An indicator is a weak acid and the pH range of its colour is 3.1 to 4.5. If the neutral point of the indictor lies in the center of the hydrogen ion concentrations corresponding to the given pH range, calculate the ionization constant of the indicator.

Explanation

The hydrogen ion concentrations of the given pH range are
For pH 3.1 , `pH=-log [H^+]` = 3.1
`[H^+] = 7.94xx10^(-4)` M For pH 4.5 ,
pH = 4.5 = – log `[H^+]` `therefore [H^+] = 3.16xx10^(-5)` M
The average of these two hydrogen ion concentrations is
`(7.9xx10^(-4))+(3.16xx10^(-5))/2=4.128xx10^(-4)` M
At this concentration of H+, we will get neutral point of the indicator, at which `[In^(–)] = [HIn]`
`therefore pH=pK_"Hin"`
or `[H^+] = K_"Him"=4.128xx10^(-4)`