F all 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4.0 1 V ibrational Spectroscopy Determining the bond dissociation energy for I2 and Br2 using UVVis spectroscopy Objective Students will collect high resolution gas phase spectra of I2 and Br2 to determine the bond dissociation energy. Logistics The duration is one week. As a class, spectra will be collected by UV Vis spectroscopy . Students will analyze results independently. Introduction In Experiment 1, Electronic Spectra of Conjugated Dyes, UV-Vis spectroscopy was used to determine the energy of the HOMO to LUMO transition in a dye molecule. In this lab we will focus our attention on smaller, simpler molecules so that we can investigate the vibrational energy of a single bond. In this lab, we will use UV -Vis spectroscopy to see the vibrational fine structure of I2 and Br2. Figure 1 shows the absorption spectrum of I2 with sufficient resolution to make out electronic transitions between vibrational levels. The convergence limit shows the continuum that appears near the bond dissociation energy. Figure 1 . Absorbance spectrum of I2 showing the vibrational fine structure. Image from LibreText CC BY -NC-SA 3.0
F all 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4.0 2 Each small peak on the spectrum corresponds to a transition between two vibrational levels and is called a band. Each band is comprised of several hundred lines , each of which involves different upper and l ower rotational quantum numbers . Th e spectrum in Figure 1 is not resolved enough to show the rotational structure. The region of maximum absorption in each band is caused by many of these lines falling together and is called the band head. The set of all of these bands is referred to as the visible band system of I2. An absorption spectrum gives information about the excited state vibrational energies. This is because most of the transitions are occurring from the same lowest energy vibrational level of spacing decreases, as shown in Figure 2. The spacing converges to zero, and at this limit bond dissociation occurs. In Figure 1, we are concerned with the higher energy transitions that will tell the convergence limit . In Figure 2 the convergence limit is shown at long inte rnuclear distance, where the I I bond is broken leaving either I + I * in the excited st ate or I + I in the ground state . One of the purposes of this experiment is to identify this convergence limit accurately and determine the bond dissociation energy of the ground state molecule , D0. Figure 2 . Energy well diagram for a diatomic molecule I2 showing vibrational levels with quantum numb ers vâ€ in the ground state (X) and quantum numbe rs vâ€™ in the excited state (B )
F all 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4.0 3 A few of the key constants from Figure 2 are defined below. citation energy c is the wavenumber of the continuum threshold D0 D0 00 el is the electronic transition energy v v The total energy of a diatomic molecule can be modelled mathematically as the sum of the electronic transition energy, el, with the vibrational energy, G( Equation 1 With I2 and Br2, the rotational energy is much smaller compared to the vibrational energy, so we . The vibrational energy G( v can be expanded . Higher order terms Equation 2 The vibration constant, e, and anharmonic constant, e are electronic state dependent and will require notation to differentiate between ground state and excited state when considering transitions between different states . Within a given state, the energy difference between the vibratio nal levels can be approximated by Equation 3 with units of wavenumbers . Equation 3 A plot of Equation 3, showing versus is called a Birge Sponer plot and will have a slope of â€“2e eintercept of e â€“ 2e e of best fit, the vibration constant of the excited state e the excited state e The x intercept gives vc vmax and should be rounded to the nearest integer. The eec values determined from the Birge Sponer plot can be used to find the dissociation energy in the excited state D0
F all 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4.0 4 Equation 4 The objective of this experiment is to determine the dissociation energy of I2 and Br2 in the ground state D0. Looking a t Figure 2, it becomes apparent that the bond dissociation energy of the ground state molecule, Do an be determined from the frequency of convergence, vc, and the atomic excitation energy, as in Equation 5. Equation 5 Since the frequency of convergence c 00 + D0 we can combine equations 4 and 5 to be able to solve for the ground state dissociation energy shown in Equation 6. Equation 6 1 1. Materials I2 and Br2 Quartz cuvette Lambda 650 Spectrophotometer Procedure Safety : Solid iodine and liquid bromine are corrosive to the skin and also stain. Always wear gloves and use tweezers and pipettes as necessary. W orking in a hood, prepare the samples by adding a few crystals of I2 to a cuvette and a small drop of Br2 to a separate cuvette. C ap and parafilm the cuvettes before removing from the hood. R ecord the UV Vis spectra from 6 60.0 nm to 480.0 nm with step sizes of 0.05 nm. Spreadsheet Assignment Plot the absorption spectra for each Br2 and I2, zooming in on the region of interest. Label each peak with the correct vibrational quantum number. Construct a Birge Sponer plot for each Br2 and I2 by plotting the change in frequency (cm1axis versus the vibrational quantum number on the xaxis . From the equation of best fit, determine the vibration cons tant of the excited state e anharmonic e Then use Equation 4 to find D0 Equation 6 to determ ine D0. Compare the ground state bond dissociation energy to literature by calculating a percent error.
F all 2020 CHE 4480 Palmer This wor k by Alycia Palme r is licensed under CC BY 4.0 5 References Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry ; McGraw Hill, Boston 2009; pp 436 . LibreText https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_110B%3 A_Physical_Chemistry_II/Text/13%3A_Molecular_Spectroscopy/1306._Electronic_Spectra_Contain_El ectronic%2C_Vibrational%2C_and_Rotational_Inform ation