Kinetics of dye fading lab answers

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EXPERIMENT B3 Kinetics of Bleaching of Methyl Orange

OBJECTIVES

The decomposition of methyl orange offers a practical example of how rates and mechanisms of chemical reactions are determined. You will study the rate of this decomposition reaction at different concentrations and temperatures to find out its rate law, rate constant, and activation energy. Experiment B3 will introduce you to Beer's law and the use of spectrophotometry in carrying out rate law analysis.

INTRODUCTION Methyl orange is an intensely colored compound used in dyeing and printing textiles. It is

also known as C.I. Acid Orange 52, C.I. 13025, helianthine B, Orange III, Gold Orange, and Tropaeolin D. Chemists use methyl orange as an indicator in the titration of weak bases with strong acids. It changes from red (at 3.1) to orange-yellow (at 4.4). The -related color changes result from changes in the way electrons are confined in the molecule when hydrogen ions are attached or detached. Here is the structure of methyl orange in acidic solution:

The molecule absorbs blue-green light, which makes its solution appear red. Notice that the nitrogen bearing the positive charge is involved in a double bond. In the basic (alkaline) form of methyl orange, a hydrogen ion is lost from the bridge between the rings, and the electrons formerly used to bind the hydrogen neutralize the positive charge on the terminal nitrogen, so that it no longer has a double bond. Solutions of this form of methyl orange in alkaline solution appear yellow:

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For this reason, methyl orange is often used as an indicator in acid-base titrations. In the present experiment, however, you will study the decomposition reaction of methyl orange as an example of how rates and mechanisms of chemical reactions are determined.

Chemical kinetics is a thriving field of research. Determining kinetic information about reactions allows scientists to understand how a reaction occurs, to be able to predict future outcomes, and to make more efficient industrial processes. Current hot areas of research include atmospheric chemistry, semiconductor processing, combustion, plasmas, and surface science. The kinetics of these systems are often studied using spectroscopic techniques, including many laser techniques. In Experiment B3, you will use a colorimetry probe to study the decomposition of methyl orange. The extensively-delocalized -electronic system of the azo compound is what gives it color; when the molecule is split in half, the products are no longer good absorbers of visible light. As a result, a solution of methyl orange fades in color as it decomposes. The absorbance of the solution is a measure of the concentration of methyl orange.

The = double bond that links the two benzene rings in azo dyes reacts with various reagents. In acid solution, methyl orange is cleanly decomposed by cations. These cations undergo electron-transfer reactions in which azo-nitrogens gain electrons and protons while tin ions lose electrons. The = linkage breaks, giving two product molecules with - bonds. The net stoichiometry of the reaction is given on the next page. But, remember that the rate law for a reaction cannot be predicted from its stoichiometry. To determine the rate law, we must explore how the concentrations of dye ( ), reducing agent ( ), and hydronium ion ( ) influence the reaction rate.

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Expecting that the rate may depend on the concentrations of all these substances, we can write a general rate law for the reaction:

= [ ] = [ ] [ ] [ ] (Eq. B3-1)

With three unknown exponents in the rate law, analysis of kinetic data would be hopelessly complicated. To simplify the task, it is convenient to use the technique of isolation (also called "flooding"). We arrange the conditions so that only the concentration of dye changes measurably during the time of our measurements. In this case, we will accomplish this by making the initial concentration of dye very much less than the initial concentration of either tin or acid:

[ ] [ ] [ ] Under these conditions, the concentrations of and stay virtually unchanged as the dye reacts. That is, at any time ,

[ ] [ ] [ ] [ ]

When we introduce these fixed concentrations into the rate expression, it has this form:

= [ ] [ ] [ ] (Eq. B3-2)

The only variable on the far right is [ ] ; the other terms (in bold) can be grouped together with the rate constant , giving a new constant :

= [ ] (Eq. B3-3)

…where,

= [ ] [ ] (Eq. B3-4)

Equation B3-3 is of a "simple" form, allowing us to analyze the kinetic data using standard techniques such as plotting or half-lives to determine the order ( ) and the rate constant ( ).

