12.9 : UV–Vis Spectroscopy: Beer–Lambert Law

The Beer-Lambert law describes the relationship between absorbance and concentration, which combines the principles established by scientists Johann Heinrich Lambert and August Beer. Lambert's law states that when light passes through a medium, the loss in intensity is directly proportional to the original intensity and the path length of the light. Beer's law proposed that the transmittance of a solution remains constant if the product of concentration and path length is constant. The modern Beer-Lambert law combines these two laws and correlates the light's absorbance, concentration, and path length.

According to the Beer-Lambert law, absorbance is concentration multiplied by the molar absorptivity coefficient and the path length. At a single wavelength, absorbance can be given by the formula,

Where A is absorbance, ε is the molar absorptivity of the compound or molecule in solution (M⁻¹cm⁻¹), the path length of the cuvette is denoted by l, and c is the concentration of the solution (M). Absorbance of a solution, is the logarithmic function of the ratio of the intensity of the incident light, I₀, to the intensity of the transmitted light, I.

The molar absorptivity, also known as the molar absorptivity coefficient, ε, is the absorbance of a compound when a 1.00 M solution is taken in a cell with a 1.00 cm path length. The absorbance of a solution is directly proportional to its concentration. The linear relationship between absorbance and concentration allows the determination of an unknown concentration by plotting the absorbance against known concentrations, creating a calibration curve.