Explain the relationship between the pH range, the end point and the pKa value of an acid-base indicator.

Bromothymol blue is a weak acid indicator with a \(\text{p}K_a\) of 7.1. The yellow acidic form (\(\text{HIn}\)) is in equilibrium with the blue basic form (\(\text{In}^-\)). Explain why the end point of bromothymol blue occurs at pH 7.1.

An acid-base indicator (HIn) has a \(\text{p}K_a\) value of 5.2. At what pH will the indicator be at its end point, where \([\text{HIn}] = [\text{In}^-]\)?

An acid-base indicator has a \(pK_a\) value of 5.2. At what pH does the indicator reach its end point?