LB Partner: HL
Absorption Spectrum of a Conjugated Dye/ Electronic Spectra of Conjugated Alkenes.
Experiment performed Sept 13, 2001
Laboratory Report Due September 27, 2001
Laboratory Report originally submitted September 27, 2001
Laboratory Report Re-submitted October 8, 2001
Abstract
This experiment was used to determine the length of the box in the particle-in-a-box model. It compared a conjugated alkene with the particle-in-a-box model, using the delocalized electron as a particle and the length of the alkene chain as the length of the box. Conjugated alkenes with phenyl groups attached were used: 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene. The length of the box is the length of the conjugated chain between the phenyl groups. A UV-vis spectrum was taken of each molecule, and the HOMO-LUMO energy gap was determined. By using this energy in the equation ΔE=((nf2-ni2)*h2)/(8mL2), the length of the box could be experimentally determined. The length for 1,4-diphenyl-1,3-butadiene was determined as .726 nm, the length for 1,6-diphenyl-1,3,5-hexatriene was determined as .888 nm, and the length for 1,8-diphenyl-1,3,5,7-octatetraene was determined as 1.039 nm. These were not as close to the calculated values for the lengths, which were determined with a computer simulation of the molecules, providing .438 nm for 1,4-diphenyl-1,3-butadiene, .540 nm for 1,6-diphenyl-1,3,5-hexatriene, and 1.804 nm for 1,8-diphenyl-1,3,5,7-octatetraene. So then the lengths were compared with theoretical lengths provided in the lab instructions themselves, which were.695 nm for 1,4-diphenyl-1,3-butadiene, .973 nm for 1,6-diphenyl-1,3,5-hexatriene, and 1.251 nm for 1,8-diphenyl-1,3,5,7-octatetraene.
Introduction
The three major concepts that were used for this lab were particle-in-a-box, molecular orbital theory and UV-Vis spectroscopy. UV-Vis spectroscopy was used to determine the absorption spectra of the molecules, which showed the energy gap between HOMO and LUMO in the molecules which were studied. The spectrometer measures the transmittance of light through a sample. This transmittance is determined by examining the intensity of the light, I0, when it goes through a sample cell with just solvent with the intensity of light, I, when it goes through a sample cell with solvent and the chemical being studied. Transmittance is defined as I/ I0. The data is then changed to measuring absorbance instead of transmittance. Absorbance, A, is defined as -log T or log(I0/I). With solutions, the absorbance is linearly related to the concentration of the solution. This relation is described with Beer's Law. Beer's Law states that A=єbc, where є is a constant called molar absortivity, b is the path length of the cell, and c is the concentration. This can be derived from the observation that the change in the intensity of the light through a sample is directly proportional to the negative concentration, the overall intensity and the change in length in the cell. Or, dI=-k*c*I*dl. The equation can then be rearranged to produce dI/I=-k*c*dl. By integrating the left hand side from I0 to I, and the right hand side form 0 to l, the equation ln(I/ I0)=-kcl is found. This equation can be changed from the natural log to log base ten by multiplying both sides by ln(10), or approximately 2.303. Then the equation 2.303 log (I/ I0)=-(2.303) kcl is found. Simplified, and by using є as the symbol for the constant, the final equation is log(I/ I0)= єcl. Since log(I/ I0) was absorbance, A= єcl, or A= єcb if the variable b is used for length instead of l. In this lab, the wavelengths of light that were absorbed by the molecules were determined using UV-Vis Spectroscopy.
