Calculate the `pH` at which an acid indicator with `K_(a) = 1.0 xx 10^(-5)` changes colour when the indicator is `1.00 xx 10^(-3)M`.

Explanation

When the indicator (Hin) is added to a solution, there exists the equilibrium, `underset("colour A")(Hin) Leftrightarrow + underset("colour B")(In^(-))`
`K_(In) =([H^+] [In^(-)])/([Hin])`
The midpoint of the colour range of an indicator Hin in the point at which `[In^(-)]=[HIn]`
`K_(In)=[H^+]=1 xx 10^(-5),pH =5`
Thus, at pH =5 of the solution, the indicator will change its colour.