An infrared spectrophotometric method for determining the concentration ratio of any two components in multicomponent mixtures is described. Although the conventional infrared spectrophotometric analysis has been carried out by making use of only positions of main absorption peaks in spectra, in the method based on a partial regression coefficient ratio, the uses of not only the main peak position but also several other positions in the absorption band are suggested. That is, absorbance values,
Am, of mixtures are measured in a certain spectral region at a given wavenumber interval, and assuming that
Am is represented by the multiple regression model, we have that:
Am=
A0β+
e…(1)
where
A0 is the absorbance data of each component, β is the partial regression coefficient, and
e is the experimental error. When the Beer's law conforms in the spectral region with respect to the absorption of each component, the partial regression coefficient, β
iof a component i in equation (1) can be given by:
β
i=
lCi/
l0iC0i…(2)
where
l and
Ci are the pathlength of the cell used and the concentration of the component, i, in the mixture respectively.
l0i and
C0i are those for the pure standard of component i. Therefore, the concentration ratio (
Ci/
Cj) of any two components, i and j, in mixtures is proportional to the partial regression coefficient ratio of the two components, i.e., ratio of β
i/β
j. This linear correlation was used for the determination of the concentration ratio of zinc and copper in the coprecipitated mixtures of zinc and copper 8-hydroxyquinolates by applying a slight difference of the absorption band due to C-O stretching frequency in these two 8-hydroxyquinolates. Though the absorption bands were not well-separated between the complexes, a plot of the partial regression coefficient ratio (β
Cu/β
Zn) against the concentration ratio(
CCu/
CZn) gave mostly a straight line. When the complexes were subjected to the measurement of an infrared spectrum by using a liquid cell 1 mm thick with KBr windows against chloroform as the reference, the reproducibility of this method was (1.1?1.3)% as a coefficient of variation in the concentration ratio range of 0.1 to 0.9, and this method gave about 10-fold enhancement in the sensitivity compared with the conventional methods.
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