When light is shown through a sample, it excites the molecules because the light has a certain amount of energy associated with it. This energy is represented with the equation DE=hn. n is the frequency of the light which causes the energy change. This can be compared with the wavelength of light detected be the spectrophotometer with the equation l=c/n, where c is the speed of light, 3*108 m/s. When molecule is excited, the energy can be released as heat through relaxation, the energy cab decompose the molecule, or the energy can be absorbed by the molecule. In conjugated alkenes like the molecules that were studied, the energy is absorbed and provides energy for electronic transitions within the molecule. The wavelength of light that is absorbed most by the molecule is the wavelength of light associated with the HOMO-LUMO transition energy within the molecule. HOMO and LUMO refer to the molecular orbitals of the compounds that were studied. HOMO is the highest occupied molecular orbital, while LUMO is the lowest unoccupied molecular orbital. In conjugated alkenes, this HOMO-LUMO transition is a π- π* transition.
A bond is created between two molecules when the atomic orbitals of the atoms overlap. When two molecules form a bond, a molecular orbital is formed for each atomic orbital participating in the bond. The electron waves from the atomic orbitals reinforce, and the atomic orbitals are added to one another to get the resulting molecular orbital, or the electron waves cancel and the atomic orbitals are subtracted to get the molecular orbitals. When the electron waves reinforce, the electron density increases which creates a more stable molecular orbital. This is the bonding orbital, and the electrons which participate in the bond fill the bonding orbital. The other molecular orbital which was created exists in a higher energy than the bonding molecular orbital, and electrons usually do not exist in this orbital. This second molecular orbital is referred to as the antibonding molecular orbital.
With conjugated systems, two atomic orbitals from each atom are participating in bonding, with one in a σ bond, and another in a π bond. Therefore, four atomic orbitals are participating, so four molecular orbitals are formed. But only the two orbitals of the lowest energy are filled with electrons, the σ and π bonds. The other two orbitals, σ * and π* , are usually empty. But when energy is applied to the system, the electrons can move into higher molecular orbitals. The energy applied to the molecules studied was the form of light energy, hn. When the energy is applied, there is a transition on the molecules from π- π*. This is because the π- π* transition is the lowest energy transition, for π bonds are weaker than σ bonds. The strength of the σ bonds creates a greater energy separation for the σ- σ* energy transition. The conjugation of the π bonds also creates different energy transition levels. The energy of the HOMO- LUMO π- π* transition decreases with an increase in the number of conjugated π bonds in the molecule.
Figure 1: Energies of the π molecular orbitals of 1,3-butadiene and 1,3,5-hexatriene
The energy levels of the molecular orbitals in the conjugated alkenes can also be drawn showing the p-orbitals, and how they overlap. When bonding orbitals overlap, the electron waves reinforce. But with more than one bond with p-orbitals, nodes where they do not overlap are created. When 4 p-orbitals combine to create 4 molecular orbitals, as is the case with a molecule like butadiene, only one of those molecular orbitals has complete overlap of the electron waves. The next highest molecular orbitals has overlap of 2 pairs of p-orbitals, with one node where they do not overlap in the middle. The number of nodes increases with an increase in the energy level of the molecular orbital, until there are four nodes in the highest level molecular orbital. These nodes are electron waves cancel. The conjugated molecules used in this experiment all act similarly. 1,4-diphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, and 1,8-diphenyl-1,3,5,7-octatetraene have 4 p-orbitals, 6 p-orbitals, and 8 p-orbitals, respectively, which overlap to create conjugated π bonds.
Figure 2: Energies and nodes for π molecular orbitals of 1,3-butadiene
These molecular orbitals can represent the particle-in-a-box model experimentally. This is done by visualizing the electrons which move freely through the conjugated system as a particle, and the length of the conjugated chain between the phenyl groups as the length of the box. The energy levels represented in the particle-in-a-box model as waves can be represented experimentally with the molecular orbitals of the molecules studied. The lowest energy π orbital corresponds to the lowest energy state in the particle-in-a-box model. In the model, the particle is viewed as a standing wave. In the lowest energy, the wave has zero nodes, such as the butadiene shown above. As the energy levels increase, the number of nodes increase. There are only distinct energy states which are allowed for the particle because it is so small that the energy levels are quantized.
Figure 3: particle-in-a-box energy levels.
The energy of the levels of the box can be represented by the equation
En= (n2h2)/(8mL2), where n is the number of the energy level, h is Plank's constant, 6.62608*10^-34 Js, m is the mass of the particle, and L is the length of the box. The change in energy in the box is represented by this equation
DE=((nf2-ni2)h2)/(8*m*L2), where nf is the final energy state, and ni is the initial energy state. As the length of the box increase, this change decreases. This corresponds with molecular orbital theory, where the energy gap between HOMO-LUMO, π- π* transition decreases with the increase in the number of π orbitals which were a part of the conjugated chain. So the larger the conjugated alkene, the smaller the energy gap, which corresponds with the particle-in-a-box theory.
This experiment was to determine the length of the box for the particle-in-a-box model. The DE associated with the light energy absorbed by the molecule can be used in the equation for particle-in-a-box mentioned above. L can then be found experimentally. This is then compared with L as determined by a computer simulation of the molecule4.
Experimental
UV-Vis spectroscopy was used extensively in this experiment. The peak absorbance levels were measured using this technique for the three compounds which were studied. A UV-Vis spectrometer essentially measures the change in intensity of light as it passes through a sample as explained above. The machine that we used was a single beamed instrument.
At the beginning of the instrument is a light source. The light source relied on energy provided by excited Deuterium. A potential difference between a metal and a metal oxide is achieved in the light source. Excited electrons move from the metal oxide to the metal. These electrons hit the Deuterium gas that fills the light source. The normally diatomic Deuterium splits into its component atoms, and a wavelength of light is emitted. Since the energy associated with the Deuterium was kinetic, it was not quantized. So a high variety of wavelengths are emitted. The light that is finally emitted from the source is composed of all the wavelengths of light that we needed for our experiment. Wavelengths from 300 to 460 nanometers were measured.
A lens then concentrates that light into a column. A shutter after the lens controls when the light will pass through the sample cell, which is next in the spectrometer. Problems arise if the sample is placed in the sample cell if there is no background done first. The cell that the sample rests in, and the solvent that the sample is dissolved in can absorb light not related to the sample itself. So a background cell, with just the solvent in it is measured first. Then the sample ell is placed in the machine. The machine saves the information from the background cell, and subtracts the effects of the background from the measurement made for the sample.
The light is then focused onto a slit. This slit, through diffraction, splits the light into its component wavelengths. These wavelengths are then measured with a photodiode array. The photodiode array is composed of numerous photodiodes, one for every 2 nanometers of light. Each diode is made from Silicon. In the Silicon, holes and electrons are placed. Holes are achieved by putting a different element in half of the Silicon which has one less valence electron. This element can be either Aluminum or Boron. In the other half of the Silicon, “electrons” are placed. These are made by putting in an element which has one more valence electron than Silicon. Phosphorous can be used for this. The overall effect is that the region of the Silicon with the holes has an overall positive charge, and the region with the electrons has an overall negative charge. When a voltage is applied to the silicon, the holes are attracted to the negative side while the electrons are attracted to the positive side. A depletion layer is created in the Silicon between the electrons and the holes, which prevents a current from flowing. In order for the current to flow, energy needs to be applied to the Silicon. In the spectrometer, this energy is in the form of light energy, of hn.
When light hits one of the photodiodes, current flows. The diode is hooked up in parallel circuit with a capacitor which holds 10pF. When the capacitor does not discharge, then current is not flowing in the diode, and light is not hitting the diode. A switch to the power supply stays open. But when the capacitor discharges, the diode does have a current, and that mans that the wavelength of light associated with that diode is hitting the diode. That switch to the power supply is then opened so that the capacitor goes back to 10 pF. The amount of current from the power supply needed to achieve this is recorded by spectrometer. When light is absorbed by the sample, less light hits the diode, and that current needed to recharge the capacitor is lessened. So by measuring which wavelengths of light do not hit the diode specific for that wavelength, or which light is lessened, then the absorption of that wavelength of light by the sample can be measured.
