This task will explore various chemical and biological processes, and one of the main physical research methods will be spectroscopy.

Spectroscopy can vary in terms of the technique used, and its capabilities range from determining the structure of substances to the movement of galaxies. As a rule, a spectrum refers to the dependence of a physical quantity (energy, radiation intensity, absorption, etc.) on the wavelength of light.

A real beam of light is always a composite object. It consists of several elementary beams of different colors—waves with different wavelengths. A real beam can be separated into elementary beams using a prism or a diffraction grating.

For example, we can use a prism to obtain a rainbow from sunlight. If we measure the intensity of different colors in the rainbow with a sensor and plot a graph of this intensity against wavelength, we get something similar to Fig. 1(a).

The resulting graph is called the spectrum of solar emission radiation in the visible range.

An incandescent lamp, a fluorescent lamp, and LEDs can be used as radiation sources. Using a prism or a diffraction grating, we can obtain rainbow-like images and measure the intensity for different colors in them (see the other graphs in Fig. 1). The graphs show the intensity with which the light source emits in a given wavelength range.

Light interacts with the objects around us, and the nature of this interaction determines the visible color of the object. In this task, we will study the absorption of light by various solutions. For example, a solution of malachite green absorbs blue light (wavelength 450 nm) and red light (wavelength 600 nm), but does not absorb green light (wavelength 500 nm). Therefore, white light passing through the solution becomes green (Fig. 2).

Now let's imagine that we shine a beam of fixed color (laser) into a solution of malachite green. The green laser will pass through the solution with virtually no absorption ($I_\mathrm{gr} \approx I_{0,\mathrm{gr}}$), while the blue laser will be strongly absorbed ($I_\mathrm{bl} \ll I_{0,\mathrm{bl}}$).
Therefore, to describe the absorption process, we need to specify the wavelength $\lambda$ we are working with:
\[A(\lambda) = \log_{10} \frac{I_0(\lambda)}{I(\lambda)}.\]The dependence $A(\lambda)$ is called the absorption spectrum. Figure 2 shows the absorption spectrum of malachite green.
The absorption spectrum $A(\lambda)$ is described by the Beer-Lambert law and depends on the substance of which the object is composed, the concentration of this substance $n$, and the thickness of the sample $b$:
\[A(\lambda) = n b \cdot \varepsilon(\lambda),\]where $\varepsilon(\lambda)$ is a coefficient unique to each substance.
If the sample consists of substances $A$ and $B$, their absorptions are added together:
\[A(\lambda) = b\left(n_A\,\varepsilon_A + n_B\,\varepsilon_B\right). \]If any substance that absorbs green light is added to a solution of malachite green, the solution will become very dark, as it will absorb almost all visible light passing through it.

To analyze the chemical processes occurring in this task, you will need to measure the absorption spectra of copper sulfate solutions and $\rm pH$ indicators in solutions of varying acidity. You will also obtain absorption spectra of photosynthetic pigments from two algae and use them to try to explain the efficiency of photosynthesis when microorganisms are illuminated with different colors.

Section I. Electrolysis of copper sulfate solution (25 points)

Part A. Oxygen generation during electrolysis (5 points)

In this part of the task, you will perform electrolysis of an aqueous solution of $\rm{CuSO_4}$ and calculate with the charge that passed through the solution during electrolysis using various methods.

During the electrolysis process, you will observe:

• the release of gaseous molecular oxygen at the anode,
• the deposition of metallic copper at the cathode,
• a decrease in the $\rm pH$ of the solution.

By analyzing the results of these observations, you will calculate the charge that contributed to a particular effect and compare it with the total charge that flowed through the solution, measured by the direct method $Q = I\cdot t$, where $I$ is the current flowing through the solution and $t$ is the time of electrolysis.

A1 Balance the equations for the reactions occurring in the solution at the anode

\[ \mathrm{H_2O} - e^- \to \mathrm{H^+ + O_2} \uparrow \]

and cathode:

\[ \mathrm{Cu^{2+}} + e^- \to \mathrm{Cu^0}.\]

Assume that no other reactions occur at the anode and cathode.

Write down and balance the overall equation for the electrolysis of an aqueous solution of $\rm{CuSO_4}$.

\[ \rm Cu SO_4 + H_2O \to\]

A2 Prepare $V_0=150$ mL of copper sulfate with a molar concentration of $c_0=0.400~\mathrm{M}$. You are given copper sulfate powder ($\rm CuSO_4 \cdot 5 H_2 O$). How many grams $m_{bs}$ of powder are needed to prepare the specified solution? It can be assumed that the volume of the resultant copper sulfate solution is the same as the volume of the added water.

We will call the resulting solution “solution A2.” Pour $5$ mL of solution A2 into Answer tube A2.

A3 In accordance with instruction G2, perform electrolysis of $120$ ml of solution A2 for $t_0=1$ h at a current of $I=1$ A.

Record the dependence of the volume of oxygen released $V_{\rm O_2}$ on time $t$. Take at least 10 measurements. Plot the resulting dependence and draw an approximation curve.

A4 After electrolysis, stir the solution remaining in the electrolyzer. In accordance with the G2 instructions, filter approximately 20-25 mL of the stirred solution after electrolysis.

We will refer to the filtered solution as “solution A4.” Pour 5 ml of solution A4 into Answer tube A4.

A5 Calculate the charge $Q$ that flowed during electrolysis based on the known value of the current.

A6 The amount of oxygen released at point A3 can be used to determine the charge flow during electrolysis. Write a formula that relates the total volume of oxygen released $V_{\rm O_2}$ to the charge flow $Q_{\rm O_2}$. Calculate the numerical value of the charge $Q_{\rm O_2}$. Assume that the experiment takes place at a pressure of $p_0=10^5$ Pa and a temperature of $T_0=298$ K. 

Part B. Determination of copper concentration (7 points)

In this part, you need to determine the concentration of copper ions in solution A4 based on how it absorbs light. The blue color of the solutions under investigation is entirely determined by the concentration of $\rm Cu^{2+}$ ions.

Prepare five solutions of $\rm CuSO_4$, each with a volume of 4 ml, in optical cuvettes.

B1 In the answer sheets, fill in the table showing what volume of solution A2 ($V_\textbf{A2}$) and water ($V_{\rm H_2O}$) need to be mixed to obtain $4$ mL of the required solutions.

Note that the initial solution A2 has very strong absorption, so in this point you calculate its dilution by a factor of 10 or more.

B2 Using the calculations made in the previous section, prepare five solutions in optical cuvettes. In accordance with instruction G1, measure the absorption spectrum of each of the five solutions.

Save the measured spectra in the “Results/B2” folder on your desktop under the names “B2.cuvette number.txt” (for example, “B2.3.txt”).

B3 Specify the wavelength $\lambda_0$ of light that is most strongly absorbed by $\rm CuSO_4$ solutions.

B4 For each cuvette, record the absorption spectra and the determine the absorption
coefficients $A$ at the wavelength $\lambda_0$ that you have chosen. Plot a graph of the dependence of absorption $A$ on the molar concentration of copper ions $[\rm Cu^{2+}]$, draw a fitting straight line $A=s\cdot [\rm Cu^{2+}]$ and determine its slope $s$.

In an optical cuvette, prepare 4 ml of a 10-fold diluted solution of A4.

B5 Measure the absorption spectrum of a 10-fold diluted solution of A4.

Save the measured spectrum in the “Results/B4” folder on your desktop under the name “B4.txt”.

B6 Determine the concentration of copper ions $[\rm Cu^{2+}]_\textbf{A4}$ in solution A4.

B7 The decrease in copper ion concentration in the solution can also be used to determine the charge passed during electrolysis. Write a formula that relates the initial concentration of copper ions $c_0$, the final concentration of copper ions $[\rm Cu^{2+}]_\textbf{A4}$, and the charge flow $Q_{\rm Cu}$. Calculate the numerical value of the charge $Q_{\rm Cu}$. Assume the volume of the solution doesn't change throughout the electrolysis.

Part C. Determination of pH (12 points)

In this part of the problem, you need to determine the $\rm pH$ in solutions A2 and A4 using indicators that change color depending on the $\rm pH$ of the solution.

