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EXPERIMENT 15 TF Notes

1. Have students log onto LoggerPro3 and start heating water as soon as they arrive 2. This reaction is easily contaminated so students must never insert the directly into the containing the reaction. Instead they should rather measure the temperature of the water and equate that to the temperature of the solution in the cuvette. 3. We will be using hot gloves in this experiment. 4. Make sure you are familiar with the calculations necessary to fill out the chart. All the necessary equations are given at the top fo the page. Note that the temperature must be converted from °C to K.

EXPERIMENT 15 Thermodynamics of Complex-Ion Equilibria

Introduction

Thermodynamic data for a reaction system provides researchers with information that is important from both theoretical and practical points of view. There are several thermodynamic properties that chemists pay close attention to when designing or carrying out experiments such as thermodynamic stability, the change in free energy of a reaction, and temperature dependence. For example, if a chemist wants to create a new type of solar cell that combines a semiconductor material with a novel conductive oxide and wants to make sure that the two materials will not react with each other, thermodynamics provide the answer. By finding the free energy change associated with the reaction, s/he can determine how stable the layers are in contact with each other and to what temperature.

In this experiment, you will learn how to determine those parameters from a controlled experiment by using spectrometry to find concentration data at various temperatures. This will allow us to determine the equilibrium constant, which can then be used to derive ΔG°, ΔH°, and ΔS°.

Scientific Background

The equilibrium we will study is the complexation of aluminum ions with xylenol orange, symbolized as – H4Q, which results in the formation of the complex ion AlQ . Because both the reactants and products strongly absorb , but at different , this reaction is ideal for spectrophotometric study.

3+ – + H4Q + Al ←→ AlQ + 4H yellow colorless red colorless

Recall that molecules are colored because they absorb certain wavelengths of visible light, while allowing other wavelengths to pass through. Xylenol orange is a yellow-colored organic molecule containing four acidic –COOH groups attached to a system of three benzene-like carbon rings (Figure 3.1). The xylenol orange acts as a ligand, which can bind to the aluminum ion through the six atoms shown in boldface type. In the process, the four protons attached to the –COOH groups are released from the molecule. The color of this complex ion AlQ– is red.

O O O O O O O OH HO O N Al N N N HO OH Al3+ O O HO O HO O O O

H3C H3C O O S S OH OH OH OH

-) Xylenol Orange (H4Q) Xylenol Orange bound to Aluminum (AlQ Yellow Red

Measuring at equilibrium using Beer’s law

– The complex AlQ absorbs very strongly at a of 550 nm. The unreacted molecule H4Q, on the other hand, absorbs much more weakly at this wavelength. The total absorbance at 550 nm can be determined by applying Beer’s law to both species and taking the sum:

– A = ε1[H4Q]L + ε2[AlQ ]L where L = 1 cm

In our experiment, we will start with a certain initial concentration of H4Q and then heat the mixture to form the complex AlQ–. The complex AlQ– does not form at room temperature, but will form as we heat the – mixture. At any moment, the sum of the concentrations of H4Q and AlQ will be constant and equal to the initial concentration of H4Q, which we can represent as [H4Q]i: – [H4Q]i = [H4Q] + [AlQ ] By combining this equation with the expression for the total absorbance, we can express the absorbance in – terms of the initial concentration [H4Q]i and the equilibrium concentration [AlQ ]: – A = ε1[H4Q]i + (ε2–ε1)[AlQ ]

Note that the quantity (ε2–ε1) is positive because ε2 is much greater than ε1, and that we have incorporated the knowledge that the path length is 1 cm. To further simplify this expression, we can define Ai as the initial absorbance before the reaction starts, when there is none of the complex AlQ– :

Ai = ε1[H4Q]i Finally, by combining this with our absorbance equation and solving for the concentration of the complex, we find that A " A [AlQ–] = i #2 "#1

4 –1 –1 The quantity (ε2–ε1) has been determined as 2.50 × 10 L mol cm . By measuring the initial absorbance Ai and the absorbance at a specific time A, the concentration of the complex AlQ– can be determined. ! Determining ΔG°, ΔH°, and ΔS° from equilibrium measurements

The equilibrium constant K for the complexation reaction is:

4 AlQ" H+ H Q + Al3+ → AlQ– + 4H+ [ ][ ] 4 ← K = 3+ [H4Q][Al ] In this experiment, we will use the spectrometer to find the equilibrium concentration of AlQ– at several + – 2– different temperatures. The concentration of H will be controlled by an HSO4 /SO4 buffer, which should maintain a pH of 2.0. The equilibrium concentrations of the! other species can be determined from the their initial concentrations using simple stoichiometric relationships:

– [H4Q] = [H4Q]i – [AlQ ] 3+ 3+ – [Al ] = [Al ]i – [AlQ ] Therefore you will be able to calculate the equilibrium constant K at several different temperatures. From this you can calculate ΔG° at each temperature from

ΔG° = –RT ln K

Finally, we can use the definition of Gibbs free energy to find ΔH° and ΔS° :

ΔG° = ΔH° – TΔS°

A plot of ΔG° as a function of temperature should give a straight line with a slope of –ΔS° and a y-intercept of ΔH°. Be sure to use the correct units in all your calculations.

