Molar attenuation coefficient

Molar attenuation coefficient, also known as molar absorptivity or molar extinction coefficient, is a measure of how strongly a chemical species attenuates light at a given wavelength. It is an intrinsic property of the substance, indicating the amount of light absorbed per unit concentration of the substance in a solution. The molar attenuation coefficient is denoted by the Greek letter epsilon (ε) and is measured in units of L mol⁻¹ cm⁻¹.

Definition

The molar attenuation coefficient is defined by the Beer-Lambert law, which describes the linear relationship between absorbance (A) of light passing through a substance and the concentration (c) of that substance, as well as the path length (l) through which the light travels. Mathematically, it is expressed as:

A = εcl

where:

• A is the absorbance (no units),
• ε is the molar attenuation coefficient (L mol⁻¹ cm⁻¹),
• c is the concentration of the compound in solution (mol L⁻¹),
• l is the path length of the cuvette in which the solution is contained (cm).

Applications

The molar attenuation coefficient is widely used in spectrophotometry, a method for measuring how much a chemical substance absorbs light, by measuring the intensity of light as a beam of light passes through sample solution. It is an essential parameter in determining the concentration of an unknown solution using the Beer-Lambert law. Applications include:

• Determining the concentration of a substance in a solution,
• Studying reaction kinetics,
• Quantifying the purity of a substance,
• Characterizing compounds in chemical analysis.

Factors Affecting Molar Attenuation Coefficient

The value of the molar attenuation coefficient depends on several factors, including:

• The wavelength of light: ε varies with wavelength, reaching a maximum at the absorption peak of the substance.
• The solvent: The nature of the solvent can affect the electronic structure of the solute, thus altering its absorption characteristics.
• Temperature: Changes in temperature can affect the absorption spectrum of a substance.
• pH of the solution: For substances that can exist in multiple protonation states, the pH can significantly affect the absorption spectrum.

Measurement

To measure the molar attenuation coefficient, a spectrophotometer is used to determine the absorbance of a series of solutions with known concentrations at a specific wavelength. The slope of the plot of absorbance versus concentration gives the molar attenuation coefficient for that wavelength.

Limitations

The Beer-Lambert law, and by extension the concept of molar attenuation coefficient, assumes that the system follows ideal behavior. Deviations can occur due to:

• High concentrations, leading to molecule-molecule interactions that alter absorbance,
• Scattering of light, particularly in turbid solutions,
• Fluorescence or phosphorescence of the sample,
• Non-homogeneous distribution of the analyte within the sample.

See Also

• Absorbance
• Spectrophotometry
• Beer-Lambert law
• Chemical analysis