ABSORBANCE: WHAT IS IT, EXAMPLES AND SOLVED EXERCISES - PHYSICAL - 2024

The absorbance is the logarithm with a negative sign of the quotient between the emergent light intensity and the incident light intensity on a sample of translucent solution that has been illuminated with monochromatic light. This quotient is the transmittance.

The physical process of light passing through a sample is called light transmission, and absorbance is a measure of it. Hence, the absorbance becomes the least logarithm of the transmittance and is an important data to determine the concentration of a sample that is generally dissolved in a solvent such as water, alcohol or any other.

Figure 1. Diagram of the absorbance process. Prepared by F. Zapata

To measure absorbance, a device called an electro-photometer is required, with which a current is measured that is proportional to the light intensity incident on its surface.

When calculating transmittance, the intensity signal corresponding to the solvent alone is generally measured first and this result is recorded as Io.

Then the dissolved sample is placed in the solvent under the same lighting conditions. The signal measured by the electro-photometer is denoted as I, which allows the transmittance T to be calculated according to the following formula:

T = I / I or

It is a dimensionless quantity. The absorbance A is thus expressed as:

A = - log (T) = - log (I / I o)

Molar absorbance and absorptivity

The molecules that make up a chemical substance are capable of absorbing light, and one measure of this is precisely absorbance. It is the result of the interaction between photons and molecular electrons.

Therefore, it is a magnitude that will depend on the density or concentration of the molecules that make up the sample and also on the optical path or distance traveled by the light.

The experimental data indicate that the absorbance A is linearly proportional to the concentration C and the distance d traveled by the light. So to calculate it based on these parameters, the following formula can be established:

A = ε⋅C⋅d

In the above formula, ε is a constant of proportionality known as molar absorptivity.

Molar absorptivity depends on the type of substance and on the wavelength at which the absorbance is measured. Molar absorptivity is also sensitive to sample temperature and sample pH.

Beer-Lambert law

This relationship between absorbance, absorptivity, concentration and distance of the thickness of the path that the light follows within the sample is known as the Beer-Lambert law.

Figure 2. Beer-Lambert's Law. Source: F. Zapata, Here are some examples of how to use it.

Examples

Example 1

During an experiment, a sample is illuminated with red light from a helium-neon laser, whose wavelength is 633 nm. An electro-photometer measures 30 mV when laser light hits directly and 10 mV when it passes through a sample.

In this case the transmittance is:

T = I / Io = 10 mV / 30 mV = ⅓.

And the absorbance is:

A = - log (⅓) = log (3) = 0.48

Example 2

If the same substance is placed in a container that is half the thickness of that used in Example 1, tell how much the electro-photometer will mark when the light from the helium-neon laser is passed through the sample.

It must be considered that if the thickness decreases by half, then the absorbance that is proportional to the optical thickness decreases by half, that is, A = 0.28. The transmittance T will be given by the following relationship:

T = 10-A = 10 ^ (- 0.28) = 0.53

The electro-photometer will read 0.53 * 30 mV = 15.74 mV.

Solved exercises

Exercise 1

We want to determine the molar absorptivity of a certain proprietary compound that is in solution. To do this, the solution is illuminated with light from a 589 nm sodium lamp. The sample will be placed in a sample holder 1.50 cm thick.

The starting point is a solution with a concentration of 4.00 × 10 ^ -4 moles per liter and the transmittance is measured, resulting in 0.06. Using these data, determine the molar absorptivity of the sample.

Solution

First, the absorbance is determined, which is defined as the least logarithm to base ten of the transmittance:

A = - log (T)

A = - log (0.06) = 1.22

Then the Lambert-Beer law is used which establishes a relationship between absorbance, molar absorptivity, concentration and optical length:

A = ε⋅C⋅d

Solving for molar absorptivity, the following relationship is obtained:

ε = A / (C⋅d)

substituting the given values ​​we have:

ε = 1.22 / (4.00 × 10 ^ -4 M⋅1.5 cm) = 2030 (M⋅cm) ^ - 1

The above result has been rounded to three significant digits.

Exercise 2

In order to improve the precision and determine the error of the measurement of the molar absorptivity of the sample in exercise 1, the sample is successively diluted to half the concentration and the transmittance is measured in each case.

Starting from Co = 4 × 10 ^ -4 M with transmittance T = 0.06, the following data sequence is obtained for transmittance and absorbance calculated from transmittance:

Co / 1–> 0.06–> 1.22

Co / 2–> 0.25–> 0.60

Co / 4–> 0.50–> 0.30

Co / 8–> 0.71–> 0.15

Co / 16–> 0.83–> 0.08

Co / 32–> 0.93–> 0.03

Co / 64–> 0.95–> 0.02

Co / 128–> 0.98–> 0.01

Co / 256–> 0.99–> 0.00

With these data perform:

a) A graph of absorbance as a function of concentration.

b) A linear fit of the data and find the slope.

c) From the slope obtained, calculate the molar absorptivity.

Solution

Figure 3. Absorbance vs Concentration. Source: F. Zapata.

The slope obtained is the product of the molar absorptivity and the optical distance, so dividing the slope by the length 1.5 cm we obtain the molar absorptivity

ε = 3049 / 1.50 = 2033 (M⋅cm) ^ - 1

Exercise 3

With the data from exercise 2:

a) Calculate the absorptivity for each piece of data.

b) Determine an average value for the molar absorptivity, its standard deviation and the statistical error associated with the average.

Solution

The molar absorptivity is calculated for each of the concentrations tested. Remember that the lighting conditions and the optical distance remain fixed.

The results for molar absorptivity are:

2033, 2007, 2007, 1983, 2158, 1681, 2376, 1,872, 1862 in units of 1 / (M * cm).

From these results we can take the average value:

<ε> = 1998 (M * cm) ^ - 1

With a standard deviation of: 184 (M * cm) ^ - 1

The mean error is the standard deviation divided by the square root of the number of data, that is:

Δ <ε> = 184/9 ^ 0.5 = 60 (M * cm) ^ - 1

Finally, it is concluded that the patented substance has a molar absorptivity at the frequency 589 nm produced by a sodium lamp of:

<ε> = (2000 ± 60) (M * cm) ^ - 1

References

1. Atkins, P. 1999. Physical Chemistry. Omega editions. 460-462.
2. The Guide. Transmittance and absorbance. Recovered from: quimica.laguia2000.com
3. Environmental Toxicology. Transmittance, absorbance and Lambert's law. Recovered from: repositorio.innovacionumh.es
4. Physical adventure. Absorbance and transmittance. Recovered from: rpfisica.blogspot.com
5. Spectophotometry. Recovered from: chem.libretexts.org
6. Environmental Toxicology. Transmittance, absorbance and Lambert's law. Recovered from: repositorio.innovacionumh.es
7. Wikipedia. Absorbance Recovered from: wikipedia.com
8. Wikipedia. Spectrophotometry. Recovered from: wikipedia.com