Chemistry
Chemistry
13th Edition
ISBN: 9781259911156
Author: Raymond Chang Dr., Jason Overby Professor
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.113QP

Consider a N2 molecule in its first excited electronic state, that is, when an electron in the highest occupied molecular orbital is promoted to the lowest empty molecular orbital. (a) Identify the molecular orbitals involved and sketch a diagram to show the transition. (b) Compare the bond order and bond length of N2* with N2, where the asterisk denotes the excited molecule. (c) Is N2* diamagnetic or paramagnetic? (d) When N2* loses its excess energy and converts to the ground state N2, it emits a photon of wavelength 470 nm, which makes up part of the auroras lights. Calculate the energy difference between these levels.

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The molecular orbital involved in transition should be identified and to sketch the transition.  Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  1 and Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  2 should be found and the bond length should be compared.  The magnetic properties of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  3should be found out.  The energy difference of the given transition should be determined

Concept Introduction:

  • In molecular orbital theory, when the bonding takes place the atomic orbitals that take part combine to get a new orbital that has the properties of the whole molecule. The newly formed orbitals are known as molecular orbitals
  • The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.
  • Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  4
  • Paramagnetic species contains at least one unpaired electrons and can be attracted towards magnetic fields. Diamagnetic species does have any unpaired electrons. That is spins of all the electrons are paired. It slightly repelled towards the magnetic fields

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  5

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  6

To identify: molecular orbital involved in transition and to sketch the transition.

Answer to Problem 10.113QP

The transition sketch is,

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  7

Explanation of Solution

In molecular orbital theory, when the bonding takes place the atomic orbitals that take part combine to get a new orbital that has the properties of the whole molecule. The newly formed orbitals are known as molecular orbitals and only contain a maximum of two electrons. The number of newly formed molecular orbital is equal to the number of atomic orbitals involved in the bonding.

There are two types of molecular orbitals,

  1. a) Bonding molecular orbitals: sharing of electron density is between the nuclei and has comparatively lower energy and fills first.
  2. b) Antibonding molecular orbitals: Two nuclei is pulled by the electrons density in opposite direction and has higher energy comparing to bonding molecular orbital.

Molecular orbital diagram of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  8 is given below

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  9

Figure 1

In the ground state of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  10 the electrons are in Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  11 orbital when the Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  12 gets excited by getting energy the electron move to Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  13 orbitals.

The diagram that showing transition is given below,

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  14

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The molecular orbital involved in transition should be identified and to sketch the transition.  Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  15 and Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  16 should be found and the bond length should be compared.  The magnetic properties of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  17should be found out.  The energy difference of the given transition should be determined

Concept Introduction:

  • In molecular orbital theory, when the bonding takes place the atomic orbitals that take part combine to get a new orbital that has the properties of the whole molecule. The newly formed orbitals are known as molecular orbitals
  • The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.
  • Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  18
  • Paramagnetic species contains at least one unpaired electrons and can be attracted towards magnetic fields. Diamagnetic species does have any unpaired electrons. That is spins of all the electrons are paired. It slightly repelled towards the magnetic fields

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  19

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  20

To identify: Bond of order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  21andChemistry, Chapter 10, Problem 10.113QP , additional homework tip  22. Also to compare its bond length

Answer to Problem 10.113QP

Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  23 and Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  24 is 3 and 2 respectively. Also the bond length of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  25 is longer than Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  26.

Explanation of Solution

Electronic configuration of excited nitrogen molecule Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  27 is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  28

The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  29

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  30

Electronic configuration of excited nitrogen molecule Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  31 is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  32

The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  33

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  34

Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  35 is 3 whereas Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  36 is 2.

Therefore, the bond length of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  37 is longer than Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  38.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The molecular orbital involved in transition should be identified and to sketch the transition.  Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  39 and Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  40 should be found and the bond length should be compared.  The magnetic properties of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  41should be found out.  The energy difference of the given transition should be determined

Concept Introduction:

  • In molecular orbital theory, when the bonding takes place the atomic orbitals that take part combine to get a new orbital that has the properties of the whole molecule. The newly formed orbitals are known as molecular orbitals
  • The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.
  • Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  42
  • Paramagnetic species contains at least one unpaired electrons and can be attracted towards magnetic fields. Diamagnetic species does have any unpaired electrons. That is spins of all the electrons are paired. It slightly repelled towards the magnetic fields

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  43

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  44

To identify: The magnetic properties of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  45

Answer to Problem 10.113QP

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  46is diamagnetic

Explanation of Solution

Paramagnetic species contains at least one unpaired electrons and can be attracted towards magnetic fields. Diamagnetic species does have any unpaired electrons. That is spins of all the electrons are paired. It slightly repelled towards the magnetic fields.

Electronic configuration of excited nitrogen molecule Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  47 is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  48

Even though there are unpaired electrons, the spin of the electrons was not change in the time of transition. All the electrons are paired so it is diamagnetic.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The molecular orbital involved in transition should be identified and to sketch the transition.  Bond order of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  49 and Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  50 should be found and the bond length should be compared.  The magnetic properties of Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  51should be found out.  The energy difference of the given transition should be determined

Concept Introduction:

  • In molecular orbital theory, when the bonding takes place the atomic orbitals that take part combine to get a new orbital that has the properties of the whole molecule. The newly formed orbitals are known as molecular orbitals
  • The bond order gives an idea about the stability of a molecule. It can be calculated using the molecular orbital theory. The stability of a molecule increase as the bond order increases.
  • Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  52
  • Paramagnetic species contains at least one unpaired electrons and can be attracted towards magnetic fields. Diamagnetic species does have any unpaired electrons. That is spins of all the electrons are paired. It slightly repelled towards the magnetic fields

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  53

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  54

To determine: The energy difference of the given transition.

Answer to Problem 10.113QP

The energy difference of the given transition is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  55

Explanation of Solution

The energy of light is calculated below.

Given,

The wavelength of light is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  56.

Planck’s constant is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  57

Speed of the light is Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  58

The energy of light is calculated is calculated by the equation,

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  59

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  60

Substituting the given values in the equation,

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  61

The energy difference of the given transition is

Chemistry, Chapter 10, Problem 10.113QP , additional homework tip  62

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