Results
|
|
1,4-diphenyl-1,3-butadiene |
1,6-diphenyl-1,3,5-hexatriene |
1,8-diphenyl-1,3,5,7-octatetraene |
|
Experimental maximum absorbance peak |
330 nm |
354 nm |
374 nm |
|
Experimental ΔE |
6.024*10-19 J |
5.61*10-19 J |
5.32*10-19 J |
|
Experimental box length |
.7073 nm |
.8666 nm |
1.010 nm |
|
Theoretical ΔE (eV) |
9.78172 eV |
9.22168 eV |
1.03967 eV |
|
Theoretical ΔE (J) |
1.567 *10-18 J |
1.447*10-18J |
1.666*10-19J |
|
Calculated theoretical box length |
.438 nm |
.540 nm |
1.804 nm |
|
Theoretical box lengths from the laboratory experiment. |
.695 nm |
.973 nm |
1.251 nm |
|
Relative error |
61.5% |
60.5% |
44.0% |
|
Relative error using theoretical values obtained from laboratory experiment. |
1.77% |
10.9% |
19.3% |
The maximum absorbance peaks from the three molecules studied were measured using UV-Vis spectroscopy. The UV-Vis spectrophotometer labeled the absorbance peaks, and gave these values.
These wavelengths can be converted into a change in energy with the equation ΔE=h(c/l), where h is Plank's constant, 6.62608*10^-34 Js, c is the speed of light, 3*108 m/s, and l is the wavelength taken from the spectrophotometer.
This energy can be used in the equation for particle-in-a-box, which was
DE=((nf2-ni2)h2)/(8*m*L2). Since it is the length, L, of the box which will be determined, the equation can be rearranged into the form: L=Ö(((nf2-ni2)(h2))/(8*m*DE)). The DE is from the values obtained above.
The actual values for the energies were found by theoretically calculating the HOMO-LUMO energy gap using a computer program, the PC Spartan Plus.
The theoretical energy change was then converted to Jules using the relationship 1eV=1.60218*10-19J.
The length of the box determined theoretically was determined with the same equation used for the experimental values for the length of the box. The theoretical energy levels were used to determine the theoretical length of the box.
These values are significantly different from the experimental values. However, the explanation of the laboratory experiment1 gave different theoretical values for the box length, which were closer to the experimental box length that were determined.
The relative error of the experimental values compared with the calculated theoretical values was calculated using the equation relative error=׀(x-xt )׀ /(xt) *100.
The relative error was also calculated using the theoretical values obtained from the explanation laboratory experiment.
Discussion
The experimental data is reasonably close to this second set of actual values for the length of the box. Since the first set of actual lengths is so different than the other lengths, it would be reasonable to assume that there is something wrong with the calculations for those lengths. The box lengths computed with the computer were off because some adjustments had to be made to the molecule in order for the energies to be calculated by the computer. The program would not calculate the alkene chains with the phenyl groups attached, so the calculations were made without the phenyl groups. This introduced error, since the bond lengths from the alkene chain to the phenyl group were not included. If, however, those bond lengths were to be assumed to be .139 nm 1, then the new values for the bond lengths would be as follows
|
|
1,4-diphenyl-1,3-butadiene |
1,6-diphenyl-1,3,5-hexatriene |
1,8-diphenyl-1,3,5,7-octatetraene. |
|
Bond length |
.716 nm |
.818 nm |
2.082 nm |
|
Relative error. |
1.1% |
5.9% |
51.5% |
The relative error between the new theoretical values and the experimental values are better than the theoretical values which were originally calculated, although the value for 1,8-diphenyl-1,3,5,7-octatetraene seems to be worse than it was originally.
The fact that the length of the box as determined with UV-Vis spectroscopy is close to the theoretical length of the box indicates that the energy associated with the HOMO-LUMO energy gap can be associated with the energy gap between energy states in the particle-in-a-box. By being able to experimentally show the particle-in-a-box model, it is easier to visualize the energy transitions.
