Spectrometric Determination of the Total Concentration of Single-Type Analytes Using Conventional Multidimensional Calibrations

Abstract

Multidimensional calibrations can be used for the spectrometric determination of the total concentration (cΣ) of similar substances; these calibrations relate the generalized signals (AΣ)j measured at different wavelengths (λj) with the concentrations of these analytes (ci) and their absorption coefficients (kij). Such calibrations are conventionally used for the separate determination of analytes, while the ci values are calculated using chemometric algorithms. To find cΣ, one should only take a sum of the found ci values. Despite the simplicity of this type of group analysis, it is rarely used, and its capabilities have not been studied. It is unclear how the accuracy of the cΣ estimate depends on the number of analytical wavelengths (AWLs), the number of standards, and other factors. The purpose of this study was to obtain relevant information using an example of model mixtures of arenes. The absorption spectra of arene mixtures were recorded in the region 230–280 nm, where these spectra are additive. We analyzed 55 hexane solutions containing three to six arenes with a total concentration of 0.1–0.5 mg/mL. The qualitative composition of the model mixtures was considered to compose the matrix of absorption coefficients of individual arenes. The ci values were found by multiple linear regression (MLR, direct calibration). With a sufficiently large number of AWLs, the found ci values were close to zero for arenes absent in the sample and close to the actual ci values for the present arenes. The summation of the found ci gave approximately correct estimates of cΣ (±5%). The single errors of the group analysis were, as a rule, smaller than the errors of the determination of the mixture components. The complication of the model (the introduction of “extra” standards and an increase in the number of AWLs) did not affect the accuracy of the results of group analysis, and the simplification of the model increased errors. If only the most typical standards were used to form the model, the values of kij of which covered the entire range of possible values of kij, the presence of components in the sample that were not taken into account by the simplified model did not lead to a noticeable increase in errors.