You are familiar with and know how to work with colored $\rm pH$ indicators such as methyl orange or bromothymol blue. These indicators change color when the acid form transits to the base form. And typically by the color change one determines that the $\rm pH$ of the solution has changed to the desired degree. However, using a spectrometer, it is possible to determine the $\rm pH$ quantitatively (this is possible near the transition point).

Let's consider how to determine the $\rm pH$ using the example of the cresol red indicator. Several cuvettes with different $\rm pH$ values (from 0.5 to 1.3) were prepared. The same amount of indicator was added to each cuvette. As a result, a color transition from red to orange/yellow is observed (Fig. 4).

Then, the absorption spectra for each of these cuvettes were measured and plotted together on a single graph (Fig. 5).

What features can be observed in the graph:

• absorption at $\lambda^{CR}_{peak}\approx 520$ nm, the value of which changes significantly with pH (this peak increases with increasing $\rm pH$);
• absorption at 430 nm, the value of which changes much less significantly with $\rm pH$ changes (this peak decreases as pH increases);
• absorption at $\lambda^{CR}_{iso}=475$ nm, the value of which remained constant with pH changes (all spectra intersected at this point, which is called the isobestic point).

Based on the absorption at the isobestic point, it is possible to calculate the concentration of the indicator, since the absorption at this point does not depend on $\rm pH$. It is clear that if the concentration of the indicator is doubled, for example, then all absorption values will also double, but the ratio $A_{peak}/A_{iso}$ will remain constant and will correspond to a certain $\rm pH$.

C1 At the end of the exercises, there is an enlarged graph (Fig. 11). Determine the absorption values $A_{peak}$ for each $\rm pH$ value on the graph. Determine the absorbance value $A_{iso}$ at the isobestic point. Calculate the ratios $A_{peak}/A_{iso}$ for each $\rm pH$ value. For convenience, a table is provided in the answer sheet. Plot a graph of $A_{peak}/A_{iso} ({\rm pH})$ and draw an approximating curve.

The resulting graph is universal and can be used as a calibration graph, since the values plotted on the axes do not depend on the initial concentration of the indicator. It can be used to determine the $\rm pH$ of solution A4.

Prepare 500 µl of undiluted solution A4 in two 2 ml test tubes. Add 25 µl of cresol red solution to one of them. Mix the solution with the indicator thoroughly.

C2 This step uses a thin glass cuvette with an adapter. Following the G1 instructions for thin cuvettes, obtain the absorption spectrum of undiluted solution A4 without indicator. Save the measured spectrum to the “Results/C2” folder on your desktop under the name “C2.txt”. 

С3 This step uses a thin glass cuvette with an adapter. Following the G1 instructions for thin cuvettes, obtain the absorption spectrum of the undiluted A4 solution with the indicator. Save the measured spectrum to the “Results/C3” folder on your desktop under the name “C3.txt”.

C4 The introduction to the problem describes how absorption spectra are combined when there are several substances in solution. Based on measurements at points C2-C3, calculate the absorption $A'_{peak}$ at wavelength $\lambda^{CR}_{peak}$ caused only by the absorption of the indicator. What is the absorption $A'_{iso}$ at a wavelength of $\lambda^{CR}_{iso}=475$ nm caused only by the absorption of the indicator?

C5 Based on the data in point C4, calculate the ratio $A'_{peak}/A'_{iso}$. Using the graph from point C1, determine the value of ${\rm pH_{fin}}$ in solution A4.

In the previous step, you determined the final $\rm pH$, i.e., the concentration of hydrogen ions in the solution after electrolysis. Next, you need to determine the initial $\rm pH$ of the solution before electrolysis. The $\rm pH$ of solution A2 is in the range from 3.00 to 5.00. In this range, the bromophenol blue indicator changes color well. Your task will be to obtain the same family of spectra for it as the authors did for cresol red (Fig. 5).

