Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN: 9781305079113
Author: David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher: Cengage Learning
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Chapter 20, Problem 14P

(a)

Interpretation Introduction

Interpretation: The moment of inertia I of HCl needs to be calculated in kg m2 .

Concept Introduction:

The moment of inertia, I for HCl can be calculated using the following formula:

  I=h8π2B

Here, h is Planck’s constant and B is Rotational constant.

(b)

Interpretation Introduction

Interpretation: The energies (in J) of the rotational levels J =1, 2 and 3 from J =0 state needs to be calculated for HCl.

Concept Introduction: For a molecule, the energy of J-state can be calculated using the following formula:

  EJ=BhJ(J+1)

Here, B is rotational constant, h is Planck’s constant and J is rotational levels.

(c)

Interpretation Introduction

Interpretation: The bond length for H-Cl needs to be calculated in angstroms.

Concept Introduction: For a molecule, the moment of inertia, Iis related to bond length as follows:

  I=μr2

Here, μ is reduced mass and r is bond length.

(d)

Interpretation Introduction

Interpretation: The initial and final J states need to be calculated for the observed absorption lines.

Concept Introduction: The frequency for the transition from J to J+1 level is represented as 2B(J+1) .

Here, B is rotational constant.

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The first three absorption lines in the pure rotational spec- trum of gaseous 12C16O are found to have the frequencies 1.15 x 1011, 2.30 × 1011, and 3.46 × 1011 s-1. Calculate: (a) The moment of inertia I of CO (in kg m²) (b) The energies of the J = 1, J = 2, and J = 3 rotational levels of CO, measured from the J = 0 state (in joules) (c) The C-O bond length (in angstroms)
The spacing of lines in the microwave spectrum of 35Cl19F is 1.033 cm−1; calculate the moment of inertia and bond length of the molecule.
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