate base

The equilibrium constant of this protolysis reaction of the base is called the base dissociation constant K_b:

It is important to realize that there is a correlation between K_a of an acid and K_b of the conjugated base. For instance:

HA(aq) + H2O(l) H3O+(aq) + A-(aq)	A-(aq) + H2O(l) HA(aq) + OH-(aq)

Summary

Dissociation Constants
An acid is a proton donor: HA(aq) + H2O(l) H3O+(aq) + A-(aq) Acid dissociation constant
A base is a proton acceptor: B(aq) + H2O(l) BH+(aq) + OH-(aq) Base dissociation constant