Chemists frequently use an instrument known as an ultraviolet-visible, or UV-Vis, spectrometer to measure the amount of ultraviolet and visible radiation absorbed by compounds. The amount of ultraviolet or visible radiation absorbed by a compound depends on three factors: the concentration, c, of the sample; the path length, l, of the sample holder, which determines the distance over which the sample and radiation interact; and the coefficient of molar absorption, e, sometimes referred to as the molar extinction coefficient. The equation is stated as A = ecl and is known as Beer’s law. The equation thus contains four variables, and to determine any of the four requires known values for three.

### Calculations

Determine the absorbance for the compound at the desired wavelength. This information may be extracted from the absorbance spectrum produced by any standard UV-Vis instrument. The spectra are normally plotted as absorbance vs. wavelength in nanometers. Generally, the appearance of any “peaks” in the spectrum indicates the wavelengths of interest.

Calculate the concentration of the sample in moles per liter, mol/L, also known as molarity, M. The general equation for molarity is

M = (grams of sample) / (molecular weight of compound) / liters of solution.

For example, a sample containing 0.10 grams of tetraphenylcyclopentadienone, with a molecular weight of 384 grams per mole, dissolved and diluted in methanol to a final volume of 1.00 liters would exhibit a molarity of:

M = (0.10 g) / (384 g/mol) / (1.00 L) = 0.00026 mol/L.

Determine the path length through the sample holder. In most cases, this is 1.0 cm. Other path lengths are possible, particularly when dealing with sample holders intended for gaseous samples. Many spectroscopists include the path length with the sample information printed on the absorbance spectrum.

Calculate the coefficient of molar absorption according to the equation A = ecl, where A is absorbance, c is concentration in moles per liter and l is path length in centimeters. Solved for e, this equation becomes e = A / (cl). Continuing the example from Step 2, tetraphenylcyclopentadienone exhibits two maxima in its absorbance spectrum: 343 nm and 512 nm. If the path length was 1.0 cm and the absorbance at 343 was 0.89, then

e(343) = A / (cl) = 0.89 / (0.00026 * 1.0) = 3423

And for the absorbance of 0.35 at 512 nm,

e(512) = 0.35 / (0.00026 * 1.0) = 1346.