Molar Absorptivity

Molar absorptivity is a term used in chemistry to measure how a particular chemical absorbs light at a particular wavelength. It is also known as molar extinction co-efficient denoted by 'ε'. This property can be calculated by using Beer- Lambert Law. The intrinsic property of the chemical known as absorbance (A), is measured using the path length (l) and concentration (c) of the species, given by the following equation,

A = εcl

Using this formula the molar absorptivity equation becomes,

ε=A/cl

To understand this property you need to understand the Beer-Lambert law.

Beer-Lambert's Law
In simple words, the law states that the absorbance (A), of an absorbing chemical species is directly proportional to the path length and concentration of the chemical. The path length is the distance source of light travels. The SI units for ε 'epsilon' are m²/mol but very commonly molar absorptivity units are expressed by, M^-1cm^-1 and also as L mol^-1 cm^-1. Many a time, this property is confused with extinction co-efficients used in physics. It is important to remember that this property is almost exclusive to chemistry. Sometimes, it so happens that there are more than one absorbing species in the chemical. In such a case, absorbance is a summation of all the individual absorbance of each absorbing species. It is given by the equation,

A= l (ε₁c₁+ε₂c₂+.....)

Here, the concentration and the molar absorptivity for each species changes whereas the path length remains the same. Certain biological components such as proteins, are known to show maximum absorption at 280nm, which is only due to the aromatic amino acids present in the protein. This explains the presence of a number of absorbing species affecting the total absorbance.

How to Calculate Molar Absorptivity
Using the Equation in an Experiment

• The simple way to calculate it is using the formula given above.
• Define all the variables with a value. Absorbance (A), is a measurement without any units, obtained from a spectrophotometer at a particular wavelength of light. Path length is usually considered to be 1, when calculating this value experimentally, unless stated otherwise. Concentration of the substance (c) should also be known.
• Substitute these values in the equation mentioned for epsilon.

Using a Graph

• In a graph, several values of A are plotted on Y axis against a number of concentrations on X axis.
• The slope of the line will be εl. Again here l path length will be 1. Thus, the slope will give you the molar absorptivity. Calculators are the easiest way to calculate these values.

Calculating Concentrations Using Known Molar Absorptivity
When this value is known, it is used to determine unknown concentrations of chemical components. For example, known molar absorptivity of iron complexes is often used to determine the iron content in the different branches of biology. Reaction between iron and phenanthroline gives a red complex whose molar absorptivity is 11,100 at the wavelength of 508nm. This method was used to estimate iron in blood. This method is reliable and sensitive, as the complex of iron is very stable once you add a reducing agent that keeps iron in the ferric state. There are various other complexes of known values that are being used to determine concentrations of biologically important chemicals.

Thus, molar absorptivity can most easily be calculated using a graph, when you have varied known concentrations of the same chemical species. Its values are constant at a particular wavelength and concentration for a given species. There are also other ways to determine this value using Avogadro's constant and absorption cross section (σ), given by,

σ = 1000ln₁₀ε/N_A=3.82 x 10^-21ε

This formula or equation can be used only when you know the absorption cross section.

This was all about the topic. It is an integral part of optics used in chemistry. It has emerged from an application of physics in chemistry, solely dedicated to the latter.