Procedure

Safety Precautions • Safety and gloves must be worn at all times. • The chemicals used in this experiment are toxic. Change gloves if you suspect that you have spilled any chemical on your gloves. Rinse for 15 minutes at an eye wash station if your eyes are accidentally exposed. • If your skin is accidentally exposed to chemicals, rinse the area with water for 15-20 minutes. • You will be working with hot beakers and . Use padded gloves to handle the hot beakers and a holder to handle the hot cuvettes.

Waste Disposal • Empty the contents of all cuvettes into the “Used Chemicals” beaker at your lab bench. Use a squirt to rinse the cuvettes with water and pour the rinse into the “Used Chemicals” beaker. • Dispose of empty cuvettes and cuvette caps in the solid waste container. • Empty the “Used Chemicals” beaker into the hazardous waste collection bucket in the back of the lab. • Leave everything else at your lab bench.

Using the Spectrometer with Logger Pro

Open the Logger Pro software (Go → Applications → LoggerPro) and look inside the spectrometer. You should see a light inside the spectrometer that has a violet color. If the spectrometer light is not on, the spectrometer USB cable may be unplugged. Quit Logger Pro, check the cable, and restart Logger Pro. If the light still does not come on, ask your TF for help.

Setting up the Reaction At your bench, you will find two nested beakers. Add distilled water to the inner beaker to the 30-ml mark. Then add water to the outer beaker so that its water level is below that of the inner beaker. Set these beakers on the and heat the water. Keep an eye on the water; it should boil gently. Add distilled water as needed if it boils too much.

Go to the center bench in the room and obtain two clean cuvettes and two square cuvette caps. Note that each cuvette has clear sides and opaque sides. Handle the cuvettes only by the opaque sides. Never touch the clear sides; fingerprints will interfere with your measurements. If the clear sides of the cuvette become marked or scratched in any way, you must repeat the experiment with new cuvettes.

Fill one cuvette with distilled water from your , and cap it with one of the square caps. This is your reference cuvette. Bring the other cuvette to the center bench in the lab. You will see two bottle-top dispensers that are calibrated to dispense exactly 1.75 ml of solution. One solution contains xylenol orange 3+ (H4Q) and the other contains aluminum ions (Al ). Carefully squirt 1.75 ml of each solution into the cuvette by smoothly pulling up the top of the dispenser and pushing it down slowly. Your cuvette should be filled almost to the top with 3.5 ml of a pale yellow solution. Put a cap on this solution; this is your sample. Again, be extremely careful not to mark or scratch the clear sides of the cuvette.

Calibrating the Spectrometer Gently insert the reference cuvette into the spectrometer. Make sure it is inserted all the way into the spectrometer. The opaque edges should be on the sides of the cuvette when it is inserted, and the light should pass through the clear sides. In Logger Pro, go to the “Experiment” menu. Select “Calibrate ▶ Spectrometer.” Once the dialog box appears, click “Finish Calibration.” You will have to wait a few seconds, and then you can click “OK.” Click on the spectrometer icon at the top of the window (this icon has a “rainbow” appearance). A new window will appear. Select the button labeled “Abs vs. Time.” In the list of check-boxes at right, uncheck any wavelengths that are already selected, and check the box for 550 nm. Make sure that only the box for “550 nm” is checked (this means that the spectrometer will measure absorbance only at 550 nm), and click “OK.”

Measuring the Initial Absorbance (Ai)

Insert your sample cuvette into the spectrometer. You should see the absorbance on the lower left-hand corner of the screen in Logger Pro. Record this value in the data section of your lab report. It is the “Initial

Absorbance (Ai)” that you will need for your calculations.

