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
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 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|