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K- 5.105 (single bond) 10. 105 (double bona) 15. 105 (triple bond) v (H2) = 4.12 4.12 V m, = (m, x m2) 7 (m; + m2) m is the mass of the atom (a) C-H (b) C-D (c) C=C

K- 5.105 (single bond) 10. 105 (double bona) 15. 105 (triple bond) v (H2) = 4.12 4.12 V m, = (m, x m2) 7 (m; + m2) m is the mass of the atom (a) C-H (b) C-D (c) C=C

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Use the formula below to estimate the stretching frequencies (wave numbers) for the following bonds
## Understanding Bond Vibrations ### Bond Vibration Frequency Formula The vibration frequency \( \nu \) (in Hertz) of a bond between two atoms can be described by the equation: \[ \nu (\text{Hz}) = 4.12 \sqrt{\frac{k}{m_r}} \] - **\( k \)** represents the force constant of the bond. - Single bond: \( k = 5 \times 10^5 \) - Double bond: \( k = 10 \times 10^5 \) - Triple bond: \( k = 15 \times 10^5 \) ### Reduced Mass \( m_r \) The reduced mass \( m_r \) of two atoms involved in the bond can be calculated using the formula: \[ m_r = \frac{(m_1 \times m_2)}{(m_1 + m_2)} \] - **\( m_1 \)** and **\( m_2 \)** are the masses of the two atoms involved in the bond. ### Important Note - \( m \) is the mass of the atom. ### Example Bonds The following are typical bond structures and their representations: (a) **C—H** (Single Bond between Carbon and Hydrogen) (b) **C—D** (Single Bond between Carbon and Deuterium) (c) **C≡C** (Triple Bond between two Carbon atoms) Understanding these principles and equations allows for the calculation of the vibration frequencies of different types of atomic bonds in molecules, which is fundamental in the study of molecular spectroscopy and chemical bonding.
Transcribed Image Text:## Understanding Bond Vibrations ### Bond Vibration Frequency Formula The vibration frequency \( \nu \) (in Hertz) of a bond between two atoms can be described by the equation: \[ \nu (\text{Hz}) = 4.12 \sqrt{\frac{k}{m_r}} \] - **\( k \)** represents the force constant of the bond. - Single bond: \( k = 5 \times 10^5 \) - Double bond: \( k = 10 \times 10^5 \) - Triple bond: \( k = 15 \times 10^5 \) ### Reduced Mass \( m_r \) The reduced mass \( m_r \) of two atoms involved in the bond can be calculated using the formula: \[ m_r = \frac{(m_1 \times m_2)}{(m_1 + m_2)} \] - **\( m_1 \)** and **\( m_2 \)** are the masses of the two atoms involved in the bond. ### Important Note - \( m \) is the mass of the atom. ### Example Bonds The following are typical bond structures and their representations: (a) **C—H** (Single Bond between Carbon and Hydrogen) (b) **C—D** (Single Bond between Carbon and Deuterium) (c) **C≡C** (Triple Bond between two Carbon atoms) Understanding these principles and equations allows for the calculation of the vibration frequencies of different types of atomic bonds in molecules, which is fundamental in the study of molecular spectroscopy and chemical bonding.
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