Molar attenuation coefficient

The molar attenuation coefficient is a measurement of how strongly a chemical species 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, it is usually taken as the M⁻¹⋅cm⁻¹ or the L⋅mol⁻¹⋅cm⁻¹. In older literature, the cm²/mol is sometimes used with corresponding values 1,000 times larger. In practice these units are the same, with the difference being expression of volume in either cm³ or in L. 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.

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

$A = \varepsilon c\ell,$

where

• ε is the molar attenuation coefficient of that material;
• c is the amount 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:

$A = \sum_{i = 1}^N A_i = \ell \sum_{i = 1}^N \varepsilon_i c_i.$

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:

$\begin{cases} A(\lambda_1) = \ell\sum_{i=1}^N \varepsilon_i(\lambda_1) c_i,\\ \ldots\\ A(\lambda_N) = \ell\sum_{i=1}^N \varepsilon_i(\lambda_N) c_i.\\ \end{cases}$

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

$\sigma = \ln(10) \frac{10^3}{N_A} \varepsilon = 3.823,532,16 \times 10^{-21}\,\varepsilon.$

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

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.

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.