# How to Find the Concentration of a Sample Using UV-Vis Spectroscopy

The Beer Lambert law is a linear relationship between the concentration of a solution and its absorbance. It is used in modern-day spectrophotometry.

The law was developed by Pierre Bouguer and Johann Heinrich Lambert. August Beer improved the law by including path length and sample concentration into the equation.

The molar extinction coefficient is specific to each chemical and is wavelength-specific.

## Absorbance

The Beer-Lambert law correlates absorbance (the negative log of transmittance) to both sample thickness and the concentration of a chemical species in the sample. This law is used in UV-visible spectroscopy to find the concentration of a sample using a spectrophotometer. First, the spectra of several different dilutions of a sample are measured. When plotted, these spectra will overlap almost perfectly. The slope of this line will give the concentration of the unknown sample.

This relationship is based on the fact that each substance has its own molar extinction coefficient, which is wavelength specific. This coefficient is also known as molar absorptivity or molar absorbance. The molar extinction coefficient and the path length are both given in units of length per wavelength, so the absorbance is also given in units of wavelength per length. If the molar extinction coefficient is not constant, the absorption will not be linear. This is because there are interactions and instrumental nonlinearities that can cause deviations from the Beer-Lambert law.

## Extinction Coefficient

The extinction coefficient () of a material is a measure of how much light the substance absorbs or reflects. It is proportional to the path length of light passing through the material, and is used in Beer’s law to calculate concentration from absorbance measurements made on a spectrophotometer or colorimeter.

The Beer Lambert law, also called Beer’s Law or the Beer-Bouguer-Lambert Law, relates the attenuation of light through a medium to its properties and is an essential part of spectroscopy. It has a number of limits and pitfalls that every spectroscopist should understand, and it is not uncommon to have spectral features that are not explained by the Beer Lambert law.

It is important to note that the linearity of Beer’s law only holds true under certain very restrictive conditions. When a solution has high concentrations the molecules tend to be close enough to interact with one another, and this causes deviations from linearity. In addition, non-linear optical processes can cause variances in measurements.

## Path Length

Path length is the distance that light travels from an initial position to a final position. It is also known as the diffraction radius and it is measured in centimeters.

The diffraction radius is defined by the ratio of the wavelength of the light used for measurement and the molar extinction coefficient of the sample. The molar extinction coefficient is unique to each chemical and is determined by wavelength-specific absorption measurements.

The Beer-Lambert law relates the intensity of a monochromatic beam of light passing through a sample to the concentration of that sample. The law was derived by Pierre Bouger in 1729 and Johann Heinrich Lambert quoted Bouger’s work in his book “Essai D’Optique Sur La Gradation De La Lumiere”. The law is often violated at high concentrations as demonstrated in the plot of concentration verses absorbance below. This violation may be due to reduced solubility of the dye at high concentrations, stray light in the flow cell or instrumental errors such as quantisation errors.

## Concentration

In chemical analysis, the concentration of a solution is related to its absorbance. The concentration of the sample is found by comparing its absorbance to a known solution of the same concentration. The Beer Lambert law, which relates absorbance to both concentration and path length, allows for this comparison.

If you have a number of different solutions with known concentration and measure their absorbance with a spectrometer, the results will be plotted on a graph. If the points fit to a linear line, their concentration can be determined from the slope of the line, which is equal to the molar absorptivity constant divided by the path length.

This relation is used in chemistry to find the concentration of chemical solutions and assess their oxidation. In physics, it is also used to determine the attenuation of radiation passing through matter, such as Earth’s atmosphere. Other names for this law include the Beer-Lambert law, Bouguer law, and the basic extinction law.