Beer's Law - Why Absorbance Depends (Almost) Linearly on Concentration

Abstract

Beer's law assumes a strictly linear dependence of the absorbance from concentration. Usually, chemical interactions and instrumental imperfection are made responsible for experimental deviations from this linearity. In this contribution we show that even in the absence of such interactions and instrumental errors, absorbance should be only approximately proportional to concentration. This can be derived from the quadratic dependence of the complex refractive index, and, by that, of the molar attenuation coefficient, from the dielectric constant and its frequency dispersion. Following dispersion theory, it is the variation of the real and the imaginary part of the dielectric function that depends linearly on concentration in the absence of interactions between the oscillators. We show that this linear correlation translates into a linear dependence of the absorbance for low concentrations or molar oscillator strengths based on an approximation provided by Lorentz in 1906. Accordingly, Beer's law can be derived from dispersion theory.

Keywords: Beer's law; absorbance; concentration; dispersion; linear dependence.