# Molar absorption coefficient

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{{short description|Measure of how strongly a chemical species absorbs a given wavelength of light}}

In [chemistry](/source/chemistry), the '''molar absorption coefficient''' or '''molar attenuation coefficient''' ({{mvar|ε}})<ref name=Chap11Sec2>{{cite web |title=Chapter 11 Section 2 - Terms and symbols used in photochemistry and in light scattering |url=https://media.iupac.org/publications/analytical_compendium/Cha11sec2.pdf |website=Compendium on Analytical Nomenclature (Orange Book)|publisher=IUPAC|date=2002|page=28}}</ref> is a measurement of how strongly a [chemical species](/source/chemical_species) absorbs, and thereby [attenuate](/source/attenuate)s, light at a given [wavelength](/source/wavelength). It is an [intrinsic property](/source/intrinsic_property) of the species. The [SI unit](/source/International_System_of_Units) of molar absorption coefficient is the square metre per [mole](/source/Mole_(unit)) ({{nowrap|m<sup>2</sup>/mol}}), but in practice, quantities are usually expressed in terms of [<span title="mol/L">M</span>](/source/Molar_concentration)<sup>−1</sup>⋅cm<sup>−1</sup> or L⋅mol<sup>−1</sup>⋅cm<sup>−1</sup> (the latter two units are both equal to {{nowrap|0.1 m<sup>2</sup>/mol}}). In older literature, the cm<sup>2</sup>/mol is sometimes used; 1 M<sup>−1</sup>⋅cm<sup>−1</sup> equals 1000&nbsp;cm<sup>2</sup>/mol. The molar absorption 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](/source/International_Union_of_Pure_and_Applied_Chemistry).<ref>{{GoldBookRef|title=Extinction|file=E02293|accessdate=2015-03-15}}</ref><ref>{{GoldBookRef|title=Absorptivity|file=A00044|accessdate=2015-03-15}}</ref>

==Beer–Lambert law==
The [absorbance](/source/absorbance) of a material that has only one absorbing species also depends on the pathlength and the concentration of the species, according to the [Beer–Lambert law](/source/Beer%E2%80%93Lambert_law)
:<math>A = \varepsilon c\ell,</math>
where
*{{mvar|ε}} is the ''molar absorption coefficient'' of that material;
*{{mvar|c}} is the [molar concentration](/source/molar_concentration) of those species;
*{{mvar|ℓ}} is the path length.

Different disciplines have different conventions as to whether [absorbance](/source/absorbance) is decadic (10-based) or Napierian (e-based), i.e., defined with respect to the transmission via [common logarithm](/source/common_logarithm) (log<sub>10</sub>) or a [natural logarithm](/source/natural_logarithm) (ln). The molar absorption coefficient is usually decadic.<ref name=Chap11Sec2/><ref>{{cite web |url=https://www.iupac.org/publications/analytical_compendium/Cha10sec213.pdf |title=Molecular Spectroscopy|website=Compendium on Analytical Nomenclature |publisher=IUPAC|date=2002}}{{cite web |url=https://www.iupac.org/publications/analytical_compendium/Cha10sec352.pdf |title=Measuring techniques|website=Compendium on Analytical Nomenclature |publisher=IUPAC|date=2002}}</ref> When ambiguity exists, it is important to indicate which one applies.

When there are ''N'' absorbing species in a solution, the overall absorbance is the sum of the absorbances for each individual species ''i'':
:<math>A = \sum_{i = 1}^N A_i = \ell \sum_{i = 1}^N \varepsilon_i c_i.</math>

The composition of a mixture of ''N'' absorbing species can be found by measuring the absorbance at ''N'' [wavelength](/source/wavelength)s (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 an ''[isosbestic point](/source/isosbestic_point)'' for a pair of species. The set of the following [simultaneous equations](/source/simultaneous_equations) can be solved to find the concentrations of each absorbing species:
:<math>\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 absorption coefficient (in units of M<sup>−1</sup>cm<sup>−1</sup>) is directly related to the [attenuation cross section](/source/Cross_section_(physics)) (in units of cm<sup>2</sup>) via the [Avogadro constant](/source/Avogadro_constant) ''N''<sub>A</sub>:<ref name=Lakowicz2006>{{cite book|last1=Lakowicz|first1=J. R.|title=Principles of Fluorescence Spectroscopy|date=2006|publisher=Springer|location=New York|isbn=9780387312781|page=59|edition=3rd}}</ref>

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

==Mass absorption coefficient==
The [mass absorption coefficient](/source/mass_absorption_coefficient) is equal to the molar absorption coefficient divided by the [molar mass](/source/molar_mass) of the absorbing species.

:{{mvar|ε<sub>m</sub>}} = {{frac|{{mvar|ε}}|{{mvar|M}}}}
where
*{{mvar|ε<sub>m</sub>}} = Mass absorption coefficient
*{{mvar|ε}} = Molar absorption coefficient
*{{mvar|M}} = Molar mass of the absorbing species

==Proteins==
In [biochemistry](/source/biochemistry), the molar absorption coefficient of a [protein](/source/protein) at {{nowrap|280 nm}} depends almost exclusively on the number of aromatic residues, particularly [tryptophan](/source/tryptophan), and can be predicted from the sequence of [amino acids](/source/amino_acids).<ref>{{cite journal|last1=Gill|first1=S. C.|last2=von Hippel|first2=P. H.|title=Calculation of protein extinction coefficients from amino acid sequence data|journal=Analytical Biochemistry|date=1989|volume=182|issue=2|pages=319–326|pmid=2610349|doi=10.1016/0003-2697(89)90602-7}}</ref> Similarly, the molar absorption coefficient of [nucleic acids](/source/nucleic_acids) at {{nowrap|260 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.

==References==
{{reflist}}

==External links==
*[http://www.microscopyu.com/articles/livecellimaging/fpintro.html Nikon MicroscopyU: Introduction to Fluorescent Proteins] includes a table of molar attenuation coefficient of [fluorescent protein](/source/fluorescent_protein)s.

{{BranchesofSpectroscopy}}

Category:Analytical chemistry
Category:Absorption spectroscopy
Category:Molar quantities

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Adapted from the Wikipedia article [Molar absorption coefficient](https://en.wikipedia.org/wiki/Molar_absorption_coefficient) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Molar_absorption_coefficient?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.