# Spectrophotometric Techniques Abstract: in this post we describe the application of the SMA Thunder Optics spectrometer and the Spectragryph software in spectrophotometry measurements. We will apply spectrophotometric techniques to measure the concentration of a solute by measuring absorbance and fluorescence. We will also apply spectrophotometry to the study of the kinetics of a chemical reaction.

### Introduction

In the previous post: Thunder Optics Spectrometer & Spectragryph, we described the Thunder Optics SMA Spectrometer (hereafter referred to as the TO spectrometer) and used it to acquire the spectra of some light sources. We now continue the experimentation activity by “exploring” with this equipment, with its accessories and with the spectragryph software, spectrophotometric techniques of absorbance and fluorescence measurement for the determination of the concentration of a substance in a liquid solution. We will also use absorbance spectrophotometry to study the kinetics of a chemical reaction.

### Determination of the concentration of a potassium permanganate solution (KMnO4) In Optics the Lambert-Beer law is an empirical relation that correlates the quantity of light absorbed by a medium, to the chemical nature, to the concentration and to the thickness of the medium crossed. When a light beam (monochromatic) of intensity I0 crosses a layer of thickness l of a medium, a part of it is absorbed by the medium itself and a part is transmitted with residual intensity I. Transmittance (T) is defined as the I/I0 ratio while the absorbance (A) as the opposite of the logarithm of the transmittance A = log (1/T).
The relationship between the intensity of the transmitted light and the incident light on the medium crossed is expressed by the following relation :

I/I0 = e-kl = T = e-A

where k is the attenuation coefficient (which is a typical constant of the medium crossed and depends on the wavelength λ) and l is the thickness of the solution crossed. The law can also be expressed in this way:

A = k l

which for a solution is further modified into:

A = ελ l M

where ελ is called the molar absorption coefficient, M is the molarity of the solution and l is the geometric path. The value of  ελ is considered constant for a given substance at a given wavelength, although it may undergo slight variations with temperature. Moreover, its constancy is guaranteed only within a given concentration range, above which the linearity between absorbance and concentration can be affected by chemical-physical phenomena.
With our absorption spectrophotometer we verified the Lambert-Beer law using dilute solutions of potassium permanganate. As known, this compound is soluble in water and the solutions have a characteristic color which, depending on the concentration, ranges from pink to dark purple.
To measure the absorbance of the solutions, the TO spectrometer coupled with the cuvette holder and the reference light source can be used (Fig. 1 a). The solutions to be examined were inserted in the classic spectrophotometry cuvettes (12x12x45 mm), made of “disposable” plastic material (Fig. 1 b). Fig. 1 – (a) Setup for absorbance measurements , (b) Cuvette with KMnO4 solutions

The standard solutions have known concentration: 8×10-4 M, 4×10-4 M, 2×10-4 M, 1×10-4 M. The solutions were obtained by weighing 0.0125 g of compound (the molar mass of the permanganate is 158 g/mol) and dissolving it in 100 ml of distilled water; thus a solution with a concentration of 8×10-4 M is obtained. For subsequent dilutions, the other concentrations are obtained. The absorbance spectra are shown in Fig. 2. Fig. 2 – Absorbance spectra of standard KMnO4 solutions

From the spectra, we can obtain the value of the maximum absorbance at a wavelength of about 525 nm for each solution. Plotting the absorbance value as a function of the concentration (molarity) of the solution we obtain the linear relation between absorbance and molarity expressed by the Lambert-Beer law: A = ελ l M (Fig. 3). Fig. 3 – Calibration curve for absorbance KMnO4 solutions Fig. 4 – Absorbance spectrum of unknown KMnO4 solution

Knowing the calibration line of our spectrophotometer for the absorbance at the wavelength of 525 nm of the potassium permanganate solution, it is possible to use the spectrophotometric measurement to determine the concentration of a solution of unknown molarity. Fig. 4 shows the measure of the “unknown” solution which gives a value equal to 0.76 for the absorbance. By inserting this value in the equation of the regression line we obtain that the concentration of the solution is 0,45×10-3 M.

