particle in a box conjugated dyes lab

In Rodds Chemistry of Carbon Compounds (pp. The potential energy of a system needs to be defined to calculate the energy levels. Images 1-3 represents graphs determined by gauss view, images 4-5 represents graphs found using particle in a box. 13. << Note that the energy levels are more closely spaced due to the fact that dye B is represented by a larger box. J. Chem. Each spectrum shows a major peak, a shoulder peak at a smaller wavelength, and a baseline with minimum noise (Figure 1). << Image 1. /Transparency L = 1 x 10-10 m a = (2j + 2)L, C: 1,1-Diethyl-2,2-dicarbocyanine Iodide, N = 2j + 2 = 2(4) + 2 = 10 pi electrons Make plots of the absorbance spectra for dyes A F. You may combine the plots in one or two page graphs. Image 2. 1985, 62, 351. 4. 6 0 1,1'-Diethyl-4,4'carbocyanine iodide (Dye E) Carry out the necessary calculations and propagate the errors involved to the final answer. The different in energy between these two levels is exactly equal to the energy a photon needs to excite the dye. because of the poor solubility of these dyes in non-polar solvents and in water. /Outlines Casaubon, J. I. and Doggett, G. J. Chem. E = 1.196 10 5 nm kJ 700nm mol = 171.kJ/mol b. the sides of the box or the walls of the well, the wave function has to go to zero. Kirksville, Missouri 63501 2001, 78, 1432. (The dyes are CONCENTRATED.) The dyes are light sensitive, and so if it is necessary to store the dye solutions, protect them from light. Figure 1: The absorption spectra of each conjugated dye. dye can be used to find the empirical parameter and the length of a conjugated system within We can read off the potential energy of the particle at any point in the box by looking at the level of the floor of the box at that point. Five-membered heterocyclic compounds with two nitrogen atoms in the ring. Thus the percentage difference was approximately 40%. The base 0000008638 00000 n 0000007528 00000 n 0000047452 00000 n Provide a sample calculation in your report. Phys. The literature procedures call for the use of methanol as a solvent.3,4 If you wish to explore the effect of solvent it is suggested that you use other polar organic solvents (e. g., tetrahydrofuran, acetonitrile, etc.) Procedure: (done by others) Absorption of blue light produces the color red while the absorption of red light produces the color blue-green. 0000044295 00000 n 0000041060 00000 n For dye 4, the absolute error is 3 nm while the experimental uncertainty is +/- 1 nm, suggesting a disagreement. 0000001086 00000 n Finally, the length of the box for each dye molecule from the absorption spectra was calculated 1,1'-Diethyl-4,4'-dicarbocyanine iodide (Dye F) The results from a classic experiment in the undergraduate physical chemistry laboratory, the particle-in-a-box model for spectroscopic transitions of conjugated dyes, is compared to computational results obtained using a molecular mechanics structural approach and the extended Hckel molecular orbital picture. ] Click here to view this article (Truman addresses and J. Chem. Then we use the number of pi electrons to determine the energy level of the highest occupied molecular orbital and the lowest unoccupied molecule orbital. Wear eye protection. The general approach to this experiment is adapted from D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 6th edition, McGraw Hill Co. Inc, NY, 1996, p378. 0000047672 00000 n 0000033368 00000 n HVKO1WJ Particle in a Box is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. and M. Kasha (1958). %PDF-1.3 % . Atkins, J,: Paula, J. /JavaScript In the free electron model, represents a constant for a series of dyes of a given type. The literature and experimental major wavelengths (max) absorbed for dyes 1, 2, and 3 agree within the experimental absolute uncertainty; however, the literature max absorbed for dye 4 falls outside the experimental absolute uncertainty (Table 1). 0000041039 00000 n For dyes 1 and 3, the absolute percent errors are 8.79% and 3.64%, respectively, while the absolute percent error is the greatest for dye 4 (21.7%). 12. 2 Dye A Dye B. 1 In this It is advisable not to try to do the peak picking in Excel; it is fairly tedious. 0000001680 00000 n Below are the dyes which we will study You will measure the absorption spectra of a series of conjugated dyes and then usethe Particle-In-A-Box (theoretical model)to explain the observed spectra. All of the conjugated dyes used have the largest absorbance at different wavelengths of light. Dye A has 6 electrons and dye B has 8 electrons in their respective pi-bond systems. 10 The energy level of a particle in a 1D box is expressed as: 2 2 =withn=1,2,3.. 