Lambert-Beer law

The Lambert-Beer law, also known as the Beer-Lambert law or simply Beer's Law, is a fundamental principle in spectroscopy and analytical chemistry. This law establishes a relationship between the absorption of light by a substance and its physical-chemical properties, providing a basis for determining the concentration of an absorbing solution.

In this article, the Lambert-Beer law will be explored in detail, including its statement, derivation, applications, and limitations.

The Lambert-Beer law articulates that the absorption of light when passing through an absorbing medium is directly proportional to the length of the path that the light travels within the medium and the concentration of the absorbent present. Mathematically, it is expressed as:

A = ε⋅c⋅l

Where:

This relationship implies that the higher the absorbent concentration or the optical path length, the higher the absorbance. It is important to note that the law assumes a linear relationship between absorbance and concentration, which is valid under specific conditions.

The Lambert-Beer law can be derived by considering two fundamental principles: Lambert's law, which states that the decrease in light intensity is proportional to the length of the optical path in a homogeneous medium, and Beer's law, which postulates that this decrease is proportional to the concentration of the absorbent.

Combining both laws, an expression is obtained that relates the intensity of the incident light (I0) and the intensity of the transmitted light (I) with the concentration and the length of the optical path:

Log(I0/I) = ε · c · l

From this equation we derive the definition of absorbance ( TO ), which is the base ten logarithm of the inverse of the transmittance ( T ), where T It is the relationship between the intensity of transmitted light and the intensity of incident light.

The Lambert-Beer law has extensive applications in different fields such as chemistry, biology, physics and engineering:

Although the Lambert-Beer law is widely used, it has limitations:

The Lambert-Beer Law is fundamental in the field of spectroscopy, an essential technique in analytical chemistry and biochemistry to determine the concentration of an absorbent solution. This law establishes a direct and proportional relationship between the absorbance of a sample and its concentration, which allows the presence of a substance in a solution to be quantified accurately and reliably.

In spectroscopic practice, the Lambert-Beer Law allows the concentration of a substance in a solution to be calculated by measuring the amount of light absorbed at a specific wavelength. This quantification capability is crucial in numerous scientific and technical contexts, from the analysis of environmental samples to the verification of the purity of pharmaceutical compounds.

The law facilitates the use of calibration curves that relate absorbance to concentration, using solutions of known concentrations as standards. These curves are essential to determine the concentration of unknown samples quickly and efficiently, providing an indispensable tool for quantitative analysis in laboratories.

In analytical chemistry, this law is used extensively to quantify the concentration of chemical solutions. For example, by measuring the intensity of light before and after passing through a solution, chemists can determine the concentration of a particular compound in that solution. This is essential for experiments ranging from determining water quality to identifying products in chemical reactions.

In biochemistry, the Lambert-Beer Law is essential for studies involving biomolecules, such as proteins and nucleic acids. For example, it allows protein quantification using the Bradford assay, a routine procedure in molecular biology laboratories. In medicine, this law facilitates the determination of the concentration of drugs in the blood, crucial for monitoring and adjusting dosages in patients.

The relevance of the Lambert-Beer Law in spectroscopy has driven the development of advanced instruments and innovative techniques. Modern spectrophotometers, for example, are designed to make precise and reproducible measurements that are based on this law, facilitating their application in research, product development and quality control.

The Lambert-Beer Law, fundamental to spectroscopy and analytical chemistry, has its roots in the individual works of two prominent scientists: Johann Heinrich Lambert and August Beer. This law, which relates the absorption of light to the properties of the material passed through, has been a pillar in the field of science, allowing significant advances in various fields of research.

Johann Heinrich Lambert, a Swiss mathematician, physicist, and astronomer, made pioneering contributions in the 18th century. In 1760, Lambert formulated a law that described how the intensity of light decreases exponentially as it passes through an absorbing medium. His work established the foundation of what would eventually become known as "Lambert's Law" of light absorption.

August Beer was a 19th-century German physicist and mathematician who extended Lambert's work. In 1852, Beer discovered that the absorption of light by a solution is proportional to the concentration of the absorbent in the solution. This relationship provided the second critical piece of the puzzle that would combine with Lambert's law to form the Lambert-Beer Law.

The Lambert-Beer Law, as we know it today, is a combination of the principles discovered by Lambert and Beer. It states that the absorbance of a sample is directly proportional to the concentration of the absorber and the optical path of light through the sample. This principle has been essential for the development of analytical spectroscopy and photometry.