Before discussing pH we must understand the equilibrium behavior of water.
H2O + H2O H3O+(aq) + OH-(aq) or H2O H+(aq) + OH-(aq)
The equilibrium constant expression for this reaction is:
Kw = [H3O+][OH-] = [H+][OH-] = 1.001x10-14 (at 25 oC, Kw is temperature dependent)
(Using [H3O+] is equivalent to using [H+].)
The equilibrium constant, Kw, is called the dissociation constant or ionization constant of water.
In pure water [H+] = [OH-] = 1.00x10-7 M. pH and pOH
Working with numbers like 1.00x10-7 M to describe a neutral solution is a rather inconvient. Acidity and basicity is described on a more convenient logarithmic scale:
pH is a shorthand notation for -log[H+] and pOH is a shorthand notation for -log[OH-].
Because of the equilibrium relationship between [H+] and [OH-], pH + pOH = 14.
Solutions are called neutral when pH = 7, [H+] = [OH-] = 1.00x10-7 acidic when pH < 7, [H+] > 1.00x10-7 basic when pH > 7, [H+] < 1.00x10-7
Example: What is the pH of a solution of 0.025 M HNO3?
HNO3 is a strong acid and for all practical purposes dissociates completely.
HNO3(aq) + H2O NO3-(aq) + H3O+(aq)
[H+] = 0.025 M
pH = -log(0.025 M) = 1.6
What is the pOH of this solution? There are 2 ways to calculate pOH:
Kw = 1.00x10-14 = [0.025 M][OH-] [OH-] = 4.00x10-13 pOH = -log(4.00x10-13) = 12.40
pOH = 14.00 - pH = 14.0 - 1.60 = 12.40
What are pH and pOH for a 0.0025 M solution of HNO3?
pH = -log(0.0025 M) = 2.60 pOH = 14.00 - 2.60 = 11.40
Notice that pH and pOH change by 1 for a factor of 10 change in [H+] and [OH-].