8 2 = 9.109x10-31kg = mass of an electron = 6.626x10-34Js = Plank's constant L = Length of the box 2. where: E is the change in energy, h is Plancks constant, m is the mass of the electron, L is the length of the box and ni and nf are the initial and final quantum numbers. $('#commentText').css('display', 'none'); The objectives of this experiment include: 1. N = 2j + 2 = 2(2) + 2 = 6 pi electrons Soltzberg, L. J. J. Chem. Use the same spectrometer settings and the same cuvette for the background and the dye solutions. j = 3 double bonds Conjugated pi-bonded system for dyes A and B. This variation may have been due to the methanol buffer in which the dye is stored. In this video you will learn how to calculate the maximum wavelength of absorption for a conjugated dye using the particle in a box (PIB) model. 0000002439 00000 n /Creator Using the spectra shown, the max is determined by observing for each dye where the absorbance was the highest. 0000001782 00000 n 0000037527 00000 n Use the references 3 and 4 to develop an experimental procedure. << A: Pinacyanol chloride, MM = 388 g/mol 0000037260 00000 n Plastic cuvettes absorb UV spectrum light, so any absorbance data that was gathered in a plastic cuvette would have . All of the conjugated dyes used have the largest Our experimental max for dyes 1, 2, and 3 agree with their respective literature values within their uncertainties. Educ. 0 As the figure below indicates these molecules possess a great deal of conjugation such that the electrons are delocalized across the chain. 3. Figure 2 shows that there is a potential energy barrier at the nitrogen atoms and there are wells at each atom; however to a reasonable degree of accuracy the potential energy of the conjugated pi-bonded system can be approximated by a particle in a box potential. Any group that produces more waste than that will be penalized accordingly. McRae, E.G. You should just be able to see a little color. Educ. The number of -electron pairs equals k + 3. HXCCDdMp+ad{3p\P>n 7hf*v[g =&X!5;$5L/9e Swenberg, Electronic Processes in Organic Crystals, (Oxford University Press, New York, 1982), Chapter 1D. 0000005322 00000 n The quantum number n = 1, 2, 3 and the spin of an electron can be either up (+1/2) or down (-1/2). ( G o o g l e) You MUST fill out the cover sheet fully and correctly to receive credit. Phys. Educ. Fourier Transform Infrared Spectroscopy (FTIR), CHEM 174 Physical Chemistry Laboratory II, Determination of the Length of a Molecular System, Pauli Exclusion Principle and Packing Electrons into the Particle in a Box. Nederlnsk - Frysk (Visser W.), Principles of Marketing (Philip Kotler; Gary Armstrong; Valerie Trifts; Peggy H. Cunningham), Mechanics of Materials (Russell C. Hibbeler; S. C. Fan), The Importance of Being Earnest (Oscar Wilde). (3) 1= 2 (4) 2=+1 2 where N is the number of electrons. Please turn in your lab writeup as a printed copy. \[\psi \left ( q_{1}, q_{1}, q_{3}, q_{4}, \right ) = - \psi \left ( q_{1}, q_{1}, q_{3}, q_{4}, \right ) \] 0000044252 00000 n In reality the pi electrons may be considered to reside across the system of conjugated pi-bond system that extends from one nitrogen atom to the other, Figure 1. subscribers only). 0000006938 00000 n subscribers only). Particle in a Box Experiment Therefore, we can replace the electron system by free electrons moving in a one dimensional box of length . 0000002026 00000 n 0000005432 00000 n 10. The purpose of this experiment is to measure the absorption spectra of two series of cyanine dyes and diphenyl polyenes, and to try to correlate the experimental observations using a simple quantum mechanical model. Calculate the length of the conjugated pi-system, L, for each of the dyes from the measured . /Contents _________________________________________________________________________________________________. endobj carbon atoms. Electrons change energy levels when radiation is absorbed. It was also seen that the lengths of the box calculated increase with the number of Band breadth of electronic transitions and the particle-in-a-box model. /St Figure 2. A ( pinacynol The absorption spectrum of each dye solution was taken at room temperature with a CARY 1G UV-Vis Spectrophotometer (Varian) at a 1 nm step size, 2 nm spectral bandwidth, 1 nm data interval, 600 nm/min scan rate, and 0.02 mm slit width. (The dyes are CONCENTRATED.). It is possible to obtain the absorption spectrum of all the dyes in Table 1 (all in the same solvent), and generate only 100 mL of waste. Question: Particle In a Box Lab Help please 1.On a single graph, plot the absorbance spectra of the three dyes. To calculate the length of the box, assume that the molecule is linear and use 154 pm and 135 pm for C-C and C = C bond lengths respectively. Using this wavelength, The spectrum of each dye was shown above. /Annots R subscribers only). The spectrum of each dye was shown above. 