Chemistry: Atoms First
Chemistry: Atoms First
3rd Edition
ISBN: 9781259638138
Author: Julia Burdge, Jason Overby Professor
Publisher: McGraw-Hill Education
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Chapter 7, Problem 7.138QP

Consider an 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 N*2 with N2, where the asterisk denotes the excited molecule, (c) Is N*2 diamagnetic or paramagnetic? (d) When N*2 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 N2 and N2* should be found and the bond length should be compared.  The magnetic properties of N2* should 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.
  • Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2
  • 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

E=hcλ

where,E=Energyh=Planck'sconstantc=speedoflightλ=wavelength of the emittedlight 

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

Answer to Problem 7.138QP

The transition sketch is,

Chemistry: Atoms First, Chapter 7, Problem 7.138QP , additional homework tip  1

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 N2 is given below

Chemistry: Atoms First, Chapter 7, Problem 7.138QP , additional homework tip  2

Figure 1

In the ground state of N2 the electrons are in σ2pz orbital when the N2 gets excited by getting energy the electron move to π*2pxorπ*2py orbitals.

The diagram that showing transition is given below,

Chemistry: Atoms First, Chapter 7, Problem 7.138QP , additional homework tip  3

(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 N2 and N2* should be found and the bond length should be compared.  The magnetic properties of N2* should 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.
  • Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2
  • 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

E=hcλ

where,E=Energyh=Planck'sconstantc=speedoflightλ=wavelength of the emittedlight 

To identify: Bond of order of N2 and N2*. Also to compare its bond length

Answer to Problem 7.138QP

Bond order of N2 and N2* is 3 and 2 respectively. Also the bond length of N2* is longer than N2.

Explanation of Solution

Electronic configuration of excited nitrogen molecule N2 is [He](σ2s)2(σ2s*)2(π2py)2(π2px)2(σ2pz)2

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.

Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2

bondorder=12(60)=3

Electronic configuration of excited nitrogen molecule N2* is [He](σ2s)2(σ2s*)2(π2py)2(π2px)2(σ2pz)1(π2py*)1

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.

Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2

bondorder=12(5-1)=2

Bond order of N2 is 3 whereas N2* is 2.

Therefore, the bond length of N2* is longer than N2.

(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 N2 and N2* should be found and the bond length should be compared.  The magnetic properties of N2* should 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.
  • Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2
  • 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

E=hcλ

where,E=Energyh=Planck'sconstantc=speedoflightλ=wavelength of the emittedlight 

To identify: The magnetic properties of N2*

Answer to Problem 7.138QP

N2* is 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 N2* is [He](σ2s)2(σ2s*)2(π2py)2(π2px)2(σ2pz)1(π2py*)1

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 N2 and N2* should be found and the bond length should be compared.  The magnetic properties of N2* should 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.
  • Bondorder=(numberofelectronsinbondingmolecularorbitals)-(numberofelectronsinantibondingmolecularorbitals)2
  • 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

E=hcλ

where,E=Energyh=Planck'sconstantc=speedoflightλ=wavelength of the emittedlight 

To determine: The energy difference of the given transition.

Answer to Problem 7.138QP

The energy difference of the given transition is 4.23×109J

Explanation of Solution

The energy of light is calculated below.

Given,

The wavelength of light is 470 nm=470 ×109m.

Planck’s constant is 6.63×1034Js

Speed of the light is 3×108ms1

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

E=hcλ

where,E=Energyh=Planck'sconstantc=speedoflightλ=wavelength of the emittedlight 

Substituting the given values in the equation,

E=hcλ=6.63×1034Js×3×108ms1470 ×109m=4.23×109J

The energy difference of the given transition is

4.23×109J

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Chapter 7 Solutions

Chemistry: Atoms First

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