(a) Interpretation: The number of IR-active vibrations for F 2 O is to be determined. Concept introduction: The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3 N − 6 .

Question

30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m²

Answer 1

Question

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

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30. We will derive the forms of the molecular partition functions for atoms and molecules shortly in class, but the partition function that describes the translational and rotational motion of a homonuclear diatomic molecule is given by Itrans (V,T) = = 2πmkBT h² V grot (T) 4π²IKBT h² Where h is Planck's constant and I is molecular moment of inertia. The overall partition function is qmolec Qtrans qrot. Find the energy, enthalpy, entropy, and Helmholtz free energy for the translational and rotational modes of 1 mole of oxygen molecules and 1 mole of iodine molecules at 50 K and at 300 K and with a volume of 1 m³. Here is some useful data: Moment of inertia: I2 I 7.46 x 10- 45 kg m² 2 O2 I 1.91 x 101 -46 kg m²

K for each reaction step. Be sure to account for all bond-breaking and bond-making steps. HI HaC Drawing Arrows! H3C OCH3 H 4 59°F Mostly sunny H CH3 HO O CH3 'C' CH3 Select to Add Arrows CH3 1 L H&C. OCH3 H H H H Select to Add Arrows Q Search Problem 30 of 20 H. H3C + :0: H CH3 CH3 20 H2C Undo Reset Done DELL

Draw the principal organic product of the following reaction.

Answer 2

Question

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

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Answer 3

Question

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

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Answer 4

Question

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

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Answer 5

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 6

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 7

Chapter 14, Problem 14.81E

Interpretation Introduction

(a)

Interpretation:

The number of IR-active vibrations for F2O is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The number of IR-active vibrations for NCl3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The number of IR-active vibrations for N(CH3)3 is to be determined.

Concept introduction:

The complex vibrations exhibit by the polyatomic molecule is known as normal modes of vibrations. The vibrational modes of a molecule are IR or Raman active. If a molecule has centre of symmetry, then the modes which are IR-active will be Raman inactive and the modes that are IR-inactive will be Raman active. The total number of vibrational degrees of freedom for nonlinear molecule is represented by 3N−6.

Answer 12

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Answer 23

Ch. 14 - Prob. 14.1E Ch. 14 - Determine if the following integrals can be...Ch. 14 - What is the frequency of light having the...Ch. 14 - What is the wavelength of light having the given...Ch. 14 - What is the energy of light having each...Ch. 14 - The Cu(H2O)62+ complex has octahedral symmetry. Is...Ch. 14 - What are the wavelength, speed, and energy of a...Ch. 14 - Prob. 14.8E Ch. 14 - Prob. 14.9E Ch. 14 - Prob. 14.10E

Solution Summary: The author determines the number of IR-active vibrations for F_2TextO.

Chapter 14 Solutions