Chapter 14, Problem 48E

(a)

Interpretation Introduction

Interpretation:

The electronic configuration of ${\text{CN}}^{+}$ should be stated. The bond order and whether is paramagentic or not should be predicted.

Concept Introduction:

Molecular orbital theory is a method that shows that how atomic orbitals combine with other or with each other to form bonding and antibonding orbitals. It is used to determine the molecular structure of a molecule. The atomic number represents the number of electrons in an atom.

Answer to Problem 48E

The electronic configuration of ${\text{CN}}^{+}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4$ . It is not paramagnetic specie and its bond order is 2.

Explanation of Solution

The given molecule is ${\text{CN}}^{+}$ . The number of electrons in C and N are 6 and 7 respectively. ${\text{CN}}^{+}$ is formed by losing an electron from $\text{CN}$ . Therefore, the total number of electrons in ${\text{CN}}^{+}$ is 12 electrons.

The molecular orbital diagram for ${\text{CN}}^{+}$ is shown below:

  

Therefore, the electronic configuration of ${\text{CN}}^{+}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4$ . All the electrons are paired. Therefore, it is not paramagnetic specie.

The bond order is calculated as follows:

  $\text{Bond}\text{order}=\frac{\text{electron}\text{in}\text{bonding}\text{MO}-\text{electrons}\text{in}\text{antibonding}\text{MO}}{\text{2}}$

Substitute electrons in antibonding MO and bonding MO for ${\text{CN}}^{+}$ in above formula.

  $\begin{array}{c}\text{Bond}\text{order}=\frac{8-4}{\text{2}}\\ =\frac{4}{\text{2}}\\ =2\end{array}$

Therefore, the bond order of ${\text{CN}}^{+}$ is 2.

(b)

Interpretation Introduction

Interpretation:

The electronic configuration of $\text{CN}$ should be stated. The bond order and whether the species is paramagentic or not should be predicted.

Concept Introduction:

Molecular orbital theory is a method that shows that how atomic orbitals combine with other or with each other to form bonding and antibonding orbitals. It is used to determine the molecular structure of a molecule. The atomic number represents the number of electrons in an atom.

Answer to Problem 48E

The electronic configuration of $\text{CN}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4{\left({\sigma }_{2p_z}\right)}^1$ . It is paramagnetic specie and its bond order is 2.5.

Explanation of Solution

The given molecule is $\text{CN}$ . The number of electrons in C and N are 6 and 7 respectively. Therefore, the total number of electrons in $\text{CN}$ is 13 electrons.

The molecular orbital diagram for $\text{CN}$ is shown below:

  

Therefore, the electronic configuration of $\text{CN}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4{\left({\sigma }_{2p_z}\right)}^1$ . There is one unpiared electron. Therefore, it is paramagnetic specie.

The bond order is calculated as follows:

  $\text{Bond}\text{order}=\frac{\text{electron}\text{in}\text{bonding}\text{MO}-\text{electrons}\text{in}\text{antibonding}\text{MO}}{\text{2}}$

Substitute electrons in antibonding MO and bonding MO for $\text{CN}$ in above formula.

  $\begin{array}{c}\text{Bond}\text{order}=\frac{9-4}{\text{2}}\\ =\frac{5}{\text{2}}\\ =2.5\end{array}$

Therefore, the bond order of $\text{CN}$ is $2.5$ .

(c)

Interpretation Introduction

Interpretation:

The electronic configuration of ${\text{CN}}^{-}$ should be stated. The bond order and specie is paramagentic or not should be predicted. The increasing order of bond length and bond energy should be stated.

Concept Introduction:

Molecular orbital theory is a method that shows that how atomic orbitals combine with other or with each other to form bonding and antibonding orbitals. It is used to determine the molecular structure of a molecule. The atomic number represents the number of electrons in an atom.

Answer to Problem 48E

The electronic configuration of ${\text{CN}}^{-}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4{\left({\sigma }_{2p_z}\right)}^2$ . It is not paramagnetic specie and its bond order is 3.

The order of increasing bond length is ${\text{CN}}^{-}<\text{CN}<{\text{CN}}^{+}$ and the order of increasing bond energy is ${\text{CN}}^{+}<\text{CN}<{\text{CN}}^{-}$ .

Explanation of Solution

The given molecule is ${\text{CN}}^{-}$ . The number of electrons in C and N are 6 and 7 respectively. Therefore, the total number of electrons in ${\text{CN}}^{-}$ is 14 electrons.

The molecular orbital diagram for ${\text{CN}}^{-}$ is shown below:

  

Therefore, the electronic configuration of ${\text{CN}}^{-}$ is ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}{}^{*}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}{}^{*}\right)}^2{\left({\pi }_{2p_x}={\pi }_{2p_y}\right)}^4{\left({\sigma }_{2p_z}\right)}^2$ . All are piared electron. Therefore, it is not paramagnetic specie.

The bond order is calculated as follows:

  $\text{Bond}\text{order}=\frac{\text{electron}\text{in}\text{bonding}\text{MO}-\text{electrons}\text{in}\text{antibonding}\text{MO}}{\text{2}}$

Substitute electrons in antibonding MO and bonding MO for ${\text{CN}}^{-}$ in above formula.

  $\begin{array}{c}\text{Bond}\text{order}=\frac{10-4}{\text{2}}\\ =\frac{6}{\text{2}}\\ =3\end{array}$

Therefore, the bond order of ${\text{CN}}^{-}$ is $3$ .

The relationship among bond energy, bond length and bond order is as follows:

  $\frac{1}{\text{Bond}\text{energy}}\propto \text{Bond}\text{length}\propto \frac{1}{\text{Bond}\text{order}}$

The bond order of ${\text{CN}}^{+}$ , $\text{CN}$ and ${\text{CN}}^{-}$ is 2, 2.5 and 3 respectively. The bond order is inversly proportional to bond length. Therefore, the order of increasing bond length is ${\text{CN}}^{-}<\text{CN}<{\text{CN}}^{+}$ .

The bond order is directly proportional to bond energy. Therefore, the order of increasing bond energy is ${\text{CN}}^{+}<\text{CN}<{\text{CN}}^{-}$ .