A Straightforward Method to Determine Equilibrium Constants from Spectrophotometric Data

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Spectrophotometry provides reliable information on the equilibrium concentration in chemically reacting mixtures. However, the widely used traditional linearized models to determine the equilibrium constant from spectrophotometric data do not provide optimal information and unnecessarily complicate data evaluation for students. In this paper we show an easy and straightforward inference method, which makes use only of Beer's Law and an elementary mathematical treatment of the problem. Though the resulting parameter estimation is nonlinear with respect to the equilibrium constant, the commercial availability of many nonlinear parameter estimation software packages eliminates the need for the student to bother with either mathematical or numerical details. Adding a suitable spectral shape function to the model describing equilibrium further facilitates the use of the proposed method and makes it an easy task to determine the components' spectra from equilibrium measurements.

Three practical examples are treated in detail in the online version. They illustrate how the method works at different complexity levels and are easy to install in undergraduate physical chemistry labs.