Acid - Base Indicators Phenolphthalein

Acid - Base indicators (also known as pH indicators) are substances which change colour with pH. They are divalent weak acids or bases, involved in protolytic water acid-base equilibrium and form two type coloured ions as Brensted-Lowry protolytical pairs.
Consider an indicator which is a weak acid, with the formula H₂In . At equilibrium, the following equilibrium equation is established with its conjugate base In^2- :

H₂In (aq)      +       2 H₂O (l)       2 H₃O⁺ (aq)     +    In^2- (aq) 
    acid                                                                              conjugate base
(colour A)                                                                              (colour B)

The acid and its conjugate base have different colours. At low pH values the concentration of H₃O⁺ is high and so the equilibrium position lies to the left. The equilibrium solution has the colour A. At high pH values, the concentration of H₃O⁺ is low - the equilibrium position thus lies to the right and the equilibrium solution has colour B.
Phenolphthalein is an example of an indicator which establishes this type of equilibrium in aqueous solution:

                    colourless (Acid)                                                              pink (Base)

Phenolphthalein (pdb version) is a colourless, weak acid which dissociates in water forming pink anions. Under acidic conditions, the equilibrium is to the left,and the concentration of the anions is too low for the pink colour to be observed. However, under alkaline conditions, the equilibrium is to the right, and the concentration of the anion becomes sufficient for the pink colour to be observed.
We can apply equilibrium law to indicator equilibria - in general for a weak acid indicator:

                 K_In = ( [H₃O⁺]²·[In^2-] / [H₂In] ) _eq

K_ln is known as the indicator dissociation constant. The colour of the indicator turns from colour A to colour B or vice versa at its turning point. At this point:

                    [H₂In]   =[In^2-] 

So from equation:

                   K_In =  [H₃O⁺]² = 10^-18.8   ;     pK_In / 2 = 9.4 = pH = -log{SQRT( [H₃O⁺]² )}

The pH of the solution at its turning point is called the pK_ln and is the pH at which half of the indicator is in its acid form and the other half in the form of its conjugate base.

Indicator Range

At a low pH, a weak acid indicator is almost entirely in the [H₂In] form, the colour of which predominates. As the pH increases - the intensity of the colour of [H₂In] decreases and the equilibrium is pushed to the right. Therefore the intensity of the colour of [In^-] increases. Physiological condition for certainly distinct colour is assumed at ratio for conjugated base form:

          [In^2-] /  [H₂In]   = 10  ; and for acid coloured form :   [In^2-] /  [H₂In]   = 1 / 10 = 0.1

      -K_In = ([H₃O⁺]²·[In^2-] / [H₂In])_eq = 10^-18.8 *10  ;  +K_In = ([H₃O⁺]²·[In^2-] / [H₂In])_eq = 10^-18.8 *0.1
 
      -pH_In = 17.8 / 2 = 8.9                                          ;   +pH_In = 19.8 / 2 = 9.9
 
An indicator is most effective if the colour change is distinct and over a low pH range. For most indicators the range is within ±0.5 of the pK_ln value: - please see the table below for examples, to the right is a model of the acid form of each indicator - with the colour of the solution at the turning point. Number 2 of involved hydrogen protons H⁺ in equilibrium .

A Universal Indicator is a mixture of indicators which give a gradual change in colour over a wide pH range - the pH of a solution can be approximately identified when a few drops of universal indicator are mixed with the solution.

Indicators are used in titration solutions to signal the completion of the acid-base reaction.