To analyze kinetic data, we need to know concentrations as a function of time. The easiest way to obtain such data is by measuring how much light the solution absorbs. A colorimeter allows us to measure light absorption. It displays the absorbance of the solution, which is linearly related to the concentration:

= [ ] [ ] =

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This relationship is called Beer's Law. It states that absorbance (how much light a solution absorbs) depends on a constant ( ), how far light travels in the solution ( ), and the concentration of the absorber. The constant , called the extinction coefficient, has a different value for every substance at every wavelength of light. While Beer's Law is valid under most conditions, solutions sometimes display non-linear behavior of absorbance with concentration. For this reason, we must verify Beer's Law by measuring the absorbance values of a set of solutions of known concentrations.

Recall that if a reaction is zeroth-order, a plot of concentration vs. time will be linear. If absorbance, , is directly proportional to concentration (Beer’s law), then a plot of versus will also be linear. Recall (also from lectures) that the “integrated rate laws” for 1st and 2nd order reactions are, respectively:

ln = ln 1 = 1 +

Hence, if the reaction is first order, a plot of ln versus will be linear; if the reaction is second order, a plot of 1/ versus will be linear.

From your measurements of [ ] (or of the absorbance of MO) versus , ln versus , or 1/ versus , you will be able to determine the likelihood that the reaction is zeroth, first, or second order by suitable plots. (Remember that if a reaction is first order, then a plot of ln vs. will be linear; however, we can’t with 100% assurance say that if a plot of ln vs. is linear, then the reaction is first order – be careful with your logic here… However, if the plot of ln vs. is VERY linear, we can have “a great deal of confidence” that the reaction is first order.

The half-life ( / ) is a quantity that is easily estimated from a graph of vs. . If a reaction is first order, the half live will be constant and, from the integrated rate law we know that,

= ln 2 /

(Eq. B3-5) By quickly examining the vs. profile, we can see if the reaction is (likely) first order. Because concentration and absorbance are linearly related for a system obeying Beer's Law, in a first order reaction, when concentration is cut in half the absorbance is also cut in half. This lets us quickly measure half-lives.

Suppose we start with a solution with an initial absorbance . For this solution, the half- life is the time taken for the absorbance to fall to /2. Now, suppose we start at this new (more dilute) solution. Its half-life is the time required for its absorbance to fall to /4 (that is, one half of one half of the initial absorbance ). Remember that if the reaction is first order, the

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half-life is independent of concentration (i.e., constant). If a constant half-life / is observed, it is easy to evaluate the rate constant from equation B3-5.

We return to the linear relationship between absorbance and concentration.

= [ ] [ ] =

If the reaction is first order,

ln[ ] = ln[ ] …or

ln = ln ln( ) ln( ) = ln( ) ln( ) Since ln( ) appears on both sides of the expression, and therefore cancels,

ln( ) = ln( ) (Eq. B3-6)

A plot of ln( ) vs. will thus give a straight line with = . Either (estimated) half- lives or plots of ln( ) vs. can be used to get rate constants for first-order kinetic behavior. In this experiment, you will use both.

A single experiment provides the value for for one set of initial concentrations of all reagents: , , and . Note that we DO NOT NEED TO KNOW THE CONCENTRATION OF to get the rate constant , but that rate constant is actually a combination of the “fundamental” rate constant multiplied by the (constant) concentrations of

and , raised to their appropriate powers (still unknown):

= [ ] [ ] from Eq. B3-4 above

If we repeat the kinetic experiment at the same concentration of acid but using different concentrations of tin, we can determine the order of the reaction with respect to tin. To see how the observed rate constants are related to the exponent , it is most convenient to take natural logs of both sides of Equation B3-4:

ln = ln( ) + ln([ ] ) + ln([ ] ) (Eq. B3-7)

For a set of solutions with the same [ ] , a plot of ln vs. ln([ ] ) should be a straight line with = .

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Similarly, if we do a series of kinetic runs at the same tin concentration but different hydronium ion concentrations, the analogous plot will have = . Thus, a series of kinetics experiments using different initial concentrations allows us to evaluate all the exponents, find the complete rate law, and THEN compute the value for the fundamental rate constant .

