By Riti Gupta — Updated March 24, 2022
Accurately determining the concentration of reagents and products is essential in any laboratory experiment. By measuring how much light a solution absorbs, scientists can infer the concentration of the absorbing species using the well‑established Beer‑Lambert Law.
The Beer‑Lambert Law describes how the intensity of light diminishes as it passes through a material. In ultraviolet–visible (UV‑Vis) spectroscopy, a beam of light is shone through a sample; the portion that is not transmitted is absorbed by the molecules in the solution.
The absorbed light is proportional to two factors: the path length of the light through the sample (l) and the concentration of the absorbing species (c). The law is expressed as:
A = log (I0 / I) = ε l c
Here, A is the absorbance (a unitless quantity), I0 is the incident light intensity, I is the transmitted light intensity, ε is the molar absorptivity (or molar extinction coefficient), and l is the path length.
To apply the equation correctly, each variable must be expressed in its standard units:
When these units are combined, the result is a dimensionless absorbance, as expected.
Suppose you wish to determine the concentration of the food dye Red #40 in a solution. The dye has a molar absorptivity of 25,900 L mol–1 cm–1 at 501 nm. You place 1 mL of the solution in a cuvette with a 1 cm path length and measure an absorbance of 0.17.
Plugging the known values into the Beer‑Lambert equation gives:
0.17 = (25,900 L mol–1 cm–1) × (1 cm) × c
Solving for concentration:
c = 6.56 × 10–6 M
For easier interpretation, this is often expressed in micromolar:
c = 6.56 µM
Thus, the Red #40 solution has a concentration of 6.56 µM.
By mastering the Beer‑Lambert Law, researchers can reliably quantify analytes in solution, track reaction progress, and ensure accurate experimental conditions.
