# Autoionization of Water

The autoionization of water describes when water reacts with water in a solution of water. This forms the basis of understanding aqueous acid base chemistry.

Do not suspect a chemical process occurs only when chemicals dissolves in water.

Despite what most people believe when they look at an ordinary glass of water, it does not peacefully sit in a state of tranquility. It exists in a state of dynamic equilibrium where water reacts with water to produce hydronium and hydroxide ions, Equation (1).

$\Large{H_2O + H_2O \rightleftarrows H_3O^{+1} + HO^{-1}}$               (1)

As a result, we assign the mass action expression in terms of concentration, which conforms to the ratio of products over reactants, (2).

$\Large{K_{eq} = \frac{[H_3O^{+1}][HO^{-1}]}{[H_2O][H_2O]}}$               (2)

## Ka Water

In particular, all acids have an equilibrium constant, Ka. This expresses the ratio of dissociated ionized acid compared to the neutral molecular acid species (3).

$\Large{K_a = \frac{[H^{+1}][A^{-1}]}{[HA]}}$                             (3)

It follows by substitution, the acid dissociation constant for water  (4).

$\Large{K_a = \frac{[H_3O^{+1}][HO^{-1}]}{[H_2O]}}$             (4)

The ionization concentration of H30+1 and OH-1 has a value of 1.00 x 10-7  M for each one. The concentration of pure water in the liquid state has a value 55.6 M, (5).

$\Large{K_a = \frac{[1 x 10^{-7} M][1 x 10^{-7}] M}{[55.6 M]} = 1.8 x 10^{-16}}$              (5)

## pKa Water

The pKa of any acid expresses the equilibrium constant in terms of the negative -log10:

$\Large{pK_a = -log[K_a]}$              (6)

$\Large{pK_a = -log[1.8 x 10^{-16}] = 15.7}$              (7)

## Kw

Similarly, we write the ion dissociation constant for water. From earlier, the actual ion concentration of H3O+1 and HO-1 has a small value compared to the concentration of water, a little less than 2 parts per billion,  Equation (8).

$\Large{K_a[H_2O] = [H_3O^{+1}][HO^{-1}] = K_w}$             (8)

Substituting numerical values for variables,,  and calculating Kw (9):

$\Large{1.8 x 10^{-16}[55.6 M] = [H_3O^{+1}][HO^{-1}] = 1.0 x 10^{-14}}$             (9)

## pH

Like pKa, you find the value of pH  by finding minus the log of the ionized acid concentration [H3O+1], (10).

Note

Sometimes students get confused over the relationship between H3O+1 and H+1. The way we write H+1 creates something of a fiction. In our depiction of the autoionization of H2O, H3O+1 makes a more accurate description. For all intents and purposes, the two ways of writing acid concentration mean the same thing: [H3O+1] = [H+1].

$\Large{pH = -log[H_30^{+1}]}$              (10)

As a result, when you plug the H3O+1 concentration into the pH equation, the pH for the autoionization of water takes the value of 7, (11).

$\Large{pH = -log(1 x 10^{-7} = 7)}$              (11)

## What Neutral Means

In conclusion, sometimes students believe a neutral solution does not contain any acid or base. You have seen that pure water contains a concentration of 1 x 10-7 M H+1.  On the other hand, it also contains 1 x 10-7 M HO-1

The correct way to understand this: a neutral solution has an equal concentration of acid and base.