# Question #586a5

Jun 14, 2015

The acid dissociation constants will express the ratio between the dissociated and undissociated forms of the acid.

#### Explanation:

A diprotic acid is an acid that has two acidic protons and thus ionizes in two steps.

The first ionization corresponds to one acid dissociation constant, more specifically to ${K}_{a 1}$, and the second ionization corresponds to another acid dissociation constant, ${K}_{a 2}$.

An acid dissociation constant simply tells you what the ratio between the ionized species that result when an acid reacts with water and the undissociated form of the acid will be.

The first dissociation equilibrium will form the bicarbonate and hydronium ions and looks like this

${\underbrace{{H}_{2} C {O}_{3 \left(a q\right)}}}_{\textcolor{b l u e}{\text{undissociated form")) + H_2O_((l)) rightleftharpoons underbrace(HCO_(3(Aq))^(-) + H_3O_((aq))^(+))_(color(green)("ionized species}}}$

The acid dissociation constant for this step will be

${K}_{a 1} = \frac{\left[H C {O}_{3}^{-}\right] \cdot \left[{H}_{3} {O}^{+}\right]}{\left[{H}_{2} C {O}_{3}\right]}$

The second dissociation equilibrium will form the carbonate and hydronium ions. Since the bicarbonate ion undergoes ionization, this time it is considered to be the undissociated form.

${\underbrace{H C {O}_{3 \left(a q\right)}^{-}}}_{\textcolor{b l u e}{\text{undissociated form")) + H_2O_((l)) rightleftharpoons underbrace(CO_(3(aq))^(2-) + H_3O_((aq))^(+))_(color(green)("ionized species}}}$

The acid dissociation constant for this step will be

${K}_{a 2} = \frac{\left[C {O}_{3}^{2 -}\right] \cdot \left[{H}_{3} {O}^{+}\right]}{\left[H C {O}_{3}^{-}\right]}$

Notice that the concentration of water is not included in the expression of the acid dissociation constants. This happens because water's concentration is so large compared with those of the other species that you can safely assume that it remains constant.

So, as a conclusion, an acid dissociation constant is always written as what the acid dissociates into divided by the form which dissociates.