We let the chemical equation for the weak acid indicator propyl red HPr be
HPr + H2O ↔ H3O+ + Pr-
Therefore, the acid dissociation constant Ka is
Ka = [H3O+][Pr-] / [HPr]
The color of this indicator turns from red to yellow or the other way around at its turning point at which
[HPr] = [Pr-]
Substituting this to the equation for Ka, we now have
Ka = [H3O+]
The pH of the solution at its turning point is
pH = -log[H3O+] = -log(Ka) = -log 3.3×10^-6 = 5.48
On this account, the pH range is pH 5.0 to 6.0.