It would be possible to prepare solutions of different $\rm pH$ values, add the same amount of indicator, and measure their spectra. However, adding the same amount of indicator is difficult, and large errors will arise in the spectra. Therefore, you can choose the following approach:

1. take a cuvette and pour $V_0=4$ ml of solution with pH = 5.0 into it;
2. add 30 µl of bromophenol blue solution to the cuvette and mix well;
3. measure the absorption spectrum of the indicator;
4. add a certain amount of $\Delta V$ of acid solution ${\rm HCl}$ to the cuvette and mix (you woll be provided with 10 and 100 mM acid solutions), which will lower the $\rm pH$;
5. measure the absorption spectrum of the modified solution;
6. continue adding concentrated acid and repeat steps 4 and 5 until we reach pH = 3.0 or lower.

The total volume of acid added will be small, so the change in indicator concentration can be neglected.

To construct a graph similar to Fig. 5 and point C1, the $\rm pH$ values of the solution after each addition of concentrated acid are missing. The table below shows the initial concentration of ${\rm HCl}$, the volume $\Delta V$ of concentrated acid added at each step, and the concentration $C_{\rm HCl}$ of the acid used. Your task is to calculate the $\rm pH$ values (to two decimal places) that the solution will have at each step of acid addition.

C6 Fill in the remaining fields in the table on the answer sheets.

С7 Perform the experiment described above, adding the specified amount $\Delta V$ of acid with concentration $C_{\rm HCl}$ at each step. Measure and save the absorption spectrum at each step according to instruction G1. Save the measured spectra in the folder on your desktop named “Results/C7” under the names “C7.step number.txt” (for example, “C7.2.txt”). You should end up with 8 spectra. Pour the remaining solution after obtaining all spectra into Answer tube C7.

C8 Display all spectra from item C7 in the program's working area. Determine the wavelength $\lambda^{BB}_{peak}$ at which absorption changes most significantly with $\rm pH$ changes. Determine the wavelength of the isosbestic point $\lambda^{BB}_{iso}$.

C9 Plot the graph of the dependence of the absorption ratio at wavelengths $\lambda^{BB}_{peak}$ and $\lambda^{BB}_{iso}$ on $\rm pH$ (i.e., the graph $A_{peak}/A_{iso} ({\rm pH})$ for bromophenol blue).

Next, do the same as in steps C2 and C3, but with a different indicator. Prepare 500 µl of undiluted solution A2 in two 2 ml test tubes. Add 20 µl of bromophenol blue solution to one of them. Mix the solution with the dye thoroughly.

С10 This step uses a thin glass cuvette with an adapter. Following the G1 instructions for thin cuvettes, obtain the absorption spectrum of the undiluted A2 solution without indicator. Save the measured spectrum to the “Results/C10” folder on your desktop under the name “C10.txt”.

С11 This step uses a thin glass cuvette with an adapter. Following the G1 instructions for thin cuvettes, obtain the absorption spectrum of the undiluted A2 solution with indicator. Save the measured spectrum to the “Results/C11” folder on your desktop under the name “C11.txt”.

С12 Based on the measurements in questions C10-C11, calculate the absorption $A'_{peak}$ at wavelength $\lambda^{BB}_{peak}$ caused only by the absorption of the indicator. What is the absorption $A'_{iso}$ at a wavelength of $\lambda^{BB}_{iso}$ nm caused only by the absorption of the indicator?

С13 Based on the data in point C12, calculate the ratio $A'_{peak}/A'_{iso}$. Using the graph from point C9, determine the value of ${\rm pH_{ini}}$ in solution A2.

С14 By increasing the concentration of hydrogen ions in the solution (i.e., decreasing the $\rm pH$), it is also possible to determine the charge passed during electrolysis. Write a formula that relates the initial ${\rm pH_{ini}}$ of the solution, the final ${\rm pH_{fin}}$ of the solution, and the charge $Q_{\rm pH}$ that has passed through. Calculate the numerical value of the charge $Q_{\rm pH}$.

Part D. Summary of results (1 point)

D1 Based on the laws you know, fill in the table on the answer sheet, checking only one of the options for each statement: true/false.

D2 Select and mark with a check mark on the answer sheet the most reliable value of the leaked charge.

