Concentrations in Multi-Component Systems

For users with the Mathcad browser jump to: (14 KB, ver. 5.0)

In analytical chemistry, the concentration of a species can be determined from its absorbance at a specific wavelength of electromagnetic radiation. In such cases the Beer-Lambert law can be applied.

If the molar absorption coefficient is known (and thickness of the sample cell), the concentration can be determined for unknown samples. This relationship can be applied even for mixtures, since the absorbance of radiation by one species is usually unaffected by the presence of other species in the solution (it is necessary that they do not interact). In other words, the absorbance at a specific wavelength is an additive value: it is the sum of the absorbances of all species in the mixture. This can be expressed as:

Apparently, for an n component mixture, n wavelengths must be selected to obtain n absorbance values for which a set of n linear equations can be written.

For the infrared spectrophotometric analysis of a four-component system, the following data were obtained:

p-xylenem-xyleneo-xyleneethylbenzene A(mixture)
13.0 0.02611.1516 00.08200.09943
13.40.0342 0.03552.5320.29330.2194
14.30.0340 0.068400.3470 0.03396
Such a set of linear equations can be solved in Mathcad in a Given/Find block or, more elegantly, using matrices .
« Home » « Mathcad Menu »