Multicomponent analysis MCA

if one or two extra measurements are performed, displaced by several nanometres with respect to the original measurement, the ratios of absorbance of the sample solution can be calculated and compared with those which have been established in the same way using a pure reference solution. If these ratios are different, it will be presumed that an impurity is present in the sample. The calculation of the concentration would not be reliable in this case. 

When a mixture of compounds whose absorption spectra are known is analysed, then the mixture s composition can be determined. The method is based on absorption spectra of pure individual components and calibrating mixtures of well-defined fraction components. According to the law of additivity (expression 9.11), the spectrum of the mixture to be measured corresponds to the weighted sum of the spectra of each of the individual constituents. The classical method of calculation is reviewed here for revision purposes since it is no longer effected long hand because it is incorporated into computer software. 

Given a mixture of three components a, b and c in solution (concentrations Q, Cj, Q). The absorbances of this mixture are measured at three wavelengths Aj, A2 and A3 giving Aj, Aj and A3. Knowing the values of the specific absorbances for each of the three compounds taken in isolation for the three wavelengths (nine values in total from to e ) through application of the additivity law, the following system of three simultaneous equations can be written (it is assumed that the optical path of the cells used is of 1 cm)  

The resolution of this mathematical system, which corresponds to a [3 x 3] matrix, leads to the three concentrations required C, Cj, and Q. 

This approach yields good results when the compounds lead to spectra, which are significantly different, otherwise it loses precision when the spectra are in close proximity as a small measurement error can lead to a large variation in the result. To avoid this risk the instruments housing diode arrays use many tens of data points. Although the system to be resolved (expression 9.14) becomes over-determined but this leads to better results. 

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Thus /(/ ) is a measure of the predictive ability of the model. For the calibration example discussed in Section 41.2, x(/ - 1) contains the slope and intercept of the straight line, and h (/) is equal to [1 c(/)] with c(j) the concentration of the calibration standard for the yth calibration measurement. For the multicomponent analysis (MCA), x(/ -1) contains the estimated concentrations of the analytes after y - 1 observations, and h (/) contains the absorptivities of the analytes at wave-lengthy. 

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