Specialized Equilibrium Constants

Many reactions are so common or useful that they have their own special equilibrium constants.

Self-Ionization of Water

The self-ionization, or autodissociation, of water is a reaction that occurs to a very small extent in neutral water. In this process, one molecule of water donates a proton to a neighboring water molecule, which yields hydronium and hydroxide ions.

Autodissociation of water

A water molecule protonates a neighboring water molecule, yielding hydronium and hydroxide ions.

The equilibrium expression for this reaction is written as follows:

$K_W=[H^+][OH^-]=1.0\times 10^{-14}$

Note that because water is a liquid, it is omitted from this equilibrium expression. The value of the dissociation constant of water, K_W, is $1.0\times 10^{-14}$. This will come into use later, in a future discussion on acids and bases.

Acid Dissociation Constant, K_a

An acid dissociation constant, K_a, is the equilibrium constant for the dissociation of an acid in aqueous solution. The general form of the balanced equation is:

$HA(aq) \rightleftharpoons H^+(aq)+A^-(aq)$

HA is a generic acid that dissociates by splitting into A⁻, known as the conjugate base of the acid, and a hydrogen ion, or proton, H⁺. As described previously, hydrogen ions actually exist as solvated hydronium ions in aqueous solutions. The equilibrium expression is given as:

$K_a=\frac{[H^+][A^-]}{[HA]}$

Recall that strong acids dissociate completely or almost completely into their ions. As such, strong acids will have large values of K_a that are greater than one, which indicates that the forward reaction of dissociation is strongly favored. Weak acids, on the other hand, will have small values of K_a that are less than one, indicating that the reverse reaction is strongly favored; weak acids dissociate only to a small extent. As such, K_a acts a relative indicator of acid strength.

Acetic acid dissociation

A ball-and-stick model of the dissociation of acetic acid to acetate. A water molecule is protonated to form a hydronium ion in the process. The acidic proton that is transferred from acetic acid to water is shown in green.

Base Dissociation Constant, K_b

The base dissociation constant, K_b, is analogous to the acid dissociation constant. For a generalized reaction of a base, B, in water, we have:

$B(aq)+H_2O(l)\rightleftharpoons BH^+(aq)+OH^-(aq)$

The equilibrium expression, K_b, is given by:

$K_b=\frac{[BH^+][OH^-]}{[B]}$

As with the acid dissociation constant, large values of K_b are indicative of a stronger base, while small values of K_b are indicative of a weaker base.