   Chapter 14, Problem 14.78E

Chapter
Section
Textbook Problem

Determine the number of IR-active vibrations for the following molecules. You may have to determine their symmetry first. (a) Hydrogen peroxide, H 2 O 2 (b) Oxalic acid, ( COOH ) 2 (c) Sulfur trioxide, SO 3 (d) Formaldehyde, H 2 CO (e) Acetone, ( CH 3 ) 2 CO (assume C 2v symmetry)

Interpretation Introduction

(a)

Interpretation:

The symmetry and the number of IR-active vibrations for H2O2 molecule are to be stated.

Concept introduction:

The number of vibrations or degree of freedom of linear molecule is 3N5 and the number of vibrations or degree of freedom of nonlinear molecule is 3N6. Only those vibrations which involve a change in dipole moment are said to be IR-active vibrations.

Explanation

Hydrogen peroxide (H2O2) is a nonlinear molecule. It is found in two isomeric forms, cis-H2O2 and trans-H2O2. The symmetry for cis-H2O2 molecule is (C2h) and for trans-H2O2 molecule is (C2v). Total number of vibrations in H2O2 molecule is calculated by the formula given below.

Total number of vibrations in H2O2=3N6 …(1)

Where,

N is the number of atoms

Interpretation Introduction

(b)

Interpretation:

The symmetry and the number of IR-active vibrations for (COOH)2 molecule is to be stated.

Concept introduction:

The number of vibrations or degree of freedom of linear molecule is 3N5 and the number of vibrations or degree of freedom of nonlinear molecule is 3N6. Only those vibrations which involve a change in dipole moment are said to be IR-active vibrations.

Interpretation Introduction

(c)

Interpretation:

The symmetry and the number of IR-active vibrations for SO3 molecule is to be stated.

Concept introduction:

The number of vibrations or degree of freedom of linear molecule is 3N5 and the number of vibrations or degree of freedom of nonlinear molecule is 3N6. Only those vibrations which involve a change in dipole moment are said to be IR-active vibrations.

Interpretation Introduction

(d)

Interpretation:

The symmetry and the number of IR-active vibrations for formaldehyde H2CO molecule is to be stated.

Concept introduction:

The number of vibrations or degree of freedom of linear molecule is 3N5 and the number of vibrations or degree of freedom of nonlinear molecule is 3N6. Only those vibrations which involve a change in dipole moment are said to be IR-active vibrations.

Interpretation Introduction

(e)

Interpretation:

The symmetry and the number of IR-active vibrations for (CH3)2CO molecule is to be stated.

Concept introduction:

The number of vibrations or degree of freedom of linear molecule is 3N5 and the number of vibrations or degree of freedom of nonlinear molecule is 3N6. Only those vibrations which involve a change in dipole moment are said to be IR-active vibrations.

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