None Calculate the energies, in Joules, of the v = 0, 1, 2, and 3 vibrational states for HCI (Mosc 2991 cm-1) and 12 (Mosc214.5 cm-1). Make a sketch of the energy levels on the same scale

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Chemistry for Engineering Students

3rd Edition

ISBN:9781285199023

Author:Lawrence S. Brown, Tom Holme

Publisher:Lawrence S. Brown, Tom Holme

Chapter5: Gases

Section: Chapter Questions

Problem 5.23PAE

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Calculate the energies, in Joules, of the v = 0, 1, 2, and 3 vibrational states for HCI (Mosc 2991 cm-1) and 12 (Mosc = 214.5 cm-1). Make a sketch of the energy levels on the same scale
Calculate the energies, in Joules, of the v = 0, 1, 2, and 3 vibrational states for HCI (osc = 2991 cm-1) and 12 (˜osc = 214.5 cm-1). Make a sketch of the energy levels on the same scale
1. [10] Consider an adsorption band in the combined rotational-vibrational spectrum of a linear molecule, where the fundamental vibrational frequency involved in the observed band is 2325 cm-¹ and the rotational constant of the molecule is B=2.4 cm³. Say hypothetically, the specific selection rules for the rotational states are AJ = ±2. At what wave numbers would the first three peaks that occur at both higher and lower wave numbers than fundamental vibrational frequency occur at? What transitions would each peak correspond to?
c) In a horizontal radiationless transition, the extent of overlap of the lu functions (probability distribution) of the initial and final states is the primary factor controlling the rate of internal conversion and intersystem crossing. Molecule (a) and molecule (c) of Figure 2 show the v = 0 vibrational level of the initial electronic state and v 7 vibrational level of the final state. Molecule (b) of Figure 2 shows the v= 0 vibrational level of the initial state and thev =1 vibrational level of the final state. Which one of the molecules (a), (b) or (c)) displays the strongest fluorescence? Explain your answer. (a) (b) (c) Figure 2: Overlap of the lyf functions for a radiationless transition between the initial (i) and finál (f) electronie states.
The vibrational levels of 23Na127I lie at the wavenumbers 142.81, 427.31, 710.31, and 991.81 cm−1. Show that they fit the expression (v + 1/2) ᷉v − (v + 1/2) 2xe ᷉v, and deduce the force constant, zero-point energy, and dissociation energy of the molecule.
What is the highest possible degeneracy of a vibration of a Cr(CO)6 molecule? Explain your answer.
Suggest a reason why the spin-lattice relaxation time of benzene (a small molecule) in a mobile, deuterated hydrocarbon solvent increases whereas that of a polymer decreases.
A sample of pure 1 H79Br gas was analysed using IR and NIR absorption spectrometers. A fundamental vibration at 2575.15 cm–1 and an overtone band at 5022.78 cm–1 were measured. (a) Using this data, calculate the equilibrium oscillation frequency (in cm–1) and the anharmonicity constant ( e x ) for pure 1 H79Br.
The fundamental vibrational wavenumber for 12C160 is 2143 cm-1. For 1 mole of these molecules, calculate the number of CO molecules in the v = 0 and v= 1 levels at the given temperatures. (a) 298 K no 6.0219479766542e n11.93307140358876 (b) 1080 K no 5.73772844591641 n1= 2.70e22 X
Suppose you were seeking the presence of (planar) S03 molecules in the microwave spectra of interstellar gas clouds. (a) You would need to know the rotational constants A and B. Calculate these parameters for 32S16O3, for which the S-O bond length is 143 pm. (b) Could you use microwavespectroscopy to distinguish the re lative abundances of 32S16O3 and 33S16O3?
The first five vibrational energy levels of ¹H¹27 I are at 1144.83, 3374.90, 5525.51, 7596.66, and 9588.35 cm¹. Treating the molecule as an anharmonic oscillator, estimate the dissociation energy of the molecule in units of reciprocal centimetres (cm-¹). [Note: m(¹H) = 1.0078 u, m(¹271) = 126.9045 u; assume the second order anharmonicity constant, Ye, to be zero.] [Note: Use graph paper in your answer.]
P11E.2 Suppose that three conformations are proposed for the nonlinear molecule H,O, (1, 2, and 3). The infrared absorption spectrum of gaseous H,O, has bands at 870, 1370, 2869, and 3417 cm. The Raman spectrum of the same sample has bands at 877, 1408, 1435, and 3407 cm. All bands correspond to fundamental vibrational wavenumbers and you may assume that: (a) the 870 and 877 cm bands arise from the same normal mode, and (b) the 3417 and 3407 cm bands arise from the same normal mode. (i) If H,O, were linear, how many normal modes of vibration would it have? (ii) Give the symmetry point group of each of the three proposed conformations of nonlinear H,O,. (iii) Determine which of the proposed conformations is inconsistent with the spectroscopic data. Explain your reasoning. 2

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Calculate the energies, in Joules, of the v = 0, 1, 2, and 3 vibrational states for HCI (Mosc 2991 cm-1) and 12 (Mosc 214.5 cm-1). Make a sketch of the energy levels on the same scale