A comparison of the experimental results to the theoretical expectations showed appreciable discrepancies. We consider possible problems in the execution of the experiment as the cause of these discrepancies.
This column is an installment in a series of our discussion of the classical least squares (CLS) approach to calibration (1–7). Where do we stand as of now? At this point, we have developed the theory of the CLS approach to calibration (1,2), described the measurement procedures and the data (3,4), and shown that when we apply the mathematical theory to the data we can reconstruct the spectra of the mixtures (5).
However, the theory of CLS only considers the relationship of the spectrum of a mixture to the spectra of the components of that mixture; the theory tells us nothing about the relationship of the spectrum to other properties of the mixture. In particular, it is silent on the question of the concentrations of the various mixture components. The numerical results of the CLS calculations are fractions, each representing the fraction that each mixture component contributes to the total mixture spectrum.
In our previous columns (5,6), we found that by computing the regression coefficients for the spectra of the pure components using the CLS algorithm and then applying those coefficients to those same pure component spectra, we were able to reproduce the spectra of mixtures of those materials very well. Our interest now is to ascertain whether the coefficients we calculated do, in fact, represent the concentrations of the corresponding materials.
Theoretically, any of the spectral regions having the absorbance bands that we previously noted should give equivalent results, the same results, and the correct results. It therefore makes sense to use both the entire spectral region we measured and each of the individual spectral regions that we previously separated out and plotted.
What do we observe in the results of Table III?
Although sporadic readings (such as toluene in sample 9) showed good agreement between the gravimetric and spectrally calculated values, for the most part the two readings disagreed markedly, often by several percent or more. We therefore have to conclude that this isn't working very well.