The box lengths computed correspond to the lengths of the molecules computed. The 1,4-diphenyl-1,3-butadiene had a smaller box length than the 1,6-diphenyl-1,3,5-hexatriene, which was smaller than the 1,8-diphenyl-1,3,5,7-octatetraene. The four-carbon chain was smaller than the 6-carbon chain, which was smaller than the 8-carbon chain. So on a surface level, the trend of the box lengths which were calculated for the particle-in-a-box model correspond with the length of the conjugated chain which represent the model in this experiment.
The trend in the energy levels is also consistent with the fact that we are modeling the particle-in-a-box model. The energy decreased with an increase in the number of carbons in the alkene chain. This corresponds with the fact that with an increase in the number of π bonds, which are created when a higher number of carbons are in the conjugated chain, there is a decrease in the HOMO-LUMO energy gap. There are 2 bonding, and 2 anti-bonding molecular orbitals in the butadiene chain which represents the length of the box in 1,4-diphenyl-1,3-butadiene. Therefore, there are only 4 energy states in our particle-in-a-box model which are being represented, and the energy transition is from n=2 to n=3.This correspond to the HOMO- LUMO energy change from the highest energy bonding molecular orbital to the lowest energy antibonding orbital, or the π- π* transition . And the energy change is greater for lower numbers of n than for higher numbers. So with the octatetraene, there are 4 bonding and 4 anti-bonding molecular orbitals. The energy transition with octatetraene in the particle-in-a-box model is from n=4 to n=5. The energy change, however, from butadiene to octatetraene shows that the energy decreases. As the n values increase in the particle-in--box model, the change in energy between he levels increases. The energy changes that are seen from the experiment are because of the length of the box being described. The length of the butadiene box is smaller than the length of the octatetraene box. And as the length of the box in the particle-in-a-box model increases, the energy transition between the energy states decreases.
Further similarities of the conjugated alkenes with the particle-in-a-box model can be seen when the HOMO and LUMO are pictured, with their respected orbitals. A wave can be drawn over the molecules (attached), with the wave going over the positive side of the orbitals. These molecular orbital diagrams represent the p-orbitals which combine to create the π bonds present in the molecules, and are similar to Figure 2. The HOMO and the LUMO are represented. These waves represent the standing waves that are found in the particle-in-a-box model.
These waves represent particles. And the particle in the experiment, the delocalized electron, are small enough to exhibit the wave/particle duality present in the particle-in-a-box model. The electron can easily be represented as a wave. It is the wave properties of the electrons which interact with eachother to create the bonds which were studied with the UV-Vis spectroscopy. The energy imparted onto the molecules by the light from the spectrophotometer excited the electrons, and changed the characteristics of the bonds between the atoms. By analyzing the absorbance of the light by the molecules, the spectrophotometer could detect the light needed to promote the electrons from bonding to antibonding molecular orbitals. This light was converted to energy, and this energy was the energy needed to promote the electrons to a higher energy level. This promotion corresponds with the promotion of particles to higher energy levels in the particle-in-a-box model.
References
1. Anderson, B. (1997). Alternative Compounds for Particle in a Box Experiment. Journal of Chemical Education,74(8),985.
2. Atkins, P. (1998). Physical Chemistry (6th ed.).New York: W.H. Freeman and Company.
3. Atkins, P., Jones, L. (1999). Chemical Principles. New York: W.H. Freeman and Company.
4. Deppmeier, B., et. al. (1997) PC Spartan Plus v. 1.3 (software), Wavefunction, Inc.
5. Hornback, J. (1998) Organic Chemistry. New York: Brooks/Cole Publishing Company.
6. Skoog, D., Holler F.J., Nieman, T.A. (1998) Principles of Instrumental Analysis (5th ed.). Philadelphia: Saunders College Publishing.