chemistry lab report

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CHEMISTRY 2500, EXERCISE C2 UV-VISIBLE SPECTRA OF CONJUGATED POLYENES: An Experimental determination of the mass of the electron A commonly found application of the “Particle in a 1-D Potential Well” model (PIDW) is the prediction of the first UV-visible transition wavelength of conjugated polyenes (i.e. poly-alkenes, with alternating C-C, C=C units, such as butadiene, hexatriene, etc.). Most quantum-mechanics texts cite the ability to model the transition wavelength of butadiene as evidence that this model is generally applicable to conjugated alkene systems. The basic premise for the use of the PIDW model for conjugated polyenes is that the -bonding system of a conjugated molecule can be considered to be separate from the sigma-bonded backbone. This idea is borne out by the large energy separation between molecular orbitals associated with σ-bonds and those with π-bonds in modern calculations. Therefore, any molecule containing conjugated C=C bonds can be thought of as having π- electrons confined to move within a pseudo-linear, one-dimensional area comprised of the overlapping p-orbitals of the sp2 carbons of the backbone. A conjugated molecule is shown below, with the conjugated region outlined:

This conceptualization closely resembles the description of a particle confined to a one-dimensional potential well (P1DW), one of the simplest and well-known quantum mechanical systems which can be solved exactly. As a result, the spectra of conjugated molecules are often crudely interpreted with this model. The properties of electrons in molecules are often conveniently probed by various types of electronic spectroscopy. Electronic spectroscopy refers to those forms of spectroscopy which probe the promotion of molecules from one electronic state (electronic configuration) to another electronic state. Changes in electronic states of molecules are understood as arising from promotion of individual electrons from one orbital to another. Thus, in simplest terms the change in energy of a molecule undergoing a transition between electronic states corresponds to the change in energy of an electron as it is promoted from one orbital to another. The energy difference associated with a change in occupation of an electron between one molecular orbital and another can therefore be effectively probed by observing the wavelength or energy of the spectroscopic absorptions that stimulate these transitions. The energy of light which can induce an electronic transition in a conjugated polyene lies in the ultraviolet or visible portion of the electromagnetic radiation spectrum. Thus, this experiment uses UV-visible spectroscopy as an analysis tool for conjugated polyene systems.

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Experimental observations of the lowest-energy electronic transitions of conjugated molecules, and the theory of the particle in a 1-D potential well (P1DW) model, can be used to directly determine the mass of the electron from spectroscopy. The theoretical development for this idea follows: The energy of an electron in a 1-D potential well is given by:

2 2

n 2

n h (1) E (n 1, 2, 3,....)

8mL  

Here m is the mass of the electron in kg, and L is the length of the box to which the electron is confined, in m. The quantum number “n” corresponds to the particular energy state in which the system exists, with the state n = 1 being the lowest energy, or ground state. The lowest energy -electron transition for a conjugated molecule involves promoting an electron from the Highest-energy Occupied Molecular Orbital (HOMO) to the Lowest-energy Unoccupied Molecular Orbital (LUMO). The energy difference between these two states is termed the “HOMO-LUMO gap”. Since there are two electrons per molecular orbital, this gap may be modelled in terms of the P1DW, if we think of each of the π-type molecular orbitals as corresponding to one of the allowed energy levels of the PIDW system. In this case the HOMO-LUMO gap can be estimated by determining the energy difference between the energy of the highest occupied level of the PIDW, and the first available level to accept an electron. The highest occupied level occurs with quantum number n = d, where d is the number of C=C bonds (since there are 2 -electrons contributed per C=C bond), and the energy of the next-highest level, for which n’ = d + 1, the first unoccupied energy level above n = d. Normally the quantum number for the lower energy orbital would be termed “n” and the quantum number for the higher energy orbital expressed in terms of that of the lower level, i.e. as n +1. Therefore, based upon these ideas and equation 1, the transition energy will be predicted by the PIDW model to be:

2 2 2 2

n 1 n 2 2

hc h h (2n 1) E h E E ((n 1) n ) (2)

8mL 8m L 

  

        

Inspection of this expression reveals that if we obtain E for a series of linear polyenes and plot it against (2n+1)/L2, the resultant plot should be linear and the best fit line should have a slope of h2/8m, from which the mass of the electron may be determined. Note that estimates of the parameter L, the length of the -network within which the electron moves, must be made to determine the mass of the electron, m.

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Procedure: You are to calculate the length of the conjugated portion of the molecule, and use it to determine the mass of the “particle” moving in the -network of the molecule which, in this case, is an electron. To begin the exercise, you will collect UV-visible spectra of a series of linear conjugated polyenes, with known structure. You are provided with solutions of alkenes diluted in hexane or ethanol as appropriate, such that their absorbances are roughly correct for performing this exercise. These should be (1) isoprene, (2) Retinol Palmitate, (3) b-carotene, (4) Amphotericin B, and (5) Astaxanthin (see structures below). Record the UV-visible spectrum of the conjugated molecules provided. Note the formula and name of each polyene provided. Instructions for use of UV/Vis spectrometer – Instructions are provided, they are also on the desktop of the lab computer, so you do not need to print them out. Sample Preparation and Spectrum Recording 1. Using hexanes or ethanol as appropriate, wash out the quartz cell, which can be

found in the black box, in the drawer below the instrument. Only touch the cells on the ground-glass sides. Avoid touching the clear surfaces with your fingers. Clean the clear surfaces with a Kimwipe. You will use this one cell for all measurements.

