Concept explainers
Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following molecules. (a) Hydrogen fluoride,
(a)
Interpretation:
For the molecule hydrogen fluoride,
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule Hydrogen fluoride,
Explanation of Solution
Hydrogen fluoride is a linear molecule. The total number of atoms present in hydrogen fluoride is
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule Hydrogen fluoride,
(b)
Interpretation:
For the molecule hydrogen telluride,
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule hydrogen telluride,
Explanation of Solution
Hydrogen telluride is a non-linear molecule. The total number of atoms present in hydrogen telluride is
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule hydrogen telluride,
(c)
Interpretation:
For the molecule Buckminsterfullerene,
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule Buckminsterfullerene,
Explanation of Solution
Buckminsterfullerene is a non-linear molecule. The total number of atoms present in Buckminsterfullerene is
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule Buckminsterfullerene,
(d)
Interpretation:
For the molecule phenylalanine,
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule Phenylalanine,
Explanation of Solution
Phenylalanine is a non-linear molecule. The total number of atoms present in phenylalanine is
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule phenylalanine,
(e)
Interpretation:
For the molecule naphthalene,
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule Naphthalene,
Explanation of Solution
Naphthalene is a non-linear molecule. The total number of atoms present in naphthalene is
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule Naphthalene,
(f)
Interpretation:
For the molecule linear isomer of the
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule the linear isomer of the
Explanation of Solution
For the linear isomer of the
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule the linear isomer of the
(g)
Interpretation:
For the molecule the bent isomer of
Concept introduction:
To describe the positions of each of the atoms in a molecule having
Answer to Problem 14.45E
For the molecule the bent isomer of
Explanation of Solution
For the bent isomer of the
The total degrees of freedom is calculated by the formula given below.
Where,
•
The value of
Substitute the value of
Since,
Therefore, the number of total degrees of freedom is
For the molecule the bent isomer of
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Chapter 14 Solutions
Physical Chemistry
- Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. a Hydrogen sulfide, H2S b Carbonyl sulfide, OCS c The sulfate ion, SO42 d Phosgene, COCl2 e Elemental chlorine, Cl2 f A linear molecule having 20 atoms g A nonlinear molecule having 20 atomsarrow_forwardWhich of the following molecules may show a pure rotational Raman spectrum: (i) H2, (ii) HCl, (iii) CH4, (iv) CH3Cl?arrow_forwardThis question pertains to rotational spectroscopy. Which of the following molecules would have a pure rotational spectrum and why? HCl, N2O, O3, SF4 What information is obtained from the rotational spectrum of a diatomic molecule and how can it be used to determine the bond length of a diatomic molecule? What is the selection rule for rotational spectroscopy? The rotational constant of 127I35Cl is 3.424 GHz. Calculate the ICl bond length.arrow_forward
- Which of the following molecules may show a pure rotational Raman spectrum: (i) CH2Cl2, (ii) CH3CH3, (iii) SF6, (iv) N2O?arrow_forwardThe vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1, whereas that in the excited state (B 3Σu−), to which there is an allowed electronic transition, is 700 cm−1. Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.arrow_forwardEstimate the centrifugal distortion constant for 1H127I, for which ᷉ B = 6.511 cm−1 and ᷉v = 2308 cm−1. By what factor would the constant change when 2H is substituted for 1H?arrow_forward
- What are the total number of degrees of freedom and the number of vibrational modes for ethanol C2H6O?arrow_forwardThe rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited vibrational states, respectively. By how much does the internuclear distance change as a result of this transition?arrow_forwardWhat is the most highly populated rotational level of Cl2 at (i) 25 °C, (ii) 100 °C? Take ᷉ B = 0.244 cm−1.arrow_forward
- Consider the vibrational mode that corresponds to the uniform expansion of the benzene ring. Is it (i) Raman, (ii) infrared active?arrow_forwardHow many normal modes of vibration are there for (a) NO2 (b) N2O, (c) cyclohexane. (d) hexane?arrow_forwardWhy does the vibrational state of a diatomic molecule affect its rotational constant? Is there an effect even if the potential is strictly parabolic?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning