Inchemistry, themolar absorption coefficient ormolar attenuation coefficient (ε)^[1] is a measurement of how strongly achemical species absorbs, and therebyattenuates, light at a givenwavelength. It is anintrinsic property of the species. TheSI unit of molar absorption coefficient is the square metre permole (m²/mol), but in practice, quantities are usually expressed in terms ofM⁻¹⋅cm⁻¹ or L⋅mol⁻¹⋅cm⁻¹ (the latter two units are both equal to0.1 m²/mol). In older literature, the cm²/mol is sometimes used; 1 M⁻¹⋅cm⁻¹ equals 1000 cm²/mol. The molar absorption coefficient is also known as themolar extinction coefficient andmolar absorptivity, but the use of these alternative terms has been discouraged by theIUPAC.^[2][3]

Theabsorbance of a material that has only one absorbing species also depends on the pathlength and the concentration of the species, according to theBeer–Lambert law

${\displaystyle A=\epsilon c\ell ,}$

where

• ε is themolar absorption coefficient of that material;
• c is themolar concentration of those species;
• ℓ is the path length.

Different disciplines have different conventions as to whetherabsorbance is decadic (10-based) or Napierian (e-based), i.e., defined with respect to the transmission viacommon logarithm (log₁₀) or anatural logarithm (ln). The molar absorption coefficient is usually decadic.^[1][4] When ambiguity exists, it is important to indicate which one applies.

When there areN absorbing species in a solution, the overall absorbance is the sum of the absorbances for each individual speciesi:

${\displaystyle A=\sum _{i=1}^N{A}_i=\ell \sum _{i=1}^N{\epsilon }_i{c}_i.}$

The composition of a mixture ofN absorbing species can be found by measuring the absorbance atNwavelengths (the values of the molar absorption coefficient 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 may be anisosbestic point for a pair of species. The set of the followingsimultaneous equations can be solved to find the concentrations of each absorbing species:

${\displaystyle \{\begin{array}{l}A({\lambda }_1)=\ell \sum _{i=1}^N{\epsilon }_i({\lambda }_1)c_i,\\ \dots \\ A({\lambda }_N)=\ell \sum _{i=1}^N{\epsilon }_i({\lambda }_N)c_i.\end{array}}$

The molar absorption coefficient (in units of M⁻¹cm⁻¹) is directly related to theattenuation cross section (in units of cm²) via theAvogadro constantN_A:^[5]

${\displaystyle \sigma =\ln (10)\frac{{10}^3}{N_{\text{A}}}\epsilon \approx 3.82353216\times {10}^{-21}\epsilon .}$

Themass absorption coefficient is equal to the molar absorption coefficient divided by themolar mass of the absorbing species.

ε_m =ε⁄M

where

• ε_m = Mass absorption coefficient
• ε = Molar absorption coefficient
• M = Molar mass of the absorbing species

Inbiochemistry, the molar absorption coefficient of aprotein at280 nm depends almost exclusively on the number of aromatic residues, particularlytryptophan, and can be predicted from the sequence ofamino acids.^[6] Similarly, the molar absorption coefficient ofnucleic acids at260 nm can be predicted given the nucleotide sequence.

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

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

• Analytical chemistry
• Absorption spectroscopy
• Molar quantities

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