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

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

Mullins1st EditionOrganic Chemistry: A Learner Centered ApproachISBN: 9780137566471Not the one you use?Change textbook

Mullins 1st Edition

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

Problem 16a

Chapter 13, Problem 16a

Calculate the reduced mass for the following bonds.
(a) C―H

Verified step by step guidance

Understand the concept of reduced mass: In a two-body system, the reduced mass (μ) is a useful quantity that simplifies the mathematical description of the system. It is defined as μ = (m₁ * m₂) / (m₁ + m₂), where m₁ and m₂ are the masses of the two bodies.

Identify the atoms involved in the bond: For the C―H bond, we have a carbon atom (C) and a hydrogen atom (H).

Find the atomic masses: The atomic mass of carbon (C) is approximately 12 atomic mass units (amu), and the atomic mass of hydrogen (H) is approximately 1 amu.

Substitute the atomic masses into the reduced mass formula: Use the formula μ = (m₁ * m₂) / (m₁ + m₂) with m₁ = 12 amu (carbon) and m₂ = 1 amu (hydrogen).

Simplify the expression: Perform the multiplication and addition operations to simplify the expression for the reduced mass. Remember that the reduced mass will be in atomic mass units (amu).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 in systems like diatomic molecules. It is calculated using the formula μ = (m1 * m2) / (m1 + m2), where m1 and m2 are the masses of the two atoms involved. This value is crucial for understanding vibrational motions in molecular systems.

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. For calculating reduced mass, knowing the atomic masses of the involved atoms, such as carbon (12 amu) and hydrogen (1 amu), is essential.

Diatomic Molecules

Diatomic molecules consist of two atoms, which can be the same or different elements, such as H2 or CO. Understanding the behavior of diatomic molecules, including their vibrational and rotational motions, often involves using the concept of reduced mass to simplify calculations related to these motions.

Recommended video:

Guided course

01:55

Reactivity of Molecules

Related Practice

Textbook Question

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

(a) C―N vs. C = N

1009

views

Textbook Question

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

1082

views

Textbook Question

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

(b) C―H vs. C―O

1108

views

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?

<IMAGE>

1515

views

Textbook Question

Calculate the reduced mass for the following bonds.

1695

views

Textbook Question

Given the IR spectrum, suggest what functional groups might correspond to the given molecular formula.

(d) C₇H₅O

<IMAGE>

1165