21.2. The pH Concept http://www.ck12.org
H 2 O(l)+H 2 O(l) H 3 O+(aq)+OH−(aq)Because the reactants are in the liquid phase, they are not included in the equilibrium constant expression. As a
result, the value of Keqfor this reaction can be calculated as follows:
Keq= [H 3 O+][OH−]Water’s ability to act as an acid or a base is relatively weak, so we would expect the reactants to be heavily favored
in this equilibrium. Indeed, at 25°C, this equilibrium constant has a value of only 1.0× 10 −^14. However, despite
the minimal extent of self-ionization, this is a fundamentally important equilibrium for any reactions that take place
in water, which includes essentially all biochemical reactions that occur inside any living organism. Because of its
particular importance, this equilibrium constant is given the special symbol Kw.
In a pure sample of water, there are no external sources of H 3 O+or OH−(no additional acids or bases), so for
each H 3 O+ion that is formed by the self-ionization of water, an OH−ion will be formed as well. As a result,
[H 3 O+] = [OH−] in pure water. Because both of these concentrations are the same, we can solve for the equilibrium
concentrations using the value of Kw. Letxbe the concentration of H 3 O+(and therefore also the concentration of
OH−):
Kw= [H 3 O+][OH−]
1. 0 × 10 −^14 = [x][x]
1. 0 × 10 −^14 =x^2
1. 0 × 10 −^7 =xAt equilibrium, [H 3 O+] = [OH−] = 1.0× 10 −^7 in a sample of pure water. An aqueous solution in which [H 3 O+] =
[OH−] is referred to as aneutral solution. However, the addition of an external acid or base will shift the relative
amounts of these two ions. Adding an acid will increase the amount of H 3 O+. As a consequence, the amount of
OH−will need to decrease in order to reestablish equilibrium (at which point the equilibrium expression for Kw
will once again have the correct value). In anacidic solution, [H 3 O+] >[OH−]. Similarly, in abasic solution, the
amount of OH−will increase and the amount of H 3 O+will decrease, so [H 3 O+] <[OH−].
Shorthand Notation for Aqueous Acids
It is very common for chemists to write H+instead of H 3 O+when talking about aqueous solutions of acids and
bases. However, H+will not exist as an isolated ion if dissolved in water. Instead, it will be closely associated with
(at least) one molecule of the solvent. It is generally acceptable to use H+, but it should be understood that this is
just a shorthand notation for H 3 O+. Consequently, the expression for Kwis often written as follows:
Kw= [H+][OH−]Acid-base reactions are also sometimes written in a way that makes use of this shorthand. For example, you might
see the following acid-dissociation reaction:
HNO 3 (aq)→H+(aq)+NO− 3 (aq)However, a better description of this process would be the following:
HNO 3 (aq)+H 2 O(l)→H 3 O+(aq)+NO− 3 (aq)H+is not just "falling off" of nitric acid. Instead, it is being pulled off by water, which is a better base than the
resulting nitrate anion. Again, the shorthand version is acceptable to use, but keep in mind that a more accurate
description would include water as a base whenever "H+" is being generated in an aqueous solution.