Explicit expressions of the general form of the titration curve in terms of concentration: Writing a single closed-form expression for the titration curve for a variety of titrations without using approximations or segmentation

Explicit expressions of the shape of a titration curve can provide insight into the feasibility of the titration and into the conditions needed for a sufficiently sharp endpoint. They also allow one to design appropriate algorithms to evaluate titration curves and allow equilibrium constants to be extracted from them.