Beer-Lambert Law

The relationship between absorbance and concentration is linear and is described by Beer-Lambert Law, shown in Figure 1.

The amount of light at a specific wavelength absorbed by a substance can be calculated in two methods. The first is to take the base 10 logarithm of the following: the intensity of light that travels towards the sample, divided by the intensity of light that travels out of the sample. The second method is multiplying the molar extinction coefficient by the sample concentration and path length.

Figure 1: The Beer-Lambert Law where c is the molar concentration of the detected substance, A is the absorbance value returned by the spectrophotometer in arbitrary units (AU), ε is the wavelength-dependent molar extinction coefficient in molar per cm (M/cm), and L is the pathlength in cm.

Note, the molar extinction coefficient is also called molar absorptivity. Also, for most spectrophotometers that use standard cuvettes, the path length is 1 cm.

This Beer-Lambert equation is easily rearranged to suit the needs of experimentation. For example, to convert absorbance values into concentration, the equation:

A = εcl

Can be rearranged to:

c = A/εl