Beer Lambert Law

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Beer Ambert Law Definition

The Beer-Lambert Law describes the relationship between the absorbance and intensity of incident light. It helps to understand the attenuation of light when it travels through a medium of varying concentrations and length of travel of light beam. This page explains what Beer-Lambert Law is and how to calculate absorbance, path length, concentration, and absorptivity coefficient.

What is absorbance?

Consider this scenario:

Let us incident a beam of light through a liquid taken in a glass container. The intensity of the light on the incident side and the receiving side differs. Why?

When light travels through any medium that has particles, it gets attenuated. In other words, as light passes through molecules and atoms of a medium, its energy keeps diminishing by the time it reaches the receiving end. This energy that the light beam loses is transferred to the particles of the medium. They get excited with this change in energy and display the excitement in the form of temperature rise or color emission.

This property of the medium to absorb the energy of the light passing through it is called absorbance. It varies with the medium and other attributes as defined by the Beer-Lambert Law.

Absorbant and Concentration Graph

As shown in the above figure:

The value of light intensity at the receiving end is less than the intensity at the incident side. They are logarithmically related by the relation: A = log (I0/I), where A is the absorbance of the medium.

What is transmittance?

Transmittance is the property of a medium that is opposite to absorbance. While absorbance indicates the amount of light energy absorbed by the medium, transmittance explains how much light is transmitted to the other end.

The formula to calculate the transmittance of a medium is given by: T = I/I0.

It is common to express transmittance in percentage. Thus, percentage transmittance = T% = 100 * (I/I0)

Key points about absorbance and transmittance:

  • The relation between absorbance and transmittance of a substance are related as A= -log 10 T.
  • For instance, if the absorbance is zero, then transmittance is 100%. Similarly, if the absorbance is one, then transmittance is 10%. This relation is often represented in the form of a graph called Beer Lambert Law graph as shown below.

    Absorbant and Concentration Graph

  • Absorbance is a logarithmic term and hence it has no units.
  • Optical density is another term that is often used synonymously to absorbance. However, IUPAC prefers absorbance over optical density.
  • The measurement of absorbance finds a key role in various industries:
    • Sugar and alcohol processing
    • Petrochemical industry
    • Dyeing industry

What is Beer Lambert’s law?

Beer Lambert’s law, also called Beer’s Law, discusses the absorbance of the light incident into a solution and the absorption coefficient of the solution.

According to Beer Lambert’s law, the absorbance of a substance is:

  • Directly proportional to the concentration of the solution, c
  • Directly proportional to the length of the path traveled by the light in the solution, l.

Often l= the length of the glass beaker that is filled with the experimental solution and is measured in centimeters (cm).

Derivation of Beer Lambert’s Law

From the above definitions of Beer Lambert’s Law,

A ∝ c A ∝ l
Thus, A ∝ cl.

This equation can be written as A=ϵcl, where ϵ is the proportionality constant called molar absorptivity or molar extinction coefficient.

Thus, A = ϵ x c x l is the Beer-Lambert Law that relates the concentration of the solution and the length of the light path with the absorbance.

The Beer Lambert’s Law can also be written as A=log10(Io/I)=ϵ x l x c.

Note: Absorbance is unitless, and the units of molar absorptivity are L mol-1cm-1

Do you know?
The container’s shape has a huge role to play in absorbance. Studies indicate that rectangular containers allow more absorption than cubic ones. Because the longer the beaker, the greater is the interaction between the molecules of the solution and the incident light beam.

FAQs about absorbance

Which substance has the highest absorbance?

Isothiazole, an organic compound comprising carbon, sulfur, nitrogen, and hydrogen, has an absorption maximum in ethanol solution at 244 nm, with a molar absorptivity of 5200.

Can absorbance be negative?

Negative absorbance has no physical significance.

Negative absorbance could be due to:

  • too much dilution of the solution,
  • the absorbance value of the reference is higher than the sample, or
  • the interchange of reference and the sample.

What are the limits of absorbance value?

Absorbance can range anywhere between zero to infinity. The absorbance of zero means the solution or the medium did not absorb any light. Similarly, the absorbance of 2 means the solution absorbed 99 percent of the beam. Ideally, absorbance values below 1 are considered normal. Any absorbance above 1.0 indicates that the solution is highly concentrated.

When do you find the most absorbance?

When the incident light beam and the color of the solution are complimentary, we find maximum absorbance.

Why does absorption increase with concentration?

As concentration increases, there are more molecules per unit length to absorb the light energy of the incident beam.

Steps to calculate absorption from Beer-Lambert Law

Step 1: Determine the molar absorption coefficient of the solution.

Step 2: Find the concentration of the solution.

Step 3: Calculate the length of the path in which the light beam travels.

Step 4: Finally, calculate absorption using the formula mentioned above.

Applications of Beer Lambert’s Law

  • Beer Lambert’s Law finds diverse applications in various studies. It helps to calculate the properties of light and the solution through which it is traveling.
  • Beer Lambert’s Law plays a significant role in spectrophotometry – an inexpensive and standard technique to find the absorption of light by a solution.
  • In chemistry, Beer Lambert’s Law is used for the study of polymer degradation and oxidation analysis.
  • Do you know that this law also helps in the calculation of earth’s radiation? Yes, the attenuation of radiation received by Earth’s atmosphere is calculated by Beer Lambert’s Law.

Limitations of Beer Lambert’s Law

Beer’s law is applicable only in cases where:

  • The length of the light path is known.
  • The concentration of the solution does not cross 0.01M.
  • The solution can absorb the light that is incident onto it.

We hope now that you are confident about Beer’s law and its significance. Use our Beer-Lambert Law absorbance calculator to simplify calculations of absorption coefficient and absorbance.

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