Please correct answer and don't use hand raiting Consider the 14N-160 molecule whose fundamental frequency has a value of 0.0064 cm¹.The equilibrium bond length for the molecule is 115 pm.a) Estimate the ratio of the number of molecules in the first excited vibrational state to thenumber in the ground state, at a temperature of 450 K.(5)b) Take 14N-160 molecule as a linear rigid rotor and determine the ratio of the number ofmolecules in the first excited rotational state to the number in the ground state, at a temperatureof 450 K(10)c) Use the Sackur-Tetrode equation to calculate the molar entropy of the molecule at 1atm and 298 K(10)

Solution:a) Ratio of molecules in the first excited vibrational state to the ground state at 450…

Answered: Consider the 14N-160 molecule whose…

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter12: Thermodynamic Processes And Thermochemistry

Section: Chapter Questions

Problem 62P

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Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?
7) Explain the basis of the Franck-Condon principle and how it leads to the formation of a vibrational progression.
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Calculate the standard deviation of the bond length ox of the diatomic molecule 'H1°F when it is in the ground state and first excited state using the quantum harmonic oscillator wavefunctions. The fundamental harmonic vibrational frequency of HF is 4,460 cm-1 and the equilibrium bond length is 0.091nm. How do you interpret the change in the ratio of average bond length to ox as a function of energy in the vibration?
A molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm³¹) of rotational transitions in the molecule.
(c) When a gas is expanded very rapidly, its temperature can fall to a few degrees Kelvin. At these low temperatures, unusual molecules like ArHCl (Argon weakly bonded to HCl) can form on mixing. For the isotopic species Ar H$CI, the following rotational transitions were observed: J (1 → 2): 6714.44 MHz J (2 → 3): 10068.90 MHz Assume the molecule can be treated as a linear diatomic molecule (ArCl). (i) Calculate the rotational constant (B) and centrifugal distortion (D) constant for this molecule.
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4. The infrared absorption spectrum of a diatomic molecule is shown in the figure. (a) Give the initial (J") and final (J') rotational quantum numbers corresponding to the peaks labeled A and B. (b) Estimate the vibrational frequency in wavenumbers (i) and the rotational constant in wavenumbers (B). (c) From the spacings of the peaks near 2700 cm and near 3050 cm, determine whether the average bond length increases or decreases with increasing vibrational quantum number. 20 18 A 14 12 2500 2600 2700 2800 2900 3000 3100 3200 wavenumber absorption intensity
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But molecules combine both vibrational and rotational states in such a way that both selection rules must be satisfied if we are only talking about absorption or emission of electromagnetic radiation (i.e. photons). 5 1 images from Krane Ch 9. Relative absorption : 0.330 L=3 to L=2 L=2 to L = 1 Electronic excited state. Electronic ground state L→ L-1 L = 1 to L = 0 Ť 0.340 0.350 SE Energy (eV) 2B 0.360 : hf L=0 L=1 L=2 to to to L = 1 L = 2 L = 3 Photo 4 1 3 1 2 1 1 0 1 1 5 0 4 0 30 20 1 0 0 0 LN L→ L+1 0.370 0.380 no emission here because AL # 0, AL = +1 AN = ±1, HCI spectra. In the middle of the gap is the energy hf that would correspond to a pure vibrational transition, which would violate the rotational selection rule. What is the value of hf for the HCI spectra?

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