2. Fill the cell with hexanes (or ethanol) and put it into the sample holder. 3. Record the spectrum of this solvent sample as your “baseline” spectrum. This

spectrum will be automatically subtracted from your sample spectrum to remove absorptions due to the solvent and cell walls, leaving the spectrum of the sample only. You must perform a baseline with the appropriate solvent, for the compound of interest. You may need to recollect a baseline for samples dissolved in a different solvent.

4. Empty and clean this cell, then fill it with your sample and place it into the sample

holder. 5. Record the spectrum of this sample, save it in a folder you will create labelled with

you and your partner’s names in the CHEM 2500 folder on the computer’s C drive. 6. You may not need this step, however, if your spectrum is too intense, i.e. too

strongly absorbing, such that the first major band with the longest wavelength has a maximum above absorbance = 3.00 units, you will need to dilute the sample. Do this by draining a portion of the sample solution away and replacing it with pure solvent. Beer’s Law states that absorbance is proportional to concentration of absorber, so reduction of concentration by ½ will result in a drop in absorbance by

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the same amount. Use this law to judge the extent to which you need to dilute your sample. Once you have the acceptable dilution and spectrum go on to the next sample, being careful to clean your cell with hexane between samples.

7. For each acquired spectrum, record the wavelength of the absorption which has the

longest-wavelength (i.e. the largest x-axis value). Please note: this may not be the most intense feature of the spectrum. For long molecules, such as -carotene, this absorption will be in the visible region (400-700 nm). Although nearly every conjugated molecule shows a strong UV absorption in the 200-250 nm region, an absorption in this region is generally not the longest-wavelength feature. At the end of the experiment, you will have one wavelength recorded for each sample. Verify your data with your TA, if you are unsure of which value to use.

Data Analysis 1) You will develop a simple equation that you can use to calculate a "geometrical"

length, L, for the -bond network of conjugated molecules. The simplest method is to count up the individual C-C and C=C bonds in the conjugated -network region of the molecule, the region over which the “box” extends. Only consider C- C and C=C bonds that are part of the conjugated region, and ignore any component that is not directly in this range. Enter these values in the provided Excel spreadsheet template file, in the correct columns. You can download this from webCT.

You will have to look up the lengths of individual C-C and C=C bonds – just find the average values, and these should be found in standard appendices at the back of general or physical chemistry textbooks, or the CRC handbook. Enter these bond lengths in the Excel template, and use them and the number of each type of bond to determine the length of the conjugated region. Since p-orbitals extend past the end of the sigma-bonded framework of the conjugated region of the molecule, your model will be more accurate if you add ½ the length of a C-C to each end of the molecule, for a total of one additional C-C bond. For example, ethene would have a length of 1*LC=C + 1*LC-C and butadiene would have a length of 2*LC=C + 2*LC-C. Include the equation you came up with to calculate the length of the region in your report.

2) In addition to the molecules you have measured in the spectrometer, include

calculations of the length of the following molecules in your data set, using the same equation you used above:

hexatriene C6H8(λmax = 256 nm) octatetraene C8H10 (λmax = 290 nm )

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C10H12 (λmax = 334 nm) C12H14 (λmax = 364 nm) lycopene (λmax = 474 nm)

These additional data points become part of your experimental data set.

3) Calculate the energy of transition for each of your observed spectroscopic transitions, and for those given as additional data above. Use the Bohr frequency relationship (See Eq. (2) in the introduction) to convert transition wavelength (λ) to transition energy, E, in Joules. A column is provided in the template given to you for this calculation.

4) Determine the appropriate value of “n” to use for each of your molecules, based

upon the discussion given in the introduction. Recall n = d, where d is the number of C=C bonds in the conjugated framework for the molecule. Enter this value in the Excel template.

5) The Excel sheet will create a graph of E vs (2n+1)/L2, and display both a trend

line over the data and the equation corresponding to the trend line. If you choose not to use the Excel Spreadsheet, you must prepare this on your own. You are expected to submit an electronic plot of this data. If you need help, please consult a teaching assistant to aid you.

6) From the slope of the trend line, determine the mass of the particle in the box in kg

using Equation (2) from the introduction. This equation is also given on the spreadsheet. How does your mass compare to the known mass of the electron? Include a discussion of this comparison, and factors affecting the quality of your value in your report discussion.

Report Once you have completed the calculations in your Excel template, you should summarize the results in your lab report. In the Results section of the report you should show a sample of each different calculation performed, the graph created in Excel, and the calculation of the mass of the electron. You should also calculate the percent difference between your calculated mass of the electron and the known value:

known

calculatedknown

mass

massmass difference

 %

In the Discussion section of your report, comment on your mass of the electron and how it compares to the known mass. Consider the mass of the electron, and alternative ways of measuring this. Is this a large, or a small number? Can you weigh this on a balance? Is your number acceptable, reasonable, unreasonable? You should be able to discuss

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possible reasons for any discrepancy, sources of error in the experimental procedure and in your performance of the exercise, and the effect that they would have on your results. There should also be a discussion of whether the model used in this exercise is an adequate model for the particle in a box, and why it is possible to use the conjugated region of a molecule as a model for the “box.” You should think about the accuracy of the model being used, as well as the accuracy of your calculations and decide whether your calculated electron mass is acceptable or if the error present in the exercise makes it unreliable. Structures of conjugated polyenes used in this exercise: Isoprene: Retinol Palmitate:    -carotene: Amphotericin B: Astaxanthin: