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
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- (a) Draw a rough schematic of the series of resonances corresponding to a vibrational transition for a diatomic. Label the P and R branches, explain what the difference is between them, and indicate what the spacing is between the resonance lines. (b) What is the main information about a diatomic molecule that one can obtain from vibrational and rotational transition frequencies (assuming that the reduced mass is known)?arrow_forwardThe average spacing between the rotational lines of the P and R branches of 12C21H2 and 12C22H2 is 2.352 cm−1 and 1.696 cm−1, respectively. Estimate the CC and CH bond lengths.arrow_forwardExplain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.arrow_forward
- This 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_forwardPredict the shape of the nitronium ion, NO2+, from its Lewis structure and the VSEPR model. It has one Raman active vibrational mode at 1400 cm−1, two strong IR active modes at 2360 and 540 cm−1, and one weak IR mode at 3735 cm−1. Are these data consistent with the predicted shape of the molecule? Assign the vibrational wavenumbers to the modes from which they arise.arrow_forwardWhich of the following molecules may show a pure rotational Raman spectrum: (i) CH2Cl2, (ii) CH3CH3, (iii) SF6, (iv) N2O?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