Beer–Lambert law

Beer–Lambert Law, also known as Beer's Law, the Lambert–Beer Law, or the Beer–Lambert–Bouguer Law, describes the linear relationship between the absorption of light by a medium and the properties of the medium through which the light is traveling. The law is a fundamental principle in the fields of spectrophotometry and photochemistry, with significant applications in chemistry, physics, and biology, particularly in the concentration determination of a solute in a solution.

Overview

The Beer–Lambert Law can be expressed by the equation:

\[A = \epsilon \cdot l \cdot c\]

where:

• \(A\) is the absorbance (no units, as it is a logarithmic measure),
• \(\epsilon\) is the molar absorptivity or extinction coefficient of the substance (measured in L mol\(^{-1}\) cm\(^{-1}\)),
• \(l\) is the path length of the light through the material (measured in cm),
• \(c\) is the concentration of the absorbing species per volume of solution (measured in mol L\(^{-1}\)).

This equation implies that the absorbance of a sample is directly proportional to the concentration of the absorbing species in the sample and the path length through which the light passes. It assumes that the system follows the criteria of homogeneity and that the light passes through the sample uniformly.

Applications

The Beer–Lambert Law is widely used in quantitative analytical chemistry to determine the concentration of a solute in a solution. It is the basis for creating calibration curves from standards of known concentration by measuring their absorbance at a specific wavelength. This method is employed in the operation of instruments like UV-Vis spectrophotometers, which are essential tools in laboratories for the analysis of DNA, proteins, and many other substances.

Limitations

While the Beer–Lambert Law provides a simple linear relationship, several factors can limit its applicability:

• High concentrations of the solute can cause deviations due to electrostatic interactions between molecules in close proximity.
• The presence of scattering particles in the sample can affect the path of light, leading to inaccuracies.
• The law assumes that the absorbing species does not undergo any chemical change during the measurement, which might not always be the case.

Historical Context

The law is named after August Beer and Johann Heinrich Lambert, who were among the first to relate the absorption of light to the properties of the material through which the light is passing. Beer's work in 1852 further refined Lambert's initial findings from the 18th century, leading to the combined form known today.

See Also

• Spectroscopy
• Absorption spectroscopy
• Molecular absorption spectroscopy
• UV/Vis spectroscopy