Theory of indicators

An acid-base indicator is a weak acid. It works by forming an anion of a different colour when it dissociates.

Take the weak acid HIn:

HIn(aq) + H₂O(l) ? H₃O⁺(aq) + In^–(aq)

HIn and In^– (its conjugate base) are different colours. The relative concentrations of these species dictates the solution’s colour:

• In a strongly acid solution: the system will shift to the left meaning HIn (or Red) dominates.
• In a strongly alkaline solution: the system will shift to the right meaning In^– (or Blue) dominates.

The colour change is not sudden at a particular pH but instead gradual over a pH range. The colour change is dependent on the ratio of [HIn] to [In^–]. In general:

• when [HIn] / [In^–] > 10, Red dominates
• when [HIn] / [In^–] < 10, Blue dominates

The pH at which these changes occur is dependent on the indicator’s K_In:

K_In = ([H₃O⁺][In^–]) / [HIn] therefore [H₃O⁺] = K_In[HIn] / [In^–]

Therefore:

• when [H₃O⁺] > 10 x K_In then [HIn] / [In^–] > 10 so Red dominates
• when [H₃O⁺] < 10 x K_In then [HIn] / [In^–] < 0.1 so Blue dominates
• when there is an intermediate concentration of when H₃O⁺ then neither colour dominates

A lot of the time the values of K_In are expressed in terms of pK_In in which pK_In = -log₁₀K_In. Therefore, in terms of pH:

pH = pK_In -log₁₀ [HIn] / [In^–]

So:

• when [HIn] / [In^–] < 0.1 the pH is less then pK -1 and Red dominates
• when [HIn] / [In^–] > 10 the pH is more than pK +1 and Blue dominates

Therefore: the colour of indicator changes over the pH range pKIn