How To Calculate Molar Absorptivity

Molar absorptivity, also known as the molar extinction coefficient, measures how well a chemical species absorbs a given wavelength of light. It is commonly used in chemistry and should not be confused with the extinction coefficient, which is used more often in physics. The standard units for molar absorptivity are square meters per mole, but it is usually expressed as square centimeters per mole.

1. Define Variables

Define the variables to calculate the molar absorptivity. The absorbance (A) is the amount of light within a given wavelength that is absorbed by the solution. The concentration (c) of the absorbing species is the amount of absorbing species per unit volume. The path length (l) is the distance light travels through the solution. Molar absorptivity is represented by "e."

2. Apply Beer-Lambert Law

Use Beer-Lambert Law to calculate the molar absorptivity of a single absorbing species. The equation is:

\(A=ecl\)

so the equation for molar absorptivity is:

\(e=\frac{A}{cl}\)

3. Calculate Total Absorbance

Calculate the total absorbance of a solution that contains more than one absorbing species. Expand the Beer-Lambert law to:

\(A=(e_1c_1+e_2c_2+...)l\)

where "e_i" is the molar absorptivity of species "i," and "c_i" is the concentration of species "i" in the solution.

4. Calculate Molar Absorptivity

Calculate the molar absorptivity from the absorption cross-section and Avogadro's Number (approximately 6.022 x 10²³);

\(d=\frac{2.303}{N}e\)

where "d" is the absorption cross section and "N" is Avogadro's Number. Therefore:

\(d=\frac{2.303}{6.022\times 10^{23}}e=3.82\times 10^{-21}e\implies e=(2.62\times 10^{20})d\)

5. Predict Molar Absorptivity of Light

Predict the molar absorptivity of light at 280 nm by a protein. The molar absorptivity under these conditions depends on the number of aromatic residues the protein has, especially tryptophan.