You are now ready to heat the reaction mixture to form the complex between aluminum and xylenol orange. Place your sample cuvette in the hot water bath (i.e. in the inner beaker). Be sure that the top of the cuvette is above the level of water in the inner beaker. You must make sure that no water gets inside the cuvette. You should heat the water bath until it boils, and then continue to heat it until the color stops changing (about 5 min). Add distilled water from a wash bottle if needed to keep the level of water up to cover most of the cuvette. Observe the cuvette and water bath during heating and write any observations in your lab report. Measuring the Equilibrium Constant of the Complexation Reaction You will measure the equilibrium constant of the complexation reaction by monitoring the absorbance of the reaction mixture as it cools slowly. Once the water bath and reaction mixture has boiled for at least 5 min, use padded gloves to carry the entire setup (beakers and all) to the lab bench where the spectrometer is located. Set the hot beakers on a paper towel underneath the clamp that holds the temperature probe. Immerse the temperature probe in the inner beaker (not inside the cuvette, which should still be capped!) Make sure that the temperature probe is immersed as far as possible. The setup should look something like that shown in the image at right.

Stir the water bath gently with the temperature probe. You should see the temperature appear on the Logger Pro screen. You will take the measurements when the temperature reaches 90°C, and every 5°C or so thereafter until the temperature has dropped to 50°C. (If the temperature is slightly below 90° when you take your first reading, that is fine, you do not need to reheat the sample.)

For each temperature measurement, you will do the following: (It will help to have one person handling the cuvette and another person recording data in the lab manual)

1. Using tweezers or a , remove the sample cuvette from the hot water bath. Quickly dry the outside of the cuvette with a paper towel. If there are lots of air bubbles in the cuvette, tap it gently to release the bubbles. Insert the cuvette into the spectrometer.

2. Record the absorbance and temperature in the data section of your lab manual, and quickly return the cuvette to the hot water bath.

3. Stir the bath gently with the temperature probe. Once the temperature has dropped another 5°C or so, you should take another measurement. Make sure that the cuvette remains capped at all times so that no water can get in to the cuvette. Repeat steps 1-3 until the temperature reaches 50°C.

Waste Disposal and Clean-up • Empty the contents of all cuvettes into the “Used Chemicals” beaker at your lab bench. Use a squirt bottle to rinse the cuvettes with water and pour the rinse into the “Used Chemicals” beaker. • Dispose of empty cuvettes and cuvette caps in the solid waste container. (Make sure that you haven’t left a cuvette inside the spectrometer!) • Empty the “Used Chemicals” beaker into the hazardous waste bucket in the back of the lab. • Put your cuvette holder back next to the spectrometer, and leave everything else at your lab bench. • Wipe down your lab bench and wash your hands before you leave the lab.

Chemistry E-1b

Experiment 15: Thermodynamics of Complex-Ion Equilibria

This page and all subsequent pages should be stapled together and submitted to your Lab TF before you leave the laboratory.

Each student should submit his/her own lab report.

Student Name: ______

Lab TF Name: ______

Lab Partner(s):______

______

Grading: Prelab: _____ / 10 Lab Report: _____ / 20 Safety: _____ / 3 Cleanup: _____ / 2

Total: _____ / 35

Data and Observations

Initial Absorbance = 0.039

Temperature (ºC) Absorbance Color 90 0.194 Pink 85 0.177 Pink 80 0.147 Pink 75 0.136 Yellow-pink 70 0.092 Yellow-pink 65 0.071 Yellow-pink 60 0.058 Yellow 55 0.043 Yellow 50 0.039 Yellow

Observations: As the cuvette is being boiled in the beaker the endothermic reaction shows that adding heat drives the reaction forward resulting in more pink product being formed from the yellow reactants. As heat is removed from the endothermic reaction, the reaction shifts left and yellow reactants are formed again

Experiment 15 Lab TF Name:______Student Name:______

Lab Report

Calculating ΔG°, ΔH°, and ΔS° from Measurements of the Equilibrium Constant

A " A [AlQ–] The concentration of AlQ– (M) [AlQ–] = i #2 "#1

– [H4Q] The concentration of H4Q (M) [H4Q] =[H4Q]i – [AlQ ]

3+ 3+ 3+ 3+ – [Al ] The concentration of Al (M) ![Al ] = [Al ]i – [AlQ ]

4 AlQ" H+ K The value of the equilibrium constant [ ][ ] K = 3+ [H4Q][Al ]

ΔG° The calculated ΔG° (kJ/mol) ΔG° = –RT ln K

! You will need the value of Ai that you measured and the following parameters: 4 –1 –1 ε2–ε1 = 2.5 × 10 L mol cm –5 [H4Q]i = 2.0 × 10 M 3+ –5 [Al ]i = 2.0 × 10 M [H+] = 0.01 M 3 1 1 R = 8.31 × 10– kJ mol– K–

