Modeling and Graphic Presentation of Acid–Base Titration Curves. Presentation of an Alternative Method

Titration curves for the acid–base-titration of polyvalent acids and bases and their mixtures can be created in a simple way and presented graphically. The method, an alternative to the existing procedures, shall be presented here for discussion. With the described method it is possible in an easy manner and for didactic purposes to show how the boundary conditions, such as concentrations, pKa values, Kw values (temperature-dependent), and mixing ratios influence the shape of titration curves. The method comes from closed mathematical formulas, which can be developed in the form: titration degree, T = f(pH). An increase in the titration volume is, therefore, not considered. It can be neglected in practice by choice of suitable volumes and concentrations. The graphic presentation can be realized with the help of a customary mathematic program, such as MathCAD 7. The titration curves are derived in the familiar form of pH = f (T). During the derivation of the equations for the titration of polyvalent acids and bases, difficult expressions appear and approximations are suggested with only small deviations from the exact formulas, which nevertheless are both simple and manageable. The procedure is presented in a series of practical examples where computed and measured titration curves are compared. When using polyvalent acids, such as malonic acid or citric acid, the appropriate activity coefficients have to be considered. If the ionic strength is constant, which can be accomplished by addition of electrolytes like KCl, this is easily accomplished and is demonstrated by examples.