Molecular Spectroscopy


Beer-Lambert Law


The Beer-Lambert law (or Beer's law) is the linear relationship between absorbance and concentration of an absorbing species. The general Beer-Lambert law is usually written as:
A = a(lambda) * b * c
where A is the measured absorbance, a(lambda) is a wavelength-dependent absorptivity coefficient, b is the path length, and c is the analyte concentration. When working in concentration units of molarity, the Beer-Lambert law is written as:
A = epsilon * b * c
where epsilon is the wavelength-dependent molar absorptivity coefficient with units of M -1 cm -1 .


Experimental measurements are usually made in terms of transmittance (T), which is defined as:
T = I / I o
where I is the light intensity after it passes through the sample and I o is the initial light intensity. The relation between A and T is:
A = -log T = - log (I / I o ).

Absorption of light by a sample

Modern absorption instruments can usually display the data as either transmittance, %-transmittance, or absorbance. An unknown concentration of an analyte can be determined by measuring the amount of light that a sample absorbs and applying Beer's law. If the absorptivity coefficient is not known, the unknown concentration can be determined using a working curve of absorbance versus concentration derived from standards.

Limitations of the Beer-Lambert law

The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of nonlinearity include:
deviations in absorptivity coefficients at high concentrations (>0.01M) due to electrostatic interactions between molecules in close proximity
scattering of light due to particulates in the sample
fluoresecence or phosphorescence of the sample
changes in refractive index at high analyte concentration
shifts in chemical equilibria as a function of concentration
non-monochromatic radiation, deviations can be minimized by using a relatively flat part of the absorption spectrum such as the maximum of an absorption band
stray light