Section II. Study of photosynthetic organisms (15 points)

Photosynthesis is a key process occurring in our planet's biosphere, allowing organisms to use the energy of sunlight to sustain life. Thanks to photosynthesis, more than 99% of organic substances are formed, which are used to feed organisms at all levels of the food chain. However, there are many different types of metabolism based on the use of light energy. If carbon dioxide is the source of carbon in photosynthesis, i.e., it is fixed with the subsequent formation of organic matter, this is referred to as carbon dioxide fixation, and such organisms are called photoautotrophs. Photosynthesis can also occur without carbon fixation, using ready-made organic substances instead of carbon dioxide; such organisms are called photoheterotrophs. Water can be used as an electron donor for the electron transport chain in photosynthetic membranes. In this case, one of the products of photosynthesis is oxygen, and this type of photosynthesis is called oxygenic. Reduced organic or inorganic compounds can also act as electron donors. In this case, the products of photosynthesis will not be gaseous, and this type of photosynthesis is called anoxygenic.

Phototrophic organisms are extremely diverse: they differ in cell structure, types of photosynthetic pigments, and many other characteristics. Phototrophic organisms often form complex communities in which they occupy different niches. In this task, you are asked to study the characteristics of photosynthesis in two microorganisms, $A$ and $B$, and draw conclusions about their physiology and ecology.

Part E. Determination of spectral efficiency of photosynthesis in cultures of two microorganisms (6.4 points)

In this task, you will determine the presence and effectiveness of oxygen release by cultures of two microorganisms, A and B, when illuminated with light of different wavelengths.

Three LED batteries serve as the light source: blue, green, and red. Each consists of three LEDs connected in series.

E1 For each LED battery, measure the voltage across the 3 LEDs connected in series
and calculate the voltage across single LED when the power source is turned
on. Fill in the table in the answer sheets.

The figure below shows the volt-ampere characteristics of LEDs.

E2 Find the current $I$ flowing through the LEDs of each color. Fill in the table in the
answer sheets.

The figure below shows the dependence of the light power $P$ emitted by LEDs on the current $I$ flowing through them.

E3 Find the power of light $P$ emitted by each of the LED. Fill in the table in the
answer sheets.

The internal cross-sectional area of the tubes is $S_0=1.77$ mm². Using the setup for studying the spectral sensitivity of photosynthesis one may measure the volume of oxygen $V$, which is released by microorganisms when exposed to light of different colors.

E4

For this task, use microorganism $A$.

Prepare the setup for measurements according to the G3 instructions.

Turn on the light source and start timing.

• If no oxygen release is observed 30 minutes after the start of the experiment, record zero values for $V_{\rm O_2$ in the table in the answer sheets.
• If oxygen release is observed 30 minutes after the start of the experiment, continue the experiment for another 1.5 hours. Record the volume of oxygen $V_{\rm O_2}$ released when illuminated by different colors of light in the table on the answer sheet.

E5 For microorganism $B$, repeat the procedure described in the previous question.
Fill in the table in the answer sheets.

To compare the photosynthetic efficiency $E$ of different microorganisms, it is necessary to obtain the average efficiency per cell and per incident radiation power:
\[E = \frac{V_{\rm O_2}}{N\cdot P},\]where $V_{\rm O_2}$ is the volume of oxygen released during exposure to light, $N$ is the number of cells exposed to light, and $P$ is the radiation power.

E6 According to instruction G4 get the image of the cells in Goryaev's chamber for both microorganisms $A$ and $B$. Save the acquired images to the “Results/E6” folder on your desktop under the name “E6.A.txt” and “E6.B.txt” respectively.

According to instruction G4, use Goryaev's chamber to count the number of cells in the four small squares $n_A$ and $n_B$ of microorganisms $A$ and $B$.

The edge of the large square of the Goryaev chamber is 0.2 mm, the depth of the chamber is 0.1 mm, and the large square consists of 16 small squares. Count the total number of cells $N_A$ and $N_B$ of microorganisms $A$ and $B$ inside a 20 ml syringe. Write down the calculation formula showing how $n_A$ and $N_A$ are related.