1. Using your data and the equations above, fill in the following table to calculate ΔG°. 5 points

Temp. (K) Abs. [AlQ-] [H4Q] [Al3+] K ΔG° 363 0.194 6.2 x 10-6 1.38 x 10-5 1.38 x 10-5 3.26 x 10-4 24.2343 358 0.177 5.5 x 10-6 1.45 x 10-5 1.45 x 10-5 2.62 x 10-4 24.5516 353 0.147 4.32 x 10-6 1.56 x 10-5 1.56 x 10-5 1.78 x 10-4 25.3466 348 0.136 3.88 x 10-6 1.61 x 10-5 1.61 x 10-5 1.50 x 10-4 25.4810 343 0.092 2.12 x 10-6 1.78 x 10-5 1.78 x 10-5 6.69 x 10-4 27.4110 338 0.071 1.28 x 10-6 1.87 x 10-5 1.87 x 10-5 3.66 x 10-5 28.7065 333 0.058 7.6 x 10-7 1.92 x 10-5 1.92 x 10-5 2.06 x 10-5 29.8712 328 0.043 1.6 x 10-7 1.98 x 10-5 1.98 x 10-5 4.08 x 10-6 33.8396 323 0.039 0 2 x 10-5 2 x 10-5 -- -

Experiment 15 Lab TF Name:______Student Name:______

2. Plot your ∆G° values as a function of Temperature on the graph below. 3 points

3. Fit a line to your data (you may do this by hand or use a computer or calculator) and determine the slope and y-intercept. Use those values to determine ΔH° and ΔS° for this reaction. 3 points

Fit from graph: ΔG°= -0.252 x T +114.5 ΔG°= -ΔS x T + ΔH°

Slope = -0.252 y-intercept = 114.5 ΔH° = 114.5 kJ/mol ΔS° = 252 J/mol K

Experiment 15 Lab TF Name:______Student Name:______

4. Did you observe any changes in the reaction mixture as it cooled? How were those changes reflected in your measurement of absorbance at 550 nm? 3 points

Yes, the reaction mixture cooled from red-pink color to yellow reflecting a decrease in absorbance at 550 nm.

5. In your prelab (question 2), you predict whether the absorbance at 550 nm would increase or decrease as the reaction mixture cooled. Was your prediction correct? If not, what was the error in your reasoning? 1 point

Accept any complete answer. Ideally, you predict that as you remove heat from the endothermic reaction less red products to form; as a result, cooling the mixture will show a decrease in absorbance at 550 nm.

6. Does the calculated sign of ΔH° correspond to the shift in the equilibrium according to LeChatelier’s Principle? Explain. 2 points

ΔH° is expected to be positive as heat was required to produce products. This corresponds well with LeChatelier’s Principle.

7. Does the calculated sign of ΔS° make sense in light of changes in entropy in the complexation reaction? You may wish to write out the balanced reaction as part of your explanation. 3 points

Entropy is increasing because the disorder of the reaction is increasing as the reaction shifts from reactants to products. This can be anticipated simply by simply considering the number of species on each side of the balanced reaction.

When you are finished, please be sure to log off from your computer. If you do not log off, the spectrometer light will remain on and the bulb will burn out.

Experiment 15 Lab TF Name:______Student Name:______Prelab To be completed and handed in as you enter the lab.

1. What color light would you expect to have a wavelength of 550 nm? If the complex AlQ– is colored red, is that consistent with our claim that it absorbs light most strongly at a wavelength of 550 nm? Explain your reasoning. 3 points

We would expect to use a wavelength of light that AlQ- will absorb. As we are investigating a red molecule and molecules absorb the opposite color from what they transmit, from the color wheel we would expect 550 nm light to be green.

2. As the reaction mixture cools, would you expect the absorbance at 550 nm to increase or decrease? Explain. 3 points

We know that we have to heat the reaction mixture to generate products, so the product concentration should decrease as the reaction mixture cools. Thus, the absorbance should decrease with temperature.

3. How do we know that [H+] in the reaction mixture is equal to 0.01 M? 2 points

The H+ concentration can be found from pH=-log [H+] 2.0=-log [H+]  [H+]=0.01 M 3+ The Al and H4Q concentrations will be half of their original concentrations Total volume = 1.75ml+1.75ml = 0.0035L 1.75mL Al 3+ (1L/1000mL) x (4x10 -5 mol Al3+/1L)= (8 x10-3 mol Al3+) /(0.0035 L) = 2 x 10-5M

4. In one experiment, the initial absorbance was 0.014. The absorbance at 86°C was 0.196. Using that data, calculate ΔG° for this complexation reaction at 86°C. 2 points

ΔG° = -RTlnK = 22.98 kJ/mol

Experiment 15