First, we will get the average pH of the two given values:
average pH = (6.4+8) / (2) = 7.2
At this average pH, the concentration of the acid from the phenol red is equal to the concentration of the base.
pH = 7.2
[H+] = 10^(-7.2) = 6.3 * 10^-8
Phenol red has the general formula HA, this gives us:
HA <.......> H+ + A-
At pH = 7.2, [H+] = [A-]
Ka = [H+][A-]/ [HA]
Ka = [H+] = 6.3 x 10^-8
