Ch. 14 - Structural Identification I: Infrared Spectroscopy and Mass Spectrometry

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 14 - Structural Identification I: Infrared Spectroscopy and Mass Spectrometry

Problem 16c

Chapter 13, Problem 16c

Calculate the reduced mass for the following bonds.
(c) C―Cl

Verified step by step guidance

Identify the atomic masses of the elements involved in the bond. For carbon (C), the atomic mass is approximately 12 amu (atomic mass units), and for chlorine (Cl), it is approximately 35.5 amu.

Use the formula for reduced mass, which is given by:

μ = \frac{m_1 m_2}{m_1 + m_2}

, where

m_1

and

m_2

are the atomic masses of the two atoms.

Substitute the atomic masses of carbon and chlorine into the reduced mass formula:

μ = \frac{12 \times 35.5}{12 + 35.5}

Simplify the expression in the numerator:

12 \times 35.5

Add the atomic masses in the denominator:

12 + 35.5

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reduced Mass

Reduced mass is a concept used in physics and chemistry to simplify the two-body problem, particularly in molecular vibrations and rotational motion. It is defined as μ = (m1 * m2) / (m1 + m2), where m1 and m2 are the masses of the two atoms involved in the bond. This value allows us to treat the two-body system as a single particle with mass μ, facilitating calculations in molecular dynamics.

Atomic Mass

Atomic mass is the mass of an atom, typically expressed in atomic mass units (amu). It is approximately equivalent to the number of protons and neutrons in the atom's nucleus. For calculating the reduced mass of a bond like C―Cl, the atomic masses of carbon (approximately 12 amu) and chlorine (approximately 35.5 amu) are used to determine the individual masses (m1 and m2) in the reduced mass formula.

Bond in Molecular Systems

In molecular systems, a bond represents the interaction between two atoms, which can be described by their shared electrons. Understanding the nature of the bond, such as C―Cl, is crucial for calculating properties like reduced mass, as it involves the specific atoms and their respective masses. This concept is fundamental in predicting molecular behavior, such as vibrational frequencies and rotational spectra.

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Textbook Question

Choose the bond in each pair that you expect to vibrate at the higher wavenumber.

(a) C―N vs. C = N

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Would you expect an acetylenic C―H to absorb at a higher or lower wavenumber than the C―H in ethene?

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Textbook Question

Choose the bond in each pair that you expect to vibrate at the higher wavenumber.

(b) C―H vs. C―O

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Textbook Question

The IR spectrum for anisole contains two C―O stretching bands in the fingerprint region. Match the band to the bond that gives rise to it. Why are these bands so intense?

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Textbook Question

Calculate the reduced mass for the following bonds.

(a) C―H

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Textbook Question

For each pair, choose the molecule that you expect to have the highest wavenumber for its C=O stretch.

(d)

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