E7 Using the data obtained in points E4, E5, and E6, calculate the photosynthetic efficiency $E$ for both microorganisms and all colors of light. Fill in the table in the answer sheets.

E8 Using the data obtained in questions E3 and E7, fill in the table in the answer sheets.

Part F. Determination of the pigment composition of the microorganisms (5.2 points)

The pigment composition largely determines the ability of photosynthetic organisms to absorb different spectral intervals of solar radiation. Pigment composition may vary among organisms of different systematic groups. The main photosynthetic pigments are chlorophylls and carotenoids. They differ in chemical structure and physical properties. The physical properties of the most important pigments, such as absorption maxima and specific mobility, are shown in the table below.

Characteristics of absorption spectra and specific mobility ($R_f$) of chlorophyll pigments on a chromatogram

Characteristics of absorption spectra and specific mobility ($R_f$) of carotenoid pigments on a chromatogram

The specific mobility value is calculated using the formula:
\[R_f=Z_x/Z_f,\] where $Z_x$ is the distance between the start line and the center of the pigment spot, and $Z_f$ is the distance between the start line and the solvent front.

The microbial culture box contains concentrated extracts of these microorganisms in small test tubes. These will be needed for chromatography and absorption spectral measurements. The volume of the extracts provided in the test tubes is approximately 150 µl. Therefore, before opening them, shake the liquid down.

F1 According to instruction G5, perform thin-layer chromatography of extracts of microorganisms $A$ and $B$.

Immediately after completing the chromatography and drying the plate, analyze the table and carefully mark the spots corresponding to chlorophylls with an “X” and the spots corresponding to carotenoids with an “O” on the plate with a pencil.

Raise the HELP sign so that an assistant can come to you and photograph the plate.

Place the marked plate in Answer tube F1.

Take three plastic cuvettes. Pour 3 ml of alcohol into each of them. Use one of the cuvettes to remove the Baseline, and add 50 µl of extracts of microorganisms $A$ and $B$ to the others. Mix the diluted extracts thoroughly.

F2 In accordance with instruction G1, obtain the absorption spectrum of extracts from microorganisms $A$ and $B$.

Save the measured spectra in the folder on the desktop “Results/F2” under the names “F2.A.txt” and “F2.B.txt” for microorganisms $A$ and $B$, respectively.

Pour 3 ml of the microorganism extract solutions you measured into Answer tube F2.A and Answer tube F2.B.

F3 Based on the chromatograms you have obtained, as well as the absorption spectra, mark whether the statements are true or false on the answer sheet.

F4 What conclusions can be drawn from the results of thin-layer chromatography and absorption spectrum analysis? Mark whether the statements are true or false on the answer sheet.

Part H. Study of Microorganism Ecology (3.4 points)

In small water bodies, the community of microorganisms is distributed according to physiological characteristics. In small water bodies with poor water mixing, a zone of oxygen concentration jump is formed, when anaerobic conditions are created in the deep layers. In the absence of oxygen, phototrophic organisms use other compounds as electron donors instead of water, such as cyanobacteria and green algae, and oxygen is not released — this type of photosynthesis is called anoxygenic.

In the water column, phototrophic microorganisms are distributed according to their relationship to oxygen (aerobic and anaerobic) and their ability to absorb light in different parts of the spectrum.

It is known, for example, that among anoxygenic phototrophic bacteria, green bacteria are anaerobic and many of them are well adapted to using low-intensity light, while purple bacteria are resistant to oxygen.

H1 Select the correct statements about microorganisms.

H2

The figure shows a diagram of a small pond with poor water circulation. Identify the zones of the pond (A-D) where the following microorganisms will live.

1. cyanobacteria and green algae
2. anaerobic decomposers of organic matter
3. green bacteria
4. purple bacteria

Write the numbers of the organisms in the table on the answer sheet.

H3 Based on the information about microorganisms $A$ and $B$ that you obtained during your research, determine in which pond zone (A-D from task H2) each of the microorganisms is most likely to live.

H4 Cyanobacterial mat consists of many phototrophic and non-phototrophic microorganisms that are arranged in layers one below the other. Indicate whether the following statements are true or false.