DISCOVER

# How to Calculate Extinction Coefficients

Updated February 21, 2017

Some chemical compounds absorb visible or ultraviolet radiation of particular wavelengths. The extent to which such a compound absorbs light at any particular wavelength is referred to as the absorbance, A. Mathematically, Beer's law governs absorbance and states that A = ecl, where c represents the concentration of the compound, l is the path length, or length of the sample through which the light travels as it's absorbed, and e is the molar extinction coefficient -- sometimes called the molar absorptivity. The experimenter controls the concentration and path length parameters, and an instrument called a spectrometer measures the absorbance at various wavelengths. The experimenter must calculate the molar extinction coefficient from the absorbance, concentration and path length.

Run an ultraviolet-visible spectrum of the sample under investigation if it is not already available.

Locate the wavelength of maximum absorbance, commonly referred to as "lambda max," on the spectrum by identifying the wavelength at which the absorbance reaches a maximum and forms a peak.

Calculate the concentration of the solution if it is not already known. By convention, chemists normally use units of molarity, or moles per litre, for concentration units in ultraviolet-visible spectroscopy. Calculate molarity by dividing the moles of substance by the total litres of solution. Moles of substance is given by dividing the grams of substance by its formula weight or molecular weight. For example, sucrose, C12H22O11, exhibits a molecular weight of 342 grams per mole, and a sample containing 0.100 grams of sucrose dissolved and diluted to 100 millilitres (0.100 litres) would contain (0.100 / 342) = 0.000292 moles. The molarity of the solution would then be 0.000292 moles / 0.100 litres = 0.000292 mol/L.

Calculate the molar extinction coefficient according to e = A / cl using the absorbance at the wavelength of maximum absorbance. Continuing the example, if a sample with a concentration of 0.000292 moles/L exhibited an absorbance of 0.65 at 550 nanometres in a cell with a 1.0-cm path length, then e = 0.75 / (0.000292 * 1.00) = 2568.

#### Things You'll Need

• Ultraviolet-Visible spectrometer