Chemistry:Molar attenuation coefficient

The molar attenuation coefficient or molar absorption coefficient is a measurement of how strongly a chemical species absorbs, and thereby attenuates, light at a given wavelength. It is an intrinsic property of the species. The SI unit of molar attenuation coefficient is the square metre per mole (m²/mol), but in practice, quantities are usually expressed in terms of M⁻¹⋅cm⁻¹ or L⋅mol⁻¹⋅cm⁻¹ (the latter two units are both equal to 0.1 m²/mol). In older literature, the cm²/mol is sometimes used; 1 M⁻¹⋅cm⁻¹ equals 1000 cm²/mol. The molar attenuation coefficient is also known as the molar extinction coefficient, and molar absorptivity, but the use of these alternative terms has been discouraged by the IUPAC.

Beer–Lambert law

The absorbance of a material that has only one attenuating species also depends on the pathlength and the concentration of the species, according to the Beer–Lambert law

[math]\displaystyle{ A = \varepsilon c\ell, }[/math]

where

• ε is the molar attenuation coefficient of that material;
• c is the molar concentration of those species;
• ℓ is the pathlength.

Different disciplines have different conventions as to whether absorbance is decadic (10-based) or Napierian (e-based), i.e., defined with respect to the transmission via common logarithm (log₁₀) or a natural logarithm (ln). The molar attenuation coefficient is usually decadic. When ambiguity exists, it is best to indicate which one applies.

When there are N attenuation species in a solution, the overall absorbance is the sum of the absorbances for each individual species i:

[math]\displaystyle{ A = \sum_{i = 1}^N A_i = \ell \sum_{i = 1}^N \varepsilon_i c_i. }[/math]

The composition of a mixture of N attenuating species can be found by measuring the absorbance at N wavelengths (the values of the molar coefficient of attenuation for each species at these wavelengths must also be known). The wavelengths chosen are usually the wavelengths of maximum absorption (absorbance maxima) for the individual species. None of the wavelengths must be an isosbestic point for a pair of species. The set of the following simultaneous equations can be solved to find the concentrations of each attenuating species:

[math]\displaystyle{ \begin{cases} A(\lambda_1) = \ell\sum_{i=1}^N \varepsilon_i(\lambda_1) c_i,\\ \ldots\\ A(\lambda_N) = \ell\sum_{i=1}^N \varepsilon_i(\lambda_N) c_i.\\ \end{cases} }[/math]

The molar attenuation coefficient (in units of cm²) is directly related to the attenuation cross section via the Avogadro constant N_A:

[math]\displaystyle{ \sigma = \ln(10) \frac{10^3}{N_\text{A}} \varepsilon \approx 3.823 532 16 \times 10^{-21}\,\varepsilon. }[/math]

Mass attenuation coefficient

The mass attenuation coefficient is equal to the molar attenuation coefficient divided by the molar mass.

Proteins

In biochemistry, the molar attenuation coefficient of a protein at 280 nm depends almost exclusively on the number of aromatic residues, particularly tryptophan, and can be predicted from the sequence of amino acids. Similarly, the extinction coefficient of nucleic acids at 260 nm can be predicted given the nucleotide sequence.

If the molar attenuation coefficient is known, it can be used to determine the concentration of a protein in solution.

External links

• Nikon MicroscopyU: Introduction to Fluorescent Proteins includes a table of molar attenuation coefficient of fluorescent proteins.