Final answer:
The measured absorbance at the point where the concentrations of HIn and In− are equal will be Ak = 0.5([HIn] + [In−]).
Step-by-step explanation:
When the concentrations of HIn and In− are equal, it implies there is an equilibrium in the context of the Henderson-Hasselbalch equation. At this point, according to Beer's Law, the absorbance will be a combined contribution of both species. If we assume that the molar absorptivity coefficients (ε) are the same for both species, the absorbance, Ak, is proportional to the total concentration of the indicator. Therefore, when [HIn] = [In−], the correct expression for absorbance would be Ak = 0.5(HIn + In−), because each species contributes equally to the total absorbance, which is in accordance with option 2 of the provided choices.