Simultaneous spectrophotometric determination and classical least squares method: a simple experiment to introduce the concept of multivariate calibration

We herein present an experiment where the concentrations of tartrazine, sunset yellow and amaranth in samples containing these three food dyes are determined by system of equations (SE) and classical least squares (CLS) multivariate calibration methods using light absorption data. Firstly, concentrations are obtained by means of the well-known SE method, that is, by solving a set of three linear equations in which the Beer-Lambert’s proportionality coefficients are obtained from analytical curves. Then, it is shown that the CLS method is a natural extension to SE, with an arbitrarily large number of equations. Nevertheless, within the CLS method, the unknown coefficients are found using mixtures with known concentrations of each dye. In order to introduce the students to the basics of algorithms and numerical computations, data treatment is performed in a command-line fashion using a freely available software. Advantages of multivariate calibration models over univariate ones are made clear, and the performance of the CLS and SE methods is compared based on the root-mean-square error.