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)**

**K**_{a} Water

_{a}Water

In particular, all acids have an equilibrium constant, **K _{a}.** 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 **H _{3}0^{+1}** and

**OH**has a value of

^{-1}**1.00 x 10**for each one. The concentration of pure water in the liquid state has a value

^{-7 }M**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)**

**pK**_{a} Water

_{a}Water

The **pK _{a}** of any acid expresses the equilibrium constant in terms of the negative

**-log**:

_{10}

\Large{pK_a = -log[K_a]}

**(6)**

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

**(7)**

**K**_{w}

_{w}

Similarly, we write the ion dissociation constant for water. From earlier, the actual ion concentration of **H _{3}O^{+1}** and

**HO**has a small value compared to the concentration of water, a little less than 2 parts per billion, Equation

^{-1}**(8)**.

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

**(8)**

Substituting numerical values for variables,, and calculating** K _{w} (9)**:

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

**(9)**

**pH**

Like **pK _{a}**, you find the value of

**pH**by finding minus the log of the ionized acid concentration

**[H**,

_{3}O^{+1}]**(10)**.

Note

Sometimes students get confused over the relationship between **H3O ^{+1}** and

**H**. The way we write

^{+1}**H**creates something of a fiction. In our depiction of the autoionization of

^{+1}**H**,

_{2}O**H**makes a more accurate description. For all intents and purposes, the two ways of writing acid concentration mean the same thing:

_{3}O^{+1}**[H**.

_{3}O^{+1}] = [H^{+1}]

\Large{pH = -log[H_30^{+1}]}

**(10)**

As a result, when you plug the **H _{3}O^{+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*.