Beers Law Definition and Equation

Beers Law is an equation that relates the attenuation of light to properties of a material. The law states that 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 Beers Law is not valid at high solution concentrations. Other Names for Beers Law Beers Law is also known as the Beer-Lambert Law, the Lambert-Beer Law, and the  Beer–Lambert–Bouguer Law. The reason there are so many names is because more than one law is involved. Basically, Pierre Bouger discovered the law in 1729 and published it in Essai doptique sur la gradation de la lumià ¨re. Lambert quoted Bougers discovery in his Photometria in 1760, saying absorbance of a sample is directly proportional to the path length of light. Even though Lambert didnt claim discovery, he was often credited with it. August Beer discovered a related law in 1852. Beers Law stated that the absorbance is proportional to the concentration of the sample. Technically, Beers Law relates only to concentration, while the Beer-Lambert Law relates absorbance to both concentration and sample thickness. Key Takeaways: Beer's Law Beers Law states that the concentration of a chemical solution is directly proportional to its absorption of light.The premise is that a beam of light becomes weaker as it passes through a chemical solution. The attenuation of light occurs either as a result of distance through solution or increasing concentration.Beers Law goes by many names, including the Beer-Lambert Law, Lambert-Beer Law, and Beer-Lambert-Bouguer Law. Equation for Beers Law Beers Law may be written simply as: A ÃŽ µbc where  A is absorbance (no units)ÃŽ µ is the molar absorptivity with units of L mol-1  cm-1 (formerly called the extinction coefficient)b is the path length of the sample, usually expressed in cmc 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: The absorbance is directly proportional to the path length of the sample (the width of the cuvette).The absorbance is directly proportional to the concentration of the sample. In this example of the Beer-Lambert law, a green laser is attenuated as it passes through a solution of Rhodamine 6G. Amirber How to Use Beers Law While many modern instruments perform Beers Law calculations by simply comparing a blank cuvette with a sample, its 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.   Beers 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 Beers Law: A ÃŽ µbc 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 Importance of Beers Law Beers Law is especially important in the fields of chemistry, physics, and meteorology. Beers Law is used in chemistry to measure the concentration of chemical solutions, to analyze oxidation, and to measure polymer degradation. The law also describes the attenuation of radiation through the Earths atmosphere. While normally applied to light, the law also helps scientists understand the attenuation of particle beams, such as neutrons. In theoretical physics, the Beer-Lambert Law is a solution to the Bhatnagar-Gross-Krook (BKG) operator, which is used in the Boltzmann equation for computational fluid dynamics. Sources Beer, August. Bestimmung der Absorption des rothen Lichts in farbigen Flà ¼ssigkeiten (Determination of the absorption of red light in colored liquids). Annalen der Physik und Chemie, vol. 86, 1852, pp. 78–88.Bouguer, Pierre. Essai doptique sur la gradation de la lumià ¨re. Claude Jombert, 1729 pp. 16–22.Ingle, J. D. J., and S. R. Crouch. Spectrochemical Analysis. Prentice Hall, 1988.Lambert, J. H. Photometria sive de mensura et gradibus luminis, colorum et umbrae [Photometry, or, On the measure and gradations of light, colors, and shade]. Augsburg (Augusta Vindelicorum). Eberhardt Klett, 1760.Mayerhà ¶fer, Thomas Gà ¼nter, and Jà ¼rgen Popp. Beers law - why absorbance depends (almost) linearly on concentration. Chemphyschem, vol. 20, no. 4, December 2018. doi:10.1002/cphc.201801073