0 If the particle in a box is used to represent these molecules then the pi electrons need to be distributed into the box. impinging photon must match the energy difference between the initial state and some excited Further, the theoretical linear regression line shows a positive linear association between the number of carbons framed by nitrogen atoms (p) and wavelength absorbed, while for experimental, the linear association breaks down when dye 4 is added (Figure 2). determine the wavelength of maximum absorbance (max) for each dye. 0000006031 00000 n Add a drop or two dye A solution. x[}@^Rh0yMbU%:HZ+*g' 4NsSRI>}fWU/:+UW^CZ={#4 \[ A = \ln \left ( \frac{I_{o}}{I} \right ) \]. R 0000034293 00000 n The figure also shows the change in state caused by the absorption of a photon. All of these systems contain long conjugated systems that can be approximated at some level to being linear and therefore can be modelled using the quantum mechanical particle in a one dimensional box . were measured and relate the absorption spectra to the particle in a box quantum mechanical obj where abs is the wavelength of the absorbed radiation and c is the speed of light, the following equations result. 0 0000012334 00000 n 0000008957 00000 n subscribers only). Repeat steps 3 5 until spectra have been recorded for all the dye solutions. << Garland, C.; Nibler, J.; Shoemaker, D. Experiments in Physical Chemistry ; ; McGraw-Hill: New York, 2003, p. 380-385. Therefore to understand how organic dyes produce color it is necessary to understand how these compounds absorb light. Note that although your spectra are experimentally determined (and so one would think that they should be shown as individual points), it is common practice to show spectra as solid lines, unless there is good reason to do otherwise. 0 1,1'-Diethyl-2,2'-carbocyanine iodide (Dye B) These dyes are typically $100-$300 per gram and so it is important not to waste the materials. Part A 0000007372 00000 n 1. https://www.sigmaaldrich.com/catalog/product/sial/323764, 2. https://www.sigmaaldrich.com/catalog/product/aldrich/201715, 3. https://www.sigmaaldrich.com/catalog/product/aldrich/392197, 4. https://www.sigmaaldrich.com/catalog/product/aldrich/d91535, 5. https://www.sigmaaldrich.com/catalog/product/aldrich/291331, 6. https://www.sigmaaldrich.com/catalog/product/aldrich/392200. Diluted solutions of each dye were analyzed using a UV/VIS spectrometer to This principle of expansion will be repeatedly utilized in the quantum mechanical treatment of more complex chemical systems later in the semester. Three things need to be considered to calculate the energy changes from Equation 5. \[ \Delta E = \frac{h^{2}}{8mL^{2}} \left ( n_{f}^{2} - n_{i}^{2} \right ) \] The literature max recorded in Sigma Aldrich is actually a range from 702 nm to 710 nm (4). Representative members of the cyanine family of conjugated dyes. /FlateDecode Physical Chemistry 10th ed. /Nums However, this trend is not observed with dye 4, whose absorption spectrum overlaps with that of dye 3. Legal. Fill out the worksheet given below as you do the following. 1 Abstract. Conjugation (delocalization) impacts the energy required for electronic transitions. Fall 2017: Andre Clayborne and Vernon Morris, /*> startxref 0 %%EOF 62 0 obj << /Type /Catalog /Pages 60 0 R /OpenAction [ 63 0 R /XYZ null null null ] /PageMode /UseNone >> endobj 90 0 obj << /S 210 /Filter /FlateDecode /Length 91 0 R >> stream 1242). Three dyes will be used in this experiment: Dark Blue Blue Green Each dye is in methanol solution of with a concentration of approximately 1 x 10-4 M. Procedure Fill a cuvette with about 2 mL of sample (dye) solution. Note: In the following work completely clean the cuvette between samples. 1 A holmium oxide (Buck Scientific) test was performed to calibrate the spectrophotometer. Elsevier. These electrons can be. %PDF-1.4 9. In specific, each AID-ssDNA structure was firstly infiltrated in a hexahedral box, with the minimum distance between the solute and box boundary set to 7 . The change in energy associated with an electron jumping from one state to another is given by equation (5). $('#pageFiles').css('display', 'none'); If the theoretical max for dye 4 yields a smaller absolute percent error when it is run with dyes 5 and 6 rather than dyes 1, 2, and 3, our hypothesis that structural difference contributes to a less-than-accurate is correct. 0000007892 00000 n 0 m"^}U%SzjFmV[luPym}jc^mvV;G;u4Xt4\VIZiYV+_;k|/l"#[bG EuL qf>Y#tLbJ( ]WIkrF'd kHP|o9ra+3Igeu * w[VI[fSQ13M4/V# UMVyTp?8f34M3)0w^p2/&xX:~ q*j BI{J9LCL'u"/|&46W'LJUuW~Fb>L Platt, J. R. J. Chem. 0 Horng, M.