BEER-LAMBERT LAW / LIMITATION/ APPLICATIONS

Beer-Lambert law is actually a combination of two laws. Beer's Law and Lambert's law.

Both of these are absorbance law

Beer's law𓀍

   The intensity of a beam of monochromatic light decreases exponentially with the increase of concentration of absorbing substance.

Lambert's law

    When a beam of light is allowed to pass through a transparent medium, the rate of decrease of intensity with a thickness of medium is directly proportional to the intensity of light.

 

Beer-Lambert law

• The law was first developed by Pierre Bouguer before 1729. It was later attributed to Johann Heinrich Lambert who cited Bouguer’s findings. The law included path length as a variable that affected absorbance. Later, Beer extended in 1852 the law to include the concentration of solutions, thus giving the law its name Beer-Lambert Law.
• The Beer-Lambert law is the linear relationship between absorbance and concentration of an absorbing species. The Beer-Lambert law, also known as Beer's law, the Lambert-Beer law, or the Beer-Lambert–Bouguer law.
• The Beer-Lambert law (also called the Beer-Lambert-Bouguer law or simply Beer's law) is the linear relationship between absorbance and concentration of an absorber of electromagnetic radiation.
• The Beer-Lambert law states that the quantity of light absorbed by a substance dissolved in a fully transmitting solvent is directly proportional to the concentration of the substance and the path length of the light through the solution.

The absorbance of a transition depends on two external assumptions.

   

1. The absorbance is directly proportional to the concentration (c$c$) of the solution of the sample used in the experiment.
2. The absorbance is directly proportional to the length of the light path (l$l$), which is equal to the width of the cell.

                                 A=ebc  = -log T = - log (I / I _o ).                   T = I / I _o    

        

                                             A = absorbance 

                                              I _o = intensity of light incident upon sample cell

                                              I = intensity of light leaving sample cell

                                              c = molar concentration of solute

                                              b= length of sample cell (cm)

                                             e = molar absorptivity

The constant 
$ϵ$ is called molar absorptivity or molar extinction coefficient and is a measure of the probability of the electronic transition. Modern absorption instruments can usually display the data as either transmittance, %-transmittance, or absorbance.

 Limitations of Beer-Lambert law

• The Beer-Lambert Law is rigorously obeyed when a single species gives rise to the observed absorption.
•  The law may not be obeyed, however, when different forms of the absorbing molecule are in equilibrium, when solute and solvent form complexes through some sort of association, when thermal equilibrium exists between the ground electronic state and a low-lying excited state, or when fluorescent compounds or compounds changed by irradiation are present.
• The Beer-Lambert law maintains linearity under specific conditions only.
• The law will make inaccurate measurements at high concentrations because the molecules of the analyte exhibit stronger intermolecular and electrostatic interactions which is due to the lesser amount of space between molecules.
• This law explains only the absorbance behavior of dilute solution only.

Applications

• Beer-Lambert law can be applied to the analysis of a mixture by spectrophotometry, without the need for extensive pre-processing of the sample. Examples include the determination of bilirubin in blood plasma samples. The spectrum of pure bilirubin is known thus the molar absorbance is known
• This law is also applied to describe the attenuation of solar or stellar radiation as it travels through the atmosphere.
• This is highly useful in many fields of medical testing, where it is applied to determine, among other things, the concentration of a chemical or substance in blood by analyzing how the blood sample absorbs light. 
• Analytical determination by absorption spectrophotometry is based on the Beer-Lambert law.