Since the indicator is a weak acid, with a Bronsted-Lowry equation of:
But, if we assume that the change between the two colored forms occurs
when we have equal amounts of each, then the transition point is when [HIn]
= [In-]. Therefore,
In other words, at the transition point, the Ka for
the indicator equals the [H3O+] of the solution we
are titrating.
Taking the negative logarithm of each side, this can be written as
pKa = pH.
This means that the best indicator, in terms of the range of its color
change range is the one in which the pKa for the indicator equals
the pH of the equivalence point. Other factors, such as ease of detection
of the color (phenolpthalein is very easy to see) may also influence the
choice of an indicator.