PKa

In chemistry and biochemistry, the acidity constant or acid dissocation constant (<math>K_a<math>) is a specific type of dissociation constant that indicates the extent of dissociation of hydrogen ions from an acid. An acid with an acidity constant near 1 is almost completely dissociated when dissolved in water; conversely, an acid with an acidity constant near 0 remains almost completely undissociated. In lay terms, the higher the <math>K_a<math>, the stronger the acid in question.

Because this number varies over many degrees of magnitude, the acidity constant is often represented by the inverse of its common logarithm, represented by <math>pK_a<math>. (cf. pH).

Given a weak acid HA, its dissolution into water is subject to the following equilibrium:

HA + H₂O ↔ H₃O⁺ + A^–

This is often written as:

HA ↔ H⁺ + A^–

The species A^– is referred to as the conjugate base of the acid. The acidity constant for the acid HA is the dissociation constant for this equilibrium. Thus:

<math>K_a = \frac{[\mbox{H}_3\mbox{O}^+][\mbox{A}^- ]} {[\mbox{HA}]}<math>

where [X] denotes the molar concentration of X in the solution.

By analogy, one can define the basicity constant (<math>K_b<math>, and similarly <math>pK_b<math>) of the conjugate base A^–:

<math>K_b = \frac{[\mbox{HA}][\mbox{OH}^-]} {[\mbox{A}^-]}<math>

For the equilibrium:

A^– + H₂O ↔ HA + OH^–

Analogously to <math>K_a<math>, the magnitude of <math>K_b<math> indicates the relative strength of the base, with <math>K_b<math> closer to 1 indicating a much stronger base.

The relation between K_a and K_b is:

<math>K_w =K_aK_b<math>

<math>pK_w = pK_a + pK_b<math>

where K_w is the dissociation constant of water, which is 1.0x10^-14 mol² dm^-6at 20 °C.

As the product of K_a and K_b must remain a constant, it follows that stronger acids will have weaker conjugate bases, and vice versa.