# Dissociation Constant

The dissociation constant specifies the tendency of a substance AxBy to reversibly dissociate (separate) in a solution into smaller components A and B:

$A_yB_y \rightleftharpoons xA + yB \tag{1}$

The dissociation constant is denoted Kd and is calculated by

$K_d =\dfrac{[A]^x[B]^y}{[A_xB_y]} \tag{2}$

where [A], [B], and [AxBy] are the molar concentraions of the entities A, B, and AxBy. The dissociation constant is an immediate consequence of the law of mass action which describes equilibria in a more general way. The dissociation constant is also sometimes called ionization constant when applied to salts. The inverse of the dissociation constant is called association constant.

#### Dissociation constant of water

Formally, the dissociation of water follows the following equation:

$H_2O \rightleftharpoons H^+ + OH^- \tag{3}$

Thus the dissociation constant is given by

$K_d = \dfrac{[H^+][OH^-]}{[H_2O]} = 2.16\times 10^{-16}\tag{4}$

However, since the concentration of undissociated water is almost unchanged by the dissociation process (due to the low Kd), we can assume that a liter of water at 25°C contains 55.39 mol undissociated water. For the sake of convenience this constant water concentration is combined with the dissociation constant Kd to form the dissociation constant of water Kw:

$K_w = [H^+][OH^-] = 2.16\times10^{-16} )(55.39) = 1.2\times 10^{-14}\tag{5}$

The value of Kw changes considerably with temperature. Consequently this variation must be taken into account when making precise measurements (i.e. when determining the pH).

 Water Temperature [°C] Kw [10-14] pKw 0 0.1 14.92 10 0.3 14.52 18 0.7 14.16 25 1.2 13.92 30 1.8 13.75 50 8.0 13.10 60 12.6 12.90 70 21.2 12.67 80 35 12.46 90 53 12.28 100 73 12.14

#### Acid base reactions

The dissociation constant can also be applied to the deprotonation of acids. In this case the dissociation constant is denoted as Ka. The greater the dissociation constant of an acid the stronger the acid. Polyprotic acids (e.g. carbonic acid or phosphoric acid) show several dissociation constants, since more than one proton can be separated (one after the other):

 H3A H+ + H2A- Ka1 = [H+][H2A-]/[H3A] pKa1 = -lg(Ka1) H2A- H+ + HA2- Ka2 = [H+][HA2-]/[H2A-] pKa2 = -lg(Ka2) HA2- H+ + A3- Ka3 = [H+][A3-]/[HA2-] pKa3 = -lg(Ka3)

A list of acid dissociation constants can be found here.

#### Other applications

The concept of the dissociation constant is applied in various fields of chemistry and pharmacology. In protein-ligand binding the dissociation constant describes the affinity between a protein and a ligand. A small dissociation constant indicates a more tightly bound the ligand. In the case of antibody-antigen binding the inverted dissociation constant is used and is called affinity constant.

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