-L. and Quitevis, E. L. J. Chem. Conjugated dyes are known sensitizers; take care when handling the dyes and wash your hands after handling them. 0000008846 00000 n If the two electrons with the same set of quantum numbers were switched then Equation (4) results. /Names The chemical structures are resonance structures; the positive charge can be equally well represented as residing on either nitrogen atom. You will measure the absorption spectra of a series of conjugated dyes and then use the Particle-In-A-Box (theoretical model) to explain the observed spectra. /Parent Gerkin, R. E. J. Chem. Potential energy of the conjugated pi-bond system for dyes A and B. 0000008795 00000 n 3 (an eigenvalue equation) by substituting eq. IMPORTANT! 11. The molar absorptivities (extinction coefficients) of these dyes are quite high, so plan your dilutions to minimize the use of the solutes and solvent. Purpose: II8b iDE;@8H%XDIc#,Olf4w73yTjHfHf`a Ch :n@| e~G) endstream endobj 55 0 obj<> endobj 56 0 obj<> endobj 57 0 obj<>/Font<>/ProcSet[/PDF/Text]>> endobj 58 0 obj<> endobj 59 0 obj<> endobj 60 0 obj[/ICCBased 84 0 R] endobj 61 0 obj<> endobj 62 0 obj[250 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 500 500 500 500 500] endobj 63 0 obj<> endobj 64 0 obj[333 303 0 667 0 0 0 0 447 447 0 667 303 379 303 538 667 667 667 667 667 667 667 667 667 667 303 0 0 667 0 568 0 727 636 651 701 576 553 674 689 242 0 0 583 788 708 735 583 735 606 606 640 667 0 947 610 610 0 447 0 447 0 0 0 553 610 545 602 576 390 610 583 235 276 538 235 894 583 606 602 602 386 509 443 583 564 780 530 572 553 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1030 0 0 0 0 0 0 515 0 492 492 0 303] endobj 65 0 obj<>stream Unfortunately, this experiment cannot be done with the equipment that we have in the laboratory, but it is possible to test a number of hypotheses using only a UV-Vis spectrometer, the dyes in Table 1 and common laboratory solvents. << $('#annoyingtags').css('display', 'none'); You will want to present a series of dyes on the same graph, and so you must clearly indicate which spectral trace arises from which dye. Be sure to read the questions raised in the texts3,4 as they may give you insight into the problem and suggest issues that you should address as part of your discussion. Specifically. The Pauli exclusion principle and the energy levels establish the electron distribution. 0000044273 00000 n 0 Journal of Chemical Education, 63(9), 756. Since a linear trend between p and experimental max is shown in both plots, and the experimental and theoretical max match for each compound in each homologous series (Figure 3), our hypothesis that PIB is predictive only when applied to a homologous series is correct. An in-house MATLAB subroutine was used to determine the optimum gamma value and calculate the PIB or theoretical wavelengths of the series of four dyes. /MediaBox In (B-F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wavefunction.The states (B,C,D) are energy eigenstates, but (E,F) are not. Shoemaker, D. P.; Garland, C. W. and Nibler, J. W. Experiments in Physical Chemistry, 7th Ed. 1. Abstract Particle in a one dimensional box laboratory experiments have traditionally used chemicals like polyenes or cyanine dyes as model systems. Molecules of a colored object absorb visible light photons when they are excited from their lowest-energy electronic state (called the ground state) to a higher-energy electronic state (called an excited state). Truman State University Conclusion : To test the robustness of the PIB model against four conjugated polymethine dyes, 1,1-diethyl-2,2-cyanine iodide (dye 1), 1,1-diethyl-2,2-carbocyanine chloride (dye 2), 1,1-diethyl-2,2-dicarbocyanine iodide (dye 3), and 1,1-diethyl-4,4-carbocyanine iodide (dye 4), I measured their absorption spectra 523 +/- 1 nm, 604 +/- 1 nm, 706 +/- 1 nm, and 706 +/- 1 nm at room temperature using a UV-Vis spectrophotometer, and calculated their PIB approximations and lengthening parameter gamma using an in-house MATLAB subroutine. 0000002720 00000 n Physical Chemistry Laboratory >> CAUTION! R The one-dimensional version of this solution, the "particle-on-a-line" is attractively simple. The solution of Schrdingers equation for the particle in a box yields the energy levels given by Equation (2). Some references from the Journal of Chemical Education are included here to help you get started,5-12 and please discuss your ideas with the instructor. spectrometer. How spectroscopic measurements may be used to derive some molecular properties (in this case the length of a conjugated pi-bonded system in dye molecules). Bring a floppy disk to record your data. obj In all four dyes we are forcing the conjugation through the chain. Therefore, if = 1, this signifies that light or any electromagnetic radiation can penetrate a significant distance into the conjugated dyes. When we run the routine, we see that for dye 4, the absolute percent error is 0.05% when run with dyes 5 and 6 (Table 2), versus 21.7% obtained when it is grouped with dyes 1, 2, and 3, suggesting that our hypothesis is correct.
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