Beer's Law Definition and Equation

Beer's Law or the Beer-Lambert Law

Lab Technician Testing Water with a Spectrophotometer
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Beer's Law is an equation that relates the attenuation of light to properties of a material. The law states the concentration of a chemical is directly proportional to the absorbance of a solution. The relation may be used to determine the concentration of a chemical species in a solution using a colorimeter or spectrophotometer. The relation is most often used in UV-visible absorption spectroscopy.

Note that Beer's Law is not valid at high solution concentrations.

Other Names for Beer's Law

Beer's Law is also known as the Beer-Lambert Law, the Lambert-Beer Law, and the Beer–Lambert–Bouguer law.

Equation for Beer's Law

Beer's Law may be written simply as:

A = εbc

where A is absorbance (no units)
ε is the molar absorbtivity with units of L mol-1 cm-1 (formerly called the extinction coefficient)
b is the path length of the sample, usually expressed in cm
c is the concentration of the compound in solution, expressed in mol L-1

Calculating the absorbance of a sample using the equation depends on two assumptions:

  1. The absorbance is directly proportional to the path length of the sample (the width of the cuvette).
  2. The absorbance is directly proportional to the concentration of the sample.

How To Use Beer's Law

While many modern instruments perform Beer's law calculations by simply comparing a blank cuvette with a sample, it's easy to prepare a graph using standard solutions to determine the concentration of a specimen.

The graphing method assumes a straight-line relationship between absorbance and concentration, which is valid for dilute solutions

Beer's Law Example Calculation

A sample is known to have a maximum absorbance value of 275 nm. Its molar absorptivity is 8400 M-1cm-1. The width of the cuvette is 1 cm.

A spectrophotometer finds A = 0.70. What is the concentration of the sample?

To solve the problem, use Beer's law:

A = εbc

0.70 = (8400 M-1cm-1)(1 cm)(c)

Divide both sides of the equation by [(8400 M-1 cm-1)(1 cm)]

c = 8.33 x 10-5 mol/L

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Helmenstine, Anne Marie, Ph.D. "Beer's Law Definition and Equation." ThoughtCo, Oct. 9, 2017, thoughtco.com/beers-law-definition-and-equation-608172. Helmenstine, Anne Marie, Ph.D. (2017, October 9). Beer's Law Definition and Equation. Retrieved from https://www.thoughtco.com/beers-law-definition-and-equation-608172 Helmenstine, Anne Marie, Ph.D. "Beer's Law Definition and Equation." ThoughtCo. https://www.thoughtco.com/beers-law-definition-and-equation-608172 (accessed November 19, 2017).