The pH Scale
Every aqueous solution is either acidic, basic or neutral. There is a quantitative relationship between the concentration of hydronium and hydroxide ions in the solution.
 
                                       Neutral solution [H3O+] = [OH-]
                                           Acid solution [H3O+] > [OH-]
                                          Basic solution [H3O+] < [OH-]
 
The brackets as usual denote molar concentrations.
 
The pH scale is a numerical scale which, for most applications extends from 0 through to 14. The numbers on the scale represent the relative acidity of solutions and can be converted into actual hydronium ion concentrations.
 
The pH scale is based on the self-ionization of pure water.
 
Two water molecules will sometimes combine into hydronium and hydroxide ions.
 
                      H2O + H2O <------>  H3O+ + OH-
 
Pure water is considered to neutral and the hydronium ion concentration is 1.0 x 10-7 mol/L which is equal to the hydroxide ion concentration.
 
 ie.               [H3O+] = [OH-] = 1.0 x 10-7 mol/L
 
The equilibrium law for this reaction should be
 
Keq = [H3O+][OH-] = (1.0 x 10-7)(1.0 x 10-7) = 1.0 x 10-14
 
You will please note that at neutrality the molarity of the hydronium ion is 10-7. The 7 plays a part in the pH scale by indicating neutrality. The scale reaches a maximum at 14. Please note again that the hydronium and hydroxide concentrations multiply out to 10-14 M. The pH scale was derived around this relationship:
 
ie.     [H3O+] = 10-pH mol/L
 
So the pH is the -log of the [hydronium ion].
 
    pH      [H3O+     [OH-     pOH 
1 10-1  10-13  13
2 10-2 10-12 12
3 10-3 10-11 11
4 10-4 10-10 10
5 10-5 10-9 9
6 10-6 10-8 8
7 10-7 10-7 7
8 10-8 10-6 6
9 10-9 10-5 5
10 10-10 10-4 4
11 10-11 10-3 3
12 10-12 10-2 2
13 10-13 10-1 1

 
Sample Problems
What is the pH of an HCl solution which has a [H3O+] = 1.0 x 10-3?
 
             pH = -log[H3O+] = -log[1.0 x 10-3] = -(-3) = 3
 
What is the pH of an acetic acid solution whose [H3O+]=2.5 x 10-4?
 
What is the hydronium concentration of nitric acid if the pH=4.0?
 
         [H3O+] = 10-pH = 10-(4) = 1.0 x 10-4 mol/L
 
What is the [H3O+] of HCl if the pH = 2.57?
 
What is the pH of 0.010 mol/L hydrochloric acid?
 
The pH of a solution may be determined by the use of an electronic instrument known as a pH meter, or through the use of chemical indicators. Acid-base indicators are dyes which undergo slight changes in molecular structure and colour when the pH value of the solution changes.
 
Specific colours correspond to specific pH values. Some examples are: litmus, phenolphthalein, bromothymol blue, etc. There is a list of acid-base indicators in the databook.