All of this will take place at one temperature, room temperature. To find out how the rate of bleaching varies with temperature, we need to duplicate one of the kinetic runs at a significantly different fixed temperature. For us, the most convenient fixed temperature other than room temperature is ice temperature. If is also determined at a lower temperature (close to ice temperature), we can use the Arrhenius Equation to compute the activation energy

of the reaction.

Recall, that since = / , where is the “Arrhenius constant” or the “pre- exponential factor” (NOT the absorbance), is the activation energy, is the molar gas constant (8.314 ) and is the temperature (in ), then for comparing two different temperatures the natural log form of the equation becomes:

ln = 1 1 (Eq. B3-8)

You will use this equation to determine .

SCHEDULE Three laboratory days are allocated for this experiment, which will be performed in pairs. The first day is devoted to learning to work with the equipment and techniques of colorimetry. Kinetics runs are on Days 2 and 3.

Day 1: Carry out solution preparation (Procedure A). Set up a LabPro kit with colorimeter probe (Procedure B). Verify Beer's Law (Procedure C). Prepare a table in your laboratory notebook, listing the concentration and absorbance for

all of the solutions in Table B3-1 for the three different wavelengths. Prepare a single Beer's Law graph for the three wavelengths analyzed (at home or in the

computer lab, any time before Day 2). Determine which wavelength provides the best response for monitoring absorbance.

Day 2: Set up a LabPro kit with colorimeter probe. Turn in your Beer's Law graph. Do kinetics runs #1 - 6 (Procedure D).

Day 3: Set up a LabPro kit with colorimeter probe. Do run #6 again (to compare with run #7). Do kinetics run #7 at ice temperature (Procedure E).

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PROCEDURE

Solution Disposal: For Procedure C, all waste can go into the “methyl orange” waste container. For Procedures D & E, we are using tin, which is damaging to the environment if disposed of improperly. Place all solution waste containing tin in the "tin waste" container. Other solution waste can be disposed of in the “aqueous waste” containers in the waste storage hood.

A. Solution Preparation – These solutions can be prepared in any order.

1) Clean a test tube. Fill it to within 2 of the top with 2 Solution. Stopper and label with your name and “ soln”. Note: the solution is used so that all of your kinetics runs will take place at the same total concentration of chloride ion, which removes one variable that might have an effect on the rate of the reaction. This solution will be used in Procedures D and E.

2) Clean your 10 graduated cylinder and a 250 Erlenmeyer flask. Measure 40 of

deionized water into the flask. Transfer 20.0 (graduated cylinder accuracy) of 6.0 (“dilute” ) to the Erlenmeyer flask, mix well with your stirring rod, stopper and label with your name and “2.0 ”.

3) Set up a test tube rack containing 6 test tubes, labeled #1 through #6. The test tubes should be

clean, rinsed with deionized water, and drain-dried but need not be fully dry. 4) From your wash bottle, add 3.0 of deionized water to your 10 graduated cylinder.

Using a Pasteur pipet, add 3.0 of 2.0 . Then pipet 4.00 of stock into the cylinder. Mix this solution well by pouring it back and forth several times between graduated cylinder and test tube #1. After mixing, the solution should be in test tube #1.

5) Prepare five solutions with the compositions given in Table B3-1. Add the indicated amount

of deionized water to your 10 graduated cylinder. Then, using a Pasteur pipet, add solution from test tube #1 to make the total volume 6.0 . Mix by pouring back and forth several times between the test tube and graduated cylinder. Rinse the graduated cylinder with deionized water before preparing the next solution. Use solution #1 carefully so you don’t run out!

Table B3-1:

Solution # 2 3 4 5 6 water 5.5 5 4 3.5 2.5 soln. #1 0.5 1 2 2.5 3.5

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6) Record in your notebook the concentration of methyl orange in the stock solution (both in units of mg/L and M, molar mass of MO is 327.33 g/mol). Use = to calculate the concentration of methyl orange in solution #1. Then use = again to calculate the concentrations of solutions #2 through #6. You need to have these values available when you begin to use the colorimeter.