### Determination of the content of Riboflavin (vitamin B2) in a multivitamin complex

Riboflavin, also known as vitamin B2, is a water-soluble vitamin of group B. It is a fundamental component of several coenzymes and is necessary for cellular respiration. Riboflavin is also a fluorescent compound. In this experiment, we use the fluorescence properties of riboflavin to determine the amount of this compound contained in a multivitamin dietary supplement. As with absorbance measurements, Beer’s law can be used for fluorescence measurements. the intensity of the light emitted, I, is directly proportional to the concentration, c, of the emitting chemical compound present in the sample:

I = k I0 c

The intensity of the light emitted depends on the intensity of the light supplied for the excitation, I0, and on the concentration, c, of the sample. The constant of proportionality k includes both the extinction coefficient (or molar absorption coefficient) at the excitation wavelength and the path length of the light beam passing through the sample.

In Fig. 1 a and Fig. 1 b, the experimental setup consisting of a spectrometer, cuvette holder and Y optical fiber is shown. The excitation source is a DPSS laser emitting at 445 nm (blue emission). The fluorescence emission is collected at right angles by the two collimators connected to the Y-shaped optical fiber. Fig. 5 – (a) Setup for fluorescence measurements, (b) Cuvette with riboflavin solution

As with absorbance spectroscopy, the fluorescence spectrometer must first be calibrated using a set of standard solutions of known concentration. By measuring the fluorescence of a set of standard solutions of known concentration, it is possible to create a calibration curve that shows how the instrument responds to changes in concentration. It is then possible to compare the response of the spectrometer to solutions of known concentration with the response of the spectrometer to a solution of unknown concentration; in this way Beer’s law allows us to determine the concentration of the unknown solution. In Fig. 6 a the sample solutions of riboflavin at known concentration are shown and in Fig. 6 b the food supplement under analysis. Fig. 6 – (a) Riboflavin solutions , (b) Multivitamin tablets

In Fig. 7 the absorbance and fluorescence spectra of riboflavin, acquired with the TO spectrometer, are shown. It is evident that the absorbance has a maximum at the wavelength of about 440 nm, this justifies the use of a blue DPSS laser as the excitation source. The fluorescence band lies between 500 nm and 600 nm with the maximum at about 520 nm. Fig. 7 – Riboflavin absorbance spectrum (orange line) and fluorescence spectrum (blue line)

The standard solutions are obtained by dissolving 100 mg of high purity riboflavin in 1 l of distilled water. Knowing the molar mass of the molecule (376.3639 g/mol) we calculate that the solution obtained has a concentration of 53×10-6 M. By further diluting the initial solution, we obtain the standard solutions at concentrations of 26, 17, 12.7 and 10.2 μM which we used as calibration solutions. Fig. 8 – Fluorescence spectra of standard riboflavin solutions

From the fluorescence spectra we obtain the maximum intensity at the wavelength of about 520 nm for each solution. Plotting the value of the fluorescence intensity as a function of the concentration (molarity) of the solution we obtain the linear relation between fluorescence and molarity expressed by Beer’s law: I = k I0 c (Fig. 9). Fig. 9 – Calibration curve for riboflavin solutions fluorescence Fig. 10 – Fluorescence spectrum of unknown solution

Knowing the calibration line of our spectrophotometer for the fluorescence of the riboflavin solution at the wavelength of 520 nm it is possible to use the spectrophotometric measurement to determine the concentration of a solution of unknown molarity. Fig. 10 shows the measure of the “unknown” solution which gives a value equal to 10.7 for the fluorescence intensity. By inserting this value in the equation of the regression line we obtain that the concentration of the solution is 8.2×10-6 M. Knowing that the solution was obtained by dissolving the contents of a tablet in 250 ml of water, we can easily obtain the quantity of riboflavin that results of 0.77 mg.

