Water as a Weak Acid

To a very small but very important extent, water is a weak acid that ionizes to hydrogen and hydroxide ions. This equilibrium reaction has the equation

H2O H+ + OH-

As with all other weak acids, this reaction has an acid dissociation constant expression:

 Ka = [H+][OH+][H2O]

In any amount of water, the concentration of water is so high (55.5 mol water molecules in 1000 mL water) and the number of ionized water molecules is so low (1.0 X 10-7 mol in 1000 mL water) that the concentration of the water molecules is a constant. Therefore we use a different expression when considering the ionization of water. This expression is an ion product called Kw, which has the value 1.0 X 10-14.

Kw = Ka[H2O] = [ H+][OH-] = 1 X 10-14

The pKw of water is the negative logarithm of this constant:

pKw = 14

In pure water, the hydrogen ion concentration, [H+], equals the hydroxide ion concentration, [OH-]. These concentrations can be calculated from the equation for the ionization of water.

H2O H+ + OH-

Let x equal the hydrogen ion concentration, [H+]. Then x also equals the hydroxide ion concentration, [OH-]. Substituting into the equilibrium expression we obtain

 [H+][OH-] = (x)(x) = 1 X 10-14 x2 = 1 X 10-14 x = 1 X 10-7 [H+] = [OH-] = 1 X 10-7 M

The pH of pure water is 7, the negative logarithm of 1 X 10-7.

A neutral solution is one that is neither acidic nor basic. The hydrogen ion concentration equals the hydroxide ion concentration, and both equal 1 X 10-7 M. In a neutral solution, then, pH = pOH = 7.

An acidic solution is one in which the hydrogen ion concentration is greater than the hydroxide ion concentration; in other words, the hydrogen ion concentration is greater than 1 X 10-7 M, and the hydroxide ion concentration is less than 1 X 10-7 M. In terms of pH, an acidic solution has a pH less than 7.

What is the hydroxide ion concentration in an acid solution? The following relationships exist whenever water is present:

[H+][OH-] = 1 X 10-14 and pH + pOH = 14

If the hydrogen ion concentration is known, the first relationship can be used to calculate the hydroxide ion concentration. Suppose the hydrogen ion concentration is 0.10 M. Substituting into and rearranging the first relationship gives

 [OH-] = 1.0 X 10-140.10 = 1 X 10-13 M

Suppose the pH of an acidic solution is 1.0. The second relationship can be used to calculate the pOH.

1.0 + pOH = 14      pOH = 13

An alkaline or basic solution is one in which the hydrogen ion concentration is less than 1 X 10-7 M. In terms of pH, an alkaline solution is one in which pH is greater than 7.0. Table 12.8 shows the relationship between pH and pOH on a scale from 0 to 14. Example:

Calculate the hydroxide ion concentration, the pH, and the pOH of 0.010 M nitric acid, HNO3.

Solution

Nitric acid is a strong acid and is therefore completely ionized in solution. Thus, [H+] = 0.010 M and pH =2. The hydroxide ion concentration can be calculated using the Kw constant:

Kw = [H+][OH-] = 1.0x10-14

Substituting and rearranging gives

0.010 x [OH-] = 1.0x10-14

 [OH-] = 1.0x10-14 0.010 = 1.0x10-12 M

Because pH + pOH = 14

pOH = 12