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Beer's Law-Why Integrated Absorbance Depends Linearly on Concentration.


ABSTRACT: As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1?%. This deviation is a consequence of a sum rule that was derived from the Kramers-Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis.

SUBMITTER: Mayerhofer TG 

PROVIDER: S-EPMC6899465 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature

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Beer's Law-Why Integrated Absorbance Depends Linearly on Concentration.

Mayerhöfer Thomas G TG   Pipa Andrei V AV   Popp Jürgen J  

Chemphyschem : a European journal of chemical physics and physical chemistry 20191010 21


As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the K  ...[more]

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