### Study of the kinetics of the chemical reaction between the “Crystal Violet” dye and Sodium Hydroxide

Crystal violet is a commonly used dye. In aqueous solution it is of an intense purple color. In the presence of a strong base (for example, sodium hydroxide NaOH), the color of the solution fades from purple to colorless. The kinetics of the chemical color change process can be analyzed using absorbance spectrophotometry in which the color intensity of the solution is recorded against time to determine the rate law.
In Fig. 11 we show the crystal violet solution and the NaOH solution. Fig. 11 – Crystal violet solution and NaOH solution

The reaction of crystal violet with sodium hydroxide produces a molecule that is colorless, the reaction can be represented in the following diagram: Fig. 12 – Reaction of Crystal Violet with NaOH

At the instant T0 the reaction product (CVOH) is absent while the concentration of the dye (CV) is maximum. As the reaction proceeds, the concentration of the dye decreases while the concentration of CVOH, which is colorless, increases: the result is that the solution becomes progressively colorless. The concentration of the CV dye can be measured by the technique of absorbance spectrometry, in this way we can monitor the kinetics of the reaction and we can measure its rate. The measures, taken every 10 seconds, are shown in the graph of Fig. 13. Fig. 13 – Absorbance spectra of solution recorded every 10 sec.

The absorbance values ​​are measured at the wavelength of 590 nm and are reported as a function of time in the semi-logarithmic scale graph of Fig. 14. The decreasing trend of absorbance is almost perfectly approximated by an exponential law with decay time of 167 seconds. Fig. 14 – Absorbance values at 590 nm in semi-logarithmic scale approximated by exponential law

From the results obtained and described above we can obtain information on the kinetics of the reaction. In general, the law on the speed of the reaction is as follows:

Rate = k [CV+]m[OH-]n (1)

Where k is a constant of proportionality, while m and n are the order of reactions of the single reactants. The values ​​of the individual reaction orders m and n must be determined experimentally.
A reaction is usually zero order, first or second order. A zero-order reaction is one in which the speed is independent of the concentration of the reactants, thus resulting constant with value k. A first order reaction is one in which the rate depends only on the concentration of a reactant and in which m = 1. In this case the rate decreases as the reaction proceeds and the concentration of the reactant [CV+] decreases. A second-order reaction can be one in which the reaction rate depends on the concentration of two different reactants (e.g. m = 1 and n = 1), or where the reaction rate depends on the concentration of only one reactant (where m = 2 ). For a second order reaction, the rate is proportional to [CV+]2 and the decrease in rate as the reaction progresses is faster than for the first order reaction.

In this experiment, CV+ reacts with OH- concentrations of orders of magnitude higher. Since sodium hydroxide has much higher concentrations, it is reasonable to assume that as [CV+] decreases over time, while [OH-] remains constant during the reaction. This creates a special condition that reduces the rate equation to the following relationship:

Rate = k’[CV+]m (2)

Where

k’ = k[OH-]n (3)

We can write

Rate = Δ[CV+] / Δt = k’[CV+]m (4)

The concentration [CV+] is measured by absorbance spectrophotometry and therefore we can derive its trend over time. From the data obtained it is evident that the concentration [CV+] decreases over time with an exponential law. Knowing that the solution of equation (4) is an exponential function we can derive that m = 1, therefore the reaction has order = 1.

### Conclusions

Our apparatus consisting of an SMA Thunder Optics spectrometer and mini light source proved to be more than adequate for the spectrophotometric analysis of absorbance and fluorescence. This allowed us to apply spectrophotometric techniques to the determination of the amount of solute present in a solution of unknown concentration. The absorbance spectrometry also allowed us to study in detail the kinetics of a chemical reaction which, involving a dye molecule, can be monitored by means of the spectrometer.

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Abstract: in questo post descriviamo l'applicazione dello spettrometro SMA Thunder Optics e del software Spectragryph nelle misure di spettrofotometria. Applicheremo le tecniche spettrofotometriche per la misura della concentrazione di un soluto mediante la misura della assorbanza e della fluorescenza. Applicheremo inoltre la spettrofotometria allo studio della cinetica di una reazione chimica.