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Determine concentrations in mixture using determinants

Please see attachment.
A solvent called "mixed xylenes" contains the o-xylene, m-xylene, p-xylene and ethyl
benzene. In the table below, the absorbances of each of the pure components and the
absorbance of a sample of "mixed xylenes" were measured at four different wavelengths.
All measurements used the same cell and, therefore, the same pathlength. What is the
concentration of each compound? (Use the determinant function in EXCEL).

For the pure compounds, where A = bX, assume X = 1

values of (molar absorptivity)b
Wavelength(m) p-xylene m-xylene o-xylene ethylbenzene unknown
12.5 1.5020 0.0514 0.000 0.0408 0.1013
13.0 0.0261 1.1516 0.000 0.0820 0.09943
13.4 0.0342 0.0355 2.532 0.2933 0.2194
14.3 0.0340 0.0684 0.000 0.3470 0.03396

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A solvent called "mixed xylenes" contains the o-xylene, m-xylene, p-xylene and ethyl
benzene. In the table below, the absorbances of each of the pure components and the
absorbance of a sample of "mixed xylenes" were measured at four different wavelengths.
All measurements used the same cell and, therefore, the same pathlength. What is the
concentration of ...

Solution Summary

The solution is given in the attachment as a step-by-step equation process and with a table.

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