Concept explainers
Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. (a) Hydrogen sulfide,
(a)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(b)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(c)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(d)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(e)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(f)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
(g)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
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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 molecules. a Hydrogen fluoride, HF b Hydrogen telluride, H2Te c Buckminsterfullerene, C60 d Phenylalanine, C6H5CH2CHNH2COOH e Naphthalene, C10H8 f The linear isomer of the C4 radical g The bent isomer of C4 radical.arrow_forwardCalculate the rotational constant (B) for the molecule H12C14N, given that the H-C and C-N bond distances are 106.6 pm and 115.3 pm respectively.arrow_forward(b) The lowest frequency rotational transition of ²H³³C1 occurs at 10.92 cm1. Determine (i) The rotational constant, B, in Hz (ii) The bond lengtharrow_forward
- 3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bondarrow_forwardExplain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.arrow_forwardThe hydrogen halides have the following fundamental vibrational wavenumbers: 4141.3 cm−1 (1H19F); 2988.9 cm−1 (1H35Cl); 2649.7 cm−1 (1H81Br); 2309.5 cm−1 (H127I). Calculate the force constants of the hydrogen–halogen bonds.arrow_forward
- How many normal modes of vibration are there for the following molecules and, in each case, briefly explain why this is so: (i) C6H6, (ii) C6H5CH3, and (iii) HC≡C−C≡CH?arrow_forwardThe vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?arrow_forwardA molecule in a liquid undergoes about 1.0 × 1013 collisions in each second. Suppose that (i) every collision is effective in deactivating the molecule vibrationally and (ii) that one collision in 100 is effective. Calculate the width (in cm−1) of vibrational transitions in the molecule.arrow_forward
- Consider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?arrow_forwardThe 14 N160 molecule undergoes a transition between its rotational ground state and its rotational first excited state. Approximating the diatomic molecule as a rigid rotor, and given that the bond length of NO is 1.152 Angstroms, calculate the energy of the transition. As your final answer, calculate the temperature T in Kelvin, such that Ethermal = kBT equals the %3D energy of the transition between NO's rotational ground state and fırst excited state.arrow_forward(3) Consider an oscillating H₂ molecule in one-dimension. (a) Show that the smaller the mass of the oscillating molecule, the greater will be its zero-point energy, for a fixed force constant. (b) Show that the spacing between adjacent energy levels is unaffected as the vibrational quantum number increases.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