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

 

 

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 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) 

pK_a Water

 

 

 

The pK_a 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)

K_w

 

 

 

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 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 [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.