MOLAR ABSORPTIVITY: HOW TO CALCULATE IT AND SOLVED EXERCISES - CHEMISTRY - 2024

The molar absorptivity is a chemical property that indicates how much light can absorb a species in solution. This concept is very important within the spectroscopic analysis of absorption of photon radiation with energies in the ultraviolet and visible (UV-vis) range.

As light is composed of photons with its own energies (or wavelengths), depending on the species or mixture analyzed, one photon can be absorbed to a greater degree than another; that is, light is absorbed at certain wavelengths characteristic of the substance.

Source: Dr. Console, from Wikimedia Commons

Thus, the value of molar absorptivity is directly proportional to the degree of absorption of light at a given wavelength. If the species absorbs little red light, its absorptivity value will be low; whereas if there is a pronounced absorption of red light, the absorptivity will have a high value.

A species that absorbs red light will reflect a green color. If the green color is very intense and dark, it means that there is a strong absorption of red light.

However, some shades of green may be due to reflections of different ranges of yellows and blues, which are mixed and perceived as turquoise, emerald, glass, etc.

What is molar absorptivity?

Molar absorptivity is also known by the following designations: specific extinction, molar attenuation coefficient, specific absorption, or Bunsen coefficient; It has even been named in other ways, which is why it has been a source of confusion.

But what exactly is molar absorptivity? It is a constant that is defined in the mathematical expression of the Lamber-Beer law, and it simply indicates how much the chemical species or mixture absorbs light. Such an equation is:

A = εbc

Where A is the absorbance of the solution at a selected wavelength λ; b is the length of the cell where the sample to be analyzed is contained, and therefore, is the distance that the light crosses within the solution; c is the concentration of the absorbent species; and ε, the molar absorptivity.

Given λ, expressed in nanometers, the value of ε remains constant; but when changing the values ​​of λ, that is, when measuring absorbances with lights of other energies, ε changes, reaching either a minimum or maximum value.

If its maximum value, ε _max, is known, λ _max is determined at the same time; that is, the light that the species absorbs the most:

Source: Gabriel Bolívar

Units

What are the units of ε? To find them, it must be known that absorbances are dimensionless values; and therefore, the multiplication of the units of b and c must be canceled.

The concentration of the absorbing species can be expressed either in g / L or mol / L, and b is usually expressed in cm or m (because it is the length of the cell that the light beam passes through). Molarity is equal to mol / L, so c is also expressed as M.

Thus, multiplying the units of b and c, we obtain: M ∙ cm. What units then must ε have to make the value of A dimensionless? Those that multiplying M ∙ cm gives a value of 1 (M ∙ cm x U = 1). Solving for U, we simply obtain M ^-1 ∙ cm ^-1, which can also be written as: L ∙ mol ^-1 ∙ cm ^-1.

In fact, using the units M ^-1 ∙ cm ^-1 or L ∙ mol ^-1 ∙ cm ^-1 speeds up calculations for determining molar absorptivity. However, it is also usually expressed in units of m ² / mol or cm ² / mol.

When expressed in these units, some conversion factors must be used to modify the units of b and c.

How to calculate it?

Direct clearance

Molar absorptivity can be calculated directly by solving it in the above equation:

ε = A / bc

If the concentration of the absorbing species, the cell length, and the absorbance obtained at a wavelength are known, ε can be calculated. However, this way of calculating it returns an inaccurate and unreliable value.

Graphing method

If you look closely at the Lambert-Beer law equation, you will notice that it looks like the equation of a line (Y = aX + b). This means that if the values ​​of A are plotted on the Y axis, and those of c on the X axis, a straight line must be obtained that passes through the origin (0,0). Thus, A would become Y, X would be c, and it would be equal to εb.

Therefore, once the line is graphed, it is enough to take any two points to determine the slope, that is, a. Once this is done, and the length of the cell, b, is known, it is easy to solve for the value of ε.

Unlike direct clearance, plotting A vs c allows the absorbance measurements to be averaged and reduces the experimental error; and also, infinite lines can pass through a single point, so direct clearance is not practical.

Likewise, experimental errors can cause a line to not pass through two, three or more points, so the line obtained after applying the least squares method is actually used (a function that is already incorporated in calculators). All this assuming a high linearity, and therefore, compliance with the Lamber-Beer law.

Solved exercises

Exercise 1

It is known that a solution of an organic compound with a concentration of 0.008739 M presented an absorbance of 0.6346, measured at λ = 500 nm and with a cell length 0.5 cm. Calculate the molar absorptivity of the complex at that wavelength.

From these data, ε can be solved directly:

ε = 0.6346 / (0.5cm) (0.008739M)

145.23 M ^-1 ∙ cm ^-1

Exercise 2

The following absorbances are measured at different concentrations of a metal complex at a wavelength of 460 nm, and with a cell of 1 cm in length:

A: 0.03010 0.1033 0.1584 0.3961 0.8093

c: 1.8 ∙ 10 ^-5 6 ∙ 10 ^-5 9.2 ∙ 10 ^-5 2.3 ∙ 10 ^-4 5.6 ∙ 10 ^-4

Calculate the molar absorptivity of the complex.

There are a total of five points. To calculate ε it is necessary to graph them by placing the values ​​of A on the Y axis, and the concentrations c on the X axis. Once this is done, the least squares line is determined, and with its equation we can determine ε.

In this case, after plotting the points and drawing the line with a coefficient of determination R ² of 0.9905, the slope is equal to 7 ∙ 10 ^-4; that is, εb = 7 ∙ 10 ^-4. Therefore, with b = 1cm, ε will be 1428.57 M ^-1.cm ^-1 (1/7 ∙ 10 ^-4).

References

1. Wikipedia. (2018). Molar attenuation coefficient. Recovered from: en.wikipedia.org
2. Science Struck. (2018). Molar Absorptivity. Recovered from: sciencestruck.com
3. Colorimetric Analysis: (Beer's law or Spectrophotometric Analysis). Recovered from: chem.ucla.edu
4. Kerner N. (nd). Experiment II - Solution Color, Absorbance, and Beer's Law. Recovered from: umich.edu
5. Day, R., & Underwood, A. Quantitative Analytical Chemistry (5th ed.). PEARSON Prentice Hall, p-472.
6. Gonzáles M. (November 17, 2010). Absorptivity Recovered from: quimica.laguia2000.com