Phenol red is an indicator that changes color over a range from ph=6.4 to ph=8.0. what is ka of phenol red?

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

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