ABSORBANCE LAW, FAILURES


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If an instrument can reveal the true shape of spectral features, the true absorbance is revealed, and it always obeys the absorbance law (equation 2, previous topic). Frequently, however, the instrumental resolving power is not high enough to reveal the true spectrum and one sees only an apparent absorbance, which does not obey the absorbance law. Basically, this deviation from the absorbance law happens because the transmittance saturates, or “bottoms out”. This is illustrated by the figure here which applies to one of the line pairs of HCl when the concentration-pathlength product is 10,000 PPM-Meters and the total sample pressure is one atmosphere. Diagram A, on the left, shows the line pair with its correct line widths of 0.2 cm-1 and the correct absorbance values. (The 3-to-1 ratio between the line intensities results from the 3-to-1 isotopic ratio of Cl-35 to Cl-37.) Diagram B shows the actual transmittance values that would be measured for the sample when using an instrument with a spectral resolution of 0.1 cm-1 or better. Diagram C shows the transmittance values that would be measured by an instrument that has a spectral resolution of 1.0 cm-1. Diagram D shows the absorbances calculated from the spectrum of Diagram C.


The area under the two lines in Diagram D is much smaller than the area under the two lines in Diagram A. This reduction of the area under the lines is the result of the instrumental smoothing over the “bottomed-out” transmittance lines. Those who use the expression Beer’s Law would describe the difference in areas between diagrams A and D as a “Beer’s law failure”. The way to avoid this “Beer’s law failure” is to measure only in spectral regions where the true transmittance is high enough so that there is no “bottoming-out” phenomenon. How high the apparent transmittance should be to avoid “bottoming out” depends on the spectral resolution, the total sample pressure and the degree of fine structure in the spectrum. In preparing the QASoft database, this has been taken in consideration. It will be noted that most of the half- wavenumber spectra in the database have apparent absorbances below 0.1 A.U (log base 10).


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