B. Setup and Colorimeter Calibration

Note: Before absorbance values can be read, it is necessary to calibrate the colorimeter every time that a new experiment is performed OR if the wavelength of detection has been changed.

1) Check out a laptop computer from the front cabinet: a) Sign your and your partner’s names to the booklet, and record other pertinent

information. b) Remove the charging connector from the computer (which is used to keep the battery

charged when the computer is not in use – you will need to replace this connection when you turn the computer in). Take the portable power cable associated with your laptop along with it.

c) Connect the power cable to the computer and the (lower) bench socket. Open the computer lid and turn on the computer.

2) Check out the LabPro box and colorimeter box (along with a plastic bag of cuvettes) from the Equipment Stockroom MH-277. (Also refer to the General Setup Procedure for the LabPro and software in the Appendix). a) Unpack the LoggerPro “green” interface box and place it on the bench. b) Remove the USB connector cable (standard USB connection on one end, “square”

connector on the other – pay attention to plug orientation!) and attach the standard USB connection to the lower USB port on the right side of the laptop computer (the upper port on the computer can be used to attach your USB drive to transfer data).

c) Connect the colorimeter cable to one of the CH# ports on the side of the interface box. d) Remove the power adapter unit from the box and connect it to the (upper) bench socket.

Connect the small end to the green interface box and wait for the green light to appear and a series of beeps to be sounded.

e) Place the large cardboard LabPro box under the computer to protect it from spills. f) Move the computer away from any faucets or chemical solution so that nothing gets

spilled onto the computer or keyboard.

3) Double-click the “LoggerPro” icon on the computer to start the software. The program should automatically detect the presence of the colorimeter, and organize the data acquisition layout accordingly. Wait for the screen to display the “Absorbance” readings of the colorimeter. If it displays “Transmittance” in large red print instead, right click that text, and

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select “Digital Meter Options”. Then change the ‘Column’ setting to “Absorbance”, and click “OK” to close the window.

4) Select the desired wavelength for your experiment using the “<” and “>” buttons on the colorimeter. Note that EVERY time you change wavelength on this device, it MUST be recalibrated with deionized water (as described in Step B.5 below).

5) Fill a cuvette three-quarters full with deionized water, dry off the outside of the cuvette with a Kimwipe, and carefully place it in the colorimeter (recall the correct orientation of cuvettes in the colorimeter). Firmly press the ‘CAL’ button on the colorimeter such that the red LED under the ‘CAL’ button flashes steadily. Once the LED flashing stops, the colorimeter is calibrated at that wavelength.

C. Verification of Beer’s Law

Precaution: Do not handle cuvettes by the clear sides. That is where the light passes through. Handle by the ridged (or frosted) sides, and wipe off any smudges or external moisture with a Kimwipe. Be certain the cuvette is oriented properly when inserted into the colorimeter.

Note: Please read the text within the Troubleshooting Tips section (Appendix C) before collecting data with the LoggerPro software!

1) Change the colorimeter detection wavelength to “565 nm”, and calibrate as described in Procedure B. You are now ready to read absorbance values. Rinse a cuvette with about 1 of the solution you will measure. Discard this rinse. Then fill the cuvette three-quarters full of the solution to be measured, insert in the compartment, and close the lid.

2) When the absorbance value has stabilized, as displayed in the bottom corner of the software,

record this absorbance value, the concentration of the solution (in / ), and the wavelength of light used in your lab notebook. Repeat this for solutions #2 through #6 at this wavelength.

3) Repeat this analysis for the other three wavelengths (430 nm, 470 nm, and 635 nm). Be sure

to recalibrate the colorimeter when changing to a different wavelength (Procedure B). 4) Prepare an overlay plot of absorbance vs. concentration and plot the best straight-line fit

through the data for each of the wavelengths analyzed. Display the equation of the line and the R2 value on the graph. Note: You are required to submit this graph to your laboratory instructor at the beginning of the next laboratory period.

5) See Cleanup and Takedown: Procedure F.

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D. Kinetics Runs

Before beginning you will need to have decided which of the three colors will provide the best response for measuring changes in absorbance of . Discuss your choice with your instructor and perform all runs at this wavelength.

