The theoretical basis for determining the optical density of a solution

Any particle, be it a molecule, atom or ion, as a result of absorption of a quantum of light, goes to a higher level of energy state. Most often, a transition is made from the ground to the excited state. This causes the appearance of certain absorption bands in the spectra.

The absorption of radiation leads to the fact that when passing it through a substance, the intensity of this radiation decreases with an increase in the number of particles of a substance having a certain optical density. This research method was proposed by V. M. Severgin back in 1795.

This method is best suited for reactions where the analyte is able to transfer to a colored compound, which causes a change in the color of the test solution. By measuring its light absorption or comparing the color with a solution of known concentration, it is easy to find the percentage of the substance in the solution.

The basic law of light absorption

The essence of photometric determination is two processes:

• the translation of the analyte into an absorbing compound;
• measuring the intensity of absorption of these very oscillations with a solution of the analyte.

Changes in the intensity of the stream of light passing through the light-absorbing substance will also be caused by light losses due to reflection and scattering. In order for the result to be reliable, parallel studies are carried out to measure the parameters at the same layer thickness, in identical cuvettes, with the same solvent. So the decrease in light intensity depends mainly on the concentration of the solution.

The decrease in the intensity of light transmitted through the solution is characterized by the light transmission coefficient (also called transmission) T:

T = I / I ₀ , where:

• I is the intensity of the light transmitted through the substance;
• I ₀ is the intensity of the incident light beam.

Thus, the transmission shows the fraction of the non-absorbed light flux passing through the studied solution. The inverse algorithm for transmittance is called the optical density of the solution (D): D = (-lgT) = (-lg) * (I / I ₀ ) = log * (I ₀ / I).

This equation shows which parameters are important for the study. These include the wavelength of light, the thickness of the cuvette, the concentration of the solution, and the optical density.

Bouguer-Lambert-Beer Law

It is a mathematical expression reflecting the dependence of the decrease in the intensity of the monochromatic light flux on the concentration of the light-absorbing substance and the thickness of the liquid layer through which it is passed:

I = I _{0 *} 10 ^{-ε · C · ι} , where:

• ε is the light absorption coefficient;
• C is the concentration of the substance, mol / l;
• ι — layer thickness of the analyzed solution, see

Having transformed, this formula can be written: I / I ₀ = 10 ^{-ε · · ι} .

The essence of the law is as follows: different solutions of the same compound, with equal concentration and layer thickness in the cell, absorb the same part of the light incident on them.

Having logarithmized the last equation, we can obtain the formula: D = ε * C * ι.

Obviously, the optical density directly depends on the concentration of the solution and the thickness of its layer. The physical meaning of the molar absorption coefficient becomes clear. It is equal to D for a unipolar solution and with a layer thickness of 1 cm.

Limitations of the application of the law

This section includes the following items:

1. It is valid exclusively for monochromatic light.
2. The coefficient ε is related to the refractive index of the medium; especially strong deviations from the law can be observed in the analysis of highly concentrated solutions.
3. The temperature when measuring the optical density should be constant (within a few degrees).
4. The light beam must be parallel.
5. pH should be constant.
6. The law is applicable for substances whose light-absorbing centers are particles of the same type.

Concentration Methods

It is worth considering the calibration graph method. For its construction, a number of solutions (5-10) with different concentrations of the test substance are prepared and their optical density is measured. According to the obtained values, a graph of the dependence of D on concentration is built. The graph is a straight line from the origin. It makes it easy to determine the concentration of a substance from the results of measurements.

There is also a supplement method. It is used less often than the previous one, but allows you to analyze solutions of complex composition, since it takes into account the influence of additional components. Its essence is to determine the optical density of the medium D _x containing the analyte of unknown concentration C _x , with re-analysis of the same solution, but with the addition of a certain amount of the investigated component (C _article ). The value of C _{x is} found using calculations or graphs.

Study conditions

In order for photometric studies to give a reliable result, several conditions must be observed:

• the reaction must end quickly and completely, selectively and reproducibly;
• the color of the resulting substance must be stable in time and not change under the influence of light;
• the test substance is taken in an amount sufficient to convert it into an analytical form;
• optical density measurements are carried out in the wavelength range at which the difference in the absorption of the starting reagents and the analyzed solution is greatest;
• the light absorption of the comparison solution is considered to be optical zero.