Mathematics of titration

Abstractly, titration is the measurement of a chemical system\u27s response to changes in its state variables. Thus, from the purely mathematical perspective, titration data is a sample of values of a function that maps system\u27s parameters into observed quantities. Understanding that function allows one to draw various conclusions about chemical composition of the system. We studied a particular type of acid-base titration which is widely used in chemical education and industry. Our titration data was comprised of measurements of pH of a mixture of acids as a function of added volume of another acid or base. The primary goal of the project was to understand and quantifY the information contained in pH curves. In particular, we wanted to see if pH curves uniquely determined chemical composition of acid mixtures as suggested by various sources. Our findings seem to contradict the conventional wisdom that software, such as Excel, can be effectively used to fit chemical composition to collected titration data. We have shown mathematically that different acid mixtures can produce identical titration data sets. Further, even when the acids in the mixture are known, finding their concentrations from pH recordings is nearly impossible because the resulting linear system of equations is extremely ill-conditioned