Note: Please read the text within the Troubleshooting Tips section (Appendix C) before collecting data with the LoggerPro software!

1) Clean your 10 graduated cylinder, two test tubes, and your 125 Erlenmeyer flask. Fill one test tube with 0.040 2 stock solution and label it “tin stock." Label the 125 flask “reagent solution.”

2) Arrange the tin stock, the stock, 2 (Step A.1), and 2.0 (Step A.2) in a

way that you can conveniently work with them. 3) Label a 250 Erlenmeyer flask (not the clean one!) “tin waste”. Place it in a convenient

spot on your bench top with a rubber stopper for disposal of your solutions. 4) Set up and calibrate the colorimeter probe as described in Procedure B, at the wavelength that

you have chosen (and verified by your instructor).

5) To carry out the Absorbance vs. time experiments it is necessary to specify several

parameters: a. Click on “Experiment” in the upper menu bar, then “Data Collection” in the

menu. Ensure that ‘Mode’ is set to “Time base”, then change the ‘Duration’ to 900 seconds and the ‘Sampling Rate’ to 5 seconds/sample, then click ‘Done’.

b. To adjust the -axis (Absorbance) range, right-click the -axis, select “Graph Options”, then select the tab titled “Axes Options”. Then define “Top” to be 1.5, and click ‘Done’.

The procedure for all room temperature kinetic runs is the same, except for the composition of the reagent solution. Proceed as follows: 6) Transfer 8.00 of stock solution into a clean test tube using a graduated cylinder. 7) Separately prepare the reagent solution for the run you wish to carry out. Measure the

quantities of the solutions listed in Table B3-2 using your clean 10 graduated cylinder, and transfer the solutions to the clean 125 Erlenmeyer flask labeled “reagent solution.”

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Table B3-2

Run #: 1 2 3 4 5 6 7 tin stock in 2.0 3.0 4.0 6.0 6.0 6.0 6.0 6.0 2.0 5.0 4.0 2.0 6.0 4.0 2.0 2.0 solution 4.0 4.0 4.0 0.0 2.0 4.0 4.0

Expected half-life, : 90 70 45 30 35 45 --

Start filling out the Worksheet provided for this experiment at the end of the lab manual. Calculate the concentrations of each reagent that will be present in the TOTAL reaction mixture when the solutions have been combined. Show this to your instructor before proceeding.

8) The following procedures should be carried out as rapidly as possible. When you are

ready for your first kinetics run, pour the 8.00 of methyl orange from the test tube into the Erlenmeyer flask containing the reagent solution (what is the total volume now?). Vigorously swirl the solution in the Erlenmeyer flask for ~10 seconds to thoroughly mix it. Quickly fill the cuvette three-quarters full, and carefully place it in the colorimeter. Click START (Green box) on the menu bar above the graph. You should see a decrease in absorbance over time. Your data ( ( ), (% ), ) will fill the table on the left as it collects the data. Do not click stop until the run is complete!

9) You do not have to let the runs go for the full 900 seconds! Let it proceed until the

absorbance is about one-quarter the original value (e.g., hypothetically starting at = 1.000, let it go long enough for the absorbance to get to about 0.250). To finish the data collection for this sample, click the red “Stop” button above the graph. (It is necessary to stop the data collection before you can copy and paste the data to MS Excel.)

10) Remove the cuvette from the compartment, and measure and record its temperature.

Discard its contents and the remaining solution in the flask in the “tin waste” flask. Rinse the reagent flask and cuvette with deionized water (this rinse should also go in the “tin waste” flask). The run is now complete.

11) Open MS Excel, then copy and paste the time, transmittance, and absorbance data into columns in Excel. Your instructor will show you how to use Excel to prepare “ln( )” and “1/ ” data columns for the zeroth, first, and second order plots that you should make. Save the file under a specific name on the laptop and on your USB drive (e.g., “KinRun1- ”).

12) Once your Excel file is saved, clear the data from the LoggerPro software by selecting “Data” from the top menu, and “Clear All Data”. This will allow you to carry out a new run.

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13) For the next run, you can rename your original data file (e.g., to “KinRun2-”) and copy and paste the new data on top of the old and expand/remove data from the previous run to update the graphs (your instructor can help you if you are unsure how to do this).

14) Remember that runs 1,2 and 3 MUST be done on the same day; you should also try to do runs 4,5 and 6 if there is time on Day 2. If not, do all three (runs 4,5,6) on Day 3 along with run 7. If you do runs 1 through 6 on Day 2, you MUST repeat run 6 on Day 3 alongside the low temperature run (run 7).

15) Thoroughly complete the worksheet provided to you and show it to your instructor for them to initial.

16) You can determine half-life directly from the Excel data table – this number should be

estimated and recorded on the data table. The “rate constant” should be the slope of the appropriate zeroth, first, OR second order graph (check with instructor if you have questions).

17) At the end of the day, transfer your tin waste and any remaining tin stock solution to the tin

waste container in the hood. Do not store your tin stock overnight in your lab drawer. See Cleanup and Takedown: Procedure F.

E. Variation in Temperature

Note: A repeat of run #6 must be done on the same laboratory day as run #7 so that the two runs can be compared with each other and both rate constants can be used to calculate the activation energy of the reaction. Be sure to record the temperature for both runs.

1) Repeat the LabPro setup procedure as described above, and fill a 400 beaker loosely with ice and add about 25 of deionized water.

2) Fill a cuvette three-quarters full of deionized water and place in the ice. This is your “blank”.

3) Prepare reagent solution #7 (see Table B3-2) and transfer this solution to a test tube. Place the test tube in the ice bath with your glass stirring rod in it.

4) Pipet 8.00 of stock solution into another test tube, and place this in the ice bath as well, with your metal spatula in it.

5) Allow the test tubes to equilibrate for at least 10 minutes in the ice bath, stirring them every two minutes. Measure and record the temperature of the reagent solution; it should be lower than 5° (if it is not, continue chilling until the temperature is below 5° ).

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6) Calibrate the colorimeter to the wavelength you have determined to be best for monitoring absorbance (refer to Procedure B for the calibration procedure). In this case, however,

use the cold “blank” to calibrate your colorimeter. When calibrating here, remove the cuvette with the blank solution from the beaker, wipe it off with a Kimwipe, and place it in the colorimeter. Note: because of its cold temperature, the cuvette may “fog up” after a few seconds in the compartment. Do not wait more than a few seconds to press “CAL”.

7) Complete the set up procedure and change the parameters as described by step D.5 and perform a test run with no sample present.

8) Carry out this step as quickly as possible. Mix reagent solution #7 with 8.00 of stock by pouring both solutions into a clean 125 Erlenmeyer flask and swirling vigorously for 10 seconds. Rinse a cuvette with 1 to 2 of this solution. Then fill the cuvette three-quarters full with solution and place it in the colorimeter. Click “Collect” (DO NOT press “Stop” until the very end of this run as instructed). Allow 2 – 3 absorbance values to be recorded, remove the cuvette, and return it to the ice bath for 60 seconds. Remove the cuvette from the ice bath, wipe it off with a Kimwipe, and return it to the colorimeter. Repeat this process for the entire duration of the run (15 ). This ensures the temperature of the solution is maintained close to that of ice water.

9) The graphical display of the data will be quite different from that of runs #1 – 6. Since the colorimeter sample chamber is actually empty for the majority of run #7 there will be intermittent sections where the absorbance reading is (near) zero. These points can be deleted after the data have been copied into MS Excel.

10) Remove the cuvette when the run is complete. Discard its contents and the remaining solution in the flask in the “tin waste” flask. Rinse the reagent flask and cuvette with deionized water.

11) Copy the data into MS Excel. Again, save the data file with a sufficiently descriptive name.

12) Refer to Procedure F for cleanup and takedown.

F. Cleanup and Takedown

1) Ensure that you have removed the last cuvette from the photometer!!!

2) Dispose of the solutions in each cuvette by pouring them into your “tin waste” flask and rinsing them with DI water. Pour the contents of your “tin waste” flask into the large “tin waste” container in the hood.

3) Pour any leftover methyl orange solutions into the aqueous waste container in the hood.