

Molecular Spectroscopy

BeerLambert Law
The BeerLambert law (or Beer's law) is the linear relationship between absorbance and
concentration of an absorbing species. The general BeerLambert law is usually written as:
A = a(lambda) * b * c
where A is the measured absorbance, a(lambda) is a wavelengthdependent absorptivity
coefficient, b is the path length, and c is the analyte concentration. When working in
concentration units of molarity, the BeerLambert law is written as:
A = epsilon * b * c
where epsilon is the wavelengthdependent 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.
The linearity of the BeerLambert 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  
nonmonochromatic 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 