Additional revision questions to accompany Prof Ashfold’s Chemistry 1A Spectroscopy course These questions, which are taken from (or based on) questions appearing in C.N. Banwell and E.M. McCash, Fundamentals of Molecular Spectroscopy, 4th edn., are intended as an advanced revision guide, and should be attempted in conjunction with the 1A course handout. They are sequenced in the same order as the material was presented in the course. 1. Convert the following spectroscopic quantities as indicated: 2000 cm-1 to µm 0.15 nm to Hz 500 nm to cm-1 9 GHz to cm-1. In what region of the electromagnetic spectrum would each appear, and to what sort of transition would each correspond? 2. The wavelength of the radiation absorbed during a particular spectroscopic transition is 10 µm. Express this as a frequency (Hz) and a wavenumber (cm-1), and calculate the energy change during the transition in both J/molecule and kJ/mole. If the energy change were twice as large, what would be the wavelength of the corresponding transition? 3. The transmittance of an aqueous solution of KMnO4 at a certain wavelength is 1% (i.e. 0.01) for a 10-3 M solution in a cell of length 1 cm. What is the molar absorption coefficient of KMnO4 at this wavelength? 4. Which of the following molecules will exhibit a pure rotational spectrum: H2, HCl, IBr, CH4, CH3Cl, CH2Cl2, H2O, CO2, SF6. 5. The rotational spectrum of 79Br19F shows a series of equidistant lines separated by 21.415 GHz. Calculate the rotational constant, B, and hence the moment of inertia and bond length of the molecule. Determine the wavenumber of the J = 9 → J = 10 transition, and find which rotational level is most populated at 300 K. Calculate the number of revolutions per second made by a 79Br19F molecule when in a level with (a) J = 0, (b) J = 1, and (c) J = 10. (atomic masses: 79Br = 131.03 × 10-27 kg; 19F = 31.55 × 10-27 kg) 6. A space probe was designed to search for the presence of CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the equilibrium bond length of CO is 1.128 × 10-10 m, at what frequencies do the first three rotational transitions appear? What spectral resolution would be needed to determine the 13C/12C isotope ratio on Saturn? (atomic masses: 12C = 19.93 × 10-27 kg; 13C = 21.59 × 10-27 kg; 16O = 26.56 × 10-27 kg) 7. The equilibrium vibrational frequency of IBr is 8.052 × 1012 Hz (268.64 cm-1), and the anharmonicity constant x = 0.003. Calculate the frequencies, wavenumbers and the relative intensities of the fundamental (i.e. v = 0 → v = 1) and the first hot band (i.e. v = 1 → v = 2) transitions for a sample maintained at 300 K. 8. How many normal modes of vibration are possible in the following molecules: HBr, O2, OCS (linear), SO2 (bent), BCl3, HCCH, CH4, CH3Br, C6H6? 9. Given the following data for 1H35Cl: Equilibrium bond length, Re = 1.275 × 10-10 m; Bond force constant, k = 516. 3 N m-1; and the atomic masses: 1H = 1.673 × 10-27 kg, 35Cl = 58.066 × 10-27 kg; Calculate (a) the zero-point energy and the frequency of the fundamental vibration; (b) the rotational constant, B, and (c) the wavenumbers of the lines P(1), P(2), P(3), R(0) and R(1). These calculated transition frequencies are slightly different from the actual values that would be measured experimentally. Suggest two contributory factors to this discrepancy. 10. A particular NMR spectrometer operates at 30.256 MHz. What magnetic fields are required to bring 1H and 13C nuclei into resonance at this frequency? (Elementary charge, e = 1.602 × 10-19 C. Mass of the proton, mP = 1.6726 × 10-27 kg. For 1H: nuclear spin quantum number, I = ½, and g = 5.585; for 13C: I = ½, g = 1.404) 11. Calculate the resonance frequency of the 1H nucleus when subjected to field strengths of 2.5 and 5.25 T, respectively. (e = 1.602 × 10-19 C. Mass of the proton, mP = 1.6726 × 10-27 kg, I = ½, g = 5.585). 12. 1 H NMR spectra of two compounds with chemical formula C3H7Cl are shown below. Suggests structures for isomers (a) and (b), and justify your reasoning. (a) (b) 4 3 δ/ppm 2